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https://en.wikipedia.org/wiki/Exponential%20sum
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In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function
Therefore, a typical exponential sum may take the form
summed over a finite sequence of real numbers xn.
Formulation
If we allow some real coefficients an, to get the form
it is the same as allowing exponents that are complex numbers. Both forms are certainly useful in applications. A large part of twentieth century analytic number theory was devoted to finding good estimates for these sums, a trend started by basic work of Hermann Weyl in diophantine approximation.
Estimates
The main thrust of the subject is that a sum
is trivially estimated by the number N of terms. That is, the absolute value
by the triangle inequality, since each summand has absolute value 1. In applications one would like to do better. That involves proving some cancellation takes place, or in other words that this sum of complex numbers on the unit circle is not of numbers all with the same argument. The best that is reasonable to hope for is an estimate of the form
which signifies, up to the implied constant in the big O notation, that the sum resembles a random walk in two dimensions.
Such an estimate can be considered ideal; it is unattainable in many of the major problems, and estimates
have to be used, where the o(N) function represents only a small saving on the trivial estimate. A typi
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https://en.wikipedia.org/wiki/1674%20in%20science
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The year 1674 in science and technology involved some significant events.
Biology
Antonie van Leeuwenhoek discovers infusoria using the microscope.
Pharmacology
Thomas Willis publishes Pharmaceutice rationalis.
Births
Deaths
Jean Pecquet, French anatomist (born 1622)
References
17th century in science
1670s in science
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https://en.wikipedia.org/wiki/List%20of%20curves%20topics
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This is an alphabetical index of articles related to curves used in mathematics.
Acnode
Algebraic curve
Arc
Asymptote
Asymptotic curve
Barbier's theorem
Bézier curve
Bézout's theorem
Birch and Swinnerton-Dyer conjecture
Bitangent
Bitangents of a quartic
Cartesian coordinate system
Caustic
Cesàro equation
Chord (geometry)
Cissoid
Circumference
Closed timelike curve
concavity
Conchoid (mathematics)
Confocal
Contact (mathematics)
Contour line
Crunode
Cubic Hermite curve
Curvature
Curve orientation
Curve fitting
Curve-fitting compaction
Curve of constant width
Curve of pursuit
Curves in differential geometry
Cusp
Cyclogon
De Boor algorithm
Differential geometry of curves
Eccentricity (mathematics)
Elliptic curve cryptography
Envelope (mathematics)
Fenchel's theorem
Genus (mathematics)
Geodesic
Geometric genus
Great-circle distance
Harmonograph
Hedgehog (curve)
Hilbert's sixteenth problem
Hyperelliptic curve cryptography
Inflection point
Inscribed square problem
intercept, y-intercept, x-intercept
Intersection number
Intrinsic equation
Isoperimetric inequality
Jordan curve
Jordan curve theorem
Knot
Limit cycle
Linking coefficient
List of circle topics
Loop (knot)
M-curve
Mannheim curve
Meander (mathematics)
Mordell conjecture
Natural representation
Opisometer
Orbital elements
Osculating circle
Osculating plane
Osgood curve
Parallel (curve)
Parallel transport
Parametric curve
Bézier curve
Spline (mathemat
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https://en.wikipedia.org/wiki/Half%20%28disambiguation%29
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One half is an irreducible fraction resulting from dividing one by two.
Half may also refer to:
half.com, a website run by eBay that sells books, movies, video games, music, etc.
Halves (band), an Irish post-rock band
Halving, the operation of division by two
A half precision floating point representation in computer sciences
"A half", a half pint of an alcoholic beverage
"Half" a song by Soundgarden on the album Superunknown
Other half, an affectionate term for a member of an intimate relationship
A person being one half Japanese, and one half gaijin
See also
Hafu (disambiguation)
Second (disambiguation)
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https://en.wikipedia.org/wiki/Superalgebra
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In mathematics and theoretical physics, a superalgebra is a Z2-graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading.
The prefix super- comes from the theory of supersymmetry in theoretical physics. Superalgebras and their representations, supermodules, provide an algebraic framework for formulating supersymmetry. The study of such objects is sometimes called super linear algebra. Superalgebras also play an important role in related field of supergeometry where they enter into the definitions of graded manifolds, supermanifolds and superschemes.
Formal definition
Let K be a commutative ring. In most applications, K is a field of characteristic 0, such as R or C.
A superalgebra over K is a K-module A with a direct sum decomposition
together with a bilinear multiplication A × A → A such that
where the subscripts are read modulo 2, i.e. they are thought of as elements of Z2.
A superring, or Z2-graded ring, is a superalgebra over the ring of integers Z.
The elements of each of the Ai are said to be homogeneous. The parity of a homogeneous element x, denoted by , is 0 or 1 according to whether it is in A0 or A1. Elements of parity 0 are said to be even and those of parity 1 to be odd. If x and y are both homogeneous then so is the product xy and .
An associative superalgebra is one whose multiplication is associative and a unital superalgebra is o
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https://en.wikipedia.org/wiki/Richard%20Vranch
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Richard Leslie Vranch (born 29 June 1959) is an English actor, improviser, comedian, writer and musician. He is known for providing the music for the British TV series Whose Line Is It Anyway?
Early life
Vranch graduated from Cambridge University with a PhD in physics. While a first-year doctoral student, he joined the Footlights in 1981 and was a contemporary of Stephen Fry, Hugh Laurie, Morwenna Banks, Tony Slattery and Neil Mullarkey. He was a researcher at the Cavendish Laboratory and a research fellow at St John's College, Oxford for nine months before going into comedy full-time.
Career
Richard Vranch improvises comedy on stage with the Comedy Store Players every Sunday at The Comedy Store in London. He performs as a stand-up comedian, and with Pippa the Ripper he is half of the hula-hoop/science double act Dr Hula. He has voiced TV and radio commercials for companies including British Airways, Lidl and Saab and he narrates TV documentaries, including the first series of Hotel Inspector. He has performed since 1979, and formed a comedy double-act with Tony Slattery in 1981. The duo hosted the Channel 4 quiz The Music Game and over 100 episodes of Cue The Music on ITV. He was the improvising pianist and guitarist on the original British television show Whose Line Is It Anyway? in 1988, but only a small proportion of his work is musical. Vranch co-wrote and performed in The Paul Merton Show at the London Palladium in 1994.
Acting work includes Dogman, The Dead Set, and
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https://en.wikipedia.org/wiki/Logarithmic%20derivative
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In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula
where is the derivative of f. Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely scaled by the current value of f.
When f is a function f(x) of a real variable x, and takes real, strictly positive values, this is equal to the derivative of ln(f), or the natural logarithm of f. This follows directly from the chain rule:
Basic properties
Many properties of the real logarithm also apply to the logarithmic derivative, even when the function does not take values in the positive reals. For example, since the logarithm of a product is the sum of the logarithms of the factors, we have
So for positive-real-valued functions, the logarithmic derivative of a product is the sum of the logarithmic derivatives of the factors. But we can also use the Leibniz law for the derivative of a product to get
Thus, it is true for any function that the logarithmic derivative of a product is the sum of the logarithmic derivatives of the factors (when they are defined).
A corollary to this is that the logarithmic derivative of the reciprocal of a function is the negation of the logarithmic derivative of the function:
just as the logarithm of the reciprocal of a positive real number is the negation of the logarithm of the number.
More generally, the logarithmic derivative of a quotient is the differe
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https://en.wikipedia.org/wiki/Peggy%20Whitson
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Peggy Annette Whitson (born February 9, 1960) is an American biochemistry researcher, retired NASA astronaut, former NASA Chief Astronaut, and an active Axiom Space astronaut. Whitson has a total of 675 days in space, more than any other American or woman.
Her first space mission was in 2002: an extended stay aboard the International Space Station as a member of Expedition 5. On her second mission, Expedition 16 in 2007-2008, she became the first woman to command the ISS. In 2009, she became the first woman to serve as NASA's Chief Astronaut, the most senior position in the NASA Astronaut Corps. In 2017, Whitson became the first woman to command the International Space Station twice. Her 289-day flight was the longest single space flight by a woman until Christina Koch's 328-day flight.
Whitson holds the records for the oldest woman spacewalker and the most spacewalks by a woman. Whitson's cumulative EVA time is 60 hours, 21 minutes, which places her in fifth place for total EVA time. At age 57 on her final NASA flight, she was the oldest woman ever in space at that time - a record broken in 2021 by Wally Funk. She is still the oldest woman to orbit the Earth, a record she broke in 2023, at 63.
