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https://en.wikipedia.org/wiki/Classification%20of%20Clifford%20algebras
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In abstract algebra, in particular in the theory of nondegenerate quadratic forms on vector spaces, the structures of finite-dimensional real and complex Clifford algebras for a nondegenerate quadratic form have been completely classified. In each case, the Clifford algebra is algebra isomorphic to a full matrix ring over R, C, or H (the quaternions), or to a direct sum of two copies of such an algebra, though not in a canonical way. Below it is shown that distinct Clifford algebras may be algebra-isomorphic, as is the case of Cl1,1(R) and Cl2,0(R), which are both isomorphic as rings to the ring of two-by-two matrices over the real numbers.
The significance of this result is that the additional structure on a Clifford algebra relative to the "underlying" associative algebra — namely, the structure given by the grade involution automorphism and reversal anti-automorphism (and their composition, the Clifford conjugation) — is in general an essential part of its definition, not a procedural artifact of its construction as the quotient of a tensor algebra by an ideal. The category of Clifford algebras is not just a selection from the category of matrix rings, picking out those in which the ring product can be constructed as the Clifford product for some vector space and quadratic form. With few exceptions, "forgetting" the additional structure (in the category theory sense of a forgetful functor) is not reversible.
Continuing the example above: Cl1,1(R) and Cl2,0(R) share the same associative algebra structure, isomorphic to (and commonly denoted as) the matrix algebra M2(R). But they are distinguished by different choices of grade involution — of which two-dimensional subring, closed under the ring product, to designate as the even subring — and therefore of which of the various anti-automorphisms of M2(R) can accurately represent the reversal anti-automorphism of the Clifford algebra. These distinguished (anti-)automorphisms are structures on the tensor algebra whi
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https://en.wikipedia.org/wiki/Diameter%20%28protocol%29
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Diameter is an authentication, authorization, and accounting protocol for computer networks. It evolved from the earlier RADIUS protocol. It belongs to the application layer protocols in the internet protocol suite.
Diameter Applications extend the base protocol by adding new commands and/or attributes, such as those for use with the Extensible Authentication Protocol (EAP).
Comparison with RADIUS
The name is a play on words, derived from the RADIUS protocol, which is the predecessor (a diameter is twice the radius). Diameter is not directly backward compatible but provides an upgrade path for RADIUS. The main features provided by Diameter but lacking in RADIUS are:
Support for SCTP
Capability negotiation
Application layer acknowledgements; Diameter defines failover methods and state machines (RFC 3539)
Extensibility; new commands can be defined
Aligned on 32 bit boundaries
Also:
Like RADIUS, it is intended to work in both local and roaming AAA situations.
It uses TCP or SCTP, unlike RADIUS which uses UDP.
Unlike RADIUS it includes no encryption but can be protected by transport-level security (IPSEC or TLS).
The base size of the AV identifier is 32 bit unlike RADIUS which uses 8 bit as the base AV identifier size.
Like RADIUS, it supports stateless as well as stateful modes.
Like RADIUS, it supports application-layer acknowledgment and defines failover.
Diameter is used for many different interfaces defined by the 3GPP standards, with each interface typically defining new commands and attributes.
Applications
A Diameter Application is not a software application but is a protocol based on the Diameter base protocol defined in RFC 6733 and RFC 7075 (Obsoletes: RFC 3588). Each application is defined by an application identifier and can add new command codes and/or new mandatory AVPs (Attribute-Value Pair). Adding a new optional AVP does not require a new application.
Examples of Diameter applications:
Diameter Mobile IPv4 Application (MobileIP, RFC 4004)
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https://en.wikipedia.org/wiki/Degaussing
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Degaussing is the process of decreasing or eliminating a remnant magnetic field. It is named after the gauss, a unit of magnetism, which in turn was named after Carl Friedrich Gauss. Due to magnetic hysteresis, it is generally not possible to reduce a magnetic field completely to zero, so degaussing typically induces a very small "known" field referred to as bias. Degaussing was originally applied to reduce ships' magnetic signatures during World War II. Degaussing is also used to reduce magnetic fields in cathode ray tube monitors and to destroy data held on magnetic storage.
Ships' hulls
The term was first used by then-Commander Charles F. Goodeve, Royal Canadian Naval Volunteer Reserve, during World War II while trying to counter the German magnetic naval mines that were wreaking havoc on the British fleet.
The mines detected the increase in the magnetic field when the steel in a ship concentrated the Earth's magnetic field over it. Admiralty scientists, including Goodeve, developed a number of systems to induce a small "N-pole up" field into the ship to offset this effect, meaning that the net field was the same as the background. Since the Germans used the gauss as the unit of the strength of the magnetic field in their mines' triggers (not yet a standard measure), Goodeve referred to the various processes to counter the mines as "degaussing". The term became a common word.
The original method of degaussing was to install electromagnetic coils into the ships, known as coiling. In addition to being able to bias the ship continually, coiling also allowed the bias field to be reversed in the southern hemisphere, where the mines were set to detect "S-pole down" fields. British ships, notably cruisers and battleships, were well protected by about 1943.
Installing such special equipment was, however, far too expensive and difficult to service all ships that would need it, so the navy developed an alternative called wiping, which Goodeve also devised, and which
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https://en.wikipedia.org/wiki/Spark-gap%20transmitter
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A spark-gap transmitter is an obsolete type of radio transmitter which generates radio waves by means of an electric spark. Spark-gap transmitters were the first type of radio transmitter, and were the main type used during the wireless telegraphy or "spark" era, the first three decades of radio, from 1887 to the end of World War I. German physicist Heinrich Hertz built the first experimental spark-gap transmitters in 1887, with which he proved the existence of radio waves and studied their properties.
A fundamental limitation of spark-gap transmitters is that they generate a series of brief transient pulses of radio waves called damped waves; they are unable to produce the continuous waves used to carry audio (sound) in modern AM or FM radio transmission. So spark-gap transmitters could not transmit audio, and instead transmitted information by radiotelegraphy; the operator switched the transmitter on and off with a telegraph key, creating pulses of radio waves to spell out text messages in Morse code.
The first practical spark gap transmitters and receivers for radiotelegraphy communication were developed by Guglielmo Marconi around 1896. One of the first uses for spark-gap transmitters was on ships, to communicate with shore and broadcast a distress call if the ship was sinking. They played a crucial role in maritime rescues such as the 1912 RMS Titanic disaster. After World War I, vacuum tube transmitters were developed, which were less expensive and produced continuous waves which had a greater range, produced less interference, and could also carry audio, making spark transmitters obsolete by 1920. The radio signals produced by spark-gap transmitters are electrically "noisy"; they have a wide bandwidth, creating radio frequency interference (RFI) that can disrupt other radio transmissions. This type of radio emission has been prohibited by international law since 1934.
Theory of operation
Electromagnetic waves are radiated by electric charges when they are
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https://en.wikipedia.org/wiki/Electrical%20wiring
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Electrical wiring is an electrical installation of cabling and associated devices such as switches, distribution boards, sockets, and light fittings in a structure.
Wiring is subject to safety standards for design and installation. Allowable wire and cable types and sizes are specified according to the circuit operating voltage and electric current capability, with further restrictions on the environmental conditions, such as ambient temperature range, moisture levels, and exposure to sunlight and chemicals.
Associated circuit protection, control, and distribution devices within a building's wiring system are subject to voltage, current, and functional specifications. Wiring safety codes vary by locality, country, or region. The International Electrotechnical Commission (IEC) is attempting to harmonise wiring standards among member countries, but significant variations in design and installation requirements still exist.
Wiring codes of practice and regulations
Wiring installation codes and regulations are intended to protect people and property from electrical shock and fire hazards. They are usually based on a model code (with or without local amendments) produced by a national or international standards organisation, such as the IEC.
Australia and New Zealand
In Australia and New Zealand, the AS/NZS 3000 standard, commonly known as the "wiring rules", specifies requirements for the selection and installation of electrical equipment, and the design and testing of such installations. The standard is mandatory in both New Zealand and Australia; therefore, all electrical work covered by the standard must comply.
Europe
In European countries, an attempt has been made to harmonise national wiring standards in an IEC standard, IEC 60364 Electrical Installations for Buildings. Hence national standards follow an identical system of sections and chapters. However, this standard is not written in such language that it can readily be adopted as a national wiring code.
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https://en.wikipedia.org/wiki/Reciprocal%20polynomial
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In algebra, given a polynomial
with coefficients from an arbitrary field, its reciprocal polynomial or reflected polynomial, denoted by or , is the polynomial
That is, the coefficients of are the coefficients of in reverse order. Reciprocal polynomials arise naturally in linear algebra as the characteristic polynomial of the inverse of a matrix.
In the special case where the field is the complex numbers, when
the conjugate reciprocal polynomial, denoted , is defined by,
where denotes the complex conjugate of , and is also called the reciprocal polynomial when no confusion can arise.
A polynomial is called self-reciprocal or palindromic if .
The coefficients of a self-reciprocal polynomial satisfy for all .
Properties
Reciprocal polynomials have several connections with their original polynomials, including:
.
is a root of a polynomial if and only if is a root of .
If then is irreducible if and only if is irreducible.
is primitive if and only if is primitive.
Other properties of reciprocal polynomials may be obtained, for instance:
A self-reciprocal polynomial of odd degree is divisible by x+1, hence is not irreducible if its degree is > 1.
Palindromic and antipalindromic polynomials
A self-reciprocal polynomial is also called palindromic because its coefficients, when the polynomial is written in the order of ascending or descending powers, form a palindrome. That is, if
is a polynomial of degree , then is palindromic if for .
Similarly, a polynomial of degree is called antipalindromic if for . That is, a polynomial is antipalindromic if .
Examples
From the properties of the binomial coefficients, it follows that the polynomials are palindromic for all positive integers , while the polynomials are palindromic when is even and antipalindromic when is odd.
Other examples of palindromic polynomials include cyclotomic polynomials and Eulerian polynomials.
Properties
If is a root of a polynomial that is either palindromic
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https://en.wikipedia.org/wiki/Linear%20no-threshold%20model
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The linear no-threshold model (LNT) is a dose-response model used in radiation protection to estimate stochastic health effects such as radiation-induced cancer, genetic mutations and teratogenic effects on the human body due to exposure to ionizing radiation. The model statistically extrapolates effects of radiation from very high doses (where they are observable) into very low doses, where no biological effects may be observed. The LNT model lies at a foundation of a postulate that all exposure to ionizing radiation is harmful, regardless of how low the dose is, and that the effect is cumulative over lifetime.
The LNT model is commonly used by regulatory bodies as a basis for formulating public health policies that set regulatory dose limits to protect against the effects of radiation. The model has also been used in the assessment of cancer risks of mutagenic chemicals. The validity of the LNT model, however, is disputed, and other significant models exist: the threshold model, which assumes that very small exposures are harmless, the radiation hormesis model, which says that radiation at very small doses can be beneficial, and the supra-linear model based on observational data. Whenever the cancer risk is estimated from real data at low doses, and not from extrapolation of observations at high doses, the supra-linear model is verified. It has been argued that the LNT model may have created an irrational fear of radiation.
Different organizations take different approaches to the LNT model. For example, the US Nuclear Regulatory Commission and United States Environmental Protection Agency endorse the model, while a number of other bodies deprecate it. One of the organizations for establishing recommendations on radiation protection guidelines internationally, the United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) that previously supported the LNT model, no longer supports the model for very low radiation doses.
Introduction
Stocha
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https://en.wikipedia.org/wiki/Radiation%20hormesis
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Radiation hormesis is the hypothesis that low doses of ionizing radiation (within the region of and just above natural background levels) are beneficial, stimulating the activation of repair mechanisms that protect against disease, that are not activated in absence of ionizing radiation. The reserve repair mechanisms are hypothesized to be sufficiently effective when stimulated as to not only cancel the detrimental effects of ionizing radiation but also inhibit disease not related to radiation exposure (see hormesis). It has been a mainstream concept since at least 2009.
While the effects of high and acute doses of ionising radiation are easily observed and understood in humans (e.g. Japanese atomic bomb survivors), the effects of low-level radiation are very difficult to observe and highly controversial. This is because the baseline cancer rate is already very high and the risk of developing cancer fluctuates 40% because of individual life style and environmental effects, obscuring the subtle effects of low-level radiation. An acute effective dose of 100 millisieverts may increase cancer risk by ~0.8%. However, children are particularly sensitive to radioactivity, with childhood leukemias and other cancers increasing even within natural and man-made background radiation levels (under 4 mSv cumulative with 1 mSv being an average annual dose from terrestrial and cosmic radiation, excluding radon which primarily doses the lung). There is limited evidence that exposures around this dose level will cause negative subclinical health impacts to neural development. Students born in regions of higher Chernobyl fallout performed worse in secondary school, particularly in mathematics. "Damage is accentuated within families (i.e., siblings comparison) and among children born to parents with low education..." who often don't have the resources to overcome this additional health challenge.
Hormesis remains largely unknown to the public. Government and regulatory bodies disagre
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https://en.wikipedia.org/wiki/Ampelography
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Ampelography (ἄμπελος, "vine" + γράφος, "writing") is the field of botany concerned with the identification and classification of grapevines, Vitis spp. Traditionally this has been done by comparing the shape and colour of the vine leaves and grape berries; more recently the study of vines has been revolutionised by DNA fingerprinting.
Early history
The grape vine is an extremely variable species and some varieties, such as Pinot, mutate particularly frequently. At the same time, the wine and table grape industries have been important since ancient times, so large sums of money can depend on the correct identification of different varieties and clones of grapevines.
The science of ampelography began seriously in the 19th century, when it became important to understand more about the different species of vine, as they had very different resistance to disease and pests such as phylloxera.
Many vine identification books were published at this time, one of which is Victor Rendu's Ampélographie française of 1857, featuring hand-colored lithographs by Eugene Grobon.
Pierre Galet
Until the Second World War, ampelography had been an art. Then Pierre Galet of the École nationale supérieure agronomique de Montpellier made a systematic assembly of criteria for the identification of vines. The Galet system was based on the shape and contours of the leaves, the characteristics of growing shoots, shoot tips, petioles, the sex of the flowers, the shape of the grape clusters and the colour, size and pips of the grapes themselves. The grapes are less affected by environmental factors than the leaves and the shoots, but are obviously not around for as long. He even included grape flavour as a criterion, but this is rather subjective.
Galet then published the definitive book, Ampélographie pratique, in 1952, featuring 9,600 types of vine. Ampélographie pratique was translated into English by Lucie Morton, published in 1979 and updated in 2000.
Illustrated Historical Universal Am
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https://en.wikipedia.org/wiki/Cell%20culture
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Cell culture or tissue culture is the process by which cells are grown under controlled conditions, generally outside of their natural environment. The term "tissue culture" was coined by American pathologist Montrose Thomas Burrows. This technique is also called micropropagation. After the cells of interest have been isolated from living tissue, they can subsequently be maintained under carefully controlled conditions. They need to be kept at body temperature (37 °C) in an incubator. These conditions vary for each cell type, but generally consist of a suitable vessel with a substrate or rich medium that supplies the essential nutrients (amino acids, carbohydrates, vitamins, minerals), growth factors, hormones, and gases (CO2, O2), and regulates the physio-chemical environment (pH buffer, osmotic pressure, temperature). Most cells require a surface or an artificial substrate to form an adherent culture as a monolayer (one single-cell thick), whereas others can be grown free floating in a medium as a suspension culture. This is typically facilitated via use of a liquid, semi-solid, or solid growth medium, such as broth or agar. Tissue culture commonly refers to the culture of animal cells and tissues, with the more specific term plant tissue culture being used for plants. The lifespan of most cells is genetically determined, but some cell-culturing cells have been “transformed” into immortal cells which will reproduce indefinitely if the optimal conditions are provided.
In practice, the term "cell culture" now refers to the culturing of cells derived from multicellular eukaryotes, especially animal cells, in contrast with other types of culture that also grow cells, such as plant tissue culture, fungal culture, and microbiological culture (of microbes). The historical development and methods of cell culture are closely interrelated to those of tissue culture and organ culture. Viral culture is also related, with cells as hosts for the viruses.
The laboratory techni
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https://en.wikipedia.org/wiki/Pentyl%20butyrate
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Pentyl butyrate, also known as pentyl butanoate or amyl butyrate, is an ester that is formed when pentanol is reacted with butyric acid, usually in the presence of sulfuric acid as a catalyst. This ester has a smell reminiscent of pear or apricot. This chemical is used as an additive in cigarettes.
References
Flavors
Butyrate esters
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https://en.wikipedia.org/wiki/Accumulation%20function
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The accumulation function a(t) is a function defined in terms of time t expressing the ratio of the value at time t (future value) and the initial investment (present value). It is used in interest theory.
Thus a(0)=1 and the value at time t is given by:
.
where the initial investment is
For various interest-accumulation protocols, the accumulation function is as follows (with i denoting the interest rate and d denoting the discount rate):
simple interest:
compound interest:
simple discount:
compound discount:
In the case of a positive rate of return, as in the case of interest, the accumulation function is an increasing function.
Variable rate of return
The logarithmic or continuously compounded return, sometimes called force of interest, is a function of time defined as follows:
which is the rate of change with time of the natural logarithm of the accumulation function.
Conversely:
reducing to
for constant .
The effective annual percentage rate at any time is:
See also
Time value of money
Mathematical finance
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https://en.wikipedia.org/wiki/Token%20bucket
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The token bucket is an algorithm used in packet-switched and telecommunications networks. It can be used to check that data transmissions, in the form of packets, conform to defined limits on bandwidth and burstiness (a measure of the unevenness or variations in the traffic flow). It can also be used as a scheduling algorithm to determine the timing of transmissions that will comply with the limits set for the bandwidth and burstiness: see network scheduler.
Overview
The token bucket algorithm is based on an analogy of a fixed capacity bucket into which tokens, normally representing a unit of bytes or a single packet of predetermined size, are added at a fixed rate. When a packet is to be checked for conformance to the defined limits, the bucket is inspected to see if it contains sufficient tokens at that time. If so, the appropriate number of tokens, e.g. equivalent to the length of the packet in bytes, are removed ("cashed in"), and the packet is passed, e.g., for transmission. The packet does not conform if there are insufficient tokens in the bucket, and the contents of the bucket are not changed. Non-conformant packets can be treated in various ways:
They may be dropped.
They may be enqueued for subsequent transmission when sufficient tokens have accumulated in the bucket.
They may be transmitted, but marked as being non-conformant, possibly to be dropped subsequently if the network is overloaded.
A conforming flow can thus contain traffic with an average rate up to the rate at which tokens are added to the bucket, and have a burstiness determined by the depth of the bucket. This burstiness may be expressed in terms of either a jitter tolerance, i.e. how much sooner a packet might conform (e.g. arrive or be transmitted) than would be expected from the limit on the average rate, or a burst tolerance or maximum burst size, i.e. how much more than the average level of traffic might conform in some finite period.
