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https://en.wikipedia.org/wiki/William%20Smyth%20%28professor%29
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William Smyth (February 2, 1797 – April 3, 1868) was an American academic and writer on mathematics and other subjects.
Early life
William Smyth was born in Pittston, Maine on February 2, 1797. He graduated from Bowdoin College in 1822, then studied theology at Andover Theological Seminary.
Career
In 1825, he became a professor of mathematics at Bowdoin College, and in 1846 became an associate professor of natural philosophy. The Bowdoin College Department of Mathematics Smyth Prize is named in his honor.
Smyth was an ardent abolitionist of slavery and supporter of the temperance movement. While at Bowdoin, Smyth supported the effort to the First Parish Church, which is now on the National Register of Historic Places.
Personal life
Smyth married Harriet Porter, daughter of Mary (née Porter) and Nathaniel Coffin. They had nine children.
He died in Brunswick, Maine in April 1868. He is interred at Pine Grove Cemetery in Brunswick.
Bibliography
Smyth wrote several widely used textbooks:
Elements of Algebra (1833) digitized version
Elementary Algebra for Schools (1850) digitized version
Treatise on Algebra" (1852) digitized version
Trigonometry, Surveying, and Navigation(1855) digitized version
Elements of Analytical Geometry" (1855)
Elements of the Differential and Integral Calculus" (1856; 2d ed., 1859) digitized version
Lectures on Modern History, edited by Jared Sparks (1849) digitized version
References
Bowdoin College Catalogue 1840-1848. Bowdoin College
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https://en.wikipedia.org/wiki/2C-T
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2C-T (or 4-methylthio-2,5-DMPEA) is a psychedelic and hallucinogenic drug of the 2C family. It is used by some as an entheogen. It has structural and pharmacodynamic properties similar to the drugs mescaline and 2C-T-2.
It was first synthesized and studied through a collaboration between David E. Nichols and Alexander Shulgin.
Chemistry
2C-T is in a class of compounds commonly known as phenethylamines, and is the 4-methylthio analogue of 2C-O, a positional isomer of mescaline. It is also the 2C analog of Aleph. The systematic name of the chemical is 2-(2,5-dimethoxy-4-(methylthio)phenyl)ethanamine. The CAS number of 2C-T is 61638-09-3.
Effects
2C-T's active dosage is around 75–150 mg and produces mescaline and MDMA-like effects that may last up to 6 hours.
Pharmacology
The mechanism that produces 2C-T’s hallucinogenic and entheogenic effects has not been specifically established, however it is most likely to result from action as a 5-HT2A serotonin receptor agonist in the brain, a mechanism of action shared by all of the hallucinogenic tryptamines and phenethylamines for which the mechanism of action is known.
Popularity
2C-T is almost unknown on the black market although it has rarely been sold by "research chemical" companies. Limited accounts of 2C-T can be found in the book PiHKAL.
Legality
Canada
As of October 31, 2016; 2C-T is a controlled substance (Schedule III) in Canada.
United States
2C-T is unscheduled and unregulated in the United States; however its
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https://en.wikipedia.org/wiki/Discovery%20Center%20of%20Springfield
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The Discovery Center of Springfield (DCS) in Springfield, Missouri, is an interactive, hands-on science center dedicated to inspiring curiosity and a life-long love of learning through memorable and engaging hands-on experiences in STEM (Science, Technology, Engineering, and Mathematics) In December of 2021, inaugural grand prize winner of the Center for Education Reform and media partner Forbes STOP Award. The Wall Street Journal editorial board wrote about the museum that became a school winning the $1 million award.
At the onset of the COVID-19 pandemic in March of 2020, the Discovery Center remained open and delivered on their mission by providing emergency, licensed childcare for the families of healthcare workers and first responders. DCS provided over 200,000 hours of free childcare and over 50,000 free meals and snacks.
Its history goes back to the late 1980s when a group of community volunteers led by the junior league of Springfield began a feasibility study for a children's hands-on museum project for Springfield and the Ozark region.
In 1991 Discovery Center of Springfield was incorporated. Over the next six years the volunteer board of directors and other committed community volunteers planned the building purchase and renovation, exhibits and program development and business operation. Since its opening in January 1998, the DCS has developed and added a great number of programs and exhibits. Collaboration has been the key to the success of this regional
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https://en.wikipedia.org/wiki/Ikeda%20map
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In physics and mathematics, the Ikeda map is a discrete-time dynamical system given by the complex map
The original map was proposed first by Kensuke Ikeda as a model of light going around across a nonlinear optical resonator (ring cavity containing a nonlinear dielectric medium) in a more general form. It is reduced to the above simplified "normal" form by Ikeda, Daido and Akimoto stands for the electric field inside the resonator at the n-th step of rotation in the resonator, and and are parameters which indicate laser light applied from the outside, and linear phase across the resonator, respectively. In particular the parameter is called dissipation parameter characterizing the loss of resonator, and in the limit of the Ikeda map becomes a conservative map.
The original Ikeda map is often used in another modified form in order to take the saturation effect of nonlinear dielectric medium into account:
A 2D real example of the above form is:
where u is a parameter and
For , this system has a chaotic attractor.
Attractor
This shows how the attractor of the system changes as the parameter is varied from 0.0 to 1.0 in steps of 0.01. The Ikeda dynamical system is simulated for 500 steps, starting from 20000 randomly placed starting points. The last 20 points of each trajectory are plotted to depict the attractor. Note the bifurcation of attractor points as is increased.
Point trajectories
The plots below show trajectories of 200 random points for various values
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https://en.wikipedia.org/wiki/Nuclear%20reactor%20physics
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Nuclear reactor physics is the field of physics that studies and deals with the applied study and engineering applications of chain reaction to induce a controlled rate of fission in a nuclear reactor for the production of energy.
Most nuclear reactors use a chain reaction to induce a controlled rate of nuclear fission in fissile material, releasing both energy and free neutrons. A reactor consists of an assembly of nuclear fuel (a reactor core), usually surrounded by a neutron moderator such as regular water, heavy water, graphite, or zirconium hydride, and fitted with mechanisms such as control rods which control the rate of the reaction.
The physics of nuclear fission has several quirks that affect the design and behavior of nuclear reactors. This article presents a general overview of the physics of nuclear reactors and their behavior.
Criticality
In a nuclear reactor, the neutron population at any instant is a function of the rate of neutron production (due to fission processes) and the rate of neutron losses (due to non-fission absorption mechanisms and leakage from the system). When a reactor’s neutron population remains steady from one generation to the next (creating as many new neutrons as are lost), the fission chain reaction is self-sustaining and the reactor's condition is referred to as "critical". When the reactor’s neutron production exceeds losses, characterized by increasing power level, it is considered "supercritical", and when losses dominate, it is
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https://en.wikipedia.org/wiki/Human%E2%80%93robot%20interaction
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Human–robot interaction (HRI) is the study of interactions between humans and robots. Human–robot interaction is a multidisciplinary field with contributions from human–computer interaction, artificial intelligence, robotics, natural language processing, design, and psychology. A subfield known as physical human–robot interaction (pHRI) has tended to focus on device design to enable people to safely interact with robotic systems.
Origins
Human–robot interaction has been a topic of both science fiction and academic speculation even before any robots existed. Because much of active HRI development depends on natural language processing, many aspects of HRI are continuations of human communications, a field of research which is much older than robotics.
The origin of HRI as a discrete problem was stated by 20th-century author Isaac Asimov in 1941, in his novel I, Robot. Asimov coined Three Laws of Robotics, namely:
A robot may not injure a human being or, through inaction, allow a human being to come to harm.
A robot must obey the orders by human beings except where such orders would conflict with the First Law.
A robot must protect its own existence as long as such protection does not conflict with the First or Second Laws.
These three laws provide an overview of the goals engineers and researchers hold for safety in the HRI field, although the fields of robot ethics and machine ethics are more complex than these three principles. However, generally human–robot interact
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https://en.wikipedia.org/wiki/Detritus
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In biology, detritus () is dead particulate organic material, as distinguished from dissolved organic material. Detritus typically includes the bodies or fragments of bodies of dead organisms, and fecal material. Detritus typically hosts communities of microorganisms that colonize and decompose (i.e. remineralize) it. In terrestrial ecosystems it is present as leaf litter and other organic matter that is intermixed with soil, which is denominated "soil organic matter". The detritus of aquatic ecosystems is organic substances that is suspended in the water and accumulates in depositions on the floor of the body of water; when this floor is a seabed, such a deposition is denominated "marine snow".
Theory
The corpses of dead plants or animals, material derived from animal tissues (e.g. molted skin), and fecal matter gradually lose their form due to physical processes and the action of decomposers, including grazers, bacteria, and fungi. Decomposition, the process by which organic matter is decomposed, occurs in several phases. Micro- and macro-organisms that feed on it rapidly consume and absorb materials such as proteins, lipids, and sugars that are low in molecular weight, while other compounds such as complex carbohydrates are decomposed more slowly. The decomposing microorganisms degrade the organic materials so as to gain the resources they require for their survival and reproduction. Accordingly, simultaneous to microorganisms' decomposition of the materials of dead pla
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https://en.wikipedia.org/wiki/Constance%20Kamii
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Constance Kamii was a Swiss-Japanese-American mathematics education scholar and psychologist. She was a professor in the Early Childhood Education Program
Department of Curriculum and Instruction at the University of Alabama in Birmingham, Alabama.
Overview
Constance Kamii was born in Geneva, Switzerland, and attended elementary schools there and in Japan. She finished high school in Los Angeles, attended Pomona College, and received her Ph.D. in education and psychology from the University of Michigan.
She was a professor of early childhood education at the University of Alabama in Birmingham. A major concern of hers since her work on the Perry Preschool Project in the 1960s was the conceptualization of goals and objectives for early childhood education on the basis of a scientific theory explaining children’s sociological and intellectual development. Convinced that the only theory in existence that explains this development from the first day of life to adolescence was that of Jean Piaget, she studied under him on and off for 15 years.
When she was not studying under Piaget in Geneva, she worked closely with teachers in the United States to develop practical ways of using his theory in classrooms. The outcome of this classroom research can be seen in Physical Knowledge in Preschool Education and Group Games in Early Education, which she wrote with Rheta DeVries. Since 1980, she had been extending this curriculum research to the primary grades and wrote Young Children Re
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https://en.wikipedia.org/wiki/Polarization
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Polarization or polarisation may refer to:
Mathematics
Polarization of an Abelian variety, in the mathematics of complex manifolds
Polarization of an algebraic form, a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables
Polarization identity, expresses an inner product in terms of its associated norm
Polarization (Lie algebra)
Physical sciences
Polarization (physics), the ability of waves to oscillate in more than one direction, in particular polarization of light, responsible for example for the glare-reducing effect of polarized sunglasses
Polarization (antenna), the state of polarization (in the above sense) of electromagnetic waves transmitted by or received by a radio antenna
Dielectric polarization, charge separation in insulating materials:
Polarization density, volume dielectric polarization
Dipolar polarization, orientation of permanent dipoles
Ionic polarization, displacement of ions in a crystal
Maxwell–Wagner–Sillars polarization, slow long-distance charge separation in dielectric spectroscopy on inhomogeneous soft matter
Polarization (electrochemistry), a change in the equilibrium potential of an electrochemical reaction
Concentration polarization, the shift of the electrochemical potential difference across an electrochemical cell from its equilibrium value
Spin polarization, the degree by which the spin of elementary particles is aligned to a given direction
Polarizability, an electrical property of atoms or mole
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https://en.wikipedia.org/wiki/Plane%20geometry%20%28disambiguation%29
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In mathematics, plane geometry may refer to the geometry of a two-dimensional geometric object called a plane.
Most times it refers to Euclidean plane geometry, the geometry of plane figures,
More specifically it can refer to:
Euclidean plane geometry:
Cartesian geometry, the study of geometry using a coordinate system
Two-dimensional space
synthetic geometry, the study of geometry using a logical deduction and compass and straightedge constructions
geometry of a projective plane,
often the real projective plane,
but possibly the complex projective plane or projective plane defined over some other field,
either infinite or finite, such as the Fano plane, or others;
geometry of an affine plane,
geometry of a non-Euclidean plane,
either the hyperbolic plane,
or the elliptic plane,
or the geometry of the related two-dimensional spherical geometry.
See also
Plane curve
Geometrography
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https://en.wikipedia.org/wiki/Elliptic%20complex
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In mathematics, in particular in partial differential equations and differential geometry, an elliptic complex generalizes the notion of an elliptic operator to sequences. Elliptic complexes isolate those features common to the de Rham complex and the Dolbeault complex which are essential for performing Hodge theory. They also arise in connection with the Atiyah-Singer index theorem and Atiyah-Bott fixed point theorem.
Definition
If E0, E1, ..., Ek are vector bundles on a smooth manifold M (usually taken to be compact), then a differential complex is a sequence
of differential operators between the sheaves of sections of the Ei such that Pi+1 ∘ Pi=0. A differential complex with first order operators is elliptic if the sequence of symbols
is exact outside of the zero section. Here π is the projection of the cotangent bundle T*M to M, and π* is the pullback of a vector bundle.
See also
Chain complex
References
Differential geometry
Elliptic partial differential equations
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https://en.wikipedia.org/wiki/Dolbeault%20cohomology
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In mathematics, in particular in algebraic geometry and differential geometry, Dolbeault cohomology (named after Pierre Dolbeault) is an analog of de Rham cohomology for complex manifolds. Let M be a complex manifold. Then the Dolbeault cohomology groups depend on a pair of integers p and q and are realized as a subquotient of the space of complex differential forms of degree (p,q).
Construction of the cohomology groups
Let Ωp,q be the vector bundle of complex differential forms of degree (p,q). In the article on complex forms, the Dolbeault operator is defined as a differential operator on smooth sections
Since
this operator has some associated cohomology. Specifically, define the cohomology to be the quotient space
Dolbeault cohomology of vector bundles
If E is a holomorphic vector bundle on a complex manifold X, then one can define likewise a fine resolution of the sheaf of holomorphic sections of E, using the Dolbeault operator of E. This is therefore a resolution of the sheaf cohomology of .