On June 15, 2018, Whitson retired from NASA. She later became a consultant for Axiom Space and is the commander of Axiom Mission 2.
Whitson was included in Time magazine's 100 Most Influential People of 2018.
Early life and background
Whitson grew up on a farm outside the town of
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https://en.wikipedia.org/wiki/Jean-Baptiste%20%C3%89lie%20de%20Beaumont
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Jean-Baptiste Armand Louis Léonce Élie de Beaumont (25 September 1798 – 21 September 1874) was a French geologist.
Biography
Élie de Beaumont was born at Canon, in Calvados. He was educated at the Lycee Henri IV where he took the first prize in mathematics and physics at the École polytechnique, where he stood first at the exit examination in 1819; and at the École des mines (1819–1822), where he began to show a decided preference for the science with which his name is associated. In 1823 he was selected along with Dufrénoy by Brochant de Villiers, the professor of geology in the École des Mines, to accompany him on a scientific tour to England and Scotland, in order to inspect the mining and metallurgical establishments of the country, and to study the principles on which George Bellas Greenough's geological map of England (1820) had been prepared, with a view to the construction of a similar map of France.
In 1835 he was appointed professor of geology at the École des Mines, in succession to Brochant de Villiers, whose assistant he had been in the duties of the chair since 1827. He held the office of engineer-in-chief of mines in France from 1833 until 1847, when he was appointed inspector-general; and in 1861 he became vice-president of the Conseil-General des Mines and a grand officer of the Legion of Honour. His growing scientific reputation secured his election to the membership of the Academy of Berlin, of the French Academy of Sciences, of the Royal Society of Edin
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https://en.wikipedia.org/wiki/Connection%20%28principal%20bundle%29
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In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G.
A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection. It gives rise to (Ehresmann) connections on any fiber bundle associated to P via the associated bundle construction. In particular, on any associated vector bundle the principal connection induces a covariant derivative, an operator that can differentiate sections of that bundle along tangent directions in the base manifold. Principal connections generalize to arbitrary principal bundles the concept of a linear connection on the frame bundle of a smooth manifold.
Formal definition
Let be a smooth principal G-bundle over a smooth manifold . Then a principal -connection on is a differential 1-form on with values in the Lie algebra of which is -equivariant and reproduces the Lie algebra generators of the fundamental vector fields on .
In other words, it is an element ω of such that
where denotes right multiplication by , and is the adjoint representation on (explicitly, );
if and is the vector field on P associated to ξ by differen
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https://en.wikipedia.org/wiki/1673%20in%20science
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The year 1673 in science and technology involved some significant events.
Mathematics
John Kersey begins publication of The Elements of that Mathematical Art Commonly Called Algebra.
Samuel Morland publishes A Perpetual Almanack and Several Useful Tables.
Microbiology
Antonie van Leeuwenhoek's observations with the microscope are first published in Philosophical Transactions of the Royal Society.
Physics
Christiaan Huygens publishes his mathematical analysis of the pendulum, Horologium Oscillatorium sive de motu pendulorum.
Births
August 10 – Johann Konrad Dippel, German theologian, alchemist and physician (died 1734)
Deaths
May 6 – Werner Rolfinck, German scientist (born 1599)
August 17 – Regnier de Graaf, Dutch physician and anatomist who discovered the ovarian follicles (born 1641)
December 15 – Margaret Cavendish, Duchess of Newcastle-upon-Tyne, English natural philosopher (born 1623)
References
17th century in science
1670s in science
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https://en.wikipedia.org/wiki/1622%20in%20science
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The year 1622 in science and technology involved some significant events.
Mathematics
The slide rule is invented by William Oughtred (1574–1660), an English mathematician, and later becomes the calculating tool of choice until the electronic calculator takes over in the early 1970s.
Physiology and medicine
Gaspare Aselli discovers the lacteal vessels of the lymphatic system.
Flemish anatomist Giulio Casserio publishes Nova anatomia in Frankfurt, containing clear copperplate engravings of the human anatomy.
Technology
February 22 – An English patent is granted for Dud Dudley's process for smelting iron ore with coke.
Births
January 28 – Adrien Auzout, French astronomer (died 1691)
March 10 – Johann Rahn, Swiss mathematician (died 1676)
April 5 – Vincenzo Viviani, Italian mathematician and scientist (died 1703)
undated – Jean Pecquet, French anatomist (died 1674)
Deaths
January 23 – William Baffin, English explorer and navigator (born 1584)
February 19 – Sir Henry Savile, English polymath and benefactor (born 1549)
April 13 – Katharina Kepler, German healer and mother of Johannes Kepler (born 1546)
May 15 – Petrus Plancius, Flemish cartographer and cosmographer (born 1552)
References
17th century in science
1620s in science
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https://en.wikipedia.org/wiki/Pierson%27s%20Puppeteers
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Pierson's Puppeteers, often known just as Puppeteers, are a fictional alien race from American author Larry Niven's Known Space books. The race first appeared in Niven’s novella Neutron Star.
Biology and sociology
The sobriquet "Pierson's" comes from the name of the human who made first contact in the early 26th century in the Known Space timeline. According to the Niven story The Soft Weapon, Pierson was a crewman aboard a spaceship at a time when there was a camp revival of the ancient Time for Beany TV show featuring Cecil the Seasick Sea Serpent, an animated character based on a hand puppet; Pierson accordingly described the alien he had met as a Puppeteer, given some resemblance of the head and neck with Cecil. Puppeteers dealing with humans usually give themselves the names of centaurs and other figures in Greek mythology, such as Nessus, Nike and Chiron. Puppeteers' names for themselves are reportedly highly complex, and unpronounceable by humans. The group name they use for their own species translates as "Citizens".
Pierson's Puppeteers are described by Niven as having two forelegs and a single hindleg ending in hoofed feet, and two snake-like heads instead of a humanoid upper body. The heads are small, containing a forked tongue, rubbery lips rimmed with finger-like knobs, and a single eye per head. The Puppeteer brain is housed not in the heads, but in the "thoracic" cavity well protected beneath the mane-covered hump from which the heads emerge. They use the "m
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https://en.wikipedia.org/wiki/Cryptographie%20ind%C3%A9chiffrable
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Cryptographie indéchiffrable (subtitle: basée sur de nouvelles combinaisons rationelles) is a French book on cryptography written by Émile Victor Théodore Myszkowski (a retired French colonel) and published in 1902.
His book described a cipher that the author had invented and claimed (incorrectly) was "undecipherable" (i.e. secure against unauthorised attempts to read it). It was based on a form of repeated-key transposition.
See also
Books on cryptography
Transposition cipher
Cryptography books
1902 non-fiction books
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https://en.wikipedia.org/wiki/Mark-8
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The Mark-8 is a microcomputer design from 1974, based on the Intel 8008 CPU (which was the world's first 8-bit microprocessor). The Mark-8 was designed by Jonathan Titus, a Virginia Tech graduate student in chemistry. After building the machine, Titus decided to share its design with the community and reached out to Radio-Electronics and Popular Electronics. He was turned down by Popular Electronics, but Radio-Electronics was interested and announced the Mark-8 as a 'loose kit' in the July 1974 issue of Radio-Electronics magazine.
Project kit
The Mark-8 was introduced as a 'build it yourself' project in Radio-Electronics'''s July 1974 cover article, offering a US$5 booklet containing circuit board layouts and DIY construction project descriptions, with Titus himself arranging for $50 circuit board sets to be made by a New Jersey company for delivery to hobbyists. Prospective Mark-8 builders had to gather the various electronics parts themselves from various sources. A couple of thousand booklets and some one-hundred circuit board sets were eventually sold.
The Mark-8 was introduced in R-E as "Your Personal Minicomputer" as the word 'microcomputer' was still far from being commonly used for microprocessor-based computers. In their announcement of their computer kit, the editors placed the Mark-8 in the same category as the era's other 'minisize' computers. As quoted by an Intel official publication, "The Mark-8 is known as one of the first computers for the home."
Influ
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https://en.wikipedia.org/wiki/Partition%20of%20an%20interval
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In mathematics, a partition of an interval on the real line is a finite sequence of real numbers such that
.
In other terms, a partition of a compact interval is a strictly increasing sequence of numbers (belonging to the interval itself) starting from the initial point of and arriving at the final point of .
Every interval of the form is referred to as a subinterval of the partition x.