Algorithm
The token bucket algorithm can be
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https://en.wikipedia.org/wiki/Columbia%20%28supercomputer%29
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Columbia was a supercomputer built by Silicon Graphics (SGI) for the National Aeronautics and Space Administration (NASA), installed in 2004 at the NASA Advanced Supercomputing (NAS) facility located at Moffett Field in California. Named in honor of the crew who died in the Space Shuttle Columbia disaster, it increased NASA's supercomputing capacity ten-fold for the agency's science, aeronautics and exploration programs.
Missions run on Columbia include high-fidelity simulations of the Space Shuttle vehicle and launch systems, hurricane track prediction, global ocean circulation, and the physics of supernova detonations.
History
Columbia debuted as the second most powerful supercomputer on the TOP500 list in November 2004 at a LINPACK rating of 51.87 teraflops, or 51.87 trillion floating point calculations per second. By June 2007 it had dropped to 13th.
It was originally composed of 20 interconnected SGI Altix 3700 512-processor multi-rack systems running SUSE Linux Enterprise, using Intel Itanium 2 Montecito and Montvale processors. In 2006, NASA and SGI added four new Altix 4700 nodes containing 256 dual-core processors, which decreased the physical footprint and the power cost of the supercomputer. The nodes were connected with InfiniBand single and double data rate (SDR and DDR) cabling with transfer speeds of up to 10 gigabits per second.
The SGI Altix platform was selected due to a positive experience with Kalpana, a single-node Altix 512-CPU system built and operated by NASA and SGI and named after Columbia astronaut Kalpana Chawla, the first Indian-born woman to fly in space. Kalpana was later integrated into the Columbia supercomputer system as the first node of twenty.
At its peak, Columbia had a total of 10,240 processors and 20 terabytes of memory, 440 terabytes of online storage, and 10 petabytes of archival tape storage. The Project Columbia team, composed mostly of computer scientists and engineers from NAS, SGI, and Intel, were awarded the Gov
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https://en.wikipedia.org/wiki/Solipsis
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Solipsis is a free and open-source system for a massively multi-participant shared virtual world designed by Joaquin Keller and Gwendal Simon at France Télécom Research and Development Labs. It aims to provide the infrastructure for a metaverse-like public virtual territory. Relying on a peer-to-peer architecture, the virtual world may potentially be inhabited by a theoretically unlimited number of participants.
Motivations
A central objective of Solipsis is to create a virtual world which is as independent as possible from the influence of private interests, such as server ownership. In order to achieve this, it is based around a peer-to-peer model rather than the traditional server-client one. Additionally, it aims to give users more flexibility in designing interfaces and content in their individual segments of the virtual world.
Main principles
A Solipsis entity is a basic element of the virtual world. To exist, an entity should run a node that may be controlled by a navigator. Nodes are self-organized in a pure peer-to-peer network, in which relationships depend on virtual proximity. A navigator is mainly a graphical user interface, but some communication services may be added to one for interaction between entities.
The virtual world is initially empty and is only filled by entities run by end users' computers. All Solipsis nodes are functionally equal, and no preordained infrastructure is required. This eliminates as far as possible any restrictions on the content or functionality of the world.
Current status
Solipsis currently consists of:
A peer-to-peer protocol over UDP. The Solipsis protocol gives a node the ability to broadcast its presence within the virtual world. Moreover, this protocol aims to guarantee the maintenance of some global properties.
A node-navigator interface, which takes the form of an API between the node and the navigator. Currently written in XML-RPC, this interface allows a navigator to control a node and to retrieve inf
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https://en.wikipedia.org/wiki/Linear%20approximation
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In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.
Definition
Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case states that
where is the remainder term. The linear approximation is obtained by dropping the remainder:
This is a good approximation when is close enough to since a curve, when closely observed, will begin to resemble a straight line. Therefore, the expression on the right-hand side is just the equation for the tangent line to the graph of at . For this reason, this process is also called the tangent line approximation. Linear approximations in this case are further improved when the second derivative of a, , is sufficiently small (close to zero) (i.e., at or near an inflection point).
If is concave down in the interval between and , the approximation will be an overestimate (since the derivative is decreasing in that interval). If is concave up, the approximation will be an underestimate.
Linear approximations for vector functions of a vector variable are obtained in the same way, with the derivative at a point replaced by the Jacobian matrix. For example, given a differentiable function with real values, one can approximate for close to by the formula
The right-hand side is the equation of the plane tangent to the graph of at
In the more general case of Banach spaces, one has
where is the Fréchet derivative of at .
Applications
Optics
Gaussian optics is a technique in geometrical optics that describes the behaviour of light rays in optical systems by using the paraxial approximation, in which only rays which make small angles with the optical axis of the system are considered. In this approximation, trigonometric functions can be expressed as l
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https://en.wikipedia.org/wiki/Jones%20polynomial
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In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable with integer coefficients.
Definition by the bracket
Suppose we have an oriented link , given as a knot diagram. We will define the Jones polynomial by using Louis Kauffman's bracket polynomial, which we denote by . Here the bracket polynomial is a Laurent polynomial in the variable with integer coefficients.
First, we define the auxiliary polynomial (also known as the normalized bracket polynomial)
where denotes the writhe of in its given diagram. The writhe of a diagram is the number of positive crossings ( in the figure below) minus the number of negative crossings (). The writhe is not a knot invariant.
is a knot invariant since it is invariant under changes of the diagram of by the three Reidemeister moves. Invariance under type II and III Reidemeister moves follows from invariance of the bracket under those moves. The bracket polynomial is known to change by a factor of under a type I Reidemeister move. The definition of the polynomial given above is designed to nullify this change, since the writhe changes appropriately by or under type I moves.
Now make the substitution in to get the Jones polynomial . This results in a Laurent polynomial with integer coefficients in the variable .
Jones polynomial for tangles
This construction of the Jones polynomial for tangles is a simple generalization of the Kauffman bracket of a link. The construction was developed by Vladimir Turaev and published in 1990.
Let be a non-negative integer and denote the set of all isotopic types of tangle diagrams, with ends, having no crossing points and no closed components (smoothings). Turaev's construction makes use of the previous construction for the Kauffman bracket and associates to each -
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https://en.wikipedia.org/wiki/Alexander%20polynomial
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In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a version of this polynomial, now called the Alexander–Conway polynomial, could be computed using a skein relation, although its significance was not realized until the discovery of the Jones polynomial in 1984. Soon after Conway's reworking of the Alexander polynomial, it was realized that a similar skein relation was exhibited in Alexander's paper on his polynomial.
Definition
Let K be a knot in the 3-sphere. Let X be the infinite cyclic cover of the knot complement of K. This covering can be obtained by cutting the knot complement along a Seifert surface of K and gluing together infinitely many copies of the resulting manifold with boundary in a cyclic manner. There is a covering transformation t acting on X. Consider the first homology (with integer coefficients) of X, denoted . The transformation t acts on the homology and so we can consider a module over the ring of Laurent polynomials . This is called the Alexander invariant or Alexander module.
The module is finitely presentable; a presentation matrix for this module is called the Alexander matrix. If the number of generators, , is less than or equal to the number of relations, , then we consider the ideal generated by all minors of the matrix; this is the zeroth Fitting ideal or Alexander ideal and does not depend on choice of presentation matrix. If , set the ideal equal to 0. If the Alexander ideal is principal, take a generator; this is called an Alexander polynomial of the knot. Since this is only unique up to multiplication by the Laurent monomial , one often fixes a particular unique form. Alexander's choice of normalization is to make the polynomial have a positive constant term.
Alexander proved that the Alexander ideal is nonzero and always p
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https://en.wikipedia.org/wiki/Catastrophic%20failure
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A catastrophic failure is a sudden and total failure from which recovery is impossible. Catastrophic failures often lead to cascading systems failure. The term is most commonly used for structural failures, but has often been extended to many other disciplines in which total and irrecoverable loss occurs, such as a head crash occurrence on a hard disk drive. Such failures are investigated using the methods of forensic engineering, which aims to isolate the cause or causes of failure.
For example, catastrophic failure can be observed in steam turbine rotor failure, which can occur due to peak stress on the rotor; stress concentration increases up to a point at which it is excessive, leading ultimately to the failure of the disc.
In firearms, catastrophic failure usually refers to a rupture or disintegration of the barrel or receiver of the gun when firing it. Some possible causes of this are an out-of-battery gun, an inadequate headspace, the use of incorrect ammunition, the use of ammunition with an incorrect propellant charge, a partially or fully obstructed barrel, or weakened metal in the barrel or receiver. A failure of this type, known colloquially as a "kaboom", or "kB" failure, can pose a threat not only to the user(s) but even many bystanders.
In chemical engineering, thermal runaway can cause catastrophic failure.
Examples
Examples of catastrophic failure of engineered structures include:
The Tay Rail Bridge disaster of 1879, where the center of the bridge was completely destroyed while a train was crossing in a storm. The bridge was badly designed and its replacement was built as a separate structure upstream of the old.
The failure of the South Fork Dam in 1889 released 4.8 billion US gallons (18 billion litres) of water and killed over 2,200 people (popularly known as the Johnstown Flood).
The collapse of the St. Francis Dam in 1928 released 12.4 billion US gallons (47 billion litres) of water, resulting in a death toll of nearly 600 people.
Th
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https://en.wikipedia.org/wiki/F-Secure
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F-Secure Corporation is a global cyber security and privacy company, which has its headquarters in Helsinki, Finland.
The company has offices in Denmark, Finland, France, Germany, India, Italy, Japan, Malaysia, Netherlands, Norway, Poland, Sweden, the United Kingdom and the United States, with a presence in more than 100 countries, and Security Lab operations in Helsinki and in Kuala Lumpur, Malaysia.
F-Secure develops and sells antivirus, VPN, password management, and other consumer cyber security products and services for computers, mobile devices, smart TVs and internet of things devices. The company also offers several free-to-use tools on its website.
History
F-Secure was first established under the name Data Fellows by Petri Allas and Risto Siilasmaa on May 16, 1988. Data Fellows trained computer users and built customized databases. Three years later, the company launched its first major software project and developed the first heuristic scanner for antivirus products. F-Secure’s first antivirus product for Windows PCs was launched in 1994. Data Fellows became F-Secure in 1999. F-Secure was the first company that developed an anti-rootkit technology called BlackLight in 2005.
In June 2015, F-Secure expanded into the enterprise market by acquiring nSense, a Danish company that specializes in security consultation and vulnerability assessment. The purchase of Inverse Path, a privately owned Italian security consultancy with experience in avionics, automative, and industrial control sectors.
F-Secure Client Security received AV-TEST Best Protection award for the fifth time in 2016.
In June 2018, F-Secure acquired security company MWR InfoSecurity for 80 million pounds ($106 million). F-Secure gained the MWR consulting business (now F-Secure Consulting), its threat hunting product, Countercept (now F-Secure Managed Detection and Response), and its suite of phishing protection services, phishd.
February 17th 2022, F-Secure announced a demerger of its cor
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https://en.wikipedia.org/wiki/Integrated%20Guided%20Missile%20Development%20Programme
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The Integrated Guided Missile Development Programme (IGMDP) was an Indian Ministry of Defence programme for the research and development of the comprehensive range of missiles. The programme was managed by the Defence Research and Development Organisation (DRDO) and Ordnance Factories Board in partnership with other Indian government political organisations. The project started in 1982–83 under the leadership of Abdul Kalam who oversaw its ending in 2008 after these strategic missiles were successfully developed.
On 8 January 2008, the DRDO formally announced the successful rated guided missile programme was completed with its design objectives achieved since most of the missiles in the programme had been developed and inducted by the Indian armed forces.
History
By the start of the 1980s, the DRDL had developed competence and expertise in the fields of propulsion, navigation and manufacture of aerospace materials based on the Soviet rocketry technologies. Thus, India's political leadership, which included Prime Minister Indira Gandhi, Defence Minister R. Venkataraman, V.S. Arunachalam (Scientific Advisor to the Defence Minister), decided that all these technologies should be consolidated.
This led to the birth of the Integrated Guided Missile Development Programme with Dr. Abdul Kalam, who had previously been the project director for the SLV-3 programme at ISRO, was inducted as the DRDL Director in 1983 to conceive and lead it. While the scientists proposed the development of each missile consecutively, the Defence Minister R. Venkataraman asked them to reconsider and develop all the missiles simultaneously. Thus, four projects, to be pursued concurrently, were born under the IGMDP:
Dr. APJ Abdul Kalam started multiple projects simultaneously to develop the following types of Indian Guided Missiles missiles.
Short Range Surface to Surface Missile (SSM) ‘Prithvi’
Long Range Surface to Surface Missile (SSM) ‘Agni’
Medium Range Surface to Air Missile (SAM) ‘A
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https://en.wikipedia.org/wiki/FLEX%20%28operating%20system%29
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FLEX is a discontinued single-tasking operating system developed by Technical Systems Consultants (TSC) of West Lafayette, Indiana, for the Motorola 6800 in 1976.
Overview
The original version was distributed on 8" floppy disks; the (smaller) version for 5.25" floppies is called mini-Flex. It was also later ported to the Motorola 6809; that version is called Flex09. All versions are text-based and intended for use on display devices ranging from printing terminals like the Teletype Model 33 ASR to smart terminals. While no graphic displays are supported by TSC software, some hardware supports elementary graphics and pointing devices.
FLEX is a disk-based operating system, using 256-byte sectors on soft-sectored floppies; the disk structure uses linkage bytes in each sector to indicate the next sector in a file or free list. The directory structure is simplified as a result. TSC (and others) provide several programming languages including BASIC in two flavors (standard and extended) and a tokenizing version of extended BASIC called Pre-compiled BASIC, FORTH, C, FORTRAN, and PASCAL.
TSC also wrote a version of FLEX, Smoke Signal DOS, for the California hardware manufacturer Smoke Signal Broadcasting; this version uses forward and reverse linkage bytes in each sector which increase disk reliability at the expense of compatibility and speed.
Later, TSC introduced the multitasking, multi-user, Unix-like UniFLEX operating system, which requires DMA disk controllers, 8" disk, and sold in small numbers. Several of the TSC computer languages were ported to UniFLEX.
During the early 1980s, FLEX was offered by Compusense Ltd as an operating system for the 6809-based Dragon 64 home computer.
Commands
The following commands are supported by different versions of the FLEX operating system.
APPEND
ASN
BACKUP
BUILD
CAT
COPY
COPYNEW
C4MAT
CLEAN
DATE
DELETE
ECHO
EXEC
FIX
GET
I
JUMP
LINK
LIST
MEMTEST1
MON
N
NEWDISK
O
P
P.COR
PO
PRINT
PROT
PSP
Q
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https://en.wikipedia.org/wiki/Packet%20over%20SONET/SDH
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Packet over SONET/SDH, abbreviated POS, is a communications protocol for transmitting packets in the form of the Point to Point Protocol (PPP) over SDH or SONET, which are both standard protocols for communicating digital information using lasers or light emitting diodes (LEDs) over optical fibre at high line rates. POS is defined by RFC 2615 as PPP over SONET/SDH. PPP is the Point to Point Protocol that was designed as a standard method of communicating over point-to-point links. Since SONET/SDH uses point-to-point circuits, PPP is well suited for use over these links. Scrambling is performed during insertion of the PPP packets into the SONET/SDH frame to solve various security attacks including denial-of-service attacks and the imitation of SONET/SDH alarms. This modification was justified as cost-effective because the scrambling algorithm was already used by the standard used to transport ATM cells over SONET/SDH. However, scrambling can optionally be disabled to allow a node to be compatible with another node that uses the now obsoleted RFC 1619 version of Packet over SONET/SDH which lacks the scrambler.
Applications of POS
The most important application of POS is to support sending of IP packets across wide area networks. Large amounts of traffic on the Internet are carried over POS links.
POS is also one of the link layers used by the Resilient Packet Ring standard known as IEEE 802.17.
History of POS
Cisco was involved in making POS an important wide area network protocol. PMC-Sierra produced an important series of early semiconductor devices which
implemented POS.
Details about the name "POS"
POS (packet over SONET) is a double-nested abbreviation. The S represents "SONET/SDH", which itself stands for "Synchronous Optical Network/Synchronous Digital Hierarchy".
Given this information, POS technically stands for "Packet over Synchronous Optical Network/Synchronous Digital Hierarchy".
Complementary Interfaces
The System Packet Interface series of stand
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https://en.wikipedia.org/wiki/Direct-view%20bistable%20storage%20tube
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Direct-view bistable storage tube (DVBST) was an acronym used by Tektronix to describe their line of storage tubes. These were cathode ray tubes (CRT) that stored information written to them using an analog technique inherent in the CRT and based upon the secondary emission of electrons from the phosphor screen itself. The resulting image was visible in the continuously glowing patterns on the face of the CRT.
DVBST technology was anticipated by Andrew Haeff of the US Naval Research Laboratory, and by Williams and Kilburn in the late 1940s. Tek's (Tektronix) Robert H. Anderson refined Haeff's concepts in the late 1950s to produce a reliable and simple DVST.
Principle
The DVBST implements two electron guns: a "flood gun" and a "writing gun". The writing gun scans across a wire grid, charging the grid to create the negative image. The flood gun then floods the grid. Previously charged areas repel the incoming electrons so that electrons only pass through the grid to the phosphor in those areas not previously charged.
The technology offered several advantages and disadvantages.
Advantages
No refreshing is needed.
Very complex pictures can be displayed at very high resolution without flicker.
The cost is much lower.
Disadvantages
They ordinarily do not display color.
Selected part of the picture can not be erased.
The erasing and redrawing process can take several seconds for complex pictures.
No animation in DVST.
Modifying any part of image requires redrawing of entire image.
Applications
Tektronix-made DVBSTs were used for analog oscilloscopes (first in the 564 oscilloscope, then the type 601 monitor (1968), the 611 monitor, the 7313 and 7514 plug-in mainframe oscilloscope, all from Tektronix) and for computer terminals such as the archetypal Tek 4010 and its several successors including the Tektronix 4014. Portions of the screen are individually written-to by a conventional electron beam gun, and "flooded" by a wide, low velocity electron gun. Eras
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https://en.wikipedia.org/wiki/Caridoid%20escape%20reaction
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The caridoid escape reaction, also known as lobstering or tail-flipping, refers to an innate escape mechanism in marine and freshwater crustaceans such as lobsters, krill, shrimp and crayfish.
The reaction, most extensively researched in crayfish, allows crustaceans to escape predators through rapid abdominal flexions that produce powerful swimming strokes—thrusting the crustacean backwards through the water and away from danger. The type of response depends on the part of the crustacean stimulated, but this behavior is complex and is regulated both spatially and temporally through the interactions of several neurons.
Discovery of the first command neuron-mediated behavior
In 1946, C. A. G. Wiersma first described the tail-flip escape in the crayfish Procambarus clarkii and noted that the giant interneurons present in the tail were responsible for the reaction. The aforementioned neuronal fibres consist of a pair of lateral giant interneurons and a pair of medial giant interneurons, and Wiersma found that stimulating just one lateral giant interneuron (LG or LGI) or one medial giant interneuron (MG or MGI) would result in the execution of a tail flip. Wiersma and K. Ikeda then proposed the term "command neuron" in their 1964 publication, and applied it to the giant interneuron's ability to command the expression of the escape response. This was the first description of a command neuron-mediated behavior and it indicated that the depolarization of a neuron could precipitate complex innate behaviors in some organisms.