In particular associated to the holomorphic structure of is a Dolbeault operator taking sections of to -forms with values in . This satisfies the characteristic Leibniz rule with respect to the Dolbeault operator on differential forms, and is therefore sometimes known as a -connection on , Therefore, in the same way that a connection on a vector bundle can be extended to the exterior covariant derivative, the Dolbeault operator of can be extended to an operator
whic
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https://en.wikipedia.org/wiki/IRF
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IRF may refer to:
General
Impulse response function
Information Retrieval Facility
Initial Reaction Force or Internal Response Force
Immediate Response Force
Institute of Space Physics (Sweden), (Institutet för rymdfysik)
Interferon Regulatory Factor (e.g. IRF6)
International Rectifier, New York Stock Exchange symbol IRF
Foundations/organizations
International Ranger Federation
International Rabbinic Fellowship
International Rogaining Federation
Islamic Research Foundation
International Rafting Federation
International Ringette Federation
Computing
Intelligent Resilient Framework, Virtual Switch Chassis Aggregation
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https://en.wikipedia.org/wiki/Set%20%28music%29
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A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.
A set by itself does not necessarily possess any additional structure, such as an ordering or permutation. Nevertheless, it is often musically important to consider sets that are equipped with an order relation (called segments); in such contexts, bare sets are often referred to as "unordered", for the sake of emphasis.
Two-element sets are called dyads, three-element sets trichords (occasionally "triads", though this is easily confused with the traditional meaning of the word triad). Sets of higher cardinalities are called tetrachords (or tetrads), pentachords (or pentads), hexachords (or hexads), heptachords (heptads or, sometimes, mixing Latin and Greek roots, "septachords"), octachords (octads), nonachords (nonads), decachords (decads), undecachords, and, finally, the dodecachord.
A time-point set is a duration set where the distance in time units between attack points, or time-points, is the distance in semitones between pitch classes.
Serial
In the theory of serial music, however, some authors (notably Milton Babbitt) use the term "set" where others woul
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https://en.wikipedia.org/wiki/Silencer%20%28genetics%29
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In genetics, a silencer is a DNA sequence capable of binding transcription regulation factors, called repressors. DNA contains genes and provides the template to produce messenger RNA (mRNA). That mRNA is then translated into proteins. When a repressor protein binds to the silencer region of DNA, RNA polymerase is prevented from transcribing the DNA sequence into RNA. With transcription blocked, the translation of RNA into proteins is impossible. Thus, silencers prevent genes from being expressed as proteins.
RNA polymerase, a DNA-dependent enzyme, transcribes the DNA sequences, called nucleotides, in the 3' to 5' direction while the complementary RNA is synthesized in the 5' to 3' direction. RNA is similar to DNA, except that RNA contains uracil, instead of thymine, which forms a base pair with adenine. An important region for the activity of gene repression and expression found in RNA is the 3' untranslated region. This is a region on the 3' terminus of RNA that will not be translated to protein but includes many regulatory regions.
Not much is yet known about silencers but scientists continue to study in hopes to classify more types, locations in the genome, and diseases associated with silencers.
Functionality
Locations within the genome
A silencer is a sequence-specific element that induces a negative effect on the transcription of its particular gene. There are many positions in which a silencer element can be located in DNA. The most common position is found ups
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https://en.wikipedia.org/wiki/Endophysics
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Endophysics literally means “physics from within”. It is the study of how the observations are affected and limited by the observer being within the universe. This is in contrast with the common exophysics assumption of a system observed from the “outside”. The term endophysics has been coined by David Finkelstein in a letter to the founder of the field Otto E. Rössler.
See also
Physics
Internal measurement (This notion is very similar to endophysics.)
References
R. J. Boskovich, De spacio et tempore, ut a nobis cognoscuntur, partial English translation in: J. M. Child (Ed.), A Theory of Natural Philosophy, Open Court (1922) and MIT Press, Cambridge, MA, 1966, pp. 203–205.
T. Toffoli, The role of the observer in uniform systems, in: G. J. Klir (Ed.), Applied General Systems Research, Recent Developments and Trends, Plenum Press, New York, London, 1978, pp. 395–400.
K. Svozil, Connections between deviations from Lorentz transformation and relativistic energy-momentum relation, Europhysics Letters 2 (1986) 83–85.
O. E. Rössler, Endophysics, in: J. L. Casti, A. Karlquist (Eds.), Real Brains, Artificial Minds, North-Holland, New York, 1987, p. 25.
O. E. Rössler, Endophysics. Die Welt des inneren Beobachters, Merwe Verlag, Berlin, 1992, with a foreword by Peter Weibel.
K. Svozil, Extrinsic-intrinsic concept and complementarity, in: H. Atmanspacker, G. J. Dalenoort (Eds.), Inside versus Outside, Springer-Verlag, Heidelberg, 1994, pp. 273–288.
External links
Karl Svozil
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https://en.wikipedia.org/wiki/Gerard%20Murphy
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Gerard Murphy may refer to:
Gerard Murphy (politician) (born 1951), Irish Fine Gael politician, TD for Cork North West
Gerard Murphy (mathematician) (1948–2006), Irish mathematics professor
Gerard Murphy (actor) (1948–2013), Irish film, television and theatre actor
See also
Gerry Murphy (disambiguation)
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https://en.wikipedia.org/wiki/Tubular%20neighborhood
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In mathematics, a tubular neighborhood of a submanifold of a smooth manifold is an open set around it resembling the normal bundle.
The idea behind a tubular neighborhood can be explained in a simple example. Consider a smooth curve in the plane without self-intersections. On each point on the curve draw a line perpendicular to the curve. Unless the curve is straight, these lines will intersect among themselves in a rather complicated fashion. However, if one looks only in a narrow band around the curve, the portions of the lines in that band will not intersect, and will cover the entire band without gaps. This band is a tubular neighborhood.
In general, let S be a submanifold of a manifold M, and let N be the normal bundle of S in M. Here S plays the role of the curve and M the role of the plane containing the curve. Consider the natural map
which establishes a bijective correspondence between the zero section of N and the submanifold S of M. An extension j of this map to the entire normal bundle N with values in M such that is an open set in M and j is a homeomorphism between N and is called a tubular neighbourhood.
Often one calls the open set rather than j itself, a tubular neighbourhood of S, it is assumed implicitly that the homeomorphism j mapping N to T exists.
Normal tube
A normal tube to a smooth curve is a manifold defined as the union of all discs such that
all the discs have the same fixed radius;
the center of each disc lies on the curve; and
eac
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https://en.wikipedia.org/wiki/Cycloheptene
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Cycloheptene is a 7-membered cycloalkene with a flash point of −6.7 °C. It is a raw material in organic chemistry and a monomer in polymer synthesis. Cycloheptene can exist as either the cis- or the trans-isomer.
{|
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| align ="center"|cis-Cycloheptene
| align ="center"|trans-Cycloheptene
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trans-Cycloheptene
With cycloheptene, the cis-isomer is always assumed but the trans-isomer does also exist. One procedure for the organic synthesis of trans-cycloheptene is by singlet photosensitization of cis-cycloheptene with methyl benzoate and ultraviolet light at −35 °C. The double bond in the trans isomer is very strained. The directly attached atoms on a simple alkene are all coplanar. In trans-cycloheptene, however, the size of the ring makes it impossible for the alkene and its two attached carbons to have this geometry because the remaining three carbons could not reach far enough to close the ring (see also Bredt's rule). There would have to be unusually large angles (angle strain), unusually long bond-lengths, or the atoms of the alkane-like loop would collide with the alkene part (steric strain). Part of the strain is relieved by pyramidalization of each alkene carbon and their rotation relative to each other. The pyramidalization angle is estimated at 37° (compared to an angle of 0° for an atom with normal trigonal–planar geometry) and the p-orbital misalignment is 30.1°. Because the barrier for rotation of the double bond in ethylene is approximately 65 kcal/mol
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https://en.wikipedia.org/wiki/ACM%20Computing%20Classification%20System
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The ACM Computing Classification System (CCS) is a subject classification system for computing devised by the Association for Computing Machinery (ACM). The system is comparable to the Mathematics Subject Classification (MSC) in scope, aims, and structure, being used by the various ACM journals to organize subjects by area.
History
The system has gone through seven revisions, the first version being published in 1964, and revised versions appearing in 1982, 1983, 1987, 1991, 1998, and the now current version in 2012.
Structure
It is hierarchically structured in four levels. For example, one branch of the hierarchy contains:
Computing methodologies
Artificial intelligence
Knowledge representation and reasoning
Ontology engineering
See also
Computer Science Ontology
Physics and Astronomy Classification Scheme
arXiv, a preprint server allowing submitted papers to be classified using the ACM CCS
Physics Subject Headings
References
.
.
.
External links
dl.acm.org/ccs is the homepage of the system, including links to four complete versions of the system:
the 1964 version
the 1991 version
the 1998 version
the current 2012 version.
The ACM Computing Research Repository uses a classification scheme that is much coarser than the ACM subject classification, and does not cover all areas of CS, but is intended to better cover active areas of research. In addition, papers in this repository are classified according to the ACM subject classification.
Computing Classific
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https://en.wikipedia.org/wiki/Thomas%20G.%20Barnes
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Thomas G. Barnes (August 14, 1911 – October 23, 2001) was an American creationist, who argued in support of his religious belief in a young earth by making the scientific claims that the Earth's magnetic field was consistently decaying.
Biography
Barnes obtained three degrees in Physics: an AB from Hardin-Simmons University in 1933, an MS from Brown University under Robert Bruce Lindsay in 1936, and an honorary Sc.D. again from Hardin-Simmons University in 1950. His detractors have questioned his credentials based on the fact that his doctorate was honorary.
At the time that Barnes joined the Creation Research Society (CRS) in the early 1960s, he was the head of the Schellenger Research Laboratories at Texas Western College (now University of Texas at El Paso), where he was completing a textbook on electricity and magnetism, and on whose faculty he served from 1938 until he retired in 1981. Barnes headed one of the first projects of the CRS, to create a creationist high school biology text. Barnes served as the president of the CRS in the mid-1970s.
Earth's magnetic field decay
Barnes claimed to calculate the half-life of the earth's magnetic field as approximately 1,400 years based on 130 years of empirical data. Some creationists have used Barnes' argument as evidence for a young earth, less than 10,000 years as suggested by the Bible. His critics have challenged this concept, claiming that Barnes failed to take experimental uncertainties into account and used an obsole
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https://en.wikipedia.org/wiki/Pumping%20lemma%20for%20context-free%20languages
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In computer science, in particular in formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, is a lemma that gives a property shared by all context-free languages and generalizes the pumping lemma for regular languages.
The pumping lemma can be used to construct a proof by contradiction that a specific language is not context-free. Conversely, the pumping lemma does not suffice to guarantee that a language is context-free; there are other necessary conditions, such as Ogden's lemma, or the Interchange lemma.
Formal statement
If a language is context-free, then there exists some integer (called a "pumping length") such that every string in that has a length of or more symbols (i.e. with ) can be written as
with substrings and , such that
1. ,
2. , and
3. for all .
Below is a formal expression of the Pumping Lemma.
Informal statement and explanation
The pumping lemma for context-free languages (called just "the pumping lemma" for the rest of this article) describes a property that all context-free languages are guaranteed to have.
The property is a property of all strings in the language that are of length at least , where is a constant—called the pumping length—that varies between context-free languages.
Say is a string of length at least that is in the language.
The pumping lemma states that can be split into five substrings, , where is non-empty and the length of is at most , such that repeatin
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https://en.wikipedia.org/wiki/Spectral%20bands
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Spectral bands are parts of the electromagnetic spectrum of specific wavelengths, which can be filtered by a standard filter. In nuclear physics, spectral bands are referred to the electromagnetic emission of polyatomic systems, including condensed materials, large molecules, etc. Each spectral line corresponds to one level in the atom splits in the molecules. When the number of atoms is large, one gets a continuum of energy levels, the so-called "spectral bands". They are often labeled in the same way as the monatomic lines.
The bands may overlap. In general, the energy spectrum can be given by a density function, describing the number of energy levels of the quantum system for a given interval. Spectral bands have constant density, and when the bands overlap, the corresponding densities are added.
Band spectra is the name given to a group of lines that are closely spaced and arranged in a regular sequence that appears to be a band. It is a colored band, separated by dark spaces on the two sides and arranged in a regular sequence. In one band, there are various sharp and wider color lines, that are closer on one side and wider on other. The intensity in each band falls off from definite limits and indistinct on the other side. In complete band spectra, there is a number lines in a band.
This spectra is produced when the emitting substance is in the molecular state. Therefore, they are also called molecular spectra.
It is emitted by a molecule in vacuum tube, C-arc core w
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https://en.wikipedia.org/wiki/E%26M
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E&M may stand for:
E and M signaling, a type of supervisory line signaling that uses DC signals on separate leads
Encrypt-and-MAC (E&M), an approach to authenticated encryption
Electromagnetism, sometimes also called electricity and magnetism, a branch of physics
Electromechanics, combines electrical engineering and mechanical engineering
Evaluation and Management Coding, a medical billing process in the United States
Exchange and Mart, a defunct long-established British sales publication
Mechatronics, a portmanteau of electronics and mechanics
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https://en.wikipedia.org/wiki/Binary%20icosahedral%20group
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In mathematics, the binary icosahedral group 2I or is a certain nonabelian group of order 120.
It is an extension of the icosahedral group I or (2,3,5) of order 60 by the cyclic group of order 2, and is the preimage of the icosahedral group under the 2:1 covering homomorphism
of the special orthogonal group by the spin group. It follows that the binary icosahedral group is a discrete subgroup of Spin(3) of order 120.
It should not be confused with the full icosahedral group, which is a different group of order 120, and is rather a subgroup of the orthogonal group O(3).
The binary icosahedral group is most easily described concretely as a discrete subgroup of the unit quaternions, under the isomorphism where Sp(1) is the multiplicative group of unit quaternions. (For a description of this homomorphism see the article on quaternions and spatial rotations.)
Elements
Explicitly, the binary icosahedral group is given as the union of all even permutations of the following vectors:
8 even permutations of
16 even permutations of
96 even permutations of
Here is the golden ratio.