Refinement of a partition
Another partition of the given interval [a, b] is defined as a refinement of the partition , if contains all the points of and possibly some other points as well; the partition is said to be “finer” than . Given two partitions, and , one can always form their common refinement, denoted , which consists of all the points of and , in increasing order.
Norm of a partition
The norm (or mesh) of the partition
is the length of the longest of these subintervals
{{math|maxxi − xi−1}} : i 1, … , n .
Applications
Partitions are used in the theory of the Riemann integral, the Riemann–Stieltjes integral and the regulated integral. Specifically, as finer partitions of a given interval are considered, their mesh approaches zero and the Riemann sum based on a given partition approaches the Riemann integral.
Tagged partitions
A tagged partition is a partition of a given interval together with a finite sequence of numbers subject to the conditions that for each ,
.
In other words, a tagged partition is a partition together with a distinguished point of every
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https://en.wikipedia.org/wiki/Ali%20Abu%20Al-Ragheb
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Ali Abu al-Ragheb () (born 1946) was the 33rd Prime Minister of Jordan from 19 June 2000 until 25 October 2003. He resigned and was replaced by Faisal al-Fayez.
Prime Minister Ali Abu Ragheb was born in Amman, Jordan in 1946. He obtained his BSc in Civil Engineering in 1967 from the University of Tennessee in the United States.
Abu al-Ragheb was partner and managing director of National Engineering and Contracting Co from 1971-1991. He later served as Minister of Industry and Trade in 1991 and in 1995. He was also appointed as Minister of Energy and Mineral Resources in 1991-1993 and was elected to the Jordanian parliament in 1993. Abu Ragheb was appointed Prime Minister and Minister of Defense on 19 June 2000.
Abu al-Ragheb's name was published in the Panama Papers that were released in early April 2016 by the International Consortium of Investigative Journalists (ICIJ).
Decorations
Grand Cordon of the Order of the Star of Jordan Al-Kawkab Al-Urduni
Grand Cordon of the Order of Al-Nahda in Jordan
Knight Grand Cross of the Order of Merit of the Italian Republic
Knight Grand Cross of the Order of St Michael and St George (GCMG) in Britain.
See also
List of prime ministers of Jordan
References
External links
Prime Ministry of Jordan website
1946 births
Living people
Prime Ministers of Jordan
Members of the House of Representatives (Jordan)
University of Tennessee alumni
Government ministers of Jordan
Industry ministers of Jordan
Defence ministers of Jordan
Trade
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https://en.wikipedia.org/wiki/Fuchsian%20group
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In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be regarded as a group acting on any of these spaces. There are some variations of the definition: sometimes the Fuchsian group is assumed to be finitely generated, sometimes it is allowed to be a subgroup of PGL(2,R) (so that it contains orientation-reversing elements), and sometimes it is allowed to be a Kleinian group (a discrete subgroup of PSL(2,C)) which is conjugate to a subgroup of PSL(2,R).
Fuchsian groups are used to create Fuchsian models of Riemann surfaces. In this case, the group may be called the Fuchsian group of the surface. In some sense, Fuchsian groups do for non-Euclidean geometry what crystallographic groups do for Euclidean geometry. Some Escher graphics are based on them (for the disc model of hyperbolic geometry).
General Fuchsian groups were first studied by , who was motivated by the paper , and therefore named them after Lazarus Fuchs.
Fuchsian groups on the upper half-plane
Let H = {z in C : Im(z) > 0} be the upper half-plane. Then H is a model of the hyperbolic plane when endowed with the metric
The group PSL(2,R) acts on H by linear fractional transformations (also known as Möbius transformations):
This action is faithful, and in
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https://en.wikipedia.org/wiki/Marker%20interface%20pattern
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The marker interface pattern is a design pattern in computer science, used with languages that provide run-time type information about objects. It provides a means to associate metadata with a class where the language does not have explicit support for such metadata.
To use this pattern, a class implements a marker interface (also called tagging interface) which is an empty interface, and methods that interact with instances of that class test for the existence of the interface. Whereas a typical interface specifies functionality (in the form of method declarations) that an implementing class must support, a marker interface need not do so. The mere presence of such an interface indicates specific behavior on the part of the implementing class. Hybrid interfaces, which both act as markers and specify required methods, are possible but may prove confusing if improperly used.
Example
An example of the application of marker interfaces from the Java programming language is the interface:package java.io;
public interface Serializable {
}A class implements this interface to indicate that its non-transient data members can be written to an . The ObjectOutputStream private method writeObject0(Object,boolean) contains a series of instanceof tests to determine writeability, one of which looks for the Serializable interface. If any of these tests fails, the method throws a NotSerializableException.
Critique
A major problem with marker interfaces is that an interface defines a cont
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https://en.wikipedia.org/wiki/Vladimir%20Prelog
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Vladimir Prelog (23 July 1906 – 7 January 1998) was a Croatian-Swiss organic chemist who received the 1975 Nobel Prize in chemistry for his research into the stereochemistry of organic molecules and reactions. Prelog was born and grew up in Sarajevo. He lived and worked in Prague, Zagreb and Zürich during his lifetime.
Early life
Prelog was born in Sarajevo, Condominium of Bosnia and Herzegovina, at that time within Austria-Hungary, to Croat parents who were working there. His father, Milan, a native of Zagreb, was a history professor at a gymnasium in Sarajevo and later at the University of Zagreb. As an 8-year-old boy, he stood near the place where the assassination of Franz Ferdinand occurred.
Education
Prelog attended elementary school in Sarajevo, but in 1915, as a child, Prelog moved to Zagreb (then part of the Austro-Hungary) with his parents. In Zagreb he graduated from elementary school. At first, he attended gymnasium in Zagreb, but soon afterwards, his father got a job in Osijek, so he continued his education there. He spent two years in Osijek gymnasium, where he became interested in chemistry under the influence of his professor Ivan Kuria.
In 1922, as a 16-year-old boy, his first scientific work was published in the German scientific journal Chemiker Zeitung. The article concerned an analytical instrument used in chemical labs. Prelog completed his high school education in Zagreb in 1924. Following his father's wishes, he moved to Prague, where he received
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https://en.wikipedia.org/wiki/Kaprekar%20number
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In mathematics, a natural number in a given number base is a -Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has digits, that add up to the original number. The numbers are named after D. R. Kaprekar.
Definition and properties
Let be a natural number. We define the Kaprekar function for base and power to be the following:
,
where and
A natural number is a -Kaprekar number if it is a fixed point for , which occurs if . and are trivial Kaprekar numbers for all and , all other Kaprekar numbers are nontrivial Kaprekar numbers.
For example, in base 10, 45 is a 2-Kaprekar number, because
A natural number is a sociable Kaprekar number if it is a periodic point for , where for a positive integer (where is the th iterate of ), and forms a cycle of period . A Kaprekar number is a sociable Kaprekar number with , and a amicable Kaprekar number is a sociable Kaprekar number with .
The number of iterations needed for to reach a fixed point is the Kaprekar function's persistence of , and undefined if it never reaches a fixed point.
There are only a finite number of -Kaprekar numbers and cycles for a given base , because if , where then
and , , and . Only when do Kaprekar numbers and cycles exist.
If is any divisor of , then is also a -Kaprekar number for base .
In base , all even perfect numbers are Kaprekar numbers. More generally, any numbers of the form or for natural numb
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https://en.wikipedia.org/wiki/Divisible%20group
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In mathematics, especially in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive integer n. Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian groups.
Definition
An abelian group is divisible if, for every positive integer and every , there exists such that . An equivalent condition is: for any positive integer , , since the existence of for every and implies that , and the other direction is true for every group. A third equivalent condition is that an abelian group is divisible if and only if is an injective object in the category of abelian groups; for this reason, a divisible group is sometimes called an injective group.
An abelian group is -divisible for a prime if for every , there exists such that . Equivalently, an abelian group is -divisible if and only if .
Examples
The rational numbers form a divisible group under addition.
More generally, the underlying additive group of any vector space over is divisible.
Every quotient of a divisible group is divisible. Thus, is divisible.
The p-primary component of , which is isomorphic to the p-quasicyclic group , is divisible.
The multiplicative group of the complex numbers is divisible.
Every existentially closed abelian group (in the model theoretic sense
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https://en.wikipedia.org/wiki/1668%20in%20science
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The year 1668 in science and technology involved some significant events.
Astronomy
Isaac Newton invents the reflecting telescope.
Biology
Francesco Redi publishes Esperienze Intorno alla Generazione degl'Insetti ("Experiments on the Generation of Insects"), disproving theories of the spontaneous generation of maggots in putrefying matter.