This concept was further fleshed out with more specific and stringent conditions in 1972 when Kupfermann and Weiss published The Command Neuron Concept. The paper stated that command neurons were neurons (or small sets of neurons) carrying the entire command signal for a natural behavioral response. According to the authors, command neurons were both necessary and sufficient in the production of a behavioral response. The concept of command neuron-m
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https://en.wikipedia.org/wiki/Unit%20of%20selection
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A unit of selection is a biological entity within the hierarchy of biological organization (for example, an entity such as: a self-replicating molecule, a gene, a cell, an organism, a group, or a species) that is subject to natural selection. There is debate among evolutionary biologists about the extent to which evolution has been shaped by selective pressures acting at these different levels.
There is debate over the relative importance of the units themselves. For instance, is it group or individual selection that has driven the evolution of altruism? Where altruism reduces the fitness of individuals, individual-centered explanations for the evolution of altruism become complex and rely on the use of game theory, for instance; see kin selection and group selection. There also is debate over the definition of the units themselves, and the roles for selection and replication, and whether these roles may change in the course of evolution.
Fundamental theory
Two useful introductions to the fundamental theory underlying the unit of selection issue and debate, which also present examples of multi-level selection from the entire range of the biological hierarchy (typically with entities at level N-1 competing for increased representation, i.e., higher frequency, at the immediately higher level N, e.g., organisms in populations or cell lineages in organisms), are Richard Lewontin's classic piece The Units of Selection and John Maynard-Smith and Eörs Szathmáry's co-authored book, The Major Transitions in Evolution. As a theoretical introduction to units of selection, Lewontin writes:
The generality of the principles of natural selection means that any entities in nature that have variation, reproduction, and heritability may evolve. ...the principles can be applied equally to genes, organisms, populations, species, and at opposite ends of the scale, prebiotic molecules and ecosystems." (1970, pp. 1-2)
Elisabeth Lloyd's book The Structure and Confirmation of Evolutio
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https://en.wikipedia.org/wiki/Motorola%206845
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The Motorola 6845, or MC6845, is a display controller that was widely used in 8-bit computers during the 1980s. Originally intended for designs based on the Motorola 6800 CPU and given a related part number, it was more widely used alongside various other processors, and was most commonly found in machines based on the Zilog Z80 and MOS 6502.
The 6845 is not an entire display solution on its own; the chip's main function is to properly time access to the display memory, and to calculate the memory address of the next portion to be drawn. Other circuitry in the machine then uses the address provided by the 6845 to fetch the pattern and then draw it. The implementation of that hardware is entirely up to the designer and varied widely among machines. The 6845 is intended for character displays, but could also be used for pixel-based graphics, with some clever programming.
Among its better-known uses is the BBC Micro, Amstrad CPC, and Videx VideoTerm display cards for the Apple II. It is also part of many early graphics adapter cards for the IBM PC, including the MDA, Hercules Graphics Card (HGC), Color Graphics Adapter (CGA) and the Plantronics Colorplus. Its functionality was duplicated and extended by custom circuits in the EGA and VGA PC video adapters.
Originally designed by Hitachi as the HD46505, Hitachi-built versions are in a wide variety of Japanese computers, from Sony, Sharp, Panasonic, and Casio. It is also known as the 6845 CRTC or the CRTC6845, meaning "cathode-ray tube controller". This version was used on the Apricot PC and Victor 9000 to provide a 800x400 resolution monochrome display.
A common clone of this CRT controller is the United Microelectronics Corporation (UMC) UM6845E CRT controller.
During the time of cold war technology embargoes, the 6845 was cloned in Bulgaria under the designation CM607.
Overview
The chip generates the signals necessary to interface with a raster display but does not generate the actual pixels, though it does con
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https://en.wikipedia.org/wiki/SGI%20O2
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The O2 was an entry-level Unix workstation introduced in 1996 by Silicon Graphics, Inc. (SGI) to replace their earlier Indy series. Like the Indy, the O2 used a single MIPS microprocessor and was intended to be used mainly for multimedia. Its larger counterpart was the SGI Octane. The O2 was SGI's last attempt at a low-end workstation.
Hardware
System architecture
Originally known as the "Moosehead" project, the O2 architecture featured a proprietary high-bandwidth Unified Memory Architecture (UMA) to connect system components. A PCI bus is bridged onto the UMA with one slot available. It had a designer case and an internal modular construction. Two SCSI drives could be mounted on special caddies (1 in the later R10000/R12000 models due to heat constraints) and an optional video capture / sound cassette mounted on the far left side.
CPU
The O2 comes in two distinct CPU flavours; the low-end MIPS 180 to 350 MHz R5000- or RM7000-based units and the higher-end 150 to 400 MHz R10000- or R12000-based units. The 200 MHz R5000 CPUs with 1 MB L2-cache are generally noticeably faster than the 180 MHz R5000s with 512 KB cache. There is a hobbyist project that has successfully retrofitted a 600 MHz RM7xxx MIPS processor into the O2.
Memory
There are eight DIMM slots on the motherboard and memory, and all O2s are expandable to 1 GB using proprietary 239-pin SDRAM DIMMs. The Memory & Rendering Engine (MRE) ASIC contains the memory controller. Memory is accessed via a 133 MHz 144-bit bus, of which 128 bits are for data and the remaining for ECC. This bus is interfaced by a set of buffers to the 66 MHz 256-bit memory system.
I/O
I/O functionality is provided by the IO Engine ASIC. The ASIC provides a 64-bit PCI bus, an ISA bus, two PS/2 ports for keyboard and mouse, and a 10/100 Base-T Ethernet port. The PCI bus has one 64-bit slot, but the ISA bus is present solely for attaching a Super I/O chip to provide serial and parallel ports.
Disks
The O2 carries an UltraWide SCSI
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https://en.wikipedia.org/wiki/Math%20League
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Math League is a math competition for elementary, middle, and high school students in the United States, Canada, and other countries. The Math League was founded in 1977 by two high school mathematics teachers, Steven R. Conrad and Daniel Flegler. Math Leagues, Inc. publishes old contests through a series of books entitled Math League Press. The purpose of the Math League Contests is to provide students "an enriching opportunity to participate in an academically-oriented activity" and to let students "gain recognition for mathematical achievement".
Math League runs three contest formats:
Grades 4-5: 30 multiple-choice questions to solve in 30 minutes, covering arithmetic and basic principles
Grades 6-8: 35 multiple-choice questions to solve in 30 minutes, covering advanced arithmetic and basic topics in geometry and algebra
Grades 9-12: Series of 6 contests. Each contest contains 6 short-answer questions to solve in 30 minutes, covering geometry, algebra, trigonometry, and other advanced pre-calculus topics.
Only plain paper, pencil or pen, and a calculator without QWERTY keyboard are allowed.
Students who score above 12 points in grades 4 and 5, and above 15 points in grades 6-8 are awarded a 'Certificate of Merit." Which means they win
References
External links
Math League Homepage
Mathematics competitions
Recurring events established in 1977
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https://en.wikipedia.org/wiki/Dump%20truck
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A dump truck, known also as a dumping truck, dump trailer, dumper trailer, dump lorry or dumper lorry or a dumper for short, is used for transporting materials (such as dirt, gravel, or demolition waste) for construction as well as coal. A typical dump truck is equipped with an open-box bed, which is hinged at the rear and equipped with hydraulic rams to lift the front, allowing the material in the bed to be deposited ("dumped") on the ground behind the truck at the site of delivery. In the UK, Australia, South Africa and India the term applies to off-road construction plants only and the road vehicle is known as a tip lorry, tipper lorry (UK, India), tipper truck, tip truck, tip trailer or tipper trailer or simply a tipper (Australia, New Zealand, South Africa).
History
The dump truck is thought to have been first conceived in the farms of late 19th century western Europe. Thornycroft developed a steam dust-cart in 1896 with a tipper mechanism. The first motorized dump trucks in the United States were developed by small equipment companies such as The Fruehauf Trailer Corporation, Galion Buggy Co. and Lauth-Juergens among many others around 1910. Hydraulic dump beds were introduced by Wood Hoist Co. shortly after. Such companies flourished during World War I due to massive wartime demand. August Fruehauf had obtained military contracts for his semi-trailer, invented in 1914 and later created the partner vehicle, the semi-truck for use in World War I. After the war, Fruehauf introduced hydraulics in his trailers. They offered hydraulic lift gates, hydraulic winches and a dump trailer for sales in the early 1920s. Fruehauf became the premier supplier of dump trailers and their famed "bathtub dump" was considered to be the best by heavy haulers, road and mining construction firms.
Companies like Galion Buggy Co. continued to grow after the war by manufacturing a number of express bodies and some smaller dump bodies that could be easily installed on either stock or
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https://en.wikipedia.org/wiki/Higman%E2%80%93Sims%20graph
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In mathematical graph theory, the Higman–Sims graph is a 22-regular undirected graph with 100 vertices and 1100 edges. It is the unique strongly regular graph srg(100,22,0,6), where no neighboring pair of vertices share a common neighbor and each non-neighboring pair of vertices share six common neighbors. It was first constructed by and rediscovered in 1968 by Donald G. Higman and Charles C. Sims as a way to define the Higman–Sims group, a subgroup of index two in the group of automorphisms of the Higman–Sims graph.
Construction
From M22 graph
Take the M22 graph, a strongly regular graph srg(77,16,0,4) and augment it with 22 new vertices corresponding to the points of S(3,6,22), each block being connected to its points, and one additional vertex C connected to the 22 points.
From Hoffman–Singleton graph
There are 100 independent sets of size 15 in the Hoffman–Singleton graph. Create a new graph with 100 corresponding vertices, and connect vertices whose corresponding independent sets have exactly 0 or 8 elements in common.
The resulting Higman–Sims graph can be partitioned into two copies of the Hoffman–Singleton graph in 352 ways.
From a cube
Take a cube with vertices labeled 000, 001, 010, ..., 111. Take all 70 possible 4-sets of vertices, and retain only the ones whose XOR evaluates to 000; there are 14 such 4-sets, corresponding to the 6 faces + 6 diagonal-rectangles + 2 parity tetrahedra. This is a 3-(8,4,1) block design on 8 points, with 14 blocks of block size 4, each point appearing in 7 blocks, each pair of points appearing 3 times, each triplet of points occurring exactly once. Permute the original 8 vertices any of 8! = 40320 ways, and discard duplicates. There are then 30 different ways to relabel the vertices (i.e., 30 different designs that are all isomorphic to each other by permutation of the points). This is because there are 1344 automorphisms, and 40320/1344 = 30.
Create a vertex for each of the 30 designs, and for each row of every design
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https://en.wikipedia.org/wiki/Bacterial%20oxidation
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Bacteria biooxidation is an oxidation process caused by microbes where the valuable metal remains (but becomes enriched) in the solid phase. In this process, the metal remains in the solid phase and the liquid can be discarded.
Bacterial oxidation is a biohydrometallurgical process developed for pre-cyanidation treatment of refractory gold ores or concentrates. The bacterial culture is a mixed culture of Acidithiobacillus ferrooxidans, Acidithiobacillus thiooxidans and Leptospirillum ferrooxidans. The bacterial oxidation process comprises contacting refractory sulfide ROM ore or concentrate with a strain of the bacterial culture for a suitable treatment period under an optimum operating environment. The bacteria oxidise the sulfide minerals, thus liberating the occluded gold for subsequent recovery via cyanidation.
The BIOX® process is a proprietary technology owned by Biomin South Africa and used under licence by a number of operating mines. The BIOX® process involves bacterial oxidation in agitated tanks for pre-treatment of refractory ores and concentrates ahead of conventional cyanide leach for gold recovery.
Under controlled continuous plant conditions, the number of bacterial cells and their activity is optimised to attain the highest rate of sulfide oxidation. The bacteria require a very acidic environment (pH 1.0 to 4.0), a temperature of between 30 and 45 °C, and a steady supply of oxygen and carbon dioxide for optimum growth and activity. The unusual operating conditions for the bacteria are not favourable for the growth of most other microbes, thus eliminating the need for sterility during the bacterial oxidation process. Because organic substances are toxic to the bacteria, they are non-pathogenic and incapable of causing disease. The bacteria employed in the process do not, therefore, pose a health risk to humans or any animals.
The bacterial oxidation of iron sulfide minerals produces iron(III) sulfate and sulfuric acid, and in the case of
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https://en.wikipedia.org/wiki/Hall%E2%80%93Janko%20graph
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In the mathematical field of graph theory, the Hall–Janko graph, also known as the Hall-Janko-Wales graph, is a 36-regular undirected graph with 100 vertices and 1800 edges.
It is a rank 3 strongly regular graph with parameters (100,36,14,12) and a maximum coclique of size 10. This parameter set is not unique, it is however uniquely determined by its parameters as a rank 3 graph. The Hall–Janko graph was originally constructed by D. Wales to establish the existence of the Hall-Janko group as an index 2 subgroup of its automorphism group.
The Hall–Janko graph can be constructed out of objects in U3(3), the simple group of order 6048:
In U3(3) there are 36 simple maximal subgroups of order 168. These are the vertices of a subgraph, the U3(3) graph. A 168-subgroup has 14 maximal subgroups of order 24, isomorphic to S4. Two 168-subgroups are called adjacent when they intersect in a 24-subgroup. The U3(3) graph is strongly regular, with parameters (36,14,4,6)
There are 63 involutions (elements of order 2). A 168-subgroup contains 21 involutions, which are defined to be neighbors.
Outside U3(3) let there be a 100th vertex C, whose neighbors are the 36 168-subgroups. A 168-subgroup then has 14 common neighbors with C and in all 1+14+21 neighbors.
An involution is found in 12 of the 168-subgroups. C and an involution are non-adjacent, with 12 common neighbors.
Two involutions are defined as adjacent when they generate a dihedral subgroup of order 8. An involution has 24 involutions as neighbors.
The characteristic polynomial of the Hall–Janko graph is . Therefore the Hall–Janko graph is an integral graph: its spectrum consists entirely of integers.
References
Group theory
Individual graphs
Regular graphs
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https://en.wikipedia.org/wiki/Modular%20representation%20theory
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Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. As well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory.
Within finite group theory, character-theoretic results proved by Richard Brauer using modular representation theory played an important role in early progress towards the classification of finite simple groups, especially for simple groups whose characterization was not amenable to purely group-theoretic methods because their Sylow 2-subgroups were too small in an appropriate sense. Also, a general result on embedding of elements of order 2 in finite groups called the Z* theorem, proved by George Glauberman using the theory developed by Brauer, was particularly useful in the classification program.
If the characteristic p of K does not divide the order |G|, then modular representations are completely reducible, as with ordinary (characteristic 0) representations, by virtue of Maschke's theorem. In the other case, when |G| ≡ 0 mod p, the process of averaging over the group needed to prove Maschke's theorem breaks down, and representations need not be completely reducible. Much of the discussion below implicitly assumes that the field K is sufficiently large (for example, K algebraically closed suffices), otherwise some statements need refinement.
History
The earliest work on representation theory over finite fields is by who showed that when p does not divide the order of the group, the representation theory is similar to that in characteristic 0. He also investigated modular invariants of some finite groups. The systematic study of modular representations, when the characteristic p divides the order of the group, was started by and was contin
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https://en.wikipedia.org/wiki/Multiplicative%20group
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In mathematics and group theory, the term multiplicative group refers to one of the following concepts:
the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations is referred to as multiplication. In the case of a field F, the group is , where 0 refers to the zero element of F and the binary operation • is the field multiplication,
the algebraic torus GL(1)..
Examples
The multiplicative group of integers modulo n is the group under multiplication of the invertible elements of . When n is not prime, there are elements other than zero that are not invertible.
The multiplicative group of positive real numbers is an abelian group with 1 its identity element. The logarithm is a group isomorphism of this group to the additive group of real numbers, .
The multiplicative group of a field is the set of all nonzero elements: , under the multiplication operation. If is finite of order q (for example q = p a prime, and ), then the multiplicative group is cyclic: .
Group scheme of roots of unity
The group scheme of n-th roots of unity is by definition the kernel of the n-power map on the multiplicative group GL(1), considered as a group scheme. That is, for any integer n > 1 we can consider the morphism on the multiplicative group that takes n-th powers, and take an appropriate fiber product of schemes, with the morphism e that serves as the identity.
The resulting group scheme is written μn (or ). It gives rise to a reduced scheme, when we take it over a field K, if and only if the characteristic of K does not divide n. This makes it a source of some key examples of non-reduced schemes (schemes with nilpotent elements in their structure sheaves); for example μp over a finite field with p elements for any prime number p.
This phenomenon is not easily expressed in the classical language of algebraic geometry. For example, it turns out to be of major importance in expressing the duality theory of abel
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https://en.wikipedia.org/wiki/Tail%20call
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In computer science, a tail call is a subroutine call performed as the final action of a procedure. If the target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize in implementations.
Tail calls can be implemented without adding a new stack frame to the call stack. Most of the frame of the current procedure is no longer needed, and can be replaced by the frame of the tail call, modified as appropriate (similar to overlay for processes, but for function calls). The program can then jump to the called subroutine. Producing such code instead of a standard call sequence is called tail-call elimination or tail-call optimization. Tail-call elimination allows procedure calls in tail position to be implemented as efficiently as goto statements, thus allowing efficient structured programming. In the words of Guy L. Steele, "in general, procedure calls may be usefully thought of as GOTO statements which also pass parameters, and can be uniformly coded as [machine code] JUMP instructions."
Not all programming languages require tail-call elimination. However, in functional programming languages, tail-call elimination is often guaranteed by the language standard, allowing tail recursion to use a similar amount of memory as an equivalent loop. The special case of tail-recursive calls, when a function calls itself, may be more amenable to call elimination than general tail calls. When the language semantics do not explicitly support general tail calls, a compiler can often still optimize sibling calls, or tail calls to functions which take and return the same types as the caller.
Description
When a function is called, the computer must "remember" the place it was called from, the return address, so that it can return to that location with the result once the call is complete. Typically, this information is saved
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https://en.wikipedia.org/wiki/Photoelectrochemical%20cell
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A "photoelectrochemical cell" is one of two distinct classes of device. The first produces electrical energy similarly to a dye-sensitized photovoltaic cell, which meets the standard definition of a photovoltaic cell. The second is a photoelectrolytic cell, that is, a device which uses light incident on a photosensitizer, semiconductor, or aqueous metal immersed in an electrolytic solution to directly cause a chemical reaction, for example to produce hydrogen via the electrolysis of water.
Both types of device are varieties of solar cell, in that a photoelectrochemical cell's function is to use the photoelectric effect (or, very similarly, the photovoltaic effect) to convert electromagnetic radiation (typically sunlight) either directly into electrical power, or into something which can itself be easily used to produce electrical power (hydrogen, for example, can be burned to create electrical power, see photohydrogen).