In total there are 120 elements, namely the unit icosians. They all have unit magnitude and therefore lie in the unit quaternion group Sp(1).
The 120 elements in 4-dimensional space match the 120 vertices the 600-cell, a regular 4-polytope.
Properties
Central extension
The binary icosahedral group, denoted by 2I, is the universal perfect central extension of the icosahedral group, and thus
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https://en.wikipedia.org/wiki/Fatou%E2%80%93Lebesgue%20theorem
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In mathematics, the Fatou–Lebesgue theorem establishes a chain of inequalities relating the integrals (in the sense of Lebesgue) of the limit inferior and the limit superior of a sequence of functions to the limit inferior and the limit superior of integrals of these functions. The theorem is named after Pierre Fatou and Henri Léon Lebesgue.
If the sequence of functions converges pointwise, the inequalities turn into equalities and the theorem reduces to Lebesgue's dominated convergence theorem.
Statement of the theorem
Let f1, f2, ... denote a sequence of real-valued measurable functions defined on a measure space (S,Σ,μ). If there exists a Lebesgue-integrable function g on S which dominates the sequence in absolute value, meaning that |fn| ≤ g for all natural numbers n, then all fn as well as the limit inferior and the limit superior of the fn are integrable and
Here the limit inferior and the limit superior of the fn are taken pointwise. The integral of the absolute value of these limiting functions is bounded above by the integral of g.
Since the middle inequality (for sequences of real numbers) is always true, the directions of the other inequalities are easy to remember.
Proof
All fn as well as the limit inferior and the limit superior of the fn are measurable and dominated in absolute value by g, hence integrable.
The first inequality follows by applying Fatou's lemma to the non-negative functions fn + g and using the linearity of the Lebesgue integral. The last
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https://en.wikipedia.org/wiki/Nearly%20free%20electron%20model
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In solid-state physics, the nearly free electron model (or NFE model and quasi-free electron model) is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual empty lattice approximation. The model enables understanding and calculation of the electronic band structures, especially of metals.
This model is an immediate improvement of the free electron model, in which the metal was considered as a non-interacting electron gas and the ions were neglected completely.
Mathematical formulation
The nearly free electron model is a modification of the free-electron gas model which includes a weak periodic perturbation meant to model the interaction between the conduction electrons and the ions in a crystalline solid. This model, like the free-electron model, does not take into account electron–electron interactions; that is, the independent electron approximation is still in effect.
As shown by Bloch's theorem, introducing a periodic potential into the Schrödinger equation results in a wave function of the form
where the function has the same periodicity as the lattice:
(where is a lattice translation vector.)
Because it is a nearly free electron approximation we can assume that
where denotes the volume of states of fixed radius (as described in Gibbs paradox).
A solution of this form can be plugged into the Schrödinger equation, resulting in the
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https://en.wikipedia.org/wiki/Fundamental%20constant
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In physics, the term fundamental constant may refer to:
Any physical constant which is part of an equation that expresses a fundamental physical law
One of the fundamental dimensionless physical constants
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https://en.wikipedia.org/wiki/Mario%20Andreacchio
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Mario Andreacchio (born 1 January 1955) is an Australian film producer/director.
Born in Leigh Creek, South Australia to Italian parents, Andreacchio graduated from Flinders University with a degree in Psychology (after originally going to University to study Experimental Physics), and then was selected to study at the Australian Film and Television School to train as a film director. He has directed nine cinema feature films, made a series of television specials, two telemovies, three children's mini-series and a variety of documentaries. In 1988, he won an International Emmy Award in the 'Children and Young People' category for Captain Johnno, an episode of the 1988 Touch the Sun TV series.
In 2008 Andreacchio founded a film production company AMPCO FILMS PTY LTD (the Adelaide Motion Picture Company), based in Norwood, South Australia.
He has served on the boards of the Australian Film Finance Corporation and the South Australian Film Corporation.
Partial filmography
Fair Game (1986)
The Dreaming (1988)
Captain Johnno (1988)
Sky Trackers (1994)
Napoleon (1995)
The Real Macaw (1998)
Sally Marshall Is Not an Alien (1999)
Young Blades (2001)
Paradise Found (2003)
Elephant Tales (2005)
The Dragon Pearl (2011)
References
Sources
Adelaide Motion Picture Company website
External links
Australian film directors
Australian people of Italian descent
1955 births
Living people
Emmy Award winners
Australian Film Television and Radio School alumni
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https://en.wikipedia.org/wiki/Scavenger%20%28chemistry%29
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A scavenger in chemistry is a chemical substance added to a mixture in order to remove or de-activate impurities and unwanted reaction products, for example oxygen, to make sure that they will not cause any unfavorable reactions. Their use is wide-ranged:
In atmospheric chemistry, the most common scavenger is the hydroxyl radical, a short-lived radical produced photolytically in the atmosphere. It is the most important oxidant for carbon monoxide, methane and other hydrocarbons, sulfur dioxide, hydrogen sulfide, and most of other contaminants, removing them from the atmosphere.
In molecular laser isotope separation, methane is used as a scavenger gas for fluorine atoms.
Hydrazine and ascorbic acid are used as oxygen scavenger corrosion inhibitors.
Tocopherol and naringenin are bioactive free radical scavengers that act as antioxidants; synthetic catalytic scavengers are their synthetic counterparts
Organotin compounds are used in polymer manufacture as hydrochloric acid scavengers.
Oxygen scavengers or oxygen absorbers are small sachets or self adhesive labels that are placed inside modified atmosphere packs to help extend product life (notably cooked meats) and help improve product appearance. They work by absorbing any oxygen left in the pack by oxidation of the iron powder contained in the sachet/label.
Glutathione in the body scavenges oxidizing free radicals and peroxides and as a thiol nucleophile, attacks dangerous alkylating electrophiles, which may be exogen
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https://en.wikipedia.org/wiki/Developable
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In mathematics, the term developable may refer to:
A developable space in general topology.
A developable surface in geometry.
A tangent developable surface of a space curve
Mathematics disambiguation pages
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https://en.wikipedia.org/wiki/School%20Mathematics%20Project
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The School Mathematics Project arose in the United Kingdom as part of the new mathematics educational movement of the 1960s. It is a developer of mathematics textbooks for secondary schools, formerly based in Southampton in the UK.
Now generally known as SMP, it began as a research project inspired by a 1961 conference chaired by Bryan Thwaites at the University of Southampton, which itself was precipitated by calls to reform mathematics teaching in the wake of the Sputnik launch by the Soviet Union, the same circumstances that prompted the wider New Math movement. It maintained close ties with the former Collaborative Group for Research in Mathematics Education at the university.
Instead of dwelling on 'traditional' areas such as arithmetic and geometry, SMP dwelt on subjects such as set theory, graph theory and logic, non-cartesian co-ordinate systems, matrix mathematics, affine transforms, Euclidean vectors, and non-decimal number systems.
Course books
SMP, Book 1
This was published in 1965. It was aimed at entry level pupils at secondary school, and was the first book in a series of 4 preparing pupils for Elementary Mathematics Examination at 'O' level.
SMP, Book 3
The computer paper tape motif on early educational material reads "THE SCHOOL MATHEMATICS PROJECT DIRECTED BY BRYAN THWAITES".
O O O O O O OO O O O O OO O O O O O
O O OOOO O O O O OO O O O O O O O
O O O OO O O OO O O O O O O OOO
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https://en.wikipedia.org/wiki/David%20Edwards%20%28quiz%20contestant%29
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David Edwards (born 1947) is a Welsh physics teacher, best known as a TV quiz contestant. On 21 April 2001 he became the first man to win the million pounds in the UK version of Who Wants to Be a Millionaire? and only the second person after Judith Keppel. He competed in both series of Are You an Egghead?, reaching the last 16 in 2008, and the final in 2009, where he lost to fellow Millionaire winner Pat Gibson.
Early career
Born in Barry, Wales, Edwards graduated in Metallurgy from Swansea University in 1969, subsequently completing a Postgraduate Certificate in Education at Keele University. He studied Advanced French as an external student at Keele University with his wife Viv Edwards. He worked as a physics teacher at Cheadle High School and Denstone College, Staffordshire, prior to his appearance on Millionaire.
Who Wants to Be a Millionaire
His million pound question was "If you planted the seeds of Quercus robur, what would grow?" The options were Trees, Flowers, Vegetables and Grain. The correct answer was Trees. He used no lifelines for this question, having used all three on a £125,000 question. The phone-a-friend he used during his run was his son, Richard Edwards, who later won £125,000 on the show in May 2004, and David returned the favour and acted as his son's phone-a-friend.
Other quiz appearances
Edwards was the Mastermind champion in 1990, and was awarded the title of Mensa Superbrain in 1985 after winning a newspaper competition.
Edwards has also part
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https://en.wikipedia.org/wiki/Overlapping%20interval%20topology
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In mathematics, the overlapping interval topology is a topology which is used to illustrate various topological principles.
Definition
Given the closed interval of the real number line, the open sets of the topology are generated from the half-open intervals with and with . The topology therefore consists of intervals of the form , , and with , together with itself and the empty set.
Properties
Any two distinct points in are topologically distinguishable under the overlapping interval topology as one can always find an open set containing one but not the other point. However, every non-empty open set contains the point 0 which can therefore not be separated from any other point in , making with the overlapping interval topology an example of a T0 space that is not a T1 space.
The overlapping interval topology is second countable, with a countable basis being given by the intervals , and with and r and s rational.
See also
List of topologies
Particular point topology, a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space
References
(See example 53)
Topological spaces
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https://en.wikipedia.org/wiki/Whitehead%20group
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Whitehead group in mathematics may mean:
A group W with Ext(W, Z)=0; see Whitehead problem
For a ring, the Whitehead group Wh(A) of a ring A, equal to
For a group, the Whitehead group Wh(G) of a group G, equal to K1(Z[G])/{±G}. Note that this is a quotient of the Whitehead group of the group ring.
The Whitehead group Wh(A) of a simplicial complex or PL-manifold A, equal to Wh(π1(A)); see Whitehead torsion.
All named after J. H. C. Whitehead.
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https://en.wikipedia.org/wiki/Chemical%20Reviews
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Chemical Reviews is peer-reviewed scientific journal published twice per month by the American Chemical Society. It publishes review articles on all aspects of chemistry. It was established in 1924 by William Albert Noyes (University of Illinois). The editor-in-chief is Sharon Hammes-Schiffer.
Abstracting and indexing
The journal is abstracted and indexed in Chemical Abstracts Service, CAB International, EBSCOhost, ProQuest, PubMed, Scopus, and the Science Citation Index. According to the Journal Citation Reports, the journal has a 2021 impact factor of 72.087.
See also
Accounts of Chemical Research
References
External links
American Chemical Society academic journals
Review journals
Monthly journals
English-language journals
Publications established in 1924
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https://en.wikipedia.org/wiki/Bryan%20Gaensler
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Bryan Malcolm Gaensler (born 1973) is an Australian astronomer based at the University of California, Santa Cruz. He studies magnetars, supernova remnants, and magnetic fields. In 2014, he was appointed as Director of the Dunlap Institute for Astronomy & Astrophysics at the University of Toronto, after James R. Graham's departure. He was the co-chair of the Canadian 2020 Long Range Plan Committee with Pauline Barmby.
In 2023, he was appointed as Dean of Physical and Biological Sciences at UC Santa Cruz.
Education
Gaensler was born in Sydney, Australia. He attended Sydney Grammar School, and studied at the University of Sydney, graduating with a BSc with first class honours in physics (1995), followed by a PhD in astrophysics (1999). His PhD thesis was completed under the supervision of Anne Green and Richard Manchester.
Career
From 1998 to 2001, Gaensler held a Hubble Fellowship at the Center for Space Research of the Massachusetts Institute of Technology. In 2001 he moved to the Smithsonian Astrophysical Observatory as a Clay Fellow. In 2002, he took up an appointment as an assistant professor in the Department of Astronomy at Harvard University.
In 2006, he moved back to Sydney as an Australian Research Council Federation Fellow in the School of Physics at the University of Sydney and in 2011 he was also appointed Director of the ARC Centre of Excellence for All-Sky Astrophysics (CAASTRO). In June 2014, Gaensler announced that he would be leaving CAASTRO and taking up
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https://en.wikipedia.org/wiki/Grygori%20N.%20Dolenko
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Grygori Nazarovych Dolenko (Gaevka, Kirovograd Oblast, February 2, 1917 - Lviv, December 16, 1990) was a Ukrainian petroleum geologist.
Graduated from Kharkiv University (1940). Worked for ChernomorNeft, KhadyzhenNeft, BuguruslanNeft, and UkrNefteRazvedka E&P companies and with Inst. of Geology and Geochemistry of Combustible Minerals of Nat'l Ac.Sci. Ukraine (NASU) since 1952 (Director, 1963–1982). NASU Corresponding Member (1964), NASU Academician (1979). Prof. Dolenko proposed the concept of mineral synthesis of oil and gas in the asthenosphere of the Earth's upper mantle. State Award laureate (1971) for the prospecting and discovery of oil and gas fields at great depths in the Dnieper-Donets basin and Carpathian Foredeep.
Selected publications
Dolenko G.N., 1962. Oil and gas geology of the Carpathians. - Kiev, Ukr.SSR Ac. Sci. Publ. - 368 p. (in Russian)
Dolenko G.N., 1966. Regularities of petroleum accumulation in the Earth's crust and the theory on inorganic oil and gas synthesis. In: Problem of oil and gas origin and formation of their commercial accumulations. - Kiev, Naukova Dumak Publ. - p. 3-25 (in Russian)
Dolenko G.N., 1975. On the problem of oil and gas origin and formation of their commercial fields. In: Problems of geology and geochemistry of endogenous petroleum. - Kiev, Naukova Dumka Publ. - p. 40-51 (in Russian)
Dolenko G.N., 1984. Origin of petroleum and its accumulation in the Earth's crust. - Kiev, Naukova Dumka Publ. - 135 p. (in Russian)
Dole
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https://en.wikipedia.org/wiki/External%20memory
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The term external memory is used with different meanings in different fields:
For the use of the term in psychology, see external memory (psychology)
For the use of the term in computing, see auxiliary memory
For the use of the term in computer science, see external memory algorithm
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https://en.wikipedia.org/wiki/Blind%20deconvolution
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In electrical engineering and applied mathematics, blind deconvolution is deconvolution without explicit knowledge of the impulse response function used in the convolution. This is usually achieved by making appropriate assumptions of the input to estimate the impulse response by analyzing the output. Blind deconvolution is not solvable without making assumptions on input and impulse response. Most of the algorithms to solve this problem are based on assumption that both input and impulse response live in respective known subspaces. However, blind deconvolution remains a very challenging non-convex optimization problem even with this assumption.