Mathematics
Nicholas Mercator and William Brouncker discover an infinite series for the logarithm while attempting to calculate the area under a hyperbolic segment.
Medicine
François Mauriceau publishes Traité des Maladies des Femmes Grosses et Accouchées in Paris, a key text in scientific obstetrics.
John Mayow publishes a tract on respiration in Oxford, recognising "spiritus nitro-aereus" as a component of air, prefiguring the isolation of oxygen.
Publications
John Wilkins publishes An Essay towards a Real Character and a Philosophical Language proposing a universal language and a uniform system of measurement for international communication between natural philosophers.
Births
December 31 – Herman Boerhaave, Dutch physician and chemist who makes Leiden a European centre of medical knowledge (died 1738)
Deaths
References
17th century in science
1660s in science
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https://en.wikipedia.org/wiki/1666%20in%20science
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The year 1666 in science and technology involved some significant events.
Events
December 22 – French Academy of Sciences first meets.
Astronomy
Publication of Stanisław Lubieniecki's Theatrum Cometicum begins in Amsterdam, the first encyclopedia and atlas of comets.
Botany
Establishment of Herrenhäuser Gärten, Hanover.
Mathematics
Isaac Newton develops differential calculus.
Samuel Morland produces several designs of pocket calculating machine and also publishes A New Method of Cryptography.
Physics
Isaac Newton uses a prism to split sunlight into the component colours of the optical spectrum, assisting understanding of the nature of light.
Robert Hooke and Giovanni Alfonso Borelli both expound gravitation as an attractive force (Hooke's lecture "On gravity" at the Royal Society of London on March 21; Borelli's Theoricae Mediceorum planetarum ex causis physicis deductae, published in Florence later in the year).
Publications
Margaret Cavendish, Duchess of Newcastle-upon-Tyne, publishes Observations upon Experimental Philosophy, including an attack on Robert Hooke's Micrographia.
Births
December – Stephen Gray, English scientist (died 1736)
Deaths
Giovanni Battista Baliani, Genoese physicist (born 1582)
Song Yingxing, Chinese encyclopedist (born 1587)
References
17th century in science
1660s in science
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https://en.wikipedia.org/wiki/Pierre%20Boutroux
|
Pierre Léon Boutroux (; 6 December 1880 – 15 August 1922) was a French mathematician and historian of science. Boutroux is chiefly known for his work in the history and philosophy of mathematics.
Biography
He was born in Paris on 6 December 1880 into a well connected family of the French intelligentsia. His father was the philosopher Émile Boutroux. His mother was Aline Catherine Eugénie Poincaré, sister of the scientist and mathematician Henri Poincaré. A cousin of Aline, Raymond Poincaré was to be President of France.
He occupied the mathematics chair at Princeton University from 1913 until 1914. He occupied the History of sciences chair from 1920 to 1922.
Boutroux published his major work Les principes de l'analyse mathématique in two volumes; Volume 1 in 1914 and Volume 2 in 1919. This is a comprehensive view of the whole field of mathematics at the time.
He was an Invited Speaker of the ICM in 1904 at Heidelberg, in 1908 at Rome, and in 1920 at Strasbourg.
He died on 15 August 1922, aged 41 years.
Works
L'Imagination et les mathématiques selon Descartes (1900)
Sur quelques propriétés des fonctions entières (1903)
Œuvres de Blaise Pascal, publiées suivant l'ordre chronologique, avec documents complémentaires, introductions et notes, par Léon Brunschvicg et Pierre Boutroux (1908)
Leçons sur les fonctions définies par les équations différentielles du premier ordre, professées au Collège de France (1908)
Les Principes de l'analyse mathématique, exposé historique e
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https://en.wikipedia.org/wiki/1657%20in%20science
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The year 1657 in science and technology involved some significant events.
Geography
Peter Heylin publishes his Cosmographie, one of the earliest attempts to describe the entire world in English and the first known description of Australia.
Mathematics
Christiaan Huygens writes the first book to be published on probability theory, De ratiociniis in ludo aleae ("On Reasoning in Games of Chance").
Medicine
Walter Rumsey invents the provang, a baleen instrument which he describes in his Organon Salutis: an instrument to cleanse the stomach.
Technology
Christiaan Huygens patents his 1656 design for a pendulum clock and the first example is made for him by Salomon Coster at The Hague.
approx. date – The anchor escapement for clocks is probably invented by Robert Hooke.
Institutions
Accademia del Cimento established in Florence.
Births
February 11 – Bernard le Bovier de Fontenelle, French scientific populariser (died 1757)
approx. date – Pierre-Charles Le Sueur, French fur trader and explorer (died 1704)
Deaths
June 3 – William Harvey, English physician who discovered the circulation of blood (born 1578)
June 16 – Fortunio Liceti, Italian Aristotelian scientific polymath (born 1577)
September 23 – Joachim Jungius, German mathematician, logician and philosopher of science (born 1587)
October 22 – Cassiano dal Pozzo, Italian scholar and patron (born 1588)
November – John French, English physician and chemist (born c. 1616)
References
17th century in science
165
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https://en.wikipedia.org/wiki/1655%20in%20science
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The year 1655 in science and technology involved some significant events.
Astronomy
March 25 – Titan, Saturn's largest moon, is discovered by Christiaan Huygens.
Biology
Botanical garden established at Uppsala University.
Thomas Muffet's Healths Improvement, or, Rules comprising and discovering the nature, method, and manner of preparing all sorts of food used in this nation is published posthumously in England, containing, inter alia, descriptions of a wide range of wildfowl to be found in the country.
Mathematics
John Wallis introduces the symbol ∞ to represent infinity.
Births
January 6 (27 December 1654 OS) – Jacob Bernoulli, Swiss mathematician (died 1705)
September 10 – Caspar Bartholin the Younger, Danish anatomist (died 1738)
Deaths
February 1 – Giovanni Baptista Ferrari, Italian Jesuit botanist and linguist (born 1584)
October 16 – Rabbi Joseph Solomon Delmedigo, Cretan-born peripatetic physician and scientist (born 1591)
October 24 – Pierre Gassendi, French physicist who played a crucial role in the revival of atomism (born 1592)
Francesco Pona, Veronese physician and poet (born 1595)
References
17th century in science
1650s in science
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https://en.wikipedia.org/wiki/Serre%27s%20multiplicity%20conjectures
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In mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain purely algebraic problems, in commutative algebra, motivated by the needs of algebraic geometry. Since André Weil's initial definition of intersection numbers, around 1949, there had been a question of how to provide a more flexible and computable theory.
Let R be a (Noetherian, commutative) regular local ring and P and Q be prime ideals of R. In 1958, Serre realized that classical algebraic-geometric ideas of multiplicity could be generalized using the concepts of homological algebra. Serre defined the intersection multiplicity of R/P and R/Q by means of the Tor functors of homological algebra, as
This requires the concept of the length of a module, denoted here by , and the assumption that
If this idea were to work, however, certain classical relationships would presumably have to continue to hold. Serre singled out four important properties. These then became conjectures, challenging in the general case. (There are more general statements of these conjectures where R/P and R/Q are replaced by finitely generated modules: see Serre's Local Algebra for more details.)
Dimension inequality
Serre proved this for all regular local rings. He established the following three properties when R is either of equal characteristic or of mixed characteristic and unramified (which in this case means that characteristic of the residue field is not an element of the square of the maximal idea
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https://en.wikipedia.org/wiki/Kirszbraun%20theorem
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In mathematics, specifically real analysis and functional analysis, the Kirszbraun theorem states that if is a subset of some Hilbert space , and is another Hilbert space, and
is a Lipschitz-continuous map, then there is a Lipschitz-continuous map
that extends and has the same Lipschitz constant as .
Note that this result in particular applies to Euclidean spaces and , and it was in this form that Kirszbraun originally formulated and proved the theorem. The version for Hilbert spaces can for example be found in (Schwartz 1969, p. 21). If is a separable space (in particular, if it is a Euclidean space) the result is true in Zermelo–Fraenkel set theory; for the fully general case, it appears to need some form of the axiom of choice; the Boolean prime ideal theorem is known to be sufficient.
The proof of the theorem uses geometric features of Hilbert spaces; the corresponding statement for Banach spaces is not true in general, not even for finite-dimensional Banach spaces. It is for instance possible to construct counterexamples where the domain is a subset of with the maximum norm and carries the Euclidean norm. More generally, the theorem fails for equipped with any norm () (Schwartz 1969, p. 20).