Two principles
The standard photovoltaic effect, as operating in standard photovoltaic cells, involves the excitation of negative charge carriers (electrons) within a semiconductor medium, and it is negative charge carriers (free electrons) which are ultimately extracted to produce power. The classification of photoelectrochemical cells which includes Grätzel cells meets this narrow definition, albeit the charge carriers are often excitonic.
The situation within a photoelectrolytic cell, on the other hand, is quite different. For example, in a water-splitting photoelectrochemical cell, the excitation, by light, of an electron in a semiconductor leaves a hole which "draws" an electron from a neighboring water molecule:
H2O(l) + [hv] + 2h+ -> 2H+ (aq) + 1/2O2(g)
This leaves positive charge carriers (protons, that is, H+ ions) in solution, which must then bond with one other proton and combine with two electrons in order to form hydrogen gas, according to:
2H+ + 2e- -> H2(g)
A photosynthetic cell is another form of photoelectrolytic cell, w
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https://en.wikipedia.org/wiki/Polyclonal%20antibodies
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Polyclonal antibodies (pAbs) are antibodies that are secreted by different B cell lineages within the body (whereas monoclonal antibodies come from a single cell lineage). They are a collection of immunoglobulin molecules that react against a specific antigen, each identifying a different epitope.
Production
The general procedure to produce polyclonal antibodies is as follows:
Antigen preparation
Adjuvant selection and preparation
Animal selection
Injection process
Blood serum extraction
An antigen/adjuvant conjugate is injected into an animal of choice to initiate an amplified immune response. After a series of injections over a specific length of time, the animal is expected to have created antibodies against the conjugate. Blood is then extracted from the animal and then purified to obtain the antibody of interest.
Inoculation is performed on a suitable mammal, such as a mouse, rabbit or goat. Larger mammals are often preferred as the amount of serum that can be collected is greater. An antigen is injected into the mammal. This induces the B-lymphocytes to produce IgG immunoglobulins specific for the antigen. This polyclonal IgG is purified from the mammal's serum.
By contrast, monoclonal antibodies are derived from a single cell line.
Many methodologies exist for polyclonal antibody production in laboratory animals. Institutional guidelines governing animal use and procedures relating to these methodologies are generally oriented around humane considerations and appropriate conduct for adjuvant (agents which modify the effect of other agents while having few if any direct effects when given by themselves) use. This includes adjuvant selection, routes and sites of administration, injection volumes per site and number of sites per animal. Institutional policies generally include allowable volumes of blood per collection and safety precautions including appropriate restraint and sedation or anesthesia of animals for injury prevention to animals or personn
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https://en.wikipedia.org/wiki/Hyperpigmentation
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Hyperpigmentation is the darkening of an area of skin or nails caused by increased melanin.
Causes
Hyperpigmentation can be caused by sun damage, inflammation, or other skin injuries, including those related to acne vulgaris. People with darker skin tones are more prone to hyperpigmentation, especially with excess sun exposure.
Many forms of hyperpigmentation are caused by an excess production of melanin. Hyperpigmentation can be diffuse or focal, affecting such areas as the face and the back of the hands. Melanin is produced by melanocytes at the lower layer of the epidermis. Melanin is a class of pigment responsible for producing color in the body in places such as the eyes, skin, and hair. The process of melanin synthesis (melanogenesis) starts with the oxidation of -tyrosine to by the enzyme tyrosine hydroxylase, then to -dopaquinone and dopachrome, which forms melanin.
As the body ages, melanocyte distribution becomes less diffuse and its regulation less controlled by the body. UV light stimulates melanocyte activity, and where concentration of the cells is greater, hyperpigmentation occurs. Another form of hyperpigmentation is post-inflammatory hyperpigmentation. These are dark and discoloured spots that appear on the skin following acne that has healed.
Diseases and conditions
Hyperpigmentation is associated with a number of diseases or conditions, including the following:
Addison's disease and other sources of adrenal insufficiency, in which hormones that stimulate melanin synthesis, such as melanocyte-stimulating hormone (MSH), are frequently elevated.
Cushing's disease or other excessive adrenocorticotropic hormone (ACTH) production, because MSH production is a byproduct of ACTH synthesis from proopiomelanocortin (POMC).
Acanthosis nigricans—hyperpigmentation of intertriginous areas associated with insulin resistance.
Melasma, also known as 'chloasma' or the “mask of pregnancy,” when it occurs in pregnant women.— It is a common skin problem that caus
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https://en.wikipedia.org/wiki/Galois%20cohomology
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In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A Galois group G associated to a field extension L/K acts in a natural way on some abelian groups, for example those constructed directly from L, but also through other Galois representations that may be derived by more abstract means. Galois cohomology accounts for the way in which taking Galois-invariant elements fails to be an exact functor.
History
The current theory of Galois cohomology came together around 1950, when it was realised that the Galois cohomology of ideal class groups in algebraic number theory was one way to formulate class field theory, at the time it was in the process of ridding itself of connections to L-functions. Galois cohomology makes no assumption that Galois groups are abelian groups, so this was a non-abelian theory. It was formulated abstractly as a theory of class formations. Two developments of the 1960s turned the position around. Firstly, Galois cohomology appeared as the foundational layer of étale cohomology theory (roughly speaking, the theory as it applies to zero-dimensional schemes). Secondly, non-abelian class field theory was launched as part of the Langlands philosophy.
The earliest results identifiable as Galois cohomology had been known long before, in algebraic number theory and the arithmetic of elliptic curves. The normal basis theorem implies that the first cohomology group of the additive group of L will vanish; this is a result on general field extensions, but was known in some form to Richard Dedekind. The corresponding result for the multiplicative group is known as Hilbert's Theorem 90, and was known before 1900. Kummer theory was another such early part of the theory, giving a description of the connecting homomorphism coming from the m-th power map.
In fact, for a while the multiplicative case of a 1-cocycle for groups that are not necessa
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https://en.wikipedia.org/wiki/English%20Electric%20KDF9
|
KDF9 was an early British 48-bit computer designed and built by English Electric (which in 1968 was merged into International Computers Limited (ICL)). The first machine came into service in 1964 and the last of 29 machines was decommissioned in 1980 at the National Physical Laboratory. The KDF9 was designed for, and used almost entirely in, the mathematical and scientific processing fields in 1967, nine were in use in UK universities and technical colleges. The KDF8, developed in parallel, was aimed at commercial processing workloads.
The KDF9 was an early example of a machine that directly supported multiprogramming, using offsets into its core memory to separate the programs into distinct virtual address spaces. Several operating systems were developed for the platform, including some that provided fully interactive use through PDP-8 machines acting as smart terminal servers. A number of compilers were available, notably both checkout and globally optimizing compilers for Algol 60.
Architecture
The logic circuits of the KDF9 were entirely solid-state. The KDF9 used transformer-coupled diode–transistor logic, built from germanium diodes, about 20,000 transistors, and about 2,000 toroid pulse transformers. They ran on a 1 MHz clock that delivered two pulses of 250 ns separated by 500 ns, in each clock cycle. The maximum configuration incorporated 32K words of 48-bit core storage (192K bytes) with a cycle time of 6 microseconds. Each word could hold a single 48-bit integer or floating-point number, two 24-bit integer or floating-point numbers, six 8-bit instruction syllables, or eight 6-bit characters. There was also provision for efficient handling of double-word (96-bit) numbers in both integer and floating point formats. However, there was no facility for byte or character addressing, so that non-numerical work suffered by comparison. Its standard character set was a version of the Friden Flexowriter paper tape code that was oriented to Algol 60, and included
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https://en.wikipedia.org/wiki/Distributed%20Universal%20Number%20Discovery
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Distributed Universal Number Discovery (DUNDi) is a VoIP routing protocol that provides directory services for Asterisk systems.
With DUNDi peered nodes share dialplan information with each other. The protocol does not actually carry any calls, but rather provides addressing information.
Peers in a DUNDi cluster query other peers for a telephone number to which a call is requested by a user. The result of the query is a dial string for the Asterisk application Dial.
The protocol was invented by Mark Spencer, the author of Asterisk.
Peers
Asterisk PBX systems that use DUNDi are peered as a cooperating system of DUNDi nodes, each having certain configuration to access a DUNDI instance on at least one other node.
In the DUNDi configuration one can limit the number of consecutive lookups between peers by setting the TTL.
A TTL of 1 means you only can ask the peers you know and they cannot ask further.
A TTL of n means that the peer you ask for a lookup can redirect your lookup to the peers it knows, only with a TTL of n-1.
Advertising extensions
Each DUNDi peer can advertise its own extensions and their context. E.g. if you can connect some local E.164 number(s), you can advertise these.
DUNDi configuration assigns a priority weight to each advertised extension.
Low values represent a high priority and must be chosen first when more than one answer is received from a lookup.
Example
In the Asterisk CLI one can do a lookup by hand to test if a DUNDi configuration works.
asterisk1*CLI> dundi lookup 301@priv bypass
1. 0 IAX2/priv:ByWFbOGKgGmZbM43BJHSZw@192.168.1.2/301 (EXISTS)
from 00:0c:29:d2:d8:ec, expires in 3600 s
DUNDi lookup completed in 113 ms
The above DUNDi lookup tells the PBX to ask the known peers if they know how to reach extension 301 in the "priv" network.
The answer consists of 6 parts:
The used protocol to communicate is IAX2.
The context-name is "priv".
The secret key of the PBX, which can redirect you to extension 301 is ByW[
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https://en.wikipedia.org/wiki/Unordered%20pair
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In mathematics, an unordered pair or pair set is a set of the form {a, b}, i.e. a set having two elements a and b with no particular relation between them, where {a, b} = {b, a}. In contrast, an ordered pair (a, b) has a as its first element and b as its second element, which means (a, b) ≠ (b, a).
While the two elements of an ordered pair (a, b) need not be distinct, modern authors only call {a, b} an unordered pair if a ≠ b.
But for a few authors a singleton is also considered an unordered pair, although today, most would say that {a, a} is a multiset. It is typical to use the term unordered pair even in the situation where the elements a and b could be equal, as long as this equality has not yet been established.
A set with precisely two elements is also called a 2-set or (rarely) a binary set.
An unordered pair is a finite set; its cardinality (number of elements) is 2 or (if the two elements are not distinct) 1.
In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing.
More generally, an unordered n-tuple is a set of the form {a1, a2,... an}.
Notes
References
.
Basic concepts in set theory
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https://en.wikipedia.org/wiki/Dry%20etching
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Dry etching refers to the removal of material, typically a masked pattern of semiconductor material, by exposing the material to a bombardment of ions (usually a plasma of reactive gases such as fluorocarbons, oxygen, chlorine, boron trichloride; sometimes with addition of nitrogen, argon, helium and other gases) that dislodge portions of the material from the exposed surface. A common type of dry etching is reactive-ion etching. Unlike with many (but not all, see isotropic etching) of the wet chemical etchants used in wet etching, the dry etching process typically etches directionally or anisotropically.
Applications
Dry etching is used in conjunction with photolithographic techniques to attack certain areas of a semiconductor surface in order to form recesses in material.
Applications include contact holes (which are contacts to the underlying semiconductor substrate), via holes (which are holes that are formed to provide an interconnect path between conductive layers in the layered semiconductor device), transistor gates for FinFET technology, or to otherwise remove portions of semiconductor layers where predominantly vertical sides are desired. Along with semiconductor manufacturing, micromachining and display production, the removal of organic residues by oxygen plasmas is sometimes correctly described as a dry etch process. The term plasma ashing can be used instead.
Dry etching is particularly useful for materials and semiconductors which are chemically resistant and could not be wet etched, such as silicon carbide or gallium nitride.
Low density plasma (LDP) is able to produce high energy reactions at a low energy cost in thanks to its low pressure, meaning dry etch requires a relatively small quantity of chemicals and electricity to function. Additionally, dry etch equipment tends to be an order of magnitude cheaper than photolithography equipment, so many manufacturers rely on dry etching strategies such as pitch doubling or quartering to gain advanc
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https://en.wikipedia.org/wiki/Random%20early%20detection
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Random early detection (RED), also known as random early discard or random early drop, is a queuing discipline for a network scheduler suited for congestion avoidance.
In the conventional tail drop algorithm, a router or other network component buffers as many packets as it can, and simply drops the ones it cannot buffer. If buffers are constantly full, the network is congested. Tail drop distributes buffer space unfairly among traffic flows. Tail drop can also lead to TCP global synchronization as all TCP connections "hold back" simultaneously, and then step forward simultaneously. Networks become under-utilized and flooded—alternately, in waves.
RED addresses these issues by pre-emptively dropping packets before the buffer becomes completely full. It uses predictive models to decide which packets to drop. It was invented in the early 1990s by Sally Floyd and Van Jacobson.
Operation
RED monitors the average queue size and drops (or marks when used in conjunction with ECN) packets based on statistical probabilities. If the buffer is almost empty, then all incoming packets are accepted. As the queue grows, the probability for dropping an incoming packet grows too. When the buffer is full, the probability has reached 1 and all incoming packets are dropped.
RED is more fair than tail drop, in the sense that it does not possess a bias against bursty traffic that uses only a small portion of the bandwidth. The more a host transmits, the more likely it is that its packets are dropped as the probability of a host's packet being dropped is proportional to the amount of data it has in a queue. Early detection helps avoid TCP global synchronization.
Problems with classic RED
According to Van Jacobson, "there are not one, but two bugs in classic RED." Improvements to the algorithm were developed, and a draft paper was prepared, but the paper was never published, and the improvements were not widely disseminated or implemented. There has been some work in trying to fini
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https://en.wikipedia.org/wiki/Paraconsistent%20mathematics
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Paraconsistent mathematics, sometimes called inconsistent mathematics, represents an attempt to develop the classical infrastructure of mathematics (e.g. analysis) based on a foundation of paraconsistent logic instead of classical logic. A number of reformulations of analysis can be developed, for example functions which both do and do not have a given value simultaneously.
Chris Mortensen claims (see references):
One could hardly ignore the examples of analysis and its special case, the calculus. There prove to be many places where there are distinctive inconsistent insights; see Mortensen (1995) for example. (1) Robinson's non-standard analysis was based on infinitesimals, quantities smaller than any real number, as well as their reciprocals, the infinite numbers. This has an inconsistent version, which has some advantages for calculation in being able to discard higher-order infinitesimals. The theory of differentiation turned out to have these advantages, while the theory of integration did not. (2)
References
McKubre-Jordens, M. and Weber, Z. (2012). "Real analysis in paraconsistent logic". Journal of Philosophical Logic 41 (5):901–922. doi: 10.1017/S1755020309990281
Mortensen, C. (1995). Inconsistent Mathematics. Dordrecht: Kluwer.
Weber, Z. (2010). "Transfinite numbers in paraconsistent set theory". Review of Symbolic Logic 3 (1):71–92. doi:10.1017/S1755020309990281
External links
Entry in the Internet Encyclopedia of Philosophy
Entry in the Stanford Encyclopedia of Philosophy
Lectures by Manuel Bremer of the University of Düsseldorf
Philosophy of mathematics
Proof theory
Paraconsistent logic
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https://en.wikipedia.org/wiki/Factorial%20number%20system
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In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations. It is also called factorial base, although factorials do not function as base, but as place value of digits. By converting a number less than n! to factorial representation, one obtains a sequence of n digits that can be converted to a permutation of n elements in a straightforward way, either using them as Lehmer code or as inversion table representation; in the
former case the resulting map from integers to permutations of n elements lists them in lexicographical order. General mixed radix systems were studied by Georg Cantor.
The term "factorial number system" is used by Knuth,
while the French equivalent "numération factorielle" was first used in 1888. The term "factoradic", which is a portmanteau of factorial and mixed radix, appears to be of more recent date.
Definition
The factorial number system is a mixed radix numeral system: the i-th digit from the right has base i, which means that the digit must be strictly less than i, and that (taking into account the bases of the less significant digits) its value is to be multiplied by ! (its place value).
From this it follows that the rightmost digit is always 0, the second can be 0 or 1, the third 0, 1 or 2, and so on . The factorial number system is sometimes defined with the 0! place omitted because it is always zero .
In this article, a factorial number representation will be flagged by a subscript "!", so for instance 3:4:1:0:1:0! stands for 354413021100, whose value is
3×5! + 4×4! + 1×3! + 0×2! + 1×1! + 0×0!
((((3×5 + 4)×4 + 1)×3 + 0)×2 + 1)×1 + 0
46310.
(The place value is the factorial of one less than the radix position, which is why the equation begins with 5! for a 6-digit factoradic number.)
General properties of mixed radix number systems also apply to the factorial number system. For instance, one can convert a number into factorial representation
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https://en.wikipedia.org/wiki/Combinatorial%20number%20system
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In mathematics, and in particular in combinatorics, the combinatorial number system of degree k (for some positive integer k), also referred to as combinadics, or the Macaulay representation of an integer, is a correspondence between natural numbers (taken to include 0) N and k-combinations. The combinations are represented as strictly decreasing sequences ck > ... > c2 > c1 ≥ 0 where each ci corresponds to the index of a chosen element in a given k-combination. Distinct numbers correspond to distinct k-combinations, and produce them in lexicographic order. The numbers less than correspond to all of }. The correspondence does not depend on the size n of the set that the k-combinations are taken from, so it can be interpreted as a map from N to the k-combinations taken from N; in this view the correspondence is a bijection.
The number N corresponding to (ck, ..., c2, c1) is given by
.
The fact that a unique sequence corresponds to any non-negative number N was first observed by D. H. Lehmer. Indeed, a greedy algorithm finds the k-combination corresponding to N: take ck maximal with , then take ck−1 maximal with , and so forth. Finding the number N, using the formula above, from the k-combination (ck, ..., c2, c1) is also known as "ranking", and the opposite operation (given by the greedy algorithm) as "unranking"; the operations are known by these names in most computer algebra systems, and in computational mathematics.
The originally used term "combinatorial representation of integers" was shortened to "combinatorial number system" by Knuth,
who also gives a much older reference;
the term "combinadic" is introduced by James McCaffrey (without reference to previous terminology or work).
Unlike the factorial number system, the combinatorial number system of degree k is not a mixed radix system: the part of the number N represented by a "digit" ci is not obtained from it by simply multiplying by a place value.
The main application of the combinatorial number s
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https://en.wikipedia.org/wiki/Wolstenholme%27s%20theorem
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In mathematics, Wolstenholme's theorem states that for a prime number , the congruence
holds, where the parentheses denote a binomial coefficient. For example, with p = 7, this says that 1716 is one more than a multiple of 343. The theorem was first proved by Joseph Wolstenholme in 1862. In 1819, Charles Babbage showed the same congruence modulo p2, which holds for . An equivalent formulation is the congruence
for , which is due to Wilhelm Ljunggren (and, in the special case , to J. W. L. Glaisher) and is inspired by Lucas' theorem.
No known composite numbers satisfy Wolstenholme's theorem and it is conjectured that there are none (see below). A prime that satisfies the congruence modulo p4 is called a Wolstenholme prime (see below).
As Wolstenholme himself established, his theorem can also be expressed as a pair of congruences for (generalized) harmonic numbers:
(Congruences with fractions make sense, provided that the denominators are coprime to the modulus.)