In image processing
In image processing, blind deconvolution is a deconvolution technique that permits recovery of the target scene from a single or set of "blurred" images in the presence of a poorly determined or unknown point spread function (PSF). Regular linear and non-linear deconvolution techniques utilize a known PSF. For blind deconvolution, the PSF is estimated from the image or image set, allowing the deconvolution to be performed. Researchers have been studying blind deconvolution methods for several decades, and have approached the problem from different directions.
Most of the work on blind deconvolution started in early 1970s. Blind deconvolution is used in astronomical imaging and medical imaging.
Blind deconvolution can be performed iteratively, whereby each iteration improves the estimation of the PSF and the scen
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https://en.wikipedia.org/wiki/Lamport%20signature
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In cryptography, a Lamport signature or Lamport one-time signature scheme is a method for constructing a digital signature. Lamport signatures can be built from any cryptographically secure one-way function; usually a cryptographic hash function is used.
Although the potential development of quantum computers threatens the security of many common forms of cryptography such as RSA, it is believed that Lamport signatures with large hash functions would still be secure in that event. Each Lamport key can only be used to sign a single message. However, many Lamport signatures can be handled by one Merkle hash tree, thus a single hash tree key can be used for many messages, making this a fairly efficient digital signature scheme.
The Lamport signature cryptosystem was invented in 1979 and named after its inventor, Leslie Lamport.
Example
Alice has a 256-bit cryptographic hash function and some kind of secure random number generator. She wants to create and use a Lamport key pair, that is, a private key and a corresponding public key.
Making the key pair
To create the private key Alice uses the random number generator to produce 256 pairs of random numbers (2×256 numbers in total), each number being 256 bits in size, that is, a total of 2×256×256 bits = 128 Kibit in total. This is her private key and she will store it away in a secure place for later use.
To create the public key she hashes each of the 512 random numbers in the private key, thus creating 512 hashes, each 2
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https://en.wikipedia.org/wiki/Donor%20number
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In chemistry a donor number (DN) is a quantitative measure of Lewis basicity. A donor number is defined as the negative enthalpy value for the 1:1 adduct formation between a Lewis base and the standard Lewis acid SbCl5 (antimony pentachloride), in dilute solution in the noncoordinating solvent 1,2-dichloroethane with a zero DN. The units are kilocalories per mole for historical reasons. The donor number is a measure of the ability of a solvent to solvate cations and Lewis acids. The method was developed by V. Gutmann in 1976. Likewise Lewis acids are characterized by acceptor numbers (AN, see Gutmann–Beckett method).
Typical solvent values are:
acetonitrile 14.1 kcal/mol (59.0 kJ/mol)
acetone 17 kcal/mol (71 kJ/mol)
methanol 19 kcal/mol (79 kJ/mol)
tetrahydrofuran 20 kcal/mol (84 kJ/mol)
dimethylformamide (DMF) 26.6 kcal/mol (111 kJ/mol)
dimethyl sulfoxide (DMSO) 29.8 kcal/mol (125 kJ/mol)
ethanol 31.5 kcal/mol (132 kJ/mol)
pyridine 33.1 kcal/mol (138 kJ/mol)
triethylamine 61 kcal/mol (255 kJ/mol)
The donor number of a solvent can be measured via calorimetry, although it is frequently measured with nuclear magnetic resonance (NMR) spectroscopy using assumptions on complexation. A critical review of the donor number concept has pointed out the serious limitations of this affinity scale. Furthermore, it has been shown that to define the order of Lewis base strength (or Lewis acid strength) at least two properties must be considered. For Pearson qualitative HSAB the
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https://en.wikipedia.org/wiki/Transcritical%20bifurcation
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In bifurcation theory, a field within mathematics, a transcritical bifurcation is a particular kind of local bifurcation, meaning that it is characterized by an equilibrium having an eigenvalue whose real part passes through zero.
A transcritical bifurcation is one in which a fixed point exists for all values of a parameter and is never destroyed. However, such a fixed point interchanges its stability with another fixed point as the parameter is varied. In other words, both before and after the bifurcation, there is one unstable and one stable fixed point. However, their stability is exchanged when they collide. So the unstable fixed point becomes stable and vice versa.
The normal form of a transcritical bifurcation is
This equation is similar to the logistic equation, but in this case we allow and to be positive or negative (while in the logistic equation and must be non-negative).
The two fixed points are at and . When the parameter is negative, the fixed point at is stable and the fixed point is unstable. But for , the point at is unstable and the point at is stable. So the bifurcation occurs at .
A typical example (in real life) could be the consumer-producer problem where the consumption is proportional to the (quantity of) resource.
For example:
where
is the logistic equation of resource growth; and
is the consumption, proportional to the resource .
References
Bifurcation theory
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https://en.wikipedia.org/wiki/Margaret%20M.%20Jacoby%20Observatory
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Margaret M. Jacoby Observatory is an astronomical observatory owned and operated by the Community College of Rhode Island. It opened in 1978 and is located in Warwick, Rhode Island, United States. The observatory was renamed in 1995 to honor Prof. Margaret M. Jacoby, the founder of the college's physics department, who secured the funding for its construction. The original 14" aperture telescope was replaced with a 16" Schmidt-Cassegrain telescope in 2009.
See also
List of observatories
References
External links
Warwick Clear Sky Chart: forecasts of observing conditions covering Jacoby Observatory.
Astronomical observatories in Rhode Island
Buildings and structures in Warwick, Rhode Island
Community College of Rhode Island
Education in Kent County, Rhode Island
Tourist attractions in Kent County, Rhode Island
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https://en.wikipedia.org/wiki/John%20Kingman
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Sir John Frank Charles Kingman (born 28 August 1939) is a British mathematician. He served as N. M. Rothschild and Sons Professor of Mathematical Sciences and Director of the Isaac Newton Institute at the University of Cambridge from 2001 until 2006, when he was succeeded by David Wallace. He is known for developing the mathematics of the Coalescent theory, a theoretical model of inheritance, which is fundamental to modern population genetics.
Education and early life
The grandson of a coal miner and son of a government scientist with a PhD in chemistry, Kingman was born in Beckenham, Kent, and grew up in the outskirts of London, where he attended Christ's College, Finchley, which was then a state grammar school. He was awarded a scholarship to read mathematics at Pembroke College, Cambridge, in 1956. On graduating in 1960, he began work on his PhD under the supervision of Peter Whittle, studying queueing theory, Markov chains and regenerative phenomena.
Career and research
Whittle left Cambridge for the University of Manchester, and, rather than follow him there, Kingman moved instead to the University of Oxford, where he resumed his work under David Kendall. After another year, Kendall was appointed a professor at Cambridge and so Kingman returned to Cambridge. He returned, however, as a member of the teaching staff (and a Fellow of Pembroke College) and never completed his PhD. He married Valerie Crompton, a historian at the University of Sussex in 1964, and in 1965 h
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https://en.wikipedia.org/wiki/Van%20Vleck%20Observatory
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Van Vleck Observatory (VVO, IAU code 298) is an astronomical observatory owned and operated by Wesleyan University. It was built in 1914 and named after the former head of the Department of Mathematics and Astronomy at the university, Prof. John M. Van Vleck. It is located in Middletown, Connecticut (USA).
This has a surviving Great refractor, a long telescope with lens popular in the late 1800s, as well as some other telescopes.
Telescopes
The University owns three telescopes. A and a are both used for weekly public observing nights, open to the Wesleyan community and the general public. The third telescope, the Perkins Telescope, is used primarily for research, including for senior and graduate student thesis projects, as well as for departmental research programs. The Perkins scope is one of the largest telescopes in New England. Wesleyan participates in a consortium of universities that operate the WIYN .9-meter telescope at the Kitt Peak National Observatory in Arizona. Students (undergraduate and graduate) and faculty have the opportunity to spend time in Arizona doing research with the telescope. Wesleyan also is a member of the Keck Northeast Astronomy Consortium (KNAC).
A 6 inch aperture refractor was acquired by Wesleyan University in 1836, and this was the largest telescope in the United States until at least 1840. The telescope was moved into the collection of the Van Vleck observatory in the 20th century.
Directors
Frederick Slocum, 1915–44
Carl Leo Ste
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https://en.wikipedia.org/wiki/Bragg%20plane
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In physics, a Bragg plane is a plane in reciprocal space which bisects a reciprocal lattice vector, , at right angles. The Bragg plane is defined as part of the Von Laue condition for diffraction peaks in x-ray diffraction crystallography.
Considering the adjacent diagram, the arriving x-ray plane wave is defined by:
Where is the incident wave vector given by:
where is the wavelength of the incident photon. While the Bragg formulation assumes a unique choice of direct lattice planes and specular reflection of the incident X-rays, the Von Laue formula only assumes monochromatic light and that each scattering center acts as a source of secondary wavelets as described by the Huygens principle. Each scattered wave contributes to a new plane wave given by:
The condition for constructive interference in the direction is that the path difference between the photons is an integer multiple (m) of their wavelength. We know then that for constructive interference we have:
where . Multiplying the above by we formulate the condition in terms of the wave vectors, and :
Now consider that a crystal is an array of scattering centres, each at a point in the Bravais lattice. We can set one of the scattering centres as the origin of an array. Since the lattice points are displaced by the Bravais lattice vectors, , scattered waves interfere constructively when the above condition holds simultaneously for all values of which are Bravais lattice vectors, the condition then becomes:
An
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https://en.wikipedia.org/wiki/Methoden%20der%20mathematischen%20Physik
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Methoden der mathematischen Physik (Methods of Mathematical Physics) is a 1924 book, in two volumes totalling around 1000 pages, published under the names of Richard Courant and David Hilbert. It was a comprehensive treatment of the "methods of mathematical physics" of the time. The second volume is devoted to the theory of partial differential equations. It contains presages of the finite element method, on which Courant would work subsequently, and which would eventually become basic to numerical analysis.
The material of the book was worked up from the content of Hilbert's lectures. While Courant played the major editorial role, many at the University of Göttingen were involved in the writing-up, and in that sense it was a collective production.
On its appearance in 1924 it apparently had little direct connection to the quantum theory questions at the centre of the theoretical physics of the time. That changed within two years, since the formulation of Schrödinger's equation made the Hilbert-Courant techniques of immediate relevance to the new wave mechanics.
There was a second edition (1931/7), wartime edition in the USA (1943), and a third German edition (1968). The English version Methods of Mathematical Physics (1953) was revised by Courant, and the second volume had extensive work done on it by the faculty of the Courant Institute. The books quickly gained the reputation as classics, and are among most highly referenced books in advanced mathematical physics course
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https://en.wikipedia.org/wiki/Costain%20Group
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Costain Group plc is a British construction and engineering company headquartered in Maidenhead, England. Founded in 1865, its history includes extensive housebuilding and mining activities, but it later focused on civil engineering and commercial construction projects. It was part of the British/French consortium which constructed the Channel Tunnel at the end of the 1980s, and has been involved in Private Finance Initiative projects.
History
19th century
The business was founded in 1865 when Richard Costain and his future brother-in-law, Richard Kneen, left the Isle of Man and moved to Liverpool as jobbing builders. The partnership lasted until 1888, when Richard Kneen left and Richard Costain's three sons (Richard, William and John) joined him. By the time of the First World War Costain had expanded through Lancashire and into South Wales, where it built houses for munitions workers.
20th century
After the First World War, Costain began to develop housing estates in Liverpool on its own account, primarily to offer continuity of employment to its workforce. With housing sites in Liverpool in short supply, Richard Costain sent his son William down to London to find new sites. He purchased the Walton Heath Land Company, and in 1923, the separate business of Richard Costain & Sons was formed.
Several executive estates in the Croydon area were developed in the middle of the 1920s. In 1929, William died: the other two brothers remained in Liverpool and William’s son, Richard
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https://en.wikipedia.org/wiki/F.%20and%20M.%20Riesz%20theorem
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In mathematics, the F. and M. Riesz theorem is a result of the brothers Frigyes Riesz and Marcel Riesz, on analytic measures. It states that for a measure μ on the circle, any part of μ that is not absolutely continuous with respect to the Lebesgue measure dθ can be detected by means of Fourier coefficients.
More precisely, it states that if the Fourier–Stieltjes coefficients of
satisfy
for all ,
then μ is absolutely continuous with respect to dθ.
The original statements are rather different (see Zygmund, Trigonometric Series, VII.8). The formulation here is as in Walter Rudin, Real and Complex Analysis, p.335. The proof given uses the Poisson kernel and the existence of boundary values for the Hardy space H1.
Expansions to this theorem were made by James E. Weatherbee in his 1968 dissertation: Some Extensions Of The F. And M. Riesz Theorem On Absolutely Continuous Measures.
References
F. and M. Riesz, Über die Randwerte einer analytischen Funktion, Quatrième Congrès des Mathématiciens Scandinaves, Stockholm, (1916), pp. 27-44.
Theorems in measure theory
Fourier series
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https://en.wikipedia.org/wiki/Syntax%20%28programming%20languages%29
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In computer science, the syntax of a computer language is the rules that define the combinations of symbols that are considered to be correctly structured statements or expressions in that language. This applies both to programming languages, where the document represents source code, and to markup languages, where the document represents data.
The syntax of a language defines its surface form. Text-based computer languages are based on sequences of characters, while visual programming languages are based on the spatial layout and connections between symbols (which may be textual or graphical). Documents that are syntactically invalid are said to have a syntax error. When designing the syntax of a language, a designer might start by writing down examples of both legal and illegal strings, before trying to figure out the general rules from these examples.