Explicit formulas
For an -valued function the extension is provided by where is the Lipschitz constant of on .
In general, an extension can also be written for -valued functions as where and conv(g) is the lower convex envelope of g.
History
The theorem w
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https://en.wikipedia.org/wiki/1614%20in%20science
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The year 1614 in science and technology involved some significant events.
Mathematics
Scottish mathematician John Napier publishes Mirifici Logarithmorum Canonis Descriptio ("Description of the Admirable Table of Logarithms"), outlining his discovery of logarithms and incorporating the decimal mark. Astronomer Johannes Kepler soon begins to employ logarithms in his description of the Solar System.
Medicine
Felix Plater gives a description of Dupuytren's contracture.
Sanctorius publishes De statica medicina, which will go through five editions in the following century.
Births
February 14 – Bishop John Wilkins, English natural philosopher, co-founder of the Royal Society (died 1672)
Deaths
July 28 – Felix Plater, Swiss physician (born 1536)
Pedro Fernandes de Queirós, Portuguese-born navigator (born 1565)
William Lee, English-born inventor (born c. 1563)
References
17th century in science
1610s in science
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https://en.wikipedia.org/wiki/Marco%20Marra
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Marco A. Marra is a Distinguished Scientist and Director of Canada's Michael Smith Genome Sciences Centre at the BC Cancer Research Centre and Professor of Medical Genetics at the University of British Columbia (UBC). He also serves as UBC Canada Research Chair in Genome Science for the Canadian Institutes of Health Research and is an inductee in the Canadian Medical Hall of Fame. Marra has been instrumental in bringing genome science to Canada by demonstrating the pivotal role that genomics can play in human health and disease research.
Education and Early Life
Canadian born and educated, Dr. Marco Marra received a B.Sc. in Molecular & Cell Biology and a PhD in Genetics from Simon Fraser University. The title of his PhD thesis: “Genome analysis in Caenorhabditis elegans: Genetic and molecular identification of genes tightly linked to unc-22(IV)”.
Marra trained as a post-doctoral fellow at the Washington University School of Medicine in St Louis, Missouri. He went on to become Group Leader of both the EST (Express Sequence Tag) Sequencing Team and Genome Fingerprinting and Mapping Teams at Washington University’s Genome Sequence Center (renamed the McDonnell Genome Institute), one of the top two sequencing centers in the world at that time.
In 1998, Nobel Laureate Dr. Michael Smith and Dr. Victor Ling set out to establish the Genome Sequence Centre in Vancouver. At their request, Marra returned to British Columbia to head the Mapping and Sequencing teams.
Career and Rese
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https://en.wikipedia.org/wiki/John%20Mashey
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John R. Mashey (born 1946) is an American computer scientist, director and entrepreneur.
Career
Mashey holds a Ph.D. in computer science from Pennsylvania State University, where he developed the ASSIST assembler language teaching software. He worked on the PWB/UNIX operating system at Bell Labs from 1973 to 1983, authoring the PWB shell, also known as the "Mashey Shell". He then moved to Silicon Valley to join Convergent Technologies, ending as director of software. He joined MIPS Computer Systems in early 1985, managing operating systems development, and helping design the MIPS RISC architecture, as well as specific CPUs, systems and software. He continued similar work at Silicon Graphics (1992–2000), contributing to the design of the NUMAflex modular computer architecture using NUMAlink, ending as VP and chief scientist.
Mashey was one of the founders of the Standard Performance Evaluation Corporation (SPEC) benchmarking group, was an ACM National Lecturer for four years, has been guest editor for IEEE Micro, and one of the long-time organizers of the Hot Chips conferences. He chaired technical conferences on operating systems and CPU chips, and gave public talks on software engineering, RISC design, performance benchmarking and supercomputing. He has been credited for being the first to spread the term and concept of big data in the 1990s. He became a consultant for venture capitalists and high-tech companies and a trustee of the Computer History Museum in 2001. In 199
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https://en.wikipedia.org/wiki/ASSIST%20%28computing%29
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ASSIST (the Assembler System for Student Instruction and Systems Teaching) is an IBM System/370-compatible assembler and interpreter developed in the early 1970s at Penn State University by Graham Campbell and John Mashey. plus student assistants.
In the late 1960s, computer science education expanded rapidly and university computer centers were faced with a large growth in usage by students, whose needs sometimes differed from professionals in batch processing environments. They needed to run short programs on decks of Punched cards with fast turnaround (minutes, not overnight) as their programs more often included syntax errors. Once they compiled, they would often fault quickly, so optimization and flexibility were far less important than low overhead.
WATFIV was a successful pioneering effort to build a FORTRAN compiler tuned for student use. Universities began running it in a dedicated "fast-batch" memory partition with a small run-time limit, such as 5 seconds on an IBM System/360 Model 67). The low limit enabled fast turnaround and avoided waste of time by programs stuck in infinite loops. WATFIV's success helped inspire development of ASSIST, PL/C and other student-oriented programs that fit the "fast-batch" model that became widely used among universities.
ASSIST was enhanced and promoted by others, such as Northern Illinois University's Wilson Singletary & Ross Overbeek and
University of Tennessee's Charles Hughes and Charles Pfleeger who reported in 1978 that A
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https://en.wikipedia.org/wiki/List%20of%20variational%20topics
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This is a list of variational topics in from mathematics and physics. See calculus of variations for a general introduction.
Action (physics)
Averaged Lagrangian
Brachistochrone curve
Calculus of variations
Catenoid
Cycloid
Dirichlet principle
Euler–Lagrange equation cf. Action (physics)
Fermat's principle
Functional (mathematics)
Functional derivative
Functional integral
Geodesic
Isoperimetry
Lagrangian
Lagrangian mechanics
Legendre transformation
Luke's variational principle
Minimal surface
Morse theory
Noether's theorem
Path integral formulation
Plateau's problem
Prime geodesic
Principle of least action
Soap bubble
Soap film
Tautochrone curve
Variations
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https://en.wikipedia.org/wiki/Configuration%20space%20%28physics%29
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In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the space defined by these coordinates is called the configuration space of the physical system. It is often the case that these parameters satisfy mathematical constraints, such that the set of actual configurations of the system is a manifold in the space of generalized coordinates. This manifold is called the configuration manifold of the system. Notice that this is a notion of "unrestricted" configuration space, i.e. in which different point particles may occupy the same position. In mathematics, in particular in topology, a notion of "restricted" configuration space is mostly used, in which the diagonals, representing "colliding" particles, are removed.
Example: a particle in 3D space
The position of a single particle moving in ordinary Euclidean 3-space is defined by the vector , and therefore its configuration space is . It is conventional to use the symbol for a point in configuration space; this is the convention in both the Hamiltonian formulation of classical mechanics, and in Lagrangian mechanics. The symbol is used to denote momenta; the symbol refers to velocities.
A particle might be constrained to move on a specific manifold. For example, if the particle is attached to a rigid linkage, free to swing about the origin, it is effectively constrained to lie on a sphere. Its configuration space is the subset of coordinates in that define
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https://en.wikipedia.org/wiki/Rashid%20Sunyaev
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Rashid Alievich Sunyaev (, ; born 1 March 1943 in Tashkent, USSR) is a German, Soviet, and Russian astrophysicist of Tatar descent. He got his MS degree from the Moscow Institute of Physics and Technology (MIPT) in 1966. He became a professor at MIPT in 1974. Sunyaev was the head of the High Energy Astrophysics Department of the Russian Academy of Sciences, and has been chief scientist of the Academy's Space Research Institute since 1992. He has also been a director of the Max Planck Institute for Astrophysics in Garching, Germany since 1996, and Maureen and John Hendricks Distinguished Visiting Professor in the School of Natural Sciences at the Institute for Advanced Study in Princeton since 2010.
Works
Sunyaev and Yakov B. Zeldovich developed the theory for the evolution of density fluctuations in the early universe. They predicted the pattern of acoustic fluctuations that have been clearly seen by WMAP and other CMB experiments in the microwave sky and in the large-scale distribution of galaxies. Sunyaev and Zeldovich stated in their 1970 paper, "A detailed investigation of the spectrum of fluctuations may, in principle, lead to an understanding of the nature of initial density perturbations since a distinct periodic dependence of the spectral density of perturbations on wavelength (mass) is peculiar to adiabatic perturbations." CMB experiments have now seen this distinctive scale in temperature and polarization measurements. Large-scale structure observations have seen t
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https://en.wikipedia.org/wiki/1617%20in%20science
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The year 1617 in science and technology involved some significant events.