For example, with p=7, the first of these says that the numerator of 49/20 is a multiple of 49, while the second says the numerator of 5369/3600 is a multiple of 7.
Wolstenholme primes
A prime p is called a Wolstenholme prime iff the following condition holds:
If p is a Wolstenholme prime, then Glaisher's theorem holds modulo p4. The only known Wolstenholme primes so far are 16843 and 2124679 ; any other Wolstenholme prime must be greater than 109. This result is consistent with the heuristic argument that the residue modulo p4 is a pseudo-random multiple of p3. This heuristic predicts that the number of Wolstenholme primes between K and N is roughly ln ln N − ln ln K. The Wolstenholme condition has been checked up to 109, and the heuristic says that there should be roughly one Wolstenholme prime between 109 and 1024. A similar heuristic predicts that there are no "doubly Wolstenholme" primes, for which the congruence would hold modulo p5.
A proof of the theorem
There is more than one way t
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https://en.wikipedia.org/wiki/System%20bus
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A system bus is a single computer bus that connects the major components of a computer system,
combining the functions of a data bus to carry information, an address bus to determine where it should be sent or read from, and a control bus to determine its operation. The technique was developed to reduce costs and improve modularity, and although popular in the 1970s and 1980s, more modern computers use a variety of separate buses adapted to more specific needs.
The system level bus (as distinct from a CPU's internal datapath busses) connects the CPU to memory and I/O devices.
Typically a system level bus is designed for use as a backplane.
Background scenario
Many of the computers were based on the First Draft of a Report on the EDVAC report published in 1945. In what became known as the Von Neumann architecture, a central control unit and arithmetic logic unit (ALU, which he called the central arithmetic part) were combined with computer memory and input and output functions to form a stored program computer. The Report presented a general organization and theoretical model of the computer, however, not the implementation of that model.
Soon designs integrated the control unit and ALU into what became known as the central processing unit (CPU).
Computers in the 1950s and 1960s were generally constructed in an ad-hoc fashion.
For example, the CPU, memory, and input/output units were each one or more cabinets connected by cables. Engineers used the common techniques of standardized bundles of wires and extended the concept as backplanes were used to hold printed circuit boards in these early machines.
The name "bus" was already used for "bus bars" that carried electrical power to the various parts of electric machines, including early mechanical calculators.
The advent of integrated circuits vastly reduced the size of each computer unit, and buses became more standardized.
Standard modules could be interconnected in more uniform ways and were easier to develop
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https://en.wikipedia.org/wiki/Hurwitz%27s%20automorphisms%20theorem
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In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface of genus g > 1, stating that the number of such automorphisms cannot exceed 84(g − 1). A group for which the maximum is achieved is called a Hurwitz group, and the corresponding Riemann surface a Hurwitz surface. Because compact Riemann surfaces are synonymous with non-singular complex projective algebraic curves, a Hurwitz surface can also be called a Hurwitz curve. The theorem is named after Adolf Hurwitz, who proved it in .
Hurwitz's bound also holds for algebraic curves over a field of characteristic 0, and over fields of positive characteristic p>0 for groups whose order is coprime to p, but can fail over fields of positive characteristic p>0 when p divides the group order. For example, the double cover of the projective line y2 = xp −x branched at all points defined over the prime field has genus g=(p−1)/2 but is acted on by the group SL2(p) of order p3−p.
Interpretation in terms of hyperbolicity
One of the fundamental themes in differential geometry is a trichotomy between the Riemannian manifolds of positive, zero, and negative curvature K. It manifests itself in many diverse situations and on several levels. In the context of compact Riemann surfaces X, via the Riemann uniformization theorem, this can be seen as a distinction between the surfaces of different topologies:
X a sphere, a compact Riemann surface of genus zero with K > 0;
X a flat torus, or an elliptic curve, a Riemann surface of genus one with K = 0;
and X a hyperbolic surface, which has genus greater than one and K < 0.
While in the first two cases the surface X admits infinitely many conformal automorphisms (in fact, the conformal automorphism group is a complex Lie group of dimension three for a sphere and of dimension one for a torus), a hyperbolic Riemann surface only admits a discrete set of automorphisms. Hu
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https://en.wikipedia.org/wiki/Mutator%20method
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In computer science, a mutator method is a method used to control changes to a variable. They are also widely known as setter methods. Often a setter is accompanied by a getter, which returns the value of the private member variable. They are also known collectively as accessors.
The mutator method is most often used in object-oriented programming, in keeping with the principle of encapsulation. According to this principle, member variables of a class are made private to hide and protect them from other code, and can only be modified by a public member function (the mutator method), which takes the desired new value as a parameter, optionally validates it, and modifies the private member variable. Mutator methods can be compared to assignment operator overloading but they typically appear at different levels of the object hierarchy.
Mutator methods may also be used in non-object-oriented environments. In this case, a reference to the variable to be modified is passed to the mutator, along with the new value. In this scenario, the compiler cannot restrict code from bypassing the mutator method and changing the variable directly. The responsibility falls to the developers to ensure the variable is only modified through the mutator method and not modified directly.
In programming languages that support them, properties offer a convenient alternative without giving up the utility of encapsulation.
In the examples below, a fully implemented mutator method can also validate the input data or take further action such as triggering an event.
Implications
The alternative to defining mutator and accessor methods, or property blocks, is to give the instance variable some visibility other than private and access it directly from outside the objects. Much finer control of access rights can be defined using mutators and accessors. For example, a parameter may be made read-only simply by defining an accessor but not a mutator. The visibility of the two methods may be differen
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https://en.wikipedia.org/wiki/Order%20%28ring%20theory%29
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In mathematics, an order in the sense of ring theory is a subring of a ring , such that
is a finite-dimensional algebra over the field of rational numbers
spans over , and
is a -lattice in .
The last two conditions can be stated in less formal terms: Additively, is a free abelian group generated by a basis for over .
More generally for an integral domain contained in a field , we define to be an -order in a -algebra if it is a subring of which is a full -lattice.
When is not a commutative ring, the idea of order is still important, but the phenomena are different. For example, the Hurwitz quaternions form a maximal order in the quaternions with rational co-ordinates; they are not the quaternions with integer coordinates in the most obvious sense. Maximal orders exist in general, but need not be unique: there is in general no largest order, but a number of maximal orders. An important class of examples is that of integral group rings.
Examples
Some examples of orders are:
If is the matrix ring over , then the matrix ring over is an -order in
If is an integral domain and a finite separable extension of , then the integral closure of in is an -order in .
If in is an integral element over , then the polynomial ring is an -order in the algebra
If is the group ring of a finite group , then is an -order on
A fundamental property of -orders is that every element of an -order is integral over .
If the integral closure of in is an -order then this result shows that must be the maximal -order in . However this hypothesis is not always satisfied: indeed need not even be a ring, and even if is a ring (for example, when is commutative) then need not be an -lattice.
Algebraic number theory
The leading example is the case where is a number field and is its ring of integers. In algebraic number theory there are examples for any other than the rational field of proper subrings of the ring of integers that are also orders. For e
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https://en.wikipedia.org/wiki/Optical%20parametric%20amplifier
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An optical parametric amplifier, abbreviated OPA, is a laser light source that emits light of variable wavelengths by an optical parametric amplification process. It is essentially the same as an optical parametric oscillator, but without the optical cavity (i.e., the light beams pass through the apparatus just once or twice, rather than many many times).
Optical parametric generation (OPG)
Optical parametric generation (OPG) (also called "optical parametric fluorescence", or "spontaneous parametric down conversion") often precedes optical parametric amplification.
In optical parametric generation, the input is one light beam of frequency ωp, and the output is two light beams of lower frequencies ωs and ωi, with the requirement ωp=ωs+ωi. These two lower-frequency beams are called the "signal" and "idler", respectively.
This light emission is based on the nonlinear optical principle. The photon of an incident laser pulse (pump) is, by a nonlinear optical crystal, divided into two lower-energy photons. The wavelengths of the signal and the idler are determined by the phase matching condition, which is changed, e.g. by temperature or, in bulk optics, by the angle between the incident pump laser ray and the optical axes of the crystal. The wavelengths of the signal and the idler photons can, therefore, be tuned by changing the phase matching condition.
Optical parametric amplification (OPA)
The output beams in optical parametric generation are usually relatively weak and have relatively spread-out direction and frequency. This problem is solved by using optical parametric amplification (OPA), also called difference frequency generation, as a second stage after the OPG.
In an OPA, the input is two light beams, of frequency ωp and ωs. The OPA will make the pump beam (ωp) weaker, and amplify the signal beam (ωs), and also create a new, so-called idler beam at the frequency ωi with ωp=ωs+ωi.
In the OPA, the pump and idler photons usually travel collinearly through a
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https://en.wikipedia.org/wiki/Battery%20eliminator%20circuit
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In battery-powered equipment, a battery eliminator circuit (BEC) is an electronic voltage regulator used to power a subsystem at a different voltage without the need for a supplemental battery. BECs are commonly used in radio-controlled models, which need separate voltages to power the motor and the R/C equipment.
Radio-controlled (R/C) models
In an electric-powered radio-controlled model, the BEC is typically part of the electronic speed control (ESC). BEC allows such a model to carry only one battery (the motive power battery) instead of two (motive power, and a separate battery to operate the R/C equipment). A BEC-equipped ESC meant for airplane use often incorporates a low-voltage-cutoff (LVC) circuit which can sense the voltage drop caused when the battery has little charge left. It then cuts the power to the 'drive' motor in order to provide the 'steering' servo(s) with enough power to be able to bring the model safely back to the operator. The power to the propeller is cut but the operation of the control surfaces would be maintained in order to perform a dead-stick landing. Without this feature, all control would be lost when the battery expired, probably resulting in the destruction of the model. In some cases, the BEC is part of the radio control receiver, instead of being part of the ESC.
R/C BECs in their simplest form use a linear fixed voltage regulator with its standard circuit suggested in the manufacturer's datasheet – usually the power supply of the receiver needs 5 V. Low-dropout types are preferred – especially for batteries with only a few cells. For small models, 1.5 to 2 A are enough; for mid-size models a 3 A type needs to be considered. BECs for large models have to provide current of 5 A or more. In this case, a more complicated switching mode regulator should be used, as the switching mode BECs are more electrically efficient than linear regulator BECs. The power dissipation losses in a linear regulator BEC are a product of the differen
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https://en.wikipedia.org/wiki/Panda%20Security
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Panda Security is a Spanish cybersecurity software company. Panda Security's core offering is antivirus software and more recently has expanded into providing and developing cybersecurity software. This includes security products and services for both businesses and home users, as well as protection tools for systems, networks, emails, and other private information. Panda Security employs around 458 people.
Overview
In 2005, Panda Security was the fourth largest antivirus vendor worldwide, with 3.2% of the marketplace. In November 2015 OPSWAT measured Panda Security's market share to be 3.6%. The company, whose shares were previously 100% held by Mikel Urizarbarrena, announced on April 24, 2007, the sale of 75% of its shares to Southern European investment group Investindustrial and private equity firm Gala Capital. On 30 July 2007, the company changed its name from Panda Software to Panda Security and Urizarbarrena was replaced by Jorge Dinares. Almost one year later, on 3 June 2008, amidst flagging sales, the board of directors voted to replace Dinares with Juan Santana, the CEO. Santana resigned in September 2011 and was replaced by José Sancho as acting CEO.
Panda Security was rated in Jan 2018 by Gartner analysts as an Endpoint Protection Visionary. Technological milestones include its launch of security systems, such as the SaaS concept (Security as a Service) or antivirus solutions that provide protection from the cloud (cloud computing) and are based on what Panda calls Collective Intelligence, a security model Panda introduced on the market in 2007. According to its CEO, the main benefit this security model provides is that it allows automatic scanning of threats instead of the manual scans carried out by other companies.
The firm has subsidiaries in the US, Italy, Switzerland, Germany, Austria, Belgium, the Netherlands, France, the UK, Sweden, Finland, Spain, and Japan. Additionally, it has franchises in another 44 countries. The US subsidiary moved its
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https://en.wikipedia.org/wiki/NEMA%20%28machine%29
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In the history of cryptography, the NEMA (NEue MAschine) ("new machine"), also designated the T-D (Tasten-Druecker-Maschine) ("key-stroke machine"), was a 10-wheel rotor machine designed by the Swiss Army during the World War II as a replacement for their Enigma machines.
History
The Swiss became aware that their current machine, a commercial Enigma (the Swiss K), had been broken by both Allied and German cryptanalysts.
A new design was begun between 1941 and 1943 by Captain Arthur Alder, a professor of mathematics at the University of Bern. The team which designed the machine also included Professors Hugo Hadwiger and Heinrich Emil Weber.
In the spring of 1944, the first prototype had become available. After some modifications, the design was accepted in March 1945, and production of 640 machines began the following month by Zellweger AG. The first machine entered service in 1947.
NEMA was declassified on 9 July 1992, and machines were offered for sale to the public on 4 May 1994.
The machine
NEMA uses 10 wheels, of which four are normal electrical rotors with 26 contacts at each end that are scramble wired in a way unique to each rotor type; one is an electrical reflector (like the Enigma's Umkehrwalze) with one set of 26 pairwise cross connected contacts; and the remaining five are "drive wheels", with mechanical cams that control the stepping of the rotors and the reflector. The wheels are assembled on an axle in pairs consisting of a drive wheel and an electrical rotor.
The NEMA machine weighs about 10 kg and measures approximately 36×32×14 cm.
See also
Fialka
Typex
SIGABA
References
Further reading
Geoff Sullivan and Frode Weierud: The Swiss NEMA Cipher Machine. Cryptologia, 23(4), October 1999, pp310–328.
Walter Schmid: Die Chiffriermaschine Nema. 109 pages, third edition, February 2005, Hombrechtikon ZH, Switzerland
External links
Frode Weierud's page on the NEMA – photographs and a simulator
David Hamer's page on NEMA – includes records of
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https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler%20divergence
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In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted , is a type of statistical distance: a measure of how one probability distribution is different from a second, reference probability distribution . A simple interpretation of the KL divergence of from is the expected excess surprise from using as a model when the actual distribution is . While it is a measure of how different two distributions are, and in some sense is thus a "distance", it is not actually a metric, which is the most familiar and formal type of distance. In particular, it is not symmetric in the two distributions (in contrast to variation of information), and does not satisfy the triangle inequality. Instead, in terms of information geometry, it is a type of divergence, a generalization of squared distance, and for certain classes of distributions (notably an exponential family), it satisfies a generalized Pythagorean theorem (which applies to squared distances).
In the simple case, a relative entropy of 0 indicates that the two distributions in question have identical quantities of information. Relative entropy is a nonnegative function of two distributions or measures. It has diverse applications, both theoretical, such as characterizing the relative (Shannon) entropy in information systems, randomness in continuous time-series, and information gain when comparing statistical models of inference; and practical, such as applied statistics, fluid mechanics, neuroscience and bioinformatics.
Introduction and context
Consider two probability distributions and . Usually, represents the data, the observations, or a measured probability distribution. Distribution represents instead a theory, a model, a description or an approximation of . The Kullback–Leibler divergence is then interpreted as the average difference of the number of bits required for encoding samples of using a code optimized for rather than one optimized for
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https://en.wikipedia.org/wiki/Safety%20testing%20of%20explosives
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The safety testing of explosives involves the determination of various properties of the different energetic materials that are used in commercial, mining, and military applications. It is highly desirable to measure the conditions under which explosives can be set off for several reasons, including: safety in handling, safety in storage, and
safety in use.
It would be very difficult to provide an absolute scale for sensitivity with respect to the different properties of explosives. Therefore, it is generally required that one or more compounds be considered a standard for comparison to those compounds being tested. For example, PETN is considered to be a primary explosive by some individuals, and a secondary explosive by others. As a general rule, PETN is considered to be either a relatively insensitive primary explosive, or one of the most sensitive secondary explosives. PETN may be detonated by striking with a hammer on a hard steel surface (a very dangerous thing to do), and is generally considered the least sensitive explosive with which this may be done. For these facts and other reasons, PETN is considered one standard by which other explosives are gauged.
Another explosive that is used as a calibration standard is TNT, which was afforded the arbitrary Figure of Insensitivity of 100. Other explosives could then be compared against this standard.
Types of safety testing
Because there are different ways to set off explosives, there are several different components to the safety testing of explosives:
Impact testing: The impact testing of explosives is performed by dropping a fixed weight onto a prepared sample of the explosive to be tested from a given distance. The weight is released, impacts upon the sample, and the result is noted. The impact distances are determined and the results are analyzed by the sensitivity test and analysis methods selected. The two most common sensitivity test and analysis methods are the Bruceton analysis and Neyer d-optimal
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https://en.wikipedia.org/wiki/Bruceton%20analysis
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A Bruceton analysis is one way of analyzing the sensitivity of explosives as described originally by Dixon and Mood in 1948. Also known as the "Up and Down Test" or "the staircase method", a Bruceton analysis relies upon two parameters: first stimulus and step size. A stimulus is provided to the sample, and the results noted. If a positive result is noted, then the stimulus is decremented by the step size. If a negative result occurs, the stimulus is increased. The test continues with each sample tested at a stimulus 1 step up or down from the previous stimulus if the previous result was negative or positive.
The results are tabulated and analyzed via Bruceton analysis, a simple computation of sums that can be performed by pencil and paper, to provide estimates of the mean and standard deviation. Confidence estimates are also produced.
Other analysis methods are the Neyer d-optimal test and Dror and Steinberg [2008] sequential procedure. Bruceton analysis has an advantage over the modern techniques being very simple to implement and analyze - as it was designed to be performed without a computer. The modern techniques offer a great improvement in efficiency, needing a much smaller sample size to obtain any desired significance level. Furthermore, these techniques enable the treatment of many other related experimental designs - such as when there is a need to learn the influence of more than one variable (say, testing the sensitivity of an explosive to both shock level and environment temperature), to models which are not only binary by nature (not only "detonate or not"), to experiments where you decide in advance (or "group") on more than one sample in each "run", and more. In fact, with the modern techniques the experimenter is not even constrained to specify a single model and can reflect uncertainty as to the form of the true model.
For mechanical threshold testing, typically on the up down method, originally proposed by Dixon, was used by SR Chaplan et al.
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https://en.wikipedia.org/wiki/Christopher%20Blizzard
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Christopher Blizzard (born 1973) is a Developer Relations lead at Facebook. Formerly, he worked as an Open Source Evangelist at the Mozilla Corporation and has contributed to other open source projects, including Red Hat and One Laptop Per Child.
Prior to his position as Open Source Evangelist he was the Software Team Lead for the One Laptop Per Child project at Red Hat and sat on the Mozilla Corporation Board of Directors. Before joining the One Laptop Per Child project he was a Systems Engineer and Open Source software developer working at Red Hat.
One Laptop Per Child
Blizzard was the OLPC Software Team Lead through Red Hat. He helped to develop the project's modified version of Fedora Core Linux. He handled all integration and community work with the OLPC project and unveiled the laptop in a video on Friday, June 2, 2006. Chris was also involved with the development of the OLPC's Sugar interface.