Syntax therefore refers to the form of the code, and is contrasted with semantics – the meaning. In processing computer languages, semantic processing generally comes after syntactic processing; however, in some cases, semantic processing is necessary for complete syntactic analysis, and these are done together or concurrently. In a compiler, the syntactic analysis comprises the frontend, while the semantic analysis comprises the backend (and middle end, if this phase is distinguished).
Levels of syntax
Computer language syntax is generally distinguished into three levels:
Words – the lexical level, determining how charac
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https://en.wikipedia.org/wiki/Robotic%20paradigm
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In robotics, a robotic paradigm is a mental model of how a robot operates. A robotic paradigm can be described by the relationship between the three basic elements of robotics: Sensing, Planning, and Acting. It can also be described by how sensory data is processed and distributed through the system, and where decisions are made.
Hierarchical/deliberative paradigm
The robot operates in a top-down fashion, heavy on planning.
The robot senses the world, plans the next action, acts; at each step the robot explicitly plans the next move.
All the sensing data tends to be gathered into one global world model.
The reactive paradigm
Sense-act type of organization.
The robot has multiple instances of Sense-Act couplings.
These couplings are concurrent processes, called behaviours, which take the local sensing data and compute the best action to take independently of what the other processes are doing.
The robot will do a combination of behaviours.
Hybrid deliberate/reactive paradigm
The robot first plans (deliberates) how to best decompose a task into subtasks (also called “mission planning”) and then what are the suitable behaviours to accomplish each subtask.
Then the behaviours starts executing as per the Reactive Paradigm.
Sensing organization is also a mixture of Hierarchical and Reactive styles; sensor data gets routed to each behaviour that needs that sensor, but is also available to the planner for construction of a task-oriented global world model.
See also
B
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https://en.wikipedia.org/wiki/Fekete%20polynomial
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In mathematics, a Fekete polynomial is a polynomial
where is the Legendre symbol modulo some integer p > 1.
These polynomials were known in nineteenth-century studies of Dirichlet L-functions, and indeed to Dirichlet himself. They have acquired the name of Michael Fekete, who observed that the absence of real zeroes t of the Fekete polynomial with 0 < t < 1 implies an absence of the same kind for the L-function
This is of considerable potential interest in number theory, in connection with the hypothetical Siegel zero near s = 1. While numerical results for small cases had indicated that there were few such real zeroes, further analysis reveals that this may indeed be a 'small number' effect.
References
Peter Borwein: Computational excursions in analysis and number theory. Springer, 2002, , Chap.5.
External links
Brian Conrey, Andrew Granville, Bjorn Poonen and Kannan Soundararajan, Zeros of Fekete polynomials, arXiv e-print math.NT/9906214, June 16, 1999.
Polynomials
Zeta and L-functions
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https://en.wikipedia.org/wiki/List%20of%20coordinate%20charts
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This article contains a non-exhaustive list of coordinate charts for Riemannian manifolds and pseudo-Riemannian manifolds. Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics.
Charts for Riemannian and pseudo-Riemannian surfaces
The following charts (with appropriate metric tensors) can be used in the stated classes of Riemannian and pseudo-Riemannian surfaces:
Radially symmetric surfaces:
Hyperspherical coordinates
Surfaces embedded in E3:
Monge chart
Certain minimal surfaces:
Asymptotic chart (see also asymptotic line)
Euclidean plane E2:
Cartesian chart
Sphere S2:
Spherical coordinates
Stereographic chart
Central projection chart
Axial projection chart
Mercator chart
Hyperbolic plane H2:
Polar chart
Stereographic chart (Poincaré model)
Upper half-space chart (Poincaré model)
Central projection chart (Klein model)
Mercator chart
AdS2 (or S1,1) and dS2 (or H1,1):
Central projection
Sn
Hopf chart
Hn
Upper half-space chart (Poincaré model)
Hopf chart
The following charts apply specifically to three-dimensional manifolds:
Axially symmetric manifolds:
Cylindrical chart
Parabolic chart
Hyperbolic chart
Toroidal chart
Three-dimensional Euclidean space E3:
Cartesian
Polar spherical chart
Cylindrical chart
Elliptical cylind
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https://en.wikipedia.org/wiki/Journal%20of%20Medicinal%20Chemistry
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The Journal of Medicinal Chemistry is a biweekly peer-reviewed medical journal covering research in medicinal chemistry. It is published by the American Chemical Society. It was established in 1959 as the Journal of Medicinal and Pharmaceutical Chemistry and obtained its current name in 1963. Philip S. Portoghese served as editor-in-chief from 1972 to 2011. In 2012, Gunda Georg (University of Minnesota) and Shaomeng Wang (University of Michigan) succeeded Portoghese (University of Minnesota). In 2021, Craig W. Lindsley (Vanderbilt University) became editor-in-chief. According to the Journal Citation Reports, the journal has a 2021 impact factor of 8.039, ranking it 1st out of 61 journals in the category "Chemistry, Medicinal".
See also
ACS Medicinal Chemistry Letters
References
External links
American Chemical Society academic journals
Medicinal chemistry journals
Biweekly journals
Academic journals established in 1959
English-language journals
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https://en.wikipedia.org/wiki/ACS%20Combinatorial%20Science
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ACS Combinatorial Science (usually abbreviated as ACS Comb. Sci.), formerly Journal of Combinatorial Chemistry (1999-2010), was a peer-reviewed scientific journal, published since 1999 by the American Chemical Society. ACS Combinatorial Science publishes articles, reviews, perspectives, accounts and reports in the field of Combinatorial Chemistry.
Anthony Czarnik served as the founding editor from 1999 to 2010. M.G. Finn served as Editor from 2010 to 2020. In 2010, ACS agreed to change the name of the journal to "Combinatorial Science" and it was the first and only ACS journal to be devoted to a way of doing science, rather than to a specific field of knowledge or application.
The journal stopped accepting new submissions in August and the last issue was published in December 2020.
Abstracting and indexing
JCS is currently indexed in:
Chemical Abstracts Service (CAS)
SCOPUS
EBSCOhost
PubMed
Web of Science
References
Combinatorial Science
Academic journals established in 1999
Monthly journals
English-language journals
Combinatorial chemistry
1999 establishments in the United States
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https://en.wikipedia.org/wiki/Organic%20Letters
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Organic Letters is a biweekly peer-reviewed scientific journal covering research in organic chemistry. It was established in 1999 and is published by the American Chemical Society. In 2014, the journal moved to a hybrid open access publishing model. The founding editor-in-chief was Amos Smith. The current editor-in-chief is Marisa C. Kozlowski. The journal is abstracted and indexed in: the Science Citation Index Expanded, Scopus, Academic Search Premier, BIOSIS Previews, Chemical Abstracts Service, EMBASE, and MEDLINE.
References
External links
American Chemical Society academic journals
Biweekly journals
Organic chemistry journals
Academic journals established in 1999
English-language journals
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https://en.wikipedia.org/wiki/Babraham
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Babraham is a village and civil parish in the South Cambridgeshire district of Cambridgeshire, England, about south-east of Cambridge on the A1307 road.
Babraham is home to the Babraham Institute which undertakes research into cell and molecular biology.
History
The parish of Babraham covers an area of and is roughly rectangular in shape. Its straight northern boundary is formed by the ancient Wool Street, separating it from Fulbourn, and its eastern border follows the Icknield Way (now the A11), separating it from Little Abington. The remaining boundaries with Stapleford, Sawston and Pampisford are formed by field boundaries and a small section of the River Granta, on which the village lies.
The course of the River Granta through the parish has been changed on numerous occasions; a watermill was listed as valueless in the 14th century when the river had changed course, and additional water channels have been dug for irrigation as well as to form an ornamental canal alongside Babraham Hall. Severe floods hit Babraham in both 1655 and 1749.
Traces of a Roman villa have been found on its parish boundary with Stapleford. It has also been suggested that the village has moved site, the principal evidence being that the church is from the present village. Babraham was comparatively wealthy during medieval times due to its wool trade, with the highest tax returns in its hundred. In the late 16th century the manor was the principal seat of the great Elizabethan merchant and fi
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https://en.wikipedia.org/wiki/MAX-3SAT
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MAX-3SAT is a problem in the computational complexity subfield of computer science. It generalises the Boolean satisfiability problem (SAT) which is a decision problem considered in complexity theory. It is defined as:
Given a 3-CNF formula Φ (i.e. with at most 3 variables per clause), find an assignment that satisfies the largest number of clauses.
MAX-3SAT is a canonical complete problem for the complexity class MAXSNP (shown complete in Papadimitriou pg. 314).
Approximability
The decision version of MAX-3SAT is NP-complete. Therefore, a polynomial-time solution can only be achieved if P = NP. An approximation within a factor of 2 can be achieved with this simple algorithm, however:
Output the solution in which most clauses are satisfied, when either all variables = TRUE or all variables = FALSE.
Every clause is satisfied by one of the two solutions, therefore one solution satisfies at least half of the clauses.
The Karloff-Zwick algorithm runs in polynomial-time and satisfies ≥ 7/8 of the clauses. While this algorithm is randomized, it can be derandomized using, e.g., the techniques from to yield a deterministic (polynomial-time) algorithm with the same approximation guarantees.
Theorem 1 (inapproximability)
The PCP theorem implies that there exists an ε > 0 such that (1-ε)-approximation of MAX-3SAT is NP-hard.
Proof:
Any NP-complete problem by the PCP theorem. For x ∈ L, a 3-CNF formula Ψx is constructed so that
x ∈ L ⇒ Ψx is satisfiable
x ∉ L ⇒ no
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https://en.wikipedia.org/wiki/Abraham%E2%80%93Lorentz%20force
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In the physics of electromagnetism, the Abraham–Lorentz force (also known as the Lorentz–Abraham force) is the recoil force (a force of equal magnitude and opposite direction) on an accelerating charged particle caused by the particle emitting electromagnetic radiation by self-interaction. It is also called the radiation reaction force, the radiation damping force, or the self-force. It is named after the physicists Max Abraham and Hendrik Lorentz.
The formula although predating the theory of special relativity, was initially calculated for non-relativistic velocity approximations was extended to arbitrary velocities by Max Abraham and was shown to be physically consistent by George Adolphus Schott. The non-relativistic form is called Lorentz self-force while the relativistic version is called the Lorentz–Dirac force or collectively known as Abraham–Lorentz–Dirac force. The equations are in the domain of classical physics, not quantum physics, and therefore may not be valid at distances of roughly the Compton wavelength or below. There are, however, two analogs of the formula that are both fully quantum and relativistic: one is called the "Abraham–Lorentz–Dirac–Langevin equation", the other is the self-force on a moving mirror.
The force is proportional to the square of the object's charge, multiplied by the jerk that it is experiencing. (Jerk is the rate of change of acceleration.) The force points in the direction of the jerk. For example, in a cyclotron, where the jer
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https://en.wikipedia.org/wiki/Outline%20of%20biochemistry
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The following outline is provided as an overview of and topical guide to biochemistry:
Biochemistry – study of chemical processes in living organisms, including living matter. Biochemistry governs all living organisms and living processes.
Applications of biochemistry
Testing
Ames test – salmonella bacteria is exposed to a chemical under question (a food additive, for example), and changes in the way the bacteria grows are measured. This test is useful for screening chemicals to see if they mutate the structure of DNA and by extension identifying their potential to cause cancer in humans.
Pregnancy test – one uses a urine sample and the other a blood sample. Both detect the presence of the hormone human chorionic gonadotropin (hCG). This hormone is produced by the placenta shortly after implantation of the embryo into the uterine walls and accumulates.
Breast cancer screening – identification of risk by testing for mutations in two genes—Breast Cancer-1 gene (BRCA1) and the Breast Cancer-2 gene (BRCA2)—allow a woman to schedule increased screening tests at a more frequent rate than the general population.
Prenatal genetic testing – testing the fetus for potential genetic defects, to detect chromosomal abnormalities such as Down syndrome or birth defects such as spina bifida.
PKU test – Phenylketonuria (PKU) is a metabolic disorder in which the individual is missing an enzyme called phenylalanine hydroxylase. Absence of this enzyme allows the buildup of phenylalanine,
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https://en.wikipedia.org/wiki/Anthrozoology
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Anthrozoology, also known as human–nonhuman-animal studies (HAS), is the subset of ethnobiology that deals with interactions between humans and other animals. It is an interdisciplinary field that overlaps with other disciplines including anthropology, ethnology, medicine, psychology, social work, veterinary medicine, and zoology. A major focus of anthrozoologic research is the quantifying of the positive effects of human–animal relationships on either party and the study of their interactions. It includes scholars from fields such as anthropology, sociology, biology, history and philosophy.
Anthrozoology scholars, such as Pauleen Bennett recognize the lack of scholarly attention given to non-human animals in the past, and to the relationships between human and non-human animals, especially in the light of the magnitude of animal representations, symbols, stories and their actual physical presence in human societies. Rather than a unified approach, the field currently consists of several methods adapted from the several participating disciplines to encompass human–nonhuman animal relationships and occasional efforts to develop sui generis methods.
Areas of study
The interaction and enhancement within captive animal interactions.
Affective (emotional) or relational bonds between humans and animals
Human perceptions and beliefs in respect of other animals
How some animals fit into human societies
How these vary between cultures, and change over times
The study of animal
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https://en.wikipedia.org/wiki/Connect6
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Connect6 (; Pinyin: liùzǐqí; ;; ) introduced in 2003 by Professor I-Chen Wu at Department of Computer Science and Information Engineering, National Chiao Tung University in Taiwan, is a two-player strategy game similar to Gomoku.
Two players, Black and White, alternately place two stones of their own colour, black and white respectively, on empty intersections of a Go-like board, except that Black (the first player) places one stone only for the first move. The one who gets six or more stones in a row (horizontally, vertically or diagonally) first wins the game.
Rules
The rules of Connect6 are very simple and similar to the traditional game of Gomoku:
Players and stones: There are two players. Black plays first, and White second. Each player plays with an appropriate color of stones, as in Go and Gomoku.
Game board: Connect6 is played on a square board made up of orthogonal lines, with each intersection capable of holding one stone. In theory, the game board can be any finite size from 1×1 up (integers only), or it could be of infinite size. However, boards that are too small may lack strategy (boards smaller than 6×6 are automatic draws), and extremely large or infinite boards are of little practical use. 19×19 Go boards might be the most convenient. For a longer and more challenging game, another suggested size is 59×59, or nine Go boards tiled in a larger square (using the join lines between the boards as additional grid lines).