Astronomy
Johannes Kepler begins to publish his Epitome astronomiæ Copernicanæ setting out his theory of elliptic orbits.
Mathematics
Napier’s Bones, a multiplication device invented by John Napier (who dies on April 4), is described in his Rabdologiæ, published in Edinburgh.
Henry Briggs publishes Logarithmorum Chilias Prima, a modification of Napier's logarithms into common logarithms.
Medicine
The Worshipful Society of Apothecaries of London is granted a royal charter, separating it from the Grocers.
Births
July 13 (bapt.) – Ralph Cudworth, Cambridge Platonist (died 1688).
Deaths
January 29 – William Butler, Irish alchemist (at sea) (born c. 1534).
February 6 – Prospero Alpini, Italian physician and botanist (born 1553).
February 11 – Giovanni Antonio Magini, Italian astronomer (born 1555).
April 4 – John Napier of Merchiston, mathematician (born 1550).
May 7 – David Fabricius, Frisian astronomer (born 1564).
December – William Butler, English physician (born 1535).
References
17th century in science
1610s in science
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https://en.wikipedia.org/wiki/1615%20in%20science
|
The year 1615 in science and technology involved some significant events.
Astronomy
Manuel Dias (Yang MaNuo), a Portuguese Jesuit missionary introduces for the first time in China the telescope in his book Tian Wen Lüe (Explicatio Sphaerae Coelestis).
Chemistry
Jean Beguin publishes an edition of his chemistry textbook Tyrocinium Chymicum including the first-ever chemical equation.
Mathematics
Summer – Henry Briggs meets John Napier for the first time in Edinburgh.
Kepler publishes Nova Stereometria (the first book printed in Linz), a significant work in pre-calculus integration.
Natural history
Posthumous publication in Mexico of Plantas y Animales de la Nueva Espana, y sus virtudes por Francisco Hernandez, y de Latin en Romance por Fr. Francisco Ximenez.
Physiology and medicine
Helkiah Crooke's Mikrokosmographia, a Description of the Body of Man, together with the controversies and figures thereto belonging; collected and translated out of all the best authors of anatomy, especially out of Gasper Bauhinus and Andreas Laurentius is published "by the Kings Maiesties especiall direction and warrant" by Crooke's patient, the printer William Jaggard, in London.
Technology
The first known solar-activated device, a water pumping machine, is invented by Salomon de Caux.
Approximate date – Croatian polymath Fausto Veranzio publishes Machinae Novae in Venice depicting around 50 machines and devices.
Births
Nicasius le Febure, French chemist (died 1669)
Frans van Scho
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https://en.wikipedia.org/wiki/Gaja%20Alaga
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Gaja Alaga (3 July 1924 – 7 September 1988) was a Croatian theoretical physicist who specialised in nuclear physics.
He was born in noble family of Bunjevac origin in the village of Lemeš (today called Svetozar Miletić) in northwestern Bačka in Kingdom of SHS (today in autonomous province Vojvodina, Serbia).
He was a corresponding member of the Croatian Academy of Sciences and Arts since 1968 and a professor at the University of Zagreb Faculty of Science (). He worked in the Ruđer Bošković Institute in Zagreb (the capital city of Croatia), the Niels Bohr Institute in Copenhagen, the University of California, Berkeley, and Ludwig-Maximilians University in Munich.
In 1955, cooperating with Kurt Alder and Ben Roy Mottelson, Alaga discovered the K-selection rules and intensity rules for beta and gamma transitions in deformed atom nuclei. This discovery was key to the development of new nuclei models which confirmed that subatomic particles can distort the shape of the nucleus. This is by the model for collective motion (based on nuclei deformed from a spherical shape, but with axial symmetry) for which Aage Bohr, Ben Roy Mottelson, and James Rainwater won the 1975 Nobel Prize.
Also in 1955 (the journal Physical Review) and in 1957 (the journal "Nuclear Physics") he discovered asymptotic selection rules for beta and gamma transitions between states of deformed nuclei. The so-called Alaga rules are in common use among specialists in nuclear structure, in comparing theoretical t
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https://en.wikipedia.org/wiki/Transformation%20geometry
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In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them. It is opposed to the classical synthetic geometry approach of Euclidean geometry, that focuses on proving theorems.
For example, within transformation geometry, the properties of an isosceles triangle are deduced from the fact that it is mapped to itself by a reflection about a certain line. This contrasts with the classical proofs by the criteria for congruence of triangles.
The first systematic effort to use transformations as the foundation of geometry was made by Felix Klein in the 19th century, under the name Erlangen programme. For nearly a century this approach remained confined to mathematics research circles. In the 20th century efforts were made to exploit it for mathematical education. Andrei Kolmogorov included this approach (together with set theory) as part of a proposal for geometry teaching reform in Russia. These efforts culminated in the 1960s with the general reform of mathematics teaching known as the New Math movement.
Pedagogy
An exploration of transformation geometry often begins with a study of reflection symmetry as found in daily life. The first real transformation is reflection in a line or reflection against an axis. The composition of two reflections results in a rotation when the lines intersect,
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https://en.wikipedia.org/wiki/Injective%20module
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In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in and are discussed in some detail in the textbook .
Injective modules have been heavily studied, and a variety of additional notions are defined in terms of them: Injective cogenerators are injective modules that faithfully represent the entire category of modules. Injective resolutions measure how far from injective a module is in terms of the injective dimension and represent modules in the derived category. Injective hulls are maximal essential extensions, and turn out to be minimal injective extensions. Over a Noetherian ring, every injective module is uniquely a direct sum of indecomposable modules, and their structure is well understood. An injective module over one ring, may not be injective over another, but there are well-understood methods of changing rings which handle special cases. Rings which are themselves injective modules have a number of interesting properties and include rings such as group rings of finite groups over fields
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https://en.wikipedia.org/wiki/Injective%20object
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In mathematics, especially in the field of category theory, the concept of injective object is a generalization of the concept of injective module. This concept is important in cohomology, in homotopy theory and in the theory of model categories. The dual notion is that of a projective object.
Definition
An object in a category is said to be injective if for every monomorphism and every morphism there exists a morphism extending to , i.e. such that .
That is, every morphism factors through every monomorphism .
The morphism in the above definition is not required to be uniquely determined by and .
In a locally small category, it is equivalent to require that the hom functor carries monomorphisms in to surjective set maps.
In Abelian categories
The notion of injectivity was first formulated for abelian categories, and this is still one of its primary areas of application. When is an abelian category, an object Q of is injective if and only if its hom functor HomC(–,Q) is exact.
If is an exact sequence in such that Q is injective, then the sequence splits.
Enough injectives and injective hulls
The category is said to have enough injectives if for every object X of , there exists a monomorphism from X to an injective object.
A monomorphism g in is called an essential monomorphism if for any morphism f, the composite fg is a monomorphism only if f is a monomorphism.
If g is an essential monomorphism with domain X and an injective codomain G, then G is c
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https://en.wikipedia.org/wiki/Mutually%20orthogonal%20Latin%20squares
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In combinatorial mathematics, two Latin squares of the same size (order) are said to be orthogonal if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are orthogonal is called a set of mutually orthogonal Latin squares. This concept of orthogonality in combinatorics is strongly related to the concept of blocking in statistics, which ensures that independent variables are truly independent with no hidden confounding correlations. "Orthogonal" is thus synonymous with "independent" in that knowing one variable's value gives no further information about another variable's likely value.
An outdated term for pair of orthogonal Latin squares is Graeco-Latin square, found in older literature.
Graeco-Latin squares
A Graeco-Latin square or Euler square or pair of orthogonal Latin squares of order over two sets and (which may be the same), each consisting of symbols, is an arrangement of cells, each cell containing an ordered pair , where is in and is in , such that every row and every column contains each element of and each element of exactly once, and that no two cells contain the same ordered pair.
The arrangement of the -coordinates by themselves (which may be thought of as Latin characters) and of the -coordinates (the Greek characters) each forms a Latin square. A Graeco-Latin square can therefore be decomposed into two orthogonal Latin squares. Orthogonality here means t
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https://en.wikipedia.org/wiki/Gaston%20Tarry
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Gaston Tarry (27 September 1843 – 21 June 1913) was a French mathematician. Born in Villefranche de Rouergue, Aveyron, he studied mathematics at high school before joining the civil service in Algeria. He pursued mathematics as an amateur.