References
Living people
American computer scientists
Computer systems engineers
Silicon Valley people
People from Mountain View, California
Mozilla developers
Open source people
Free software programmers
Mozilla people
1973 births
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https://en.wikipedia.org/wiki/Rejection%20of%20evolution%20by%20religious%20groups
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Recurring cultural, political, and theological rejection of evolution by religious groups exists regarding the origins of the Earth, of humanity, and of other life. In accordance with creationism, species were once widely believed to be fixed products of divine creation, but since the mid-19th century, evolution by natural selection has been established by the scientific community as an empirical scientific fact.
Any such debate is universally considered religious, not scientific, by professional scientific organizations worldwide: in the scientific community, evolution is accepted as fact, and efforts to sustain the traditional view are universally regarded as pseudoscience. While the controversy has a long history, today it has retreated to be mainly over what constitutes good science education, with the politics of creationism primarily focusing on the teaching of creationism in public education. Among majority-Christian countries, the debate is most prominent in the United States, where it may be portrayed as part of a culture war. Parallel controversies also exist in some other religious communities, such as the more fundamentalist branches of Judaism and Islam. In Europe and elsewhere, creationism is less widespread (notably, the Catholic Church and Anglican Communion both accept evolution), and there is much less pressure to teach it as fact.
Christian fundamentalists reject the evidence of common descent of humans and other animals as demonstrated in modern paleontology, genetics, histology and cladistics and those other sub-disciplines which are based upon the conclusions of modern evolutionary biology, geology, cosmology, and other related fields. They argue for the Abrahamic accounts of creation, and, in order to attempt to gain a place alongside evolutionary biology in the science classroom, have developed a rhetorical framework of "creation science". In the landmark Kitzmiller v. Dover, the purported basis of scientific creationism was judged to be a
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https://en.wikipedia.org/wiki/General%20Leibniz%20rule
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In calculus, the general Leibniz rule, named after Gottfried Wilhelm Leibniz, generalizes the product rule (which is also known as "Leibniz's rule"). It states that if and are -times differentiable functions, then the product is also -times differentiable and its th derivative is given by
where is the binomial coefficient and denotes the jth derivative of f (and in particular ).
The rule can be proven by using the product rule and mathematical induction.
Second derivative
If, for example, , the rule gives an expression for the second derivative of a product of two functions:
More than two factors
The formula can be generalized to the product of m differentiable functions f1,...,fm.
where the sum extends over all m-tuples (k1,...,km) of non-negative integers with and
are the multinomial coefficients. This is akin to the multinomial formula from algebra.
Proof
The proof of the general Leibniz rule proceeds by induction. Let and be -times differentiable functions. The base case when claims that:
which is the usual product rule and is known to be true. Next, assume that the statement holds for a fixed that is, that
Then,
And so the statement holds for and the proof is complete.
Multivariable calculus
With the multi-index notation for partial derivatives of functions of several variables, the Leibniz rule states more generally:
This formula can be used to derive a formula that computes the symbol of the composition of differential operators. In fact, let P and Q be differential operators (with coefficients that are differentiable sufficiently many times) and Since R is also a differential operator, the symbol of R is given by:
A direct computation now gives:
This formula is usually known as the Leibniz formula. It is used to define the composition in the space of symbols, thereby inducing the ring structure.
See also
References
Articles containing proofs
Differentiation rules
Gottfried Wilhelm Leibniz
Mathematical identities
Theorems in
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https://en.wikipedia.org/wiki/Smoke%20ring
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A smoke ring is a visible vortex ring formed by smoke in a clear atmosphere.
Smokers may blow smoke rings from the mouth, intentionally or accidentally. Smoke rings may also be formed by sudden bursts of fire (such as lighting and immediately putting out a cigarette lighter), by shaking a smoke source (such as an incense stick) up and down, by firing certain types of artillery, or by the use of special devices, such as vortex ring guns and vortex ring toys. The head of a mushroom cloud is a large smoke ring.
A smoke ring is commonly formed when a puff of smoke is suddenly injected into clear air, especially through a narrow opening. The outer parts of the puff are slowed by the still air (or by edges of the opening) relative to the central part, imparting it the characteristic poloidal flow pattern.
The smoke makes the ring visible, but does not significantly affect the flow. The same phenomenon occurs with any fluid, producing vortex rings which are invisible but otherwise entirely similar to smoke rings.
Smoking and breathing
A smoker may produce rings by taking smoke into their mouth and expelling it with a tongue flick, by closing the jaw, tapping the cheek, or producing a sudden burst of air with the lungs and throat. The smoker may also use any of those methods to blow into a cloud of smoke outside their mouth.
A trick often performed in conjunction with mouth-blown smoke rings is the French inhale.
It is also possible to produce a vapour ring by using the same techniques on a cold day by exhaling.
The most famous such steam rings were those produced during the mid-20th century by Douglas Leigh's billboard on the Hotel Claridge in New York City's Times Square, advertising Camel cigarettes. An automated steam chamber behind the billboard produced puffs of steam every four seconds, giving the appearance of smoke rings leaving the smoker's open mouth and drifting away. Inspired by a World War II-era prohibition on lighted advertising, the Camel smoke
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https://en.wikipedia.org/wiki/Discrepancy%20theory
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In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be in. It is also called the theory of irregularities of distribution. This refers to the theme of classical discrepancy theory, namely distributing points in some space such that they are evenly distributed with respect to some (mostly geometrically defined) subsets. The discrepancy (irregularity) measures how far a given distribution deviates from an ideal one.
Discrepancy theory can be described as the study of inevitable irregularities of distributions, in measure-theoretic and combinatorial settings. Just as Ramsey theory elucidates the impossibility of total disorder, discrepancy theory studies the deviations from total uniformity.
A significant event in the history of discrepancy theory was the 1916 paper of Weyl on the uniform distribution of sequences in the unit interval.
Theorems
Discrepancy theory is based on the following classic theorems:
The theorem of van Aardenne–Ehrenfest
Axis-parallel rectangles in the plane (Roth, Schmidt)
Discrepancy of half-planes (Alexander, Matoušek)
Arithmetic progressions (Roth, Sarkozy, Beck, Matousek & Spencer)
Beck–Fiala theorem
Six Standard Deviations Suffice (Spencer)
Major open problems
The unsolved problems relating to discrepancy theory include:
Axis-parallel rectangles in dimensions three and higher (folklore)
Komlós conjecture
Heilbronn triangle problem on the minimum area of a triangle determined by three points from an n-point set
Applications
Applications for discrepancy theory include:
Numerical integration: Monte Carlo methods in high dimensions.
Computational geometry: Divide-and-conquer algorithm.
Image processing: Halftoning
Random trial formulation: Randomized controlled trial
See also
Discrepancy of hypergraphs
References
Further reading
Diophantine approximation
Unsolved problems in mathematics
Discrepancy theory
Measure theory
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https://en.wikipedia.org/wiki/Atomic%20commit
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In the field of computer science, an atomic commit is an operation that applies a set of distinct changes as a single operation. If the changes are applied, then the atomic commit is said to have succeeded. If there is a failure before the atomic commit can be completed, then all of the changes completed in the atomic commit are reversed. This ensures that the system is always left in a consistent state. The other key property of isolation comes from their nature as atomic operations. Isolation ensures that only one atomic commit is processed at a time. The most common uses of atomic commits are in database systems and version control systems.
The problem with atomic commits is that they require coordination between multiple systems. As computer networks are unreliable services, this means no algorithm can coordinate with all systems as proven in the Two Generals Problem. As databases become more and more distributed, this coordination will increase the difficulty of making truly atomic commits.
Usage
Atomic commits are essential for multi-step updates to data. This can be clearly shown in a simple example of a money transfer between two checking accounts.
This example is complicated by a transaction to check the balance of account Y during a transaction for transferring 100 dollars from account X to Y. To start, first 100 dollars is removed from account X. Second, 100 dollars is added to account Y. If the entire operation is not completed as one atomic commit, then several problems could occur. If the system fails in the middle of the operation, after removing the money from X and before adding into Y, then 100 dollars has just disappeared. Another issue is if the balance of Y is checked before the 100 dollars is added, the wrong balance for Y will be reported.
With atomic commits neither of these cases can happen, in the first case of the system failure, the atomic commit would be rolled back and the money returned to X. In the second case, the request of the
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https://en.wikipedia.org/wiki/Albino%20Blacksheep
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Albino Blacksheep (ABS) is an animation website made by Steven Lerner in Toronto, Ontario on January 4, 1999. It publishes member submitted digital media made with Adobe Flash. The website also features image galleries, audio files, and text files, along with a mobile section that provided ring tones, screensavers, and wallpaper for mobile phones.
History
Albino Blacksheep was founded on January 4, 1999, by Steven Lerner, to promote his band of the same name, which was started in 1996. Very little information on the band Albino Blacksheep exists. In 2000, Steven took a web design course and redesigned the website. This new incarnation contained rants, graphical images, and a video stream from Lerner's video camera.
Perhaps Lerner's first famous work was in 2003, with his site's Google bomb for French military victories. Between then and 2006, the site had been growing in popularity, receiving about 1.50 million pageviews per day.
Albino Blacksheep is also famous for being a major portal for Flash animation and animutation (a Flash animation style created by Neil Cicierega in 2001). The popular Web game Musical Lantern can be found on this site. The website also helped the band Tally Hall achieve some notability after posting their music video Banana Man.
On April 1, 2007, Lerner changed the homepage to a joke homepage, designed to make people think that the site had been bought and turned into "Google Animations". The joke was reinforced by a fake blog stating that "Albino Blacksheep has been acquired by Google Inc. for roughly $32 million in stock options. The deal was discussed over a casual breakfast in Mountain View, California between the Canadian-born founder of Albino Blacksheep and the Google co-founders and CEO. Plans are underway for Google Inc. to tie its services and software into the former Albino Blacksheep website which will go by the new name Google Animation."
Notes and references
External links
Albino Blacksheep
1999 establishments in Ontar
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https://en.wikipedia.org/wiki/Lyapunov%20time
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In mathematics, the Lyapunov time is the characteristic timescale on which a dynamical system is chaotic. It is named after the Russian mathematician Aleksandr Lyapunov. It is defined as the inverse of a system's largest Lyapunov exponent.
Use
The Lyapunov time mirrors the limits of the predictability of the system. By convention, it is defined as the time for the distance between nearby trajectories of the system to increase by a factor of e. However, measures in terms of 2-foldings and 10-foldings are sometimes found, since they correspond to the loss of one bit of information or one digit of precision respectively.
While it is used in many applications of dynamical systems theory, it has been particularly used in celestial mechanics where it is important for the problem of the stability of the Solar System. However, empirical estimation of the Lyapunov time is often associated with computational or inherent uncertainties.
Examples
Typical values are:
See also
Belousov–Zhabotinsky reaction
Molecular chaos
Three-body problem
References
Dynamical systems
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https://en.wikipedia.org/wiki/ISO%206346
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ISO 6346 is an international standard covering the coding, identification and marking of intermodal (shipping) containers used within containerized intermodal freight transport by the International Organization for Standardization (ISO). The standard establishes a visual identification system for every container that includes a unique serial number (with check digit), the owner, a country code, a size, type and equipment category as well as any operational marks. The register of container owners is managed by the International Container Bureau (BIC).
Identification system
Example of an ISO 6346 compliant container number:
The illustrated example is a code for a container owned by Hapag-Lloyd AG.
Owner code
The owner code consists of three capital letters of the Latin alphabet to indicate the owner or principal operator of the container. Such code needs to be registered at the Bureau International des Containers in Paris to ensure uniqueness worldwide. An owner can apply for more than one code, as normally the first 2 letters are used as the owner code and the third is used to indicate pool (e.g. HLA, HLB, HLX are some Hapag-Lloyd codes to indicate whether container is standard, reefer...)
Equipment category identifier
The equipment category identifier consists of one of the following capital letters of the Latin alphabet:
U for all freight containers
J for detachable freight container-related equipment
Z for trailers and chassis
Presently, all official BIC container codes end in "U". However, the Association of American Railroads recognizes similar codes for their containers and trailers travelling by rail in North America, though these are not recognized by the BIC and lack check digits.
Under the ISO code, then, only U, J, and Z are in use. The refrigerated (reefer) container is identified by means of the size type code.
Serial number
The serial number consists of 6 numeric digits, assigned by the owner or operator, uniquely identifying the container within
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https://en.wikipedia.org/wiki/OSI%20protocols
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The Open Systems Interconnection protocols are a family of information exchange standards developed jointly by the ISO and the ITU-T. The standardization process began in 1977.
While the seven-layer OSI model is often used as a reference for teaching and documentation, the protocols originally conceived for the model did not gain popularity, and only X.400, X.500, and IS-IS have achieved lasting impact. The goal of an open-standard protocol suite instead has been met by the Internet protocol suite, maintained by the Internet Engineering Task Force (IETF).
Overview
The OSI protocol stack is structured into seven conceptual layers. The layers form a hierarchy of functionality starting with the physical hardware components to the user interfaces at the software application level. Each layer receives information from the layer above, processes it and passes it down to the next layer. Each layer adds encapsulation information (header) to the incoming information before it is passed to the lower layer. Headers generally include address of source and destination, error control information, protocol identification and protocol parameters such as flow control options and sequence numbers.
Layer 1: physical layer
This layer deals with the physical plugs and sockets and electrical specification of signals only.
This is the medium over which the digital signals are transmitted. It can be twisted pair, coaxial cable, optical fiber, wireless, or other transmission media.
Layer 2: data link layer
The data link layer packages raw bits from the physical layer into frames (logical, structured packets for data). It is specified in ITU-T Rec. X.212 [ISO/IEC 8886], ITU-T Rec. X.222 and others. This layer is responsible for transferring frames from one host to another. It might perform error checking. This layer further consists of two sublayers: MAC and LLC.
Layer 3: network layer
Connectionless Network Service (CLNS) – ITU-T Rec. X.213 [ISO/IEC 8348]. SCCP is based on X.213
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https://en.wikipedia.org/wiki/Xpress%20Transport%20Protocol
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Xpress Transport Protocol (XTP) is a transport layer protocol for high-speed networks promoted by the XTP Forum developed to replace TCP. XTP provides protocol options for error control, flow control, and rate control. Instead of separate protocols for each type of communication, XTP controls packet exchange patterns to produce different models, e.g. reliable datagrams, transactions, unreliable streams, and reliable multicast connections.
Long latency is one of the major problems in satellite communications. Couple this with possible environmental variables and sometimes asymmetrical bandwidth conditions, the quality of service in satellite communications is sometimes lacking. XTP addresses these issues in a variety of ways such as a Selective Retransmission algorithm that deals with loss recovery. This works by the receiver detecting missing data packets and transmitting a list of those missing packets to the sender, who then is able to quickly resend missing packets as needed. As stated, XTP also provides rate control in which the maximum bandwidth can be specified as well as what size burst data can be accepted. XTP also offers a reliable multicast protocol, and the flexibility to match any specific application needs.
XTP does not employ congestion avoidance algorithms. XTP is a real-time option at Layer 4 for the US Navy SAFENET LAN Profile.
See also
T/TCP
SCTP
References
Caini, C., Firrincieli, R., Marchese, M., de Cola, T., Luglio, M., Roseti, C., et al. (2006). Transport layer protocols and architectures for satellite networks. International Journal of Satellite Communications and Networking, 25, 1-26. Retrieved March 9, 2009 from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.73.7647&rep=rep1&type=pdf
W. Timothy Strayer, Bert J. Dempsey, Alfred C. Weaver. XTP: The Xpress Transfer Protocol. Addison-Wesley, Reading, Mass 1992.
Internet protocols
Internet Standards
Transport layer protocols
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https://en.wikipedia.org/wiki/Apple%20Computer%2C%20Inc.%20v.%20Franklin%20Computer%20Corp.
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Apple Computer, Inc. v. Franklin Computer Corp., 714 F.2d 1240 (3d Cir. 1983), was the first time an appellate level court in the United States held that a computer's BIOS could be protected by copyright. As second impact, this ruling clarified that binary code, the machine readable form of software and firmware, was copyrightable too and not only the human-readable source code form of software.
Franklin Computer Corporation introduced the Franklin Ace 1000, a clone of Apple Computer's Apple II, in 1982. Apple quickly determined that substantial portions of the Franklin ROM and operating system had been copied directly from Apple's versions, and on May 12, 1982, filed suit in the United States District Court for the Eastern District of Pennsylvania. It cited the presence of some of the same embedded strings, such as the name "James Huston" (an Apple programmer), and "Applesoft," on both the Apple and Franklin system disks.
Franklin admitted that it had copied Apple's software but argued that it would have been impractical to independently write its own versions of the software and maintain compatibility, although it said it had written its own version of Apple's copy utility and was working on its own versions of other software. Franklin argued that because Apple's software existed only in machine-readable form, and not in printed form, and because some of the software did not contain copyright notices, it could be freely copied. The Apple II firmware was likened to a machine part whose form was dictated entirely by the requirements of compatibility (that is, an exact copy of Apple's ROM was the only part that would "fit" in an Apple-compatible computer and enable its intended function), and was therefore not copyrightable.
The district court found in favor of Franklin. However, Apple appealed the ruling to the United States Court of Appeals for the Third Circuit which, in a separate case decided three days after Franklin won at the lower level, had determined t
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https://en.wikipedia.org/wiki/IP%20aliasing
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IP aliasing is associating more than one IP address to a network interface. With this, one node on a network can have multiple connections to a network, each serving a different purpose.
In the Linux kernel, it was first implemented by Juan José Ciarlante in 1995. On Solaris IP aliasing was called logical network interface and was first available in Solaris 2.5 in 1995. It has also been possible in Microsoft Windows NT since (at least) Windows NT 3.51, released in 1995.
IP aliasing can be used to provide multiple network addresses on a single physical interface. This demonstrates using IP version 4 addresses only. One reason for using this could be to make a computer look as though it is multiple computers, so for example you could have one server that is acting as both a gateway (router) and a DHCP server and DNS using three different IP addresses, perhaps with a future plan to use a hardware router and to move the functionality to separate DNS and DHCP servers. Or indeed the opposite you could decide to replace the three different hardware devices with a single server to reduce the administration overhead. In this case you can have three different addresses which are all on the same computer without having to install many physical network interfaces. Another reason to use IP aliasing could be to have the computer on two different logical network subnets whilst using a single physical interface.
References
Internet architecture
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https://en.wikipedia.org/wiki/Automatic%20programming
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In computer science, automatic programming is a type of computer programming in which some mechanism generates a computer program to allow human programmers to write the code at a higher abstraction level.
There has been little agreement on the precise definition of automatic programming, mostly because its meaning has changed over time. David Parnas, tracing the history of "automatic programming" in published research, noted that in the 1940s it described automation of the manual process of punching paper tape. Later it referred to translation of high-level programming languages like Fortran and ALGOL. In fact, one of the earliest programs identifiable as a compiler was called Autocode. Parnas concluded that "automatic programming has always been a euphemism for programming in a higher-level language than was then available to the programmer."