Game moves: Black plays first, pu
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https://en.wikipedia.org/wiki/David%20Ruelle
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David Pierre Ruelle (; born 20 August 1935) is a Belgian mathematical physicist, naturalized French. He has worked on statistical physics and dynamical systems. With Floris Takens, Ruelle coined the term strange attractor, and developed a new theory of turbulence.
Biography
Ruelle studied physics at the Université Libre de Bruxelles, obtaining a PhD degree in 1959 under the supervision of Res Jost. He spent two years (1960–1962) at the ETH Zurich, and another two years (1962–1964) at the Institute for Advanced Study in Princeton, New Jersey. In 1964, he became professor at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France. Since 2000, he has been an emeritus professor at IHES and distinguished visiting professor at Rutgers University.
David Ruelle made fundamental contributions in various aspects of mathematical physics. In quantum field theory, the most important contribution is the rigorous formulation of scattering processes based on Wightman's axiomatic theory. This approach is known as the Haag–Ruelle scattering theory. Later Ruelle helped to create a rigorous theory of statistical mechanics of equilibrium, that includes the study of the thermodynamic limit, the equivalence of ensembles, and the convergence of Mayer's series. A further result is the Asano-Ruelle lemma, which allows the study of the zeros of certain polynomial functions that are recurrent in statistical mechanics.
The study of infinite systems led to the local definition of Gibb
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https://en.wikipedia.org/wiki/LwIP
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lwIP (lightweight IP) is a widely used open-source TCP/IP stack designed for embedded systems. lwIP was originally developed by Adam Dunkels at the Swedish Institute of Computer Science and is now developed and maintained by a worldwide network of developers.
lwIP is used by many manufacturers of embedded systems, including Intel/Altera, Analog Devices, Xilinx, TI, ST and Freescale.
lwIP network stack
The focus of the lwIP network stack implementation is to reduce resource usage while still having a full-scale TCP stack. This makes lwIP suitable for use in embedded systems with tens of kilobytes of free RAM and room for around 40 kilobytes of code ROM.
lwIP protocol implementations
Aside from the TCP/IP stack, lwIP has several other important parts, such as a network interface, an operating system emulation layer, buffers and a memory management section. The operating system emulation layer and the network interface allow the network stack to be transplanted into an operating system, as it provides a common interface between lwIP code and the operating system kernel.
The network stack of lwIP includes an IP (Internet Protocol) implementation at the Internet layer that can handle packet forwarding over multiple network interfaces. Both IPv4 and IPv6 are supported dual stack since lwIP v2.0.0 . For network maintenance and debugging, lwIP implements ICMP (Internet Control Message Protocol). IGMP (Internet Group Management Protocol) is supported for multicast traffic manag
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https://en.wikipedia.org/wiki/Toyota%20Technological%20Institute%20at%20Chicago
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Toyota Technological Institute at Chicago (TTIC or TTI-Chicago) is a private graduate school and research institute focused on computer science and located in Chicago, Illinois within the University of Chicago campus. It is supported by the earnings on an endowment of approximately $255 million as well as by the income from research awards received by its faculty.
History
TTIC was founded by the Toyota Technological Institute (TTI), in Nagoya in Japan, a small private engineering school with an endowment provided by the Toyota Motor Corporation. TTI established TTIC as an independent computer science institute with the intention of creating a world-class institution. In addition to historical ties, there remains active collaboration between TTIC and TTI in Nagoya. However, TTIC has no formal ties with either TTI or the Toyota Motor Corporation.
TTIC officially opened for operation in September 2003 and three students entered its Ph.D. program in September 2004.
Academics
Research
TTIC focuses primarily on the following areas within computer science:
Machine learning
Theoretical Computer Science—Algorithms & Complexity
Computer Vision
Speech and Language Technologies
Computational Biology
Robotics
PhD program
TTIC offers a graduate program leading to a doctorate in computer science, with graduate students conducting research primarily within its areas of focus. TTIC has degree-granting authority in the state of Illinois and is accredited by the Higher Learning Commi
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https://en.wikipedia.org/wiki/Hirzebruch%20surface
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In mathematics, a Hirzebruch surface is a ruled surface over the projective line. They were studied by .
Definition
The Hirzebruch surface is the -bundle, called a Projective bundle, over associated to the sheafThe notation here means: is the -th tensor power of the Serre twist sheaf , the invertible sheaf or line bundle with associated Cartier divisor a single point. The surface is isomorphic to , and is isomorphic to blown up at a point so is not minimal.
GIT quotient
One method for constructing the Hirzebruch surface is by using a GIT quotientwhere the action of is given byThis action can be interpreted as the action of on the first two factors comes from the action of on defining , and the second action is a combination of the construction of a direct sum of line bundles on and their projectivization. For the direct sum this can be given by the quotient varietywhere the action of is given byThen, the projectivization is given by another -action sending an equivalence class toCombining these two actions gives the original quotient up top.
Transition maps
One way to construct this -bundle is by using transition functions. Since affine vector bundles are necessarily trivial, over the charts of defined by there is the local model of the bundleThen, the transition maps, induced from the transition maps of give the mapsendingwhere is the affine coordinate function on .
Properties
Projective rank 2 bundles over P1
Note that by Grothendieck's theorem,
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https://en.wikipedia.org/wiki/Schwarz%20reflection%20principle
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In mathematics, the Schwarz reflection principle is a way to extend the domain of definition of a complex analytic function, i.e., it is a form of analytic continuation. It states that if an analytic function is defined on the upper half-plane, and has well-defined (non-singular) real values on the real axis, then it can be extended to the conjugate function on the lower half-plane. In notation, if is a function that satisfies the above requirements, then its extension to the rest of the complex plane is given by the formula,
That is, we make the definition that agrees along the real axis.
The result proved by Hermann Schwarz is as follows. Suppose that F is a continuous function on the closed upper half plane , holomorphic on the upper half plane , which takes real values on the real axis. Then the extension formula given above is an analytic continuation to the whole complex plane.
In practice it would be better to have a theorem that allows F certain singularities, for example F a meromorphic function. To understand such extensions, one needs a proof method that can be weakened. In fact Morera's theorem is well adapted to proving such statements. Contour integrals involving the extension of F clearly split into two, using part of the real axis. So, given that the principle is rather easy to prove in the special case from Morera's theorem, understanding the proof is enough to generate other results.
The principle also adapts to apply to harmonic functions.
See also
K
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https://en.wikipedia.org/wiki/B%C3%B4cher%27s%20theorem
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In mathematics, Bôcher's theorem is either of two theorems named after the American mathematician Maxime Bôcher.
Bôcher's theorem in complex analysis
In complex analysis, the theorem states that the finite zeros of the derivative of a non-constant rational function that are not multiple zeros are also the positions of equilibrium in the field of force due to particles of positive mass at the zeros of and particles of negative mass at the poles of , with masses numerically equal to the respective multiplicities, where each particle repels with a force equal to the mass times the inverse distance.
Furthermore, if C1 and C2 are two disjoint circular
regions which contain respectively all the zeros and all the poles of , then C1 and C2 also contain all the critical
points of .
Bôcher's theorem for harmonic functions
In the theory of harmonic functions, Bôcher's theorem states that a positive harmonic function in a punctured domain (an open domain minus one point in the interior) is a linear combination of a harmonic function in the unpunctured domain with a scaled fundamental solution for the Laplacian in that domain.
See also
Marden's theorem
External links
(Review of Joseph L. Walsh's book.)
Theorems in complex analysis
Harmonic functions
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https://en.wikipedia.org/wiki/Ontology%20language
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In computer science and artificial intelligence, ontology languages are formal languages used to construct ontologies. They allow the encoding of knowledge about specific domains and often include reasoning rules that support the processing of that knowledge. Ontology languages are usually declarative languages, are almost always generalizations of frame languages, and are commonly based on either first-order logic or on description logic.
Classification of ontology languages
Classification by syntax
Traditional syntax ontology languages
Common Logic - and its dialects
CycL
DOGMA (Developing Ontology-Grounded Methods and Applications)
F-Logic (Frame Logic)
FO-dot (First-order logic extended with types, arithmetic, aggregates and inductive definitions)
KIF (Knowledge Interchange Format)
Ontolingua based on KIF
KL-ONE
KM programming language
LOOM (ontology)
OCML (Operational Conceptual Modelling Language)
OKBC (Open Knowledge Base Connectivity)
PLIB (Parts LIBrary)
RACER
Markup ontology languages
These languages use a markup scheme to encode knowledge, most commonly with XML.
DAML+OIL
Ontology Inference Layer (OIL)
Web Ontology Language (OWL)
Resource Description Framework (RDF)
RDF Schema (RDFS)
SHOE
Controlled natural languages
Attempto Controlled English
Open vocabulary natural languages
Executable English
Classification by structure (logic type)
Frame-based
Three languages are completely or partially frame-based languages.
F-Logic
OKBC
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https://en.wikipedia.org/wiki/Hausdorff%20moment%20problem
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In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence be the sequence of moments
of some Borel measure supported on the closed unit interval . In the case , this is equivalent to the existence of a random variable supported on , such that .
The essential difference between this and other well-known moment problems is that this is on a bounded interval, whereas in the Stieltjes moment problem one considers a half-line , and in the Hamburger moment problem one considers the whole line . The Stieltjes moment problems and the Hamburger moment problems, if they are solvable, may have infinitely many solutions (indeterminate moment problem) whereas a Hausdorff moment problem always has a unique solution if it is solvable (determinate moment problem). In the indeterminate moment problem case, there are infinite measures corresponding to the same prescribed moments and they consist of a convex set. The set of polynomials may or may not be dense in the associated Hilbert spaces if the moment problem is indeterminate, and it depends on whether measure is extremal or not. But in the determinate moment problem case, the set of polynomials is dense in the associated Hilbert space.
Completely monotonic sequences
In 1921, Hausdorff showed that is such a moment sequence if and only if the sequence is completely monotonic, that is, its difference sequences satisfy the equation
for all . Here, i
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https://en.wikipedia.org/wiki/Hamburger%20moment%20problem
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In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m0, m1, m2, ...), does there exist a positive Borel measure μ (for instance, the measure determined by the cumulative distribution function of a random variable) on the real line such that
In other words, an affirmative answer to the problem means that (m0, m1, m2, ...) is the sequence of moments of some positive Borel measure μ.
The Stieltjes moment problem, Vorobyev moment problem, and the Hausdorff moment problem are similar but replace the real line by (Stieltjes and Vorobyev; but Vorobyev formulates the problem in the terms of matrix theory), or a bounded interval (Hausdorff).
Characterization
The Hamburger moment problem is solvable (that is, (mn) is a sequence of moments) if and only if the corresponding Hankel kernel on the nonnegative integers
is positive definite, i.e.,
for every arbitrary sequence (cj)j ≥ 0 of complex numbers that are finitary (i.e. cj = 0 except for finitely many values of j).
For the "only if" part of the claims simply note that
which is non-negative if is non-negative.
We sketch an argument for the converse. Let Z+ be the nonnegative integers and F0(Z+) denote the family of complex valued sequences with finitary support. The positive Hankel kernel A induces a (possibly degenerate) sesquilinear product on the family of complex-valued sequences with finite support. This in turn gives a Hilbert space
whose typi
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https://en.wikipedia.org/wiki/Cupillari%20Observatory
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Thomas G. Cupillari Observatory is an astronomical observatory in Fleetville, Pennsylvania, owned and operated by Keystone College.
It is named after Thomas G. Cupillari, a professor of physics, mathematics, and astronomy at Keystone College, who founded it in 1973 after purchasing its dome and telescope from television personality Dave Garroway. Cupillari retired as a professor in 2007, stepped down as director of the observatory in 2015, and died of cancer in 2021.
See also
List of astronomical observatories
References
External links
Cupillari Observatory Clear Sky Clock Forecasts of observing conditions.
Astronomical observatories in Pennsylvania
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https://en.wikipedia.org/wiki/Intensity
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Intensity may refer to:
In colloquial use
Strength (disambiguation)
Amplitude
Level (disambiguation)
Magnitude (disambiguation)
In physical sciences
Physics
Intensity (physics), power per unit area (W/m2)
Field strength of electric, magnetic, or electromagnetic fields (V/m, T, etc.)
Intensity (heat transfer), radiant heat flux per unit area per unit solid angle (W·m−2·sr−1)
Electric current, whose value is sometimes called current intensity in older books
Optics
Radiant intensity, power per unit solid angle (W/sr)
Luminous intensity, luminous flux per unit solid angle (lm/sr or cd)
Irradiance, power per unit area (W/m2)
Astronomy
Radiance, power per unit solid angle per unit projected source area (W·sr−1·m−2)
Seismology
Mercalli intensity scale, a measure of earthquake impact
Japan Meteorological Agency seismic intensity scale, a measure of earthquake impact
Peak ground acceleration, a measure of earthquake acceleration (g or m/s2)
Acoustics
Sound intensity, sound power per unit area
Other uses
Value intensity in philosophy and ethics
In video luminous emittance, the luminous flux per unit area (lm/m2 or lux)
Energy intensity, an economic measure of energy consumed per unit of GDP (J/$, etc.)
Carbon intensity, any of several measures of release of carbon into the environment
Floor area ratio, the ratio of the total floor area of buildings on a certain location to the size of the land of that location, or the zoning limit imposed on such a ratio
Intensity (measure theo
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https://en.wikipedia.org/wiki/Statistics%20Online%20Computational%20Resource
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The Statistics Online Computational Resource (SOCR) is an online multi-institutional research and education organization. SOCR designs, validates and broadly shares a suite of online tools for statistical computing, and interactive materials for hands-on learning and teaching concepts in data science, statistical analysis and probability theory. The SOCR resources are platform agnostic based on HTML, XML and Java, and all materials, tools and services are freely available over the Internet.
The core SOCR components include interactive distribution calculators, statistical analysis modules, tools for data modeling, graphics visualization, instructional resources, learning activities and other resources.