In 1901 Tarry confirmed Leonhard Euler's conjecture that no 6×6 Graeco-Latin square was possible (the 36 officers problem).
See also
List of amateur mathematicians
Prouhet-Tarry-Escott problem
Tarry point
Tetramagic square
References
External links
People from Villefranche-de-Rouergue
1843 births
1913 deaths
Combinatorialists
19th-century French mathematicians
20th-century French mathematicians
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https://en.wikipedia.org/wiki/Giovanni%20Amelino-Camelia
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Giovanni Amelino-Camelia (born 14 December 1965, Naples) is an Italian physicist of the University of Naples Federico II who works on quantum gravity.
He is the first proposer of doubly special relativity, that is the idea of introducing the Planck length in physics as an observer-independent quantity, obtaining a relativistic theory (like Galileian relativity and Einstein's special relativity). The principles of doubly special relativity probably imply the loss of the notion of classical (Riemannian) spacetime; this led Amelino-Camelia to the study of non-commutative geometry as a feasible theory of quantum spacetime.
Amelino-Camelia is the initiator of "quantum-gravity phenomenology", for being the first to show that with some experiments under reach of current technology sensitivity to Planck-scale effects is feasible (see Fermi Gamma-ray Space Telescope).
References
External links
Homepage at the INFN of Rome, ITALY
Works published at arXiv.org
"Are we at the dawn of quantum-gravity phenomenology?" (1999, Slides)
Small interview at "Essential Science Indicators" (2003, with photo)
"Quantum Gravity Phenomenology" Living Reviews in Relativity (2008)
1965 births
Living people
20th-century Italian astronomers
Quantum gravity physicists
21st-century Italian astronomers
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https://en.wikipedia.org/wiki/Rodolfo%20Gambini
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Rodolfo Gambini (born 11 May 1946) is a physicist and professor of the Universidad de la Republica in Montevideo, Uruguay and a visiting professor at the Horace Hearne Institute for Theoretical Physics at the Louisiana State University.
He works on loop quantum gravity. He got his PhD in Université de Paris VI working with Achilles Papapetrou. From there he moved to the Universidad Simón Bolívar in Venezuela where he rose through the professorial ranks. It was there that together with fellow physicist Antoni Trías he invented the loop representation for Yang-Mills theories in 1986.
Gambini returned to Uruguay in 1987 after democracy had returned to the country. Gambini has published over 100 scientific articles ranging from philosophy of science and foundations of quantum mechanics to lattice gauge theories to quantum gravity. He was head of the Pedeciba, the main funding agency for basic sciences in Uruguay (2003–2008). He is a fellow of the American Physical Society and of the American Association for Advancement of Science, a member of the Third World Academy of Sciences, the Latin American Academy of Sciences and the Academy of Exact and Natural Sciences of Argentina. He is the 2003 winner of the Third World Academy of Sciences prize in physics and has received numerous distinctions in Uruguay. In particular he was awarded the 2004 Presidential Medal of Science, the Prize to the Intellectual Work in 2011 and made an honorary doctorate of the University of the Republic i
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https://en.wikipedia.org/wiki/Integral%20equation
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In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: where is an integral operator acting on u. Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals. A direct comparison can be seen with the mathematical form of the general integral equation above with the general form of a differential equation which may be expressed as follows:where may be viewed as a differential operator of order i. Due to this close connection between differential and integral equations, one can often convert between the two. For example, one method of solving a boundary value problem is by converting the differential equation with its boundary conditions into an integral equation and solving the integral equation. In addition, because one can convert between the two, differential equations in physics such as Maxwell's equations often have an analog integral and differential form. See also, for example, Green's function and Fredholm theory.
Classification and overview
Various classification methods for integral equations exist. A few standard classifications include distinctions between linear and nonlinear; homogenous and inhomogeneous; Fredholm and Volterra; first order, second order, and third order; and singular and regular integral equations.
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https://en.wikipedia.org/wiki/Pseudo-spectral%20method
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Pseudo-spectral methods, also known as discrete variable representation (DVR) methods, are a class of numerical methods used in applied mathematics and scientific computing for the solution of partial differential equations. They are closely related to spectral methods, but complement the basis by an additional pseudo-spectral basis, which allows representation of functions on a quadrature grid. This simplifies the evaluation of certain operators, and can considerably speed up the calculation when using fast algorithms such as the fast Fourier transform.
Motivation with a concrete example
Take the initial-value problem
with periodic conditions . This specific example is the Schrödinger equation for a particle in a potential , but the structure is more general. In many practical partial differential equations, one has a term that involves derivatives (such as a kinetic energy contribution), and a multiplication with a function (for example, a potential).
In the spectral method, the solution is expanded in a suitable set of basis functions, for example plane waves,
Insertion and equating identical coefficients yields a set of ordinary differential equations for the coefficients,
where the elements are calculated through the explicit Fourier-transform
The solution would then be obtained by truncating the expansion to basis functions, and finding a solution for the . In general, this is done by numerical methods, such as Runge–Kutta methods. For the numerical solutions,
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https://en.wikipedia.org/wiki/Glycosylation
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Glycosylation is the reaction in which a carbohydrate (or 'glycan'), i.e. a glycosyl donor, is attached to a hydroxyl or other functional group of another molecule (a glycosyl acceptor) in order to form a glycoconjugate. In biology (but not always in chemistry), glycosylation usually refers to an enzyme-catalysed reaction, whereas glycation (also 'non-enzymatic glycation' and 'non-enzymatic glycosylation') may refer to a non-enzymatic reaction.
Glycosylation is a form of co-translational and post-translational modification. Glycans serve a variety of structural and functional roles in membrane and secreted proteins. The majority of proteins synthesized in the rough endoplasmic reticulum undergo glycosylation. Glycosylation is also present in the cytoplasm and nucleus as the O-GlcNAc modification. Aglycosylation is a feature of engineered antibodies to bypass glycosylation. Five classes of glycans are produced:
N-linked glycans attached to a nitrogen of asparagine or arginine side-chains. N-linked glycosylation requires participation of a special lipid called dolichol phosphate.
O-linked glycans attached to the hydroxyl oxygen of serine, threonine, tyrosine, hydroxylysine, or hydroxyproline side-chains, or to oxygens on lipids such as ceramide.
Phosphoglycans linked through the phosphate of a phosphoserine.
C-linked glycans, a rare form of glycosylation where a sugar is added to a carbon on a tryptophan side-chain. Aloin is one of the few naturally occurring substances.
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https://en.wikipedia.org/wiki/Spatial%20scale
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Spatial scale is a specific application of the term scale for describing or categorizing (e.g. into orders of magnitude) the size of a space (hence spatial), or the extent of it at which a phenomenon or process occurs.
For instance, in physics an object or phenomenon can be called microscopic if too small to be visible. In climatology, a micro-climate is a climate which might occur in a mountain, valley or near a lake shore. In statistics, a megatrend is a political, social, economical, environmental or technological trend which involves the whole planet or is supposed to last a very large amount of time. The concept is also used in geography, astronomy, and meteorology.
These divisions are somewhat arbitrary; where, on this table, mega- is assigned global scope, it may only apply continentally or even regionally in other contexts. The interpretations of meso- and macro- must then be adjusted accordingly.
See also
Astronomical units of length
Cosmic distance ladder
List of examples of lengths
Orders of magnitude (length)
Scale (analytical tool)
Scale (geography)
Scale (map)
Scale (ratio)
Location of Earth
References
Concepts in physics
Geography terminology
Cartography
Length
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https://en.wikipedia.org/wiki/Udi%20Manber
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Udi Manber () is an Israeli computer scientist. He is one of the authors of agrep and GLIMPSE. After a career in engineering and management, he worked on medical research.
Education
He earned both his bachelor's degree in 1975 in mathematics and his master's degree in 1978 from the Technion in Israel. At the University of Washington, he earned another master's degree in 1981 and his PhD in computer science in 1982.
Career
He has won a Presidential Young Investigator Award in 1985, 3 best-paper
awards, and the Usenix annual Software Tools User Group Award software award in 1999. Together with Gene Myers he developed the suffix array, a data structure for string matching.
He was a professor at the University of Arizona and authored several articles while there, including "Using Induction to Design Algorithms" summarizing his textbook (which remains in print) Introduction to Algorithms: A Creative Approach.
He became the chief scientist at Yahoo! in 1998.