Program synthesis is one type of automatic programming where a procedure is created from scratch, based on mathematical requirements.
Origin
Mildred Koss, an early UNIVAC programmer, explains: "Writing machine code involved several tedious steps—breaking down a process into discrete instructions, assigning specific memory locations to all the commands, and managing the I/O buffers. After following these steps to implement mathematical routines, a sub-routine library, and sorting programs, our task was to look at the larger programming process. We needed to understand how we might reuse tested code and have the machine help in programming. As we programmed, we examined the process and tried to think of ways to abstract these steps to incorporate them into higher-level language. This led to the development of interpreters, assemblers, compilers, and generators—programs designed to operate on or produce other programs, that is, automatic programming."
Generative programming
Generative programming and the related term meta-programming are concepts whereby programs can be written "to manufacture software components in an autom
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https://en.wikipedia.org/wiki/Journal%20of%20Recreational%20Mathematics
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The Journal of Recreational Mathematics was an American journal dedicated to recreational mathematics, started in 1968. It had generally been published quarterly by the Baywood Publishing Company, until it ceased publication with the last issue (volume 38, number 2) published in 2014. The initial publisher (of volumes 1–5) was Greenwood Periodicals.
Harry L. Nelson was primary editor for five years (volumes 9 through 13, excepting volume 13, number 4, when the initial editor returned as lead) and Joseph Madachy, the initial lead editor and editor of a predecessor called Recreational Mathematics Magazine which ran during the years 1961 to 1964, was the editor for many years. Charles Ashbacher and Colin Singleton took over as editors when Madachy retired (volume 30 number 1). The final editors were Ashbacher and Lamarr Widmer. The journal has from its inception also listed associate editors, one of whom was Leo Moser.
The journal contains:
Original articles
Book reviews
Alphametics And Solutions To Alphametics
Problems And Conjectures
Solutions To Problems And Conjectures
Proposer's And Solver's List For Problems And Conjectures
Indexing
The journal is indexed in:
Academic Search Premier
Book Review Index
International Bibliography of Periodical Literature
International Bibliography of Book Reviews
Readers' Guide to Periodical Literature
The Gale Group
References
Recreational mathematics
Mathematics journals
Academic journals established in 1968
Publications disestablished in 2014
Quarterly journals
Defunct journals of the United States
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https://en.wikipedia.org/wiki/Terence%20Tao
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Terence Chi-Shen Tao (; born 17 July 1975) is an Australian mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory.
Tao was born to ethnic Chinese immigrant parents and raised in Adelaide. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014. He is also a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers. He is widely regarded as one of the greatest living mathematicians and has been referred to as the "Mozart of mathematics."
Life and career
Family
Tao's parents are first-generation immigrants from Hong Kong to Australia. Tao's father, Billy Tao, was a Chinese paediatrician who was born in Shanghai and earned his medical degree (MBBS) from the University of Hong Kong in 1969. Tao's mother, Grace Leong, was born in Hong Kong; she received a first-class honours degree in mathematics and physics at the University of Hong Kong. She was a secondary school teacher of mathematics and physics in Hong Kong. Billy and Grace met as students at the University of Hong Kong. They then emigrated from Hong Kong to Australia in 1972.
Tao also has two brothers, Trevor and Nigel, who are living in Australia. Both formerly represented the states at the International Mathematical Olympiad. Furthermore, Trevor has been representing Australia internationally in chess and holds the title of Chess International Master. Tao speaks Cantonese but cannot write Chinese. Tao is married to Laura Tao, an electrical engineer at NASA's Jet Propulsion Laboratory. They live in Los Angeles, California, and have two children: Riley and daughter Madeleine.
Childhood
A child prodigy, Tao
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https://en.wikipedia.org/wiki/Linearization
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In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.
Linearization of a function
Linearizations of a function are lines—usually lines that can be used for purposes of calculation. Linearization is an effective method for approximating the output of a function at any based on the value and slope of the function at , given that is differentiable on (or ) and that is close to . In short, linearization approximates the output of a function near .
For example, . However, what would be a good approximation of ?
For any given function , can be approximated if it is near a known differentiable point. The most basic requisite is that , where is the linearization of at . The point-slope form of an equation forms an equation of a line, given a point and slope . The general form of this equation is: .
Using the point , becomes . Because differentiable functions are locally linear, the best slope to substitute in would be the slope of the line tangent to at .
While the concept of local linearity applies the most to points arbitrarily close to , those relatively close work relatively well for linear approximations. The slope should be, most accurately, the slope of the tangent line at .
Visually, the accompanying diagram shows the tangent line of at . At , where is any small positive or negative value, is very nearly the value of the tangent line at the point .
The final equation for the linearization of a function at is:
For , . The derivative of is , and the slope of at is .
Example
To find , we can use the fact that . The li
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https://en.wikipedia.org/wiki/Arbitrarily%20large
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In mathematics, the phrases arbitrarily large, arbitrarily small and arbitrarily long are used in statements to make clear of the fact that an object is large, small and long with little limitation or restraint, respectively. The use of "arbitrarily" often occurs in the context of real numbers (and its subsets thereof), though its meaning can differ from that of "sufficiently" and "infinitely".
Examples
The statement
" is non-negative for arbitrarily large ."
is a shorthand for:
"For every real number , is non-negative for some value of greater than ."
In the common parlance, the term "arbitrarily long" is often used in the context of sequence of numbers. For example, to say that there are "arbitrarily long arithmetic progressions of prime numbers" does not mean that there exists any infinitely long arithmetic progression of prime numbers (there is not), nor that there exists any particular arithmetic progression of prime numbers that is in some sense "arbitrarily long". Rather, the phrase is used to refer to the fact that no matter how large a number is, there exists some arithmetic progression of prime numbers of length at least .
Similar to arbitrarily large, one can also define the phrase " holds for arbitrarily small real numbers", as follows:
In other words:
However small a number, there will be a number smaller than it such that holds.
Arbitrarily large vs. sufficiently large vs. infinitely large
While similar, "arbitrarily large" is not equivalent to "sufficiently large". For instance, while it is true that prime numbers can be arbitrarily large (since there are infinitely many of them due to Euclid's theorem), it is not true that all sufficiently large numbers are prime.
As another example, the statement " is non-negative for arbitrarily large ." could be rewritten as:
However, using "sufficiently large", the same phrase becomes:
Furthermore, "arbitrarily large" also does not mean "infinitely large". For example, although prime number
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https://en.wikipedia.org/wiki/Soil%20classification
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Soil classification deals with the systematic categorization of soils based on distinguishing characteristics as well as criteria that dictate choices in use.
Overview
Soil classification is a dynamic subject, from the structure of the system, to the definitions of classes, to the application in the field. Soil classification can be approached from the perspective of soil as a material and soil as a resource.
Inscriptions at the temple of Horus at Edfu outline a soil classification used by Tanen to determine what kind of temple to build at which site. Ancient Greek scholars produced a number of classification based on several different qualities of the soil.
Engineering
Geotechnical engineers classify soils according to their engineering properties as they relate to use for foundation support or building material. Modern engineering classification systems are designed to allow an easy transition from field observations to basic predictions of soil engineering properties and behaviors.
The most common engineering classification system for soils in North America is the Unified Soil Classification System (USCS). The USCS has three major classification groups: (1) coarse-grained soils (e.g. sands and gravels); (2) fine-grained soils (e.g. silts and clays); and (3) highly organic soils (referred to as "peat"). The USCS further subdivides the three major soil classes for clarification. It distinguishes sands from gravels by grain size, classifying some as "well-graded" and the rest as "poorly-graded". Silts and clays are distinguished by the soils' Atterberg limits, and thus the soils are separated into "high-plasticity" and "low-plasticity" soils. Moderately organic soils are considered subdivisions of silts and clays and are distinguished from inorganic soils by changes in their plasticity properties (and Atterberg limits) on drying. The European soil classification system (ISO 14688) is very similar, differing primarily in coding and in adding an "intermediate-p
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https://en.wikipedia.org/wiki/Nonribosomal%20peptide
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Nonribosomal peptides (NRP) are a class of peptide secondary metabolites, usually produced by microorganisms like bacteria and fungi. Nonribosomal peptides are also found in higher organisms, such as nudibranchs, but are thought to be made by bacteria inside these organisms. While there exist a wide range of peptides that are not synthesized by ribosomes, the term nonribosomal peptide typically refers to a very specific set of these as discussed in this article.
Nonribosomal peptides are synthesized by nonribosomal peptide synthetases, which, unlike the ribosomes, are independent of messenger RNA. Each nonribosomal peptide synthetase can synthesize only one type of peptide. Nonribosomal peptides often have cyclic and/or branched structures, can contain non-proteinogenic amino acids including D-amino acids, carry modifications like N-methyl and N-formyl groups, or are glycosylated, acylated, halogenated, or hydroxylated. Cyclization of amino acids against the peptide "backbone" is often performed, resulting in oxazolines and thiazolines; these can be further oxidized or reduced. On occasion, dehydration is performed on serines, resulting in dehydroalanine. This is just a sampling of the various manipulations and variations that nonribosomal peptides can perform. Nonribosomal peptides are often dimers or trimers of identical sequences chained together or cyclized, or even branched.
Nonribosomal peptides are a very diverse family of natural products with an extremely broad range of biological activities and pharmacological properties. They are often toxins, siderophores, or pigments. Nonribosomal peptide antibiotics, cytostatics, and immunosuppressants are in commercial use.
Examples
Antibiotics
Actinomycin
Bacitracin
Calcium dependent antibiotic
Daptomycin
Vancomycin
Teixobactin
Tyrocidine
Gramicidin
Zwittermicin A
Antibiotic precursors
ACV-Tripeptide
Cytostatics
Epothilone
Fabclavine
Bleomycin
Immunosuppressants
Ciclosporin (Cyclosporine A)
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https://en.wikipedia.org/wiki/Multi%20Router%20Traffic%20Grapher
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The Multi Router Traffic Grapher (MRTG) is free software for monitoring and measuring the traffic load on network links. It allows the user to see traffic load on a network over time in graphical form.
It was originally developed by Tobias Oetiker and Dave Rand to monitor router traffic, but has developed into a tool that can create graphs and statistics for almost anything.
MRTG is written in Perl and can run on Windows, Linux, Unix, Mac OS and NetWare.
How it works
SNMP
MRTG uses the Simple Network Management Protocol (SNMP) to send requests with two object identifiers (OIDs) to a device. The device, which must be SNMP-enabled, will have a management information base (MIB) to look up the OIDs specified. After collecting the information it will send back the raw data encapsulated in an SNMP protocol. MRTG records this data in a log on the client along with previously recorded data for the device. The software then creates an HTML document from the logs, containing a list of graphs detailing traffic for the selected devices in the server.
Script output
Alternatively, MRTG can be configured to run a script or command, and parse its output for counter values. The MRTG website contains a large library of external scripts to enable monitoring of SQL database statistics, firewall rules, CPU fan RPMs, or virtually any integer-value data.
Features
Measures two values (I for Input, O for Output) per target.
Gets its data via an SNMP agent, or through the output of a command line.
Typically collects data every five minutes (it can be configured to collect data less frequently).
Creates an HTML page per target that features four graphs (GIF or PNG images).
Results are plotted vs time into day, week, month and year graphs, with the I plotted as a full green area, and the O as a blue line.
Automatically scales the Y axis of the graphs to show the most detail.
Adds calculated Max, Average and Current values for both I and O to the target's HTML page.
Can also sen
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https://en.wikipedia.org/wiki/FileZilla
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FileZilla is a free and open-source, cross-platform FTP application, consisting of FileZilla Client and FileZilla Server. Clients are available for Windows, Linux, and macOS. Both server and client support FTP and FTPS (FTP over SSL/TLS), while the client can in addition connect to SFTP servers. FileZilla's source code is hosted on SourceForge.
History
FileZilla was started as a computer science class project in the second week of January 2001 by Tim Kosse and two classmates.
Before they started to write the code, they discussed under which license they should release it. They decided to make FileZilla an open-source project because many FTP clients were already available, and they didn't think that they would sell a single copy if they made FileZilla commercial. Since its initial development in 2001, FileZilla has been released under the GNU General Public License (GPL). The FileZilla client is currently released under GPL-2.0-or-later, and the server package under AGPL-3.0-or-later.
FileZilla featured as SourceForge's Project of the Month in November 2003.
Features
These are some features of FileZilla Client:
Transfer files using FTP and encrypted FTP such as FTPS (server and client) and SFTP.
Support IPv6 which is the latest version of internet protocol
Supports resume which means the file transfer process can be paused and continued
Ability to overwrite existing files only if the source file is newer
Ability to overwrite existing files only if the file size does not match
Ability to preserve the time stamps of transferred files, given support by local system (downloading) or target server (uploading).
Tabbed user interface for multitasking, to allow browsing more than one server or even transfer files simultaneously between multiple servers.
Site Manager to manage server lists and transfer queue for ordering file transfer tasks
Bookmarks for easy access to most frequent use
Drag and drop to download and upload.
Directory comparison for comparing l
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https://en.wikipedia.org/wiki/No-win%20situation
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A no-win situation, also called a lose-lose situation, is one where a person has choices, but no choice leads to a net gain. For example, if a company finds a dangerous fault in one of its products, they can either issue a product recall and take some reputational damage, or allow the product to harm people: the company is in a no-win situation.
In game theory
In game theory, a "no-win" situation is a circumstance in which no player benefits from any outcome, hence ultimately losing the match. This may be because of any or all of the following:
Unavoidable or unforeseeable circumstances causing the situation to change after decisions have been made. This is common in text adventures.
Zugzwang, as in chess, when any move a player chooses makes them worse off than before such as losing a piece or being checkmated.
A situation in which the player has to accomplish two mutually dependent tasks each of which must be completed before the other or that are mutually exclusive (a Catch-22).
Ignorance of other players' actions, meaning the best decision for all differs from that for any one player (as in the prisoner's dilemma).
In history
Carl von Clausewitz's advice never to launch a war that one has not already won characterizes war as a no-win situation. A similar example is the Pyrrhic victory in which a military victory is so costly that the winning side actually ends up worse off than before it started. Looking at the victory as a part of a larger situation, the situation could either be no-win, or more of a win for the other side than the one that won the "victory", or victory at such cost that the gains are outweighed by the cost and are no longer a source of joy.
For example, the "victorious" side may have accomplished their objective, which may have been worthless; it may also lose a strategic advantage in manpower or positioning. For example, the British Empire was one of the victorious powers of the Second World War but was so weakened that it could no lon
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https://en.wikipedia.org/wiki/Logarithmic%20distribution
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In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion
From this we obtain the identity
This leads directly to the probability mass function of a Log(p)-distributed random variable:
for k ≥ 1, and where 0 < p < 1. Because of the identity above, the distribution is properly normalized.
The cumulative distribution function is
where B is the incomplete beta function.
A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution, and Xi, i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log(p) distribution, then
has a negative binomial distribution. In this way, the negative binomial distribution is seen to be a compound Poisson distribution.
R. A. Fisher described the logarithmic distribution in a paper that used it to model relative species abundance.
See also
Poisson distribution (also derived from a Maclaurin series)
References
Further reading
Discrete distributions
Logarithms
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https://en.wikipedia.org/wiki/CHIP-8
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CHIP-8 is an interpreted programming language, developed by Joseph Weisbecker made on his 1802 Microprocessor. It was initially used on the COSMAC VIP and Telmac 1800 8-bit microcomputers in the mid-1970s. CHIP-8 programs are run on a CHIP-8 virtual machine. It was made to allow video games to be more easily programmed for these computers. The simplicity of CHIP-8, and its long history and popularity, has ensured that CHIP-8 emulators and programs are still being made to this day. It also gave inspiration to similar systems with certain limitations and compatibility independent of hardware called fantasy consoles.
Roughly fifteen years after CHIP-8 was introduced, derived interpreters appeared for some models of graphing calculators (from the late 1980s onward, these handheld devices in many ways have more computing power than most mid-1970s microcomputers for hobbyists).
An active community of users and developers existed in the late 1970s, beginning with ARESCO's "VIPer" newsletter whose first three issues revealed the machine code behind the CHIP-8 interpreter.
CHIP-8 applications
There are a number of classic video games ported to CHIP-8, such as Pong, Space Invaders, Tetris, and Pac-Man. There are also applications like a random maze generator and Conway's Game of Life.
CHIP-8 extensions and variations
During the 1970s and 1980s, CHIP-8 users shared CHIP-8 programs, but also changes and extensions to the CHIP-8 interpreter, in the COSMAC VIP users' newsletter, VIPER magazine. These extensions included CHIP-10 and Hi-Res CHIP-8, which introduced a higher resolution than the standard 64x32, and CHIP-8C and CHIP-8X, which extended the monochrome display capabilities to support limited color, among other features. These extensions were mostly backwards compatible, as they were based on the original interpreter, although some repurposed rarely used opcodes for new instructions.
In 1979, Electronics Australia ran a series of articles on building a kit computer
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https://en.wikipedia.org/wiki/Telmac%201800
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The Telmac 1800 was an early microcomputer delivered in kit form. It was introduced in 1977 by Telercas Oy, the Finnish importer of RCA microchips. Most of the 2,000 kits manufactured over four years were bought by electronics enthusiasts in Finland, Sweden and Norway.
An expansion board, OSCOM, later became available, and included an alphanumeric video display, and up to of memory. A Tiny BASIC could be run on this configuration.
The first-ever commercial video game to be developed in Finland, Chesmac (fi), was developed by Raimo Suonio on a Telmac 1800 computer in 1979.
The Telmac 1800 was followed by the Oscom Nano and the Telmac 2000.
Major features
RCA 1802 (COSMAC) microprocessor CPU @ 1.75 MHz
Cassette tape interface
2 kB RAM, expandable to 4 kB
RCA CDP1861 'Pixie' video chip, 64×128 pixels display resolution
Sound limited to a fixed frequency tone
Able to run a CHIP-8 interpreter
References
External links
Revival Studios Developer of new Chip-8/SuperChip/MegaChip8 games.
Telmac 1800 schematics.
See also
Telmac TMC-600
Early microcomputers
8-bit computers
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https://en.wikipedia.org/wiki/Interleukin%202
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Interleukin-2 (IL-2) is an interleukin, a type of cytokine signaling molecule in the immune system. It is a 15.5–16 kDa protein that regulates the activities of white blood cells (leukocytes, often lymphocytes) that are responsible for immunity. IL-2 is part of the body's natural response to microbial infection, and in discriminating between foreign ("non-self") and "self". IL-2 mediates its effects by binding to IL-2 receptors, which are expressed by lymphocytes. The major sources of IL-2 are activated CD4+ T cells and activated CD8+ T cells. Put shortly the function of IL-2 is to stimulate the growth of helper, cytotoxic and regulatory T cells.
IL-2 receptor
IL-2 is a member of a cytokine family, each member of which has a four alpha helix bundle; the family also includes IL-4, IL-7, IL-9, IL-15 and IL-21. IL-2 signals through the IL-2 receptor, a complex consisting of three chains, termed alpha (CD25), beta (CD122) and gamma (CD132). The gamma chain is shared by all family members.