All SOCR resources are licensed under either the Lesser GNU Public License or CC BY; peer-reviewed, integrated internally and interoperate with independent digital libraries developed by other professional societies and scientific organizations like NSDL, Open Educational Resources, Mathematical Association of America, California Digital Library, LONI Pipeline, etc.
See also
List of statistical packages
Comparison of statistical packages
External links
SOCR University of Michigan site
SOCR UCLA site
References
Educational math software
Research institutes in the United States
Statistical software
University of Michigan
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https://en.wikipedia.org/wiki/Steven%20Pemberton
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Steven Pemberton is a researcher affiliated with the Distributed and Interactive Systems group at the Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands.
He was one of the designers of ABC, a programming language released in 1987, and editor-in-chief of the Special Interest Group on Computer–Human Interaction (SIGCHI)'s Bulletin from 1993-1999 and the Association for Computing Machinery (ACM)'s Interactions from 1998-2004.
Contributions to web standards
Pemberton was a contributing author of HyperText Markup Language (HTML) 4.0 and HTML 4.01, and chair of the World Wide Web Consortium (W3C) HTML Working Group. He was a contributing author of the Extensible HyperText Markup Language (XHTML) specifications 1.0 in 2000 and 1.1 in 2001, and chair of the XHTML 2 Working Group from 2006-9.
He chaired the first W3C workshop on style sheets in 1995, and was a contributing author of the Cascading Style Sheets (CSS) Level 1 specification in 1996, Level 2 in 1998, and CSS Color Module Level 3 in 2002.
Pemberton was co-chair of the W3C XForms Working Group from 2000-2007, and in 2003 co-authored the XForms 1.0 specification. In 2009 he co-authored the XForms 1.1 and XML Events specifications. He was co-chair of the W3C Forms Working Group from 2010-2012.
Awards
2009: SIGCHI Lifetime Service Award.
2022: SIGCHI Lifetime Practice Award.
References
External links
Personal website
Living people
Year of bir
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https://en.wikipedia.org/wiki/CRAM-MD5
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In cryptography, CRAM-MD5 is a challenge–response authentication mechanism (CRAM) based on the HMAC-MD5 algorithm. As one of the mechanisms supported by the Simple Authentication and Security Layer (SASL), it is often used in email software as part of SMTP Authentication and for the authentication of POP and IMAP users, as well as in applications implementing LDAP, XMPP, BEEP, and other protocols.
When such software requires authentication over unencrypted connections, CRAM-MD5 is preferred over mechanisms that transmit passwords "in the clear," such as LOGIN and PLAIN. However, it can't prevent derivation of a password through a brute-force attack, so it is less effective than alternative mechanisms that avoid passwords or that use connections encrypted with Transport Layer Security (TLS).
Protocol
The CRAM-MD5 protocol involves a single challenge and response cycle, and is initiated by the server:
Challenge: The server sends a base64-encoded string to the client. Before encoding, it could be any random string, but the standard that currently defines CRAM-MD5 says that it is in the format of a Message-ID email header value (including angle brackets) and includes an arbitrary string of random digits, a timestamp, and the server's fully qualified domain name.
Response: The client responds with a string created as follows.
The challenge is base64-decoded.
The decoded challenge is hashed using HMAC-MD5, with a shared secret (typically, the user's password, or a hash there
|
https://en.wikipedia.org/wiki/Free%20will%20theorem
|
The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006. In 2009, the authors published a stronger version of the theorem in the Notices of the American Mathematical Society. Later, in 2017, Kochen elaborated some details.
Axioms
The proof of the theorem as originally formulated relies on three axioms, which Conway and Kochen call "fin", "spin", and "twin". The spin and twin axioms can be verified experimentally.
Fin: There is a maximal speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality.
Spin: The squared spin component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0).
Twin: It is possible to "entangle" two elementary particles and separate them by a significant distance, so that they have the same squared spin results if measured in parallel directions. This is a consequence of quantum entanglement, but full entanglement is not necessary for the twin axiom to hold (entanglement is sufficient but not necessary).
In their later 2009 paper, "The Strong Free Will Theorem", Conway and Kochen replace the Fin axiom by a weaker one called Min, thereby strengthening the theorem. The Min axiom asserts only tha
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https://en.wikipedia.org/wiki/Symmetric%20derivative
|
In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative. It is defined as
The expression under the limit is sometimes called the symmetric difference quotient. A function is said to be symmetrically differentiable at a point x if its symmetric derivative exists at that point.
If a function is differentiable (in the usual sense) at a point, then it is also symmetrically differentiable, but the converse is not true. A well-known counterexample is the absolute value function , which is not differentiable at , but is symmetrically differentiable here with symmetric derivative 0. For differentiable functions, the symmetric difference quotient does provide a better numerical approximation of the derivative than the usual difference quotient.
The symmetric derivative at a given point equals the arithmetic mean of the left and right derivatives at that point, if the latter two both exist.
Neither Rolle's theorem nor the mean-value theorem hold for the symmetric derivative; some similar but weaker statements have been proved.
Examples
The absolute value function
For the absolute value function , using the notation for the symmetric derivative, we have at that
Hence the symmetric derivative of the absolute value function exists at and is equal to zero, even though its ordinary derivative does not exist at that point (due to a "sharp" turn in the curve at ).
Note that in this example both the left and right derivatives at 0 exist, but t
|
https://en.wikipedia.org/wiki/Hans%20Conrad%20Leipelt
|
Hans Conrad Leipelt (18 July 1921 – 29 January 1945) was an Austrian member of the White Rose resistance group in Nazi Germany.
Background
Leipelt was born in Vienna. His father, Konrad Leipelt, was a graduate in civil engineering, while his mother Katharina was a chemist from a Christian family with Jewish roots. In 1925, Hans father accepted the post of factory director of Tin Works in Wilhelmsburg, leading the family's migration to Hamburg. Due to the Jewish origins of Katharina Leipelt, the family suffered the repressions of the Nuremberg race laws from 1935.
Leipelt graduated high school with his Abitur in 1938, and then reported to the Reichsarbeitsdienst and the Wehrmacht. During the western campaign, he met Karl Ludwig Schneider, with whom he soon developed a strong friendship. In June 1940, he was decorated with the Iron Cross second class and the Tank Destruction Badge during the French campaign. He was later dishonourably discharged from the Wehrmacht because he was a Mischling first grade.
In the autumn of 1940, he began his chemistry studies at the University of Hamburg, but transferred in the 1941–1942 winter semester to the University of Munich, as a student of Heinrich Otto Wieland. Leipelt was only allowed to study at Munich due to the influence of Professor Wieland who, as the winner of the Nobel Prize in Chemistry in 1927, had personal freedom to select his students. Via Schneider, Leipelt had also come into contact with Margaretha Rothe and Heinz Kuchar
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https://en.wikipedia.org/wiki/Bucknell%20Observatory
|
Bucknell Observatory is an astronomical observatory owned and operated by Bucknell University. It is located in Lewisburg, Pennsylvania.
History
In 2019, the observatory offered classes in observational astrophysics taught by Katelyn Allers, associate professor of physics and astronomy at Bucknell who is a member of the team of astronomers credited with the discovery of the rogue planet PSO J318.5-22.
In 2018, the observatory offered the class, "Physics for Future Leaders," which was taught by professor of physics Brian Utter, and was designed to help future inventors and business managers ponder such questions as:
"Should we deregulate the oil industry or enact policies to favor a more sustainable energy of the future? Do our choices as individual consumers matter? Is it advisable — or even possible — to plan for a colony on Mars the way JFK boldly announced that 'we choose to go to the Moon?'"
See also
List of astronomical observatories
References
External links
Bucknell Observatory Clear Sky Clock Forecasts of observing conditions for Bucknell.
Astronomical observatories in Pennsylvania
|
https://en.wikipedia.org/wiki/How%20People%20Learn
|
How People Learn is the title of an educational psychology book edited by John D. Bransford, Ann L. Brown, and Rodney R. Cocking and published by the United States National Academy of Sciences' National Academies Press. The committee on How People Learn also wrote How Students Learn: History, Mathematics, and Science in the Classroom as a follow-up. An updated edition How People Learn II was released in October 2018.
The book draws the following conclusions, among others:
Learners and Learning:
"Effective comprehension and thinking require a coherent understanding of the organizing principles in any subject matter," and
"In-depth understanding requires detailed knowledge of the facts within a domain. The key attribute of expertise is a detailed and organized understanding of the important facts within a specific domain."
Thus, the debate within education between advocates of deep conceptual understanding and advocates of broad factual understanding misses the point. In-depth understanding is necessary to truly understand the content, but broad factual understanding is also necessary as it allows a person to remember and organize what they have learned.
Teachers and Teaching:
"Teachers need expertise in both subject matter content and in teaching," and "Teachers need to develop models of their own professional development that are based on lifelong learning, rather than on an 'updating' model of learning, in order to have frameworks to guide their career planning." These
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https://en.wikipedia.org/wiki/Weitkamp%20Observatory
|
Weitkamp Observatory is an astronomical observatory owned and operated by Otterbein College. Donated in 1955 by Alfred Henry Weitkamp in memory of Mary Geeding Weitkamp, it is located in Westerville, Ohio (USA).
See also
List of observatories
References
External links
Otterbein University Home > Academics > Departments > Physics > Facilities - Weitkamp Observatory
Otterbein University campus map - in the text on the Facilities page linked above the location of the observatory is given as being "on the fifth floor of the McFadden-Schear science building at Otterbein University, 155 W. Main St., Westerville, Ohio (building 37 on the campus map)"; on the campus map this location is in fact shown as building 47, the Shear-McFadden Science Hall; the coordinate used in the article is that of the domed structure on the roof of this building.
Astronomical observatories in Ohio
Otterbein University
Buildings and structures in Franklin County, Ohio
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https://en.wikipedia.org/wiki/Keeble%20Observatory
|
Keeble Observatory is an astronomical observatory owned and operated by Randolph-Macon College. It is located in Ashland, Virginia (USA), named for Dr. William Houston Keeble, distinguished Professor of Physics at Randolph-Macon College from 1919 until his retirement in 1952. He was a member of Phi Beta Kappa, the American Physical Society, the American Association of Physics Teachers, the American Astronomical Society, and was a fellow of the American Association for the Advancement of Science.
The first structure was opened in 1963 and housed a 12-inch Newtonian telescope. This building was razed in 2016. A new taller structure went into service the following year and houses a 40cm Ritchey-Chretien.
See also
List of astronomical observatories
References
External links
Keeble Observatory Clear Sky Clock Forecasts of observing conditions.
Astronomical observatories in Virginia
Randolph–Macon College
1963 establishments in Virginia
Buildings and structures in Hanover County, Virginia
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https://en.wikipedia.org/wiki/Tyler%20Volk
|
Tyler Volk is Professor Emeritus of Environmental Studies and Biology at New York University.
His areas of interest include principles of form and function in systems (described as metapatterns), environmental challenges to global prosperity, CO2 and global change, biosphere theory and the role of life in earth dynamics.
Books
Tyler Volk has authored seven books, most recently, Quarks to Culture: How We Came to Be
Quarks to Culture explores the rhythm within what Tyler Volk calls the "grand sequence," a series of levels of sizes and innovations building from elementary quanta to globalized human civilization. The key is "combogenesis," the building-up from combination and integration to produce new things with innovative relations. Themes unfold in how physics and chemistry led to biological evolution, and biological evolution to cultural evolution. Volk develops an inclusive natural philosophy that brings clarity to our place in the world, a roadmap for our minds." Quarks to Culture was reviewed in Science in January 2018.
His previous books include: CO2 Rising: The World’s Greatest Environmental Challenge, What is Death?: A Scientist Looks at the Cycle of Life, Gaia's Body: Toward a Physiology of Earth, and Metapatterns: Across Space, Time, and Mind.
Environmental studies and teaching
With Dale Jamieson, Christopher Schlottmann, and others, Volk helped plan and develop the interdisciplinary Environmental Studies Program launched at New York University in Fall 2007. In
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https://en.wikipedia.org/wiki/Francesca%20Chiara
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Francesca Chiara Palamara (born March 25, 1972, in Padua, Italy, as Francesca Chiara Casellati) is the singer and songwriter of the Italian band The LoveCrave.
Biography
Francesca Chiara's parents are teachers (English and Mathematics) and they still live in Padova, where Francesca was born. Her grandparents lived in Venice, and she descends from a Venetian noble family, the Pisani. Her grandmother's name was Adriana Pisani.
Francesca Chiara spent her childhood going to Venice every weekend and this is why she has always been fascinated by dark and silent atmospheres, where her music finds inspiration. Her first child, where born in 2010 and Chiara is married to Tancredi Palamara.
Musical career
She wrote her first novel at the age of 10 and she wrote her first song at 13 years old. It was called "Survivor".
At 17 years old she spent one year in San Francisco, California graduating at Castro Valley High School and she began to sing seriously and to play guitar.
She returned to Italy and founded the band Mystery, with Simon Dredo and Mauro Lentola, producing a four-song hard rock EP.
At 19 years old she moved from Padova to Milan and started studying music for three years in a music school but then she left it. She worked in a wedding agency, sold wine through the phone and worked in a concert agency to survive and pay the rent.
She met Tank Palamara in a metal club and they started to collaborate. Their first band was called The Flu in 1996 and it was a new punk meta
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https://en.wikipedia.org/wiki/Kirkwood%20Observatory
|
Kirkwood Observatory is an astronomical observatory owned and operated by Indiana University. It is located in Bloomington, Indiana, United States. It is named for Daniel Kirkwood (1814–1895) an astronomer and professor of mathematics at Indiana University who discovered the divisions of the asteroid belt known as the Kirkwood Gaps.
Description
Built in 1900 and dedicated on May 15, 1901, the observatory was thoroughly renovated during the 2001–02 academic year. Although the facility is no longer used for research, its original refracting telescope, built by Warner & Swasey Company with a 12-inch (0.3-meter) Brashear objective lens, also received a complete restoration. The telescope is now used regularly for outreach events and undergraduate-level classes. Kirkwood Observatory also has an instructional solar telescope.