In 2002, he joined Amazon.com, where he became "chief algorithms officer" and a vice president. He later was appointed CEO of the Amazon subsidiary company A9.com. He filed a patent on behalf of Amazon. In 2004, Google promoted sponsored listings for its own recruiting whenever someone searched for his name on Google's search engine.
In 2006, he was hired by Google as one of their vice presidents of engineering. In December 2007, he announced Knol, Google's project to create a knowledge repository.
In October 2010, he
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https://en.wikipedia.org/wiki/Ultra-high-energy%20cosmic%20ray
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In astroparticle physics, an ultra-high-energy cosmic ray (UHECR) is a cosmic ray with an energy greater than 1 EeV (1018 electronvolts, approximately 0.16 joules), far beyond both the rest mass and energies typical of other cosmic ray particles.
These particles are extremely rare; between 2004 and 2007, the initial runs of the Pierre Auger Observatory (PAO) detected 27 events with estimated arrival energies above , that is, about one such event every four weeks in the 3000 km2 area surveyed by the observatory.
An extreme-energy cosmic ray (EECR) is an UHECR with energy exceeding (about 8 joule, or the energy of a proton traveling at ≈ % the speed of light), the so-called Greisen–Zatsepin–Kuzmin limit (GZK limit). This limit should be the maximum energy of cosmic ray protons that have traveled long distances (about 160 million light years), since higher-energy protons would have lost energy over that distance due to scattering from photons in the cosmic microwave background (CMB). It follows that EECR could not be survivors from the early universe, but are cosmologically "young", emitted somewhere in the Local Supercluster by some unknown physical process.
If an EECR is not a proton, but a nucleus with A nucleons, then the GZK limit applies to its nucleons, which carry only a fraction of the total energy of the nucleus. There is evidence that these highest-energy cosmic rays might be iron nuclei, rather than the protons that make up most cosmic rays.
For an iron nucle
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https://en.wikipedia.org/wiki/Program%20derivation
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In computer science, program derivation is the derivation of a program from its specification, by mathematical means.
To derive a program means to write a formal specification, which is usually non-executable, and then apply mathematically correct rules in order to obtain an executable program satisfying that specification. The program thus obtained is then correct by construction. Program and correctness proof are constructed together.
The approach usually taken in formal verification is to first write a program, and then provide a proof that it conforms to a given specification. The main problems with this are that:
the resulting proof is often long and cumbersome;
no insight is given as to how the program was developed; it appears "like a rabbit out of a hat";
should the program happen to be incorrect in some subtle way, the attempt to verify it is likely to be long and certain to be fruitless.
Program derivation tries to remedy these shortcomings by:
keeping proofs shorter, by development of appropriate mathematical notations;
making design decisions through formal manipulation of the specification.
Terms that are roughly synonymous with program derivation are: transformational programming, algorithmics, deductive programming.
The Bird-Meertens Formalism is an approach to program derivation.
Approaches to achieving correctness in Distributed computing include research languages such as the P programming language.
See also
Automatic programming
Hoare logic
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https://en.wikipedia.org/wiki/Skipjack%20%28cipher%29
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In cryptography, Skipjack is a block cipher—an algorithm for encryption—developed by the U.S. National Security Agency (NSA). Initially classified, it was originally intended for use in the controversial Clipper chip. Subsequently, the algorithm was declassified.
History of Skipjack
Skipjack was proposed as the encryption algorithm in a US government-sponsored scheme of key escrow, and the cipher was provided for use in the Clipper chip, implemented in tamperproof hardware. Skipjack is used only for encryption; the key escrow is achieved through the use of a separate mechanism known as the Law Enforcement Access Field (LEAF).
The algorithm was initially secret, and was regarded with considerable suspicion by many for that reason. It was declassified on 24 June 1998, shortly after its basic design principle had been discovered independently by the public cryptography community.
To ensure public confidence in the algorithm, several academic researchers from outside the government were called in to evaluate the algorithm. The researchers found no problems with either the algorithm itself or the evaluation process. Moreover, their report gave some insight into the (classified) history and development of Skipjack:
In March 2016, NIST published a draft of its cryptographic standard which no longer certifies Skipjack for US government applications.
Description
Skipjack uses an 80-bit key to encrypt or decrypt 64-bit data blocks. It is an unbalanced Feistel network with 32 round
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https://en.wikipedia.org/wiki/Legendre%20transform%20%28integral%20transform%29
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In mathematics, Legendre transform is an integral transform named after the mathematician Adrien-Marie Legendre, which uses Legendre polynomials as kernels of the transform. Legendre transform is a special case of Jacobi transform.
The Legendre transform of a function is
The inverse Legendre transform is given by
Associated Legendre transform
Associated Legendre transform is defined as
The inverse Legendre transform is given by
Some Legendre transform pairs
References
Integral transforms
Mathematical physics
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https://en.wikipedia.org/wiki/Particle%20in%20a%20ring
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In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring (technically, whose configuration space is the circle ) is
Wave function
Using polar coordinates on the 1-dimensional ring of radius R, the wave function depends only on the angular coordinate, and so
Requiring that the wave function be periodic in with a period (from the demand that the wave functions be single-valued functions on the circle), and that they be normalized leads to the conditions
,
and
Under these conditions, the solution to the Schrödinger equation is given by
Energy eigenvalues
The energy eigenvalues are quantized because of the periodic boundary conditions, and they are required to satisfy
, or
The eigenfunction and eigenenergies are
where
Therefore, there are two degenerate quantum states for every value of (corresponding to ). Therefore, there are 2n+1 states with energies up to an energy indexed by the number n.
The case of a particle in a one-dimensional ring is an instructive example when studying the quantization of angular momentum for, say, an electron orbiting the nucleus. The azimuthal wave functions in that case are identical to the energy eigenfunctions of the particle on a ring.
The statement that any wavefunction for the particle on a ring can be written as a superposition of energy eigenfunctions is exactly identical to the Fourier theorem a
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https://en.wikipedia.org/wiki/Diving%20physics
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Diving physics, or the physics of underwater diving is the basic aspects of physics which describe the effects of the underwater environment on the underwater diver and their equipment, and the effects of blending, compressing, and storing breathing gas mixtures, and supplying them for use at ambient pressure. These effects are mostly consequences of immersion in water, the hydrostatic pressure of depth and the effects of pressure and temperature on breathing gases. An understanding of the physics is useful when considering the physiological effects of diving, breathing gas planning and management, diver buoyancy control and trim, and the hazards and risks of diving.
Changes in density of breathing gas affect the ability of the diver to breathe effectively, and variations in partial pressure of breathing gas constituents have profound effects on the health and ability to function underwater of the diver.
Aspects of physics with particular relevance to diving
The main laws of physics that describe the influence of the underwater diving environment on the diver and diving equipment include:
Buoyancy
Archimedes' principle (Buoyancy) - Ignoring the minor effect of surface tension, an object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Thus, when in water, the weight of the volume of water displaced as compared to the weight of the diver's body and the diver's equipment, determine whether the dive
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https://en.wikipedia.org/wiki/Geometric%20hashing
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In computer science, geometric hashing is a method for efficiently finding two-dimensional objects represented by discrete points that have undergone an affine transformation, though extensions exist to other object representations and transformations. In an off-line step, the objects are encoded by treating each pair of points as a geometric basis. The remaining points can be represented in an invariant fashion with respect to this basis using two parameters. For each point, its quantized transformed coordinates are stored in the hash table as a key, and indices of the basis points as a value. Then a new pair of basis points is selected, and the process is repeated. In the on-line (recognition) step, randomly selected pairs of data points are considered as candidate bases. For each candidate basis, the remaining data points are encoded according to the basis and possible correspondences from the object are found in the previously constructed table. The candidate basis is accepted if a sufficiently large number of the data points index a consistent object basis.
Geometric hashing was originally suggested in computer vision for object recognition in 2D and 3D, but later was applied to different problems such as structural alignment of proteins.
Geometric hashing in computer vision
Geometric hashing is a method used for object recognition. Let’s say that we want to check if a model image can be seen in an input image. This can be accomplished with geometric hashing. The meth
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https://en.wikipedia.org/wiki/MoD%20Lyneham
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Ministry of Defence Lyneham or MOD Lyneham is a Ministry of Defence site in Wiltshire, England, about north-east of Chippenham and south-west of Swindon. The site houses the Defence School of Electronic and Mechanical Engineering. Also here is Prince Philip Barracks, housing the regimental headquarters of the Royal Electrical and Mechanical Engineers (REME), 8 Training Battalion REME and