The IL-2 receptor (IL-2R) α subunit binds IL-2 with low affinity (Kd~ 10−8 M). Interaction of IL-2 and CD25 alone does not lead to signal transduction due to its short intracellular chain but has the ability (when bound to the β and γ subunit) to increase the IL-2R affinity 100-fold. Heterodimerization of the β and γ subunits of IL-2R is essential for signalling in T cells. IL-2 can signalize either via intermediate-affinity dimeric CD122/CD132 IL-2R (Kd~ 10−9 M) or high-affinity trimeric CD25/CD122/CD132 IL-2R (Kd~ 10−11 M). Dimeric IL-2R is expressed by memory CD8+ T cells and NK cells, whereas regulatory T cells and activated T cells express high levels of trimeric IL-2R.
IL-2 signaling pathways and regulation
Instructions to express proteins in response to an IL-2 signal (called IL-2 transduction) can take place via 3 different signaling pathways; they are: (1) the JAK-STAT pathway, (2) the PI3K/Akt/mTOR pathway and (3) the MAPK/ERK pathway. The signalling is commenced by IL
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https://en.wikipedia.org/wiki/Index%20of%20oncology%20articles
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This is a list of terms related to oncology. The original source for this list was the US National Cancer Institute's public domain Dictionary of Cancer Terms.
0–9
10-propargyl-10-deazaaminopterin
– 12-O-tetradecanoylphorbol-13-acetate
– 13-cis retinoic acid
– 17-N-allylamino-17-demethoxygeldanamycin
– 18F-EF5
– 1H-nuclear magnetic resonance spectroscopic imaging
– 2-methoxyestradiol
– 2IT-BAD monoclonal antibody 170
– 3-aminopyridine-2-carboxaldehyde thiosemicarbazone
– 3-AP
– 3-dimensional conformal radiation therapy
– 3-dimensional radiation therapy
– 4-demethoxydaunorubicin
– 4-hydroxytamoxifen
– 4-nitroquinoline 1-oxide
– 4-NQO
– 5-FU
– 5-hydroxyindoleacetic acid
– 5-hydroxytryptamine
– 506U78
– 5Q- syndrome
– 6-hydroxymethylacylfulvene
– 9-cis retinoic acid
– 90Y-DOTA-biotin
A
A33 monoclonal antibody
– AAP
– abarelix
– ABCD rating
– ABI-007
– ABT-510
– ABT-751
– ABX-EGF
– accelerated phase
– ACE inhibitor
– acetylcysteine
– achlorhydria
– acitretin
– acoustic neurofibromatosis
– acridine carboxamide
– acrylonitrile
– actinic keratosis
– action study
– Activase
– acute erythroid leukemia
– acute lymphoblastic leukemia
– acute lymphocytic leukemia
– acute myelogenous leukemia
– acute myeloid leukemia
– acute nonlymphocytic leukemia
– AD 32
– adenocarcinoma
– adenoid cystic cancer
– adenoma
– adenopathy
– adenosine triphosphate
– adenovirus
– adjunct agent
– adjunctive therapy
– adjuvant therapy
– adrenocortical
– Adriamycin
– adult T-cell leukemia/lymphoma
– AE-941
– AEE788
– aerobic metabolism
– aerobic respiration
– aerodigestive tract
– aerosolize
– aflatoxin
– AFP
– AG013736
– AG2037
– AG3340
– AG337
– agent study
– agglutinin
– aggressive lymphoma
– agnogenic myeloid metaplasia
– agonist
– agranulocytosis
– AJCC staging system
– alanine aminopeptidase
– alanine transferase
– alanosine
– aldesleukin
– alemtuzumab
– alendronate sodium
– alkalinization
– alkylating agent
– ALL
– all-trans retinoic acid
– allogeneic
– allogeneic bone marrow transplantation
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https://en.wikipedia.org/wiki/International%20Union%20of%20Biological%20Sciences
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The International Union of Biological Sciences (IUBS) is a non-profit organization and non-governmental organization, founded in 1919, that promotes the biological sciences internationally. As a scientific umbrella organization it was a founding member of the International Council for Science (ICSU).
Objectives
The union has several key objectives:
to promote the study of biological sciences;
to initiate, facilitate and coordinate research and other scientific activities necessitating international, interdisciplinary cooperation;
to ensure the discussion and dissemination of the results of cooperative research, particularly in connection with IUBS scientific programmes;
to support the organisation of international conferences and assist in the publication of their reports.
Networking and cooperation
The Union was a founding member of the ICSU Scientific Committee and works closely with UNESCO. It also maintains relations with the World Health Organization (WHO), the Food and Agriculture Organization (FAO) and the United Nations Environment Programme (UNEP). It cooperates with the European Commission and numerous other organizations, agencies and foundations.
Organisation
The Union currently consists of:
44 national members, consisting of national science academies, research and scientific organizations,
80 scientific members, including international scientific associations, societies or commissions of the various biological disciplines, from biology to zoology. New members are allowed under strict scientific guidelines.
The national and the academic members identify promising areas of biological science and bring them to the attention of the Union and in the reverse, promote the programs of the Union in their own country to stimulate research projects. The Union reviews the member's suggestions, checks them against the international academic and scientific-political background and develops the programs, if they have sufficient support. Approval is given
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https://en.wikipedia.org/wiki/DeskMate
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DeskMate is a software application that provides a graphical operating environment. It originally was for Tandy Corporation's TRSDOS Operating System for their TRS-80 line of computers, but eventually shifted to MS-DOS. Like GEM from Digital Research, it is not a full operating system, but runs on top an existing system. Initial ports only ran on Tandy's PCs such as the Tandy 1000, but later became available for true IBM PC compatibles and competed with early versions of Microsoft Windows.
Some non-Tandy software uses DeskMate to provide the user interface via a runtime version of the operating environment for those without it. This includes Activision's The Music Studio and a version of Lotus 1-2-3.
DeskMate 1.0
DeskMate version 1.0 was included with the original Tandy 1000 and did not work correctly on non-Tandy computers. This was mainly due to the use of the function keys - as most non-Tandy PCs either did not come with an F12 button or with one that did not act in the same way as a Tandy F12 function key (Tandy adopted F11/F12 before IBM did).
DeskMate was popular, increasing sales of the Tandy 1000 to homes and schools.
DeskMate 2
By the time Personal DeskMate was released with the Tandy 1000 EX, it was a GUI that acted as a portal for many other office productivity applications. The DeskMate application would run on top of MS-DOS. The user interface was made up of text. The applications that made up the suite were:
a basic word processor ("Text")
a spreadsheet ("Worksheet")
a calendar
a basic database program ("Filer")
The programs all fit on a 360K floppy disk. With careful manipulation, it was possible to isolate the individual applications and remove the others, placing them on separate floppies to be swapped when required. DeskMate was still required, as the individual programs could not be accessed directly.
DeskMate 3
DeskMate 3 added a number of basic applications:
a drawing program ("Draw")
a simple digital audio editing program ("Sound")
a sim
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https://en.wikipedia.org/wiki/Schur%20multiplier
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In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group of a group G. It was introduced by in his work on projective representations.
Examples and properties
The Schur multiplier of a finite group G is a finite abelian group whose exponent divides the order of G. If a Sylow p-subgroup of G is cyclic for some p, then the order of is not divisible by p. In particular, if all Sylow p-subgroups of G are cyclic, then is trivial.
For instance, the Schur multiplier of the nonabelian group of order 6 is the trivial group since every Sylow subgroup is cyclic. The Schur multiplier of the elementary abelian group of order 16 is an elementary abelian group of order 64, showing that the multiplier can be strictly larger than the group itself. The Schur multiplier of the quaternion group is trivial, but the Schur multiplier of dihedral 2-groups has order 2.
The Schur multipliers of the finite simple groups are given at the list of finite simple groups. The covering groups of the alternating and symmetric groups are of considerable recent interest.
Relation to projective representations
Schur's original motivation for studying the multiplier was to classify projective representations of a group, and the modern formulation of his definition is the second cohomology group . A projective representation is much like a group representation except that instead of a homomorphism into the general linear group , one takes a homomorphism into the projective general linear group . In other words, a projective representation is a representation modulo the center.
showed that every finite group G has associated to it at least one finite group C, called a Schur cover, with the property that every projective representation of G can be lifted to an ordinary representation of C. The Schur cover is also known as a covering group or Darstellungsgruppe. The Schur covers of the finite simple groups are known, and each is an example of
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https://en.wikipedia.org/wiki/Axiom%20of%20real%20determinacy
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In mathematics, the axiom of real determinacy (abbreviated as ADR) is an axiom in set theory. It states the following:
The axiom of real determinacy is a stronger version of the axiom of determinacy (AD), which makes the same statement about games where both players choose integers; ADR is inconsistent with the axiom of choice. It also implies the existence of inner models with certain large cardinals.
ADR is equivalent to AD plus the axiom of uniformization.
See also
AD+
Axiom of projective determinacy
Topological game
Axioms of set theory
Determinacy
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https://en.wikipedia.org/wiki/List%20of%20web%20browsers
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The following is a list of web browsers that are notable.
Historical
Layout engines
Gecko is developed by the Mozilla Foundation.
Goanna is a fork of Gecko developed by Moonchild Productions.
Servo is an experimental web browser layout engine being developed cooperatively by Mozilla and Samsung. In 2020 the engine's development was transferred to the Linux Foundation.
Presto was developed by Opera Software for use in Opera. Development stopped as Opera transitioned to Blink.
Trident is developed by Microsoft for use in the Windows versions of Internet Explorer 4 to Internet Explorer 11.
EdgeHTML is the engine developed by Microsoft for Edge. It is a largely rewritten fork of Trident with all legacy code removed.
Tasman was developed by Microsoft for use in Internet Explorer 5 for Macintosh.
KHTML is developed by the KDE project.
WebKit is a fork of KHTML by Apple Inc. used in Apple Safari, and formerly in Chromium and Google Chrome.
Blink is a 2013 fork of WebKit's WebCore component by Google used in Chromium, Google Chrome, Microsoft Edge, Opera, and Vivaldi.
Graphical
Current and maintained projects are listed in boldface.
Trident shells
Other software publishers have built browsers and other products around Microsoft's Trident engine. The following browsers are all based on that rendering engine:
360 Secure Browser
AOL Explorer
Bento Browser (built into Winamp)
Deepnet Explorer
GreenBrowser
Internet Explorer
MediaBrowser
MSN Explorer
NeoPlanet
NetCaptor
RealPlayer
Tencent Traveler
Gecko-based
Camino for Mac OS X (formerly Chimera)
Conkeror, (keyboard-driven browser)
Galeon, (GNOME's old default browser)
K-Meleon (Windows)
K-MeleonCCF ME (for Windows based on K-Meleon core, mostly written in Lua)
K-Ninja for Windows (based on K-Meleon)
MicroB (for Maemo)
Minimo (for mobile)
Mozilla Firefox (formerly Firebird and Phoenix, developed by the Mozilla foundation)
AT&T Pogo (based on Firefox)
Cliqz, (a fork of the Fir
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https://en.wikipedia.org/wiki/Dedekind%20sum
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In mathematics, Dedekind sums are certain sums of products of a sawtooth function, and are given by a function D of three integer variables. Dedekind introduced them to express the functional equation of the Dedekind eta function. They have subsequently been much studied in number theory, and have occurred in some problems of topology. Dedekind sums have a large number of functional equations; this article lists only a small fraction of these.
Dedekind sums were introduced by Richard Dedekind in a commentary on fragment XXVIII of Bernhard Riemann's collected papers.
Definition
Define the sawtooth function as
We then let
be defined by
the terms on the right being the Dedekind sums. For the case a = 1, one often writes
s(b, c) = D(1, b; c).
Simple formulae
Note that D is symmetric in a and b, and hence
and that, by the oddness of (( )),
D(−a, b; c) = −D(a, b; c),
D(a, b; −c) = D(a, b; c).
By the periodicity of D in its first two arguments, the third argument being the length of the period for both,
D(a, b; c) = D(a+kc, b+lc; c), for all integers k,l.
If d is a positive integer, then
D(ad, bd; cd) = dD(a, b; c),
D(ad, bd; c) = D(a, b; c), if (d, c) = 1,
D(ad, b; cd) = D(a, b; c), if (d, b) = 1.
There is a proof for the last equality making use of
Furthermore, az = 1 (mod c) implies D(a, b; c) = D(1, bz; c).
Alternative forms
If b and c are coprime, we may write s(b, c) as
where the sum extends over the c-th roots of unity other than 1, i.e. over all such that and .
If b, c > 0 are coprime, then
Reciprocity law
If b and c are coprime positive integers then
Rewriting this as
it follows that the number 6c s(b,c) is an integer.
If k = (3, c) then
and
A relation that is prominent in the theory of the Dedekind eta function is the following. Let q = 3, 5, 7 or 13 and let n = 24/(q − 1). Then given integers a, b, c, d with ad − bc = 1 (thus belonging to the modular group), with c chosen so that c = kq for some integer k > 0, define
Then nδ
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https://en.wikipedia.org/wiki/Hauppauge%20Computer%20Works
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Hauppauge Computer Works ( ) is a US manufacturer and marketer of electronic video hardware for personal computers. Although it is most widely known for its WinTV line of TV tuner cards for PCs, Hauppauge also produces personal video recorders, digital video editors, digital media players, hybrid video recorders and digital television products for both Windows and Mac. The company is named after the hamlet of Hauppauge, New York, in which it is based.
In addition to its headquarters in New York, Hauppauge also has sales and technical support offices in France, Germany, the Netherlands, Sweden, Italy, Poland, Australia, Japan, Singapore, Indonesia, Taiwan, Spain and the UK.
Company history
Hauppauge was co-founded by Kenneth Plotkin and Kenneth Aupperle, and became incorporated in 1982.
Starting in 1983, the company followed Microway, the company that a year earlier provided the software needed by scientists and engineers to modify the IBM PC Fortran compiler so that it could transparently employ Intel 8087 coprocessors. The 80-bit Intel 8087 math coprocessor ran a factor of 50 faster than the 8/16-bit 8088 CPU that the IBM PC software came with. However, in 1982, the speed-up in floating-point-intensive applications was only a factor of 10 as the initial software developed by Microway and Hauppauge continued to call floating point libraries to do computations instead of placing inline x87 instructions inline with the 8088's instructions that allowed the 8088 to drive the 8087 directly. By 1984, inline compilers made their way into the market providing increased speed ups. Hauppauge provided similar software products in competition with Microway that they bundled with math coprocessors and remained in the Intel math coprocessor business until 1993 when the Intel Pentium came out with a built-in math coprocessor. However, like other companies that entered the math coprocessor business, Hauppauge produced other products that contributed to a field that is today call
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https://en.wikipedia.org/wiki/Gyroelongated%20square%20pyramid
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In geometry, the gyroelongated square pyramid is one of the Johnson solids (). As its name suggests, it can be constructed by taking a square pyramid and "gyroelongating" it, which in this case involves joining a square antiprism to its base.
Applications
The Gyroelongated square pyramid represents the capped square antiprismatic molecular geometry:
Dual polyhedron
The dual of the gyroelongated square pyramid has 9 faces: 4 kites, 1 square and 4 pentagonal.
See also
Gyroelongated square bipyramid
External links
Johnson solids
Pyramids and bipyramids
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https://en.wikipedia.org/wiki/Shift%20JIS%20art
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Shift_JIS art is artwork created from characters in the Shift JIS character set, a superset of the ASCII encoding standard intended for Japanese usage. Shift_JIS art has become popular on web-based bulletin boards, notably 2channel, and has even made its way into mainstream media and commercial advertising in Japan.
In Japanese media
The Shift JIS character set is a Japanese Industrial Standards (JIS) superset of JIS X 0201 (in turn almost a superset of ASCII) intended for Japanese usage. Unlike Western ASCII art, which is generally designed to be viewed with a monospaced font, Shift_JIS art is designed around the proportional-width MS PGothic font supplied with Microsoft Windows, which is the default font for web sites in Japanese versions of Windows. This dependency has led to the development of the free Mona Font, in which each character is the same width as its counterpart in MS PGothic. This is useful on operating systems lacking the PGothic font, such as Linux.
Within the Japanese community, Shift_JIS art is sometimes abbreviated as SJIS art, but is most commonly referred to as "AA" meaning ASCII art, although it rarely restricts itself to the 95 printable characters within the ASCII standard. As with ANSI art, SJIS art is sometimes used for animation. However, due to technical advances, SJIS art also appears in the form of Adobe Flash files and animated GIFs.
The Japanese movie and television show, , frequently included Shift_JIS art, both during screen transitions and within the story itself. One of the recurring characters in the TV series was a Shift_JIS artist who would often draw full-screen Shift_JIS works of art as a way of expressing his support and encouraging the lead character. When they got engaged, posts began flowing in congratulating the new couple, and extravagant Shift JIS art pictures were posted.
The Touhou Project meme "Yukkuri shiteitte ne!!!" traces back to Shift JIS art of Reimu Hakurei's outfit in Curiosities of Lotus Asia tha
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https://en.wikipedia.org/wiki/Elongated%20pentagonal%20pyramid
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In geometry, the elongated pentagonal pyramid is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal pyramid () by attaching a pentagonal prism to its base.
Formulae
The following formulae for the height (), surface area () and volume () can be used if all faces are regular, with edge length :
Dual polyhedron
The dual of the elongated pentagonal pyramid has 11 faces: 5 triangular, 1 pentagonal and 5 trapezoidal. It is topologically identical to the Johnson solid.
See also
Elongated pentagonal bipyramid
References
External links
Johnson solids
Self-dual polyhedra
Pyramids and bipyramids
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https://en.wikipedia.org/wiki/Gyroelongated%20pentagonal%20pyramid
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In geometry, the gyroelongated pentagonal pyramid is one of the Johnson solids (). As its name suggests, it is formed by taking a pentagonal pyramid and "gyroelongating" it, which in this case involves joining a pentagonal antiprism to its base.
It can also be seen as a diminished icosahedron, an icosahedron with the top (a pentagonal pyramid, ) chopped off by a plane. Other Johnson solids can be formed by cutting off multiple pentagonal pyramids from an icosahedron: the pentagonal antiprism and metabidiminished icosahedron (two pyramids removed), and the tridiminished icosahedron (three pyramids removed).
Dual polyhedron
The dual of the gyroelongated pentagonal pyramid has 11 faces: 5 kites, 1 regular pentagonal and 5 irregular pentagons.
External links
Johnson solids
Pyramids and bipyramids
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https://en.wikipedia.org/wiki/Tridiminished%20icosahedron
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In geometry, the tridiminished icosahedron is one of the Johnson solids (). The name refers to one way of constructing it, by removing three pentagonal pyramids () from a regular icosahedron, which replaces three sets of five triangular faces from the icosahedron with three mutually adjacent pentagonal faces.
Related polytopes
The tridiminished icosahedron is the vertex figure of the snub 24-cell, a uniform 4-polytope (4-dimensional polytope).
See also
Diminished icosahedron (J11)
Metabidiminished icosahedron (J62)
External links
Johnson solids
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