Directors
John A. Miller (1901–06)
Wilbur A. Cogshall (1907–44)
Frank K. Edmondson (1944–78)
See also
1764 Cogshall, asteroid named after W. A. Cogshall
List of observatories
References
External links
Topographical map from TopoQuest
Bloomington Clear Sky Clock Forecasts of observing conditions covering Kirkwood Observatory.
Astronomical observatories in Indiana
Indiana University Bloomington
Tourist attractions in Bloomington, Indiana
Buildings and structures in Bloomington, Indiana
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https://en.wikipedia.org/wiki/2E6
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2E6 may refer to:
EIA Class 2 dielectric
2E6 group in mathematics
|
https://en.wikipedia.org/wiki/Steven%20Vogel
|
Steven Vogel (April 7, 1940 – November 24, 2015) was an American biomechanics researcher, the James B. Duke professor in the Department of Biology at Duke University.
Life
Vogel was born in Beacon, New York, and educated there and in Poughkeepsie. He graduated from Tufts University and was awarded his graduate degrees from Harvard University. Vogel joined Duke University as an assistant professor in the Zoology department in 1966, and taught there for 40 years, eventually retiring as professor emeritus.
Over the course of his professional career, Vogel, along with Stephen Wainwright and R. McNeil Alexander, played a fundamental role in the establishment of the discipline of biomechanics, and was a prolific author of popular works on the intersection of physics and biology. His research projects included studies of ventilation currents in prairie dog burrows, flight in tiny insects, leaf streamlining, air movement through feathery moth antennae, and the mechanics of jet propulsion in squid and scallops. Vogel died of cancer in Durham, North Carolina on November 24, 2015.
Works
In English:
Life in Moving Fluids: The Physical Biology of Flow. Princeton University Press (1981; 2nd ed. 1996).
Life's Devices: The Physical World of Animals and Plants. Princeton University Press (1988).
Vital Circuits: On Pumps, Pipes, and the Workings of Circulatory Systems. Oxford University Press (1993).
Cats' Paws and Catapults: Mechanical Worlds of Nature and People. W.W. Norton (1998).
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https://en.wikipedia.org/wiki/List%20of%20lay%20Catholic%20scientists
|
Many Catholics have made significant contributions to the development of science and mathematics from the Middle Ages to today. These scientists include Galileo Galilei, René Descartes, Louis Pasteur, Blaise Pascal, André-Marie Ampère, Charles-Augustin de Coulomb, Pierre de Fermat, Antoine Laurent Lavoisier, Alessandro Volta, Augustin-Louis Cauchy, Pierre Duhem, Jean-Baptiste Dumas, Alois Alzheimer, Georgius Agricola and Christian Doppler.
Lay Catholic scientists
A
Maria Gaetana Agnesi (1718–1799) – mathematician who wrote on differential and integral calculus
Georgius Agricola (1494–1555) – father of mineralogy
Ulisse Aldrovandi (1522–1605) – father of natural history
Rudolf Allers (1883–1963) – Austrian psychiatrist; the only Catholic member of Sigmund Freud's first group, later a critic of Freudian psychoanalysis
Alois Alzheimer (1864–1915) – credited with identifying the first published case of presenile dementia, which is now known as Alzheimer's disease
André-Marie Ampère (1775–1836) – one of the main discoverers of electromagnetism
Leopold Auenbrugger (1722–1809) – first to use percussion as a diagnostic technique in medicine
Adrien Auzout (1622–1691) – astronomer who contributed to the development of the telescopic micrometer
Amedeo Avogadro (1776–1856) – Italian scientist noted for contributions to molecular theory and Avogadro's Law
B
Jacques Babinet (1794–1872) – French physicist, mathematician, and astronomer who is best known for his contributions to
|
https://en.wikipedia.org/wiki/Symmetrically%20continuous%20function
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In mathematics, a function is symmetrically continuous at a point x if
The usual definition of continuity implies symmetric continuity, but the converse is not true. For example, the function is symmetrically continuous at , but not continuous.
Also, symmetric differentiability implies symmetric continuity, but the converse is not true just like usual continuity does not imply differentiability.
The set of the symmetrically continuous functions, with the usual scalar multiplication can be easily shown to have the structure of a vector space over , similarly to the usually continuous functions, which form a linear subspace within it.
References
Differential calculus
Theory of continuous functions
Types of functions
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https://en.wikipedia.org/wiki/David%20Gavaghan
|
David J. Gavaghan (born 10 February 1966) is Professor of Computational Biology in the Department of Computer Science at the University of Oxford. He is also the director of the Life Sciences Interface Doctoral Training Centre, Principal Investigator of the Integrative Biology project and Research Fellow in Mathematics at New College, Oxford.
Education
Gavaghan completed his undergraduate degree in Mathematics at Durham University in 1986. This was followed by a Master of Science in Numerical Analysis and Mathematical Modelling in 1987 and his Doctor of Philosophy on the development of Parallel Numerical Algorithms in 1991 at Linacre College at the University of Oxford.
Research and career
Gavaghan's research is interdisciplinary and involves the application of mathematical and computational techniques to problems in the biomedical sciences. Gavaghan serves on the advisory board chair for the Software Sustainability Institute (SSI).
References
1966 births
Living people
British bioinformaticians
Alumni of Grey College, Durham
Fellows of New College, Oxford
Members of the Department of Computer Science, University of Oxford
Alumni of Linacre College, Oxford
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https://en.wikipedia.org/wiki/Sturt
|
Sturt may refer to:
Sturt (surname)
Sturt (biology), a unit of measurement in embryology named for Alfred Sturtevant
Places and things named after Charles Sturt, a British explorer of Australia, include:
Australia
Sturt Highway, a national highway in New South Wales, Victoria, and South Australia.
New South Wales
Sturt National Park, New South Wales
Charles Sturt University, a university in Wagga Wagga
Queensland
Sturt, Queensland, a locality in the Shire of Boulia
South Australia
Sturt, South Australia, a suburb of Adelaide
Sturt Football Club, an Australian Rules Football club
Sturt River, Adelaide
Sturt Street, Adelaide
City of Charles Sturt, a city
Point Sturt, a town
Division of Sturt, a federal electoral district in South Australia
Electoral district of Sturt (New South Wales), former New South Wales Legislative Assembly electorate
Electoral district of Sturt (South Australia), former South Australian House of Assembly electorate
See also
Stuart (disambiguation)
Sterte
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https://en.wikipedia.org/wiki/ECC%20patents
|
Patent-related uncertainty around elliptic curve cryptography (ECC), or ECC patents, is one of the main factors limiting its wide acceptance. For example, the OpenSSL team accepted an ECC patch only in 2005 (in OpenSSL version 0.9.8), despite the fact that it was submitted in 2002.
According to Bruce Schneier as of May 31, 2007, "Certicom certainly can claim ownership of ECC. The algorithm was developed and patented by the company's founders, and the patents are well written and strong. I don't like it, but they can claim ownership." Additionally, NSA has licensed MQV and other ECC patents from Certicom in a US$25 million deal for NSA Suite B algorithms. (ECMQV is no longer part of Suite B.)
However, according to RSA Laboratories, "in all of these cases, it is the implementation technique that is patented, not the prime or representation, and there are alternative, compatible implementation techniques that are not covered by the patents." Additionally, Daniel J. Bernstein has stated that he is "not aware of" patents that cover the Curve25519 elliptic curve Diffie–Hellman algorithm or its implementation. , published in February 2011, documents ECC techniques, some of which were published so long ago that even if they were patented, any such patents for these previously published techniques would now be expired.
Known patents
Certicom holds a patent on efficient GF(2n) multiplication in normal basis representation; expired in 2016.
Certicom holds multiple patents which
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https://en.wikipedia.org/wiki/Reflection%20principle
|
In set theory, a branch of mathematics, a reflection principle says that it is possible to find sets that, with respect to any given property, resemble the class of all sets. There are several different forms of the reflection principle depending on exactly what is meant by "resemble". Weak forms of the reflection principle are theorems of ZF set theory due to , while stronger forms can be new and very powerful axioms for set theory.
The name "reflection principle" comes from the fact that properties of the universe of all sets are "reflected" down to a smaller set.
Motivation
A naive version of the reflection principle states that "for any property of the universe of all sets we can find a set with the same property". This leads to an immediate contradiction: the universe of all sets contains all sets, but there is no set with the property that it contains all sets. To get useful (and non-contradictory) reflection principles we need to be more careful about what we mean by "property" and what properties we allow.
Reflection principles are associated with attempts to formulate the idea that no one notion, idea, or statement can capture our whole view of the universe of sets. Kurt Gödel described it as follows:
Georg Cantor expressed similar views on Absolute Infinity: All cardinality properties are satisfied in this number, in which held by a smaller cardinal.
To find non-contradictory reflection principles we might argue informally as follows. Suppose that we have some
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https://en.wikipedia.org/wiki/Double%20crossover
|
Double crossover may refer to:
Two pairs of railway switches forming two connections that cross over between two parallel tracks
An artificial nucleic acid structural motif used in DNA nanotechnology
|
https://en.wikipedia.org/wiki/Sublunary%20sphere
|
In Aristotelian physics and Greek astronomy, the sublunary sphere is the region of the geocentric cosmos below the Moon, consisting of the four classical elements: earth, water, air, and fire.
The sublunary sphere was the realm of changing nature. Beginning with the Moon, up to the limits of the universe, everything (to classical astronomy) was permanent, regular and unchanging—the region of aether where the planets and stars are located. Only in the sublunary sphere did the powers of physics hold sway.
Evolution of concept
Plato and Aristotle helped to formulate the original theory of a sublunary sphere in antiquity, the idea usually going hand in hand with geocentrism and the concept of a spherical Earth.
Avicenna carried forward into the Middle Ages the Aristotelian idea of generation and corruption being limited to the sublunary sphere. Medieval scholastics like Thomas Aquinas, who charted the division between celestial and sublunary spheres in his work Summa Theologica, also drew on Cicero and Lucan for an awareness of the great frontier between Nature and Sky, sublunary and aetheric spheres. The result for medieval/Renaissance mentalities was a pervasive awareness of the existence, at the Moon, of what C.S. Lewis called 'this "great divide"...from aether to air, from 'heaven' to 'nature', from the realm of gods (or angels) to that of daemons, from the realm of necessity to that of contingence, from the incorruptible to the corruptible"
However, the theories of Coper
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https://en.wikipedia.org/wiki/Coadjoint%20representation
|
In mathematics, the coadjoint representation of a Lie group is the dual of the adjoint representation. If denotes the Lie algebra of , the corresponding action of on , the dual space to , is called the coadjoint action. A geometrical interpretation is as the action by left-translation on the space of right-invariant 1-forms on .
The importance of the coadjoint representation was emphasised by work of Alexandre Kirillov, who showed that for nilpotent Lie groups a basic role in their representation theory is played by coadjoint orbits.
In the Kirillov method of orbits, representations of are constructed geometrically starting from the coadjoint orbits. In some sense those play a substitute role for the conjugacy classes of , which again may be complicated, while the orbits are relatively tractable.
Formal definition
Let be a Lie group and be its Lie algebra. Let denote the adjoint representation of . Then the coadjoint representation is defined by
for
where denotes the value of the linear functional on the vector .
Let denote the representation of the Lie algebra on induced by the coadjoint representation of the Lie group . Then the infinitesimal version of the defining equation for reads:
for
where is the adjoint representation of the Lie algebra .
Coadjoint orbit
A coadjoint orbit for in the dual space of may be defined either extrinsically, as the actual orbit inside , or intrinsically as the homogeneous space where is the stabilizer of wit
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https://en.wikipedia.org/wiki/Ketyl
|
A ketyl group in organic chemistry is an anion radical that contains a group R2C−O•. It is the product of the 1-electron reduction of a ketone.
Another mesomeric structure has the radical position on carbon and the negative charge on oxygen.
Ketyls can be formed as radical anions by one-electron reduction of carbonyls with alkali metals. Sodium and potassium metal reduce benzophenone in THF solution to the soluble ketyl radical. Ketyls are also invoked as intermediates in the pinacol coupling reaction.
Reactions
Water
The ketyl radicals derived from the reaction of sodium and benzophenone is a common laboratory desiccant. Ketyls react quickly with the water, peroxides, and with oxygen. Thus, the deep purple coloration qualitatively indicates dry, peroxide-free, and oxygen-free conditions. The method for drying is still popular in many laboratories due to its ability to produce such pure solvent quickly. An alternative option for chemists interested only in water-free solvent is the use of molecular sieves. This is a much safer method than using an alkali metal still, produces solvent as dry as sodium-ketyl (though not as dry as potassium, or potassium-sodium alloy) but takes longer.
Oxygen
Sodium benzophenone ketyl reacts with oxygen to give the sodium benzoate and sodium phenoxide.
Reducing agent
Potassium-benzophenone ketyl is used as a reductant for the preparation of organoiron compounds.
References
Functional groups
Free radicals
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https://en.wikipedia.org/wiki/Ring%20expansion%20and%20contraction
|
Ring expansion and ring contraction reactions expand or contract rings, usually in organic chemistry. The term usually refers to reactions involve making and breaking C-C bonds, Diverse mechanisms lead to these kinds of reactions.
Demyanov ring contraction and expansion
These reactions entail diazotization of aminocyclobutanes and aminocyclopropanes. Loss of N2 from the diazo cations results in secondary carbocations, which tend to rearrange and then undergo hydrolysis. The reaction converts aminocyclobutane into a mixture of hydroxycyclobutane and hydroxymethylcyclopropane. These reactions produce an equilibrating mixture of two carbocations:
Carbenoid ring contractions
In the Arndt–Eistert reaction, an α-diazoketone is induced to release N2, resulting in a highly reactive sextet carbon center adjacent to the carbonyl. Such species convert by a Wolff rearrangement to give an ester in the presence of alcohols. When applied to cyclic α-diazoketones, ring contraction occurs. In the case of steroids, this reaction has been used to convert cyclopenanone groups to cyclobutanyl derivatives.
Ring expansion reactions
Ring expansions can allow access to larger systems that can be difficult to synthesize otherwise. Rings can be expanded by attack of the ring onto an outside group already appended to the ring (a migration/insertion), opening of a bicycle to a single larger ring, or coupling a ring closing with an expansion. These expansions can be further broken down by wha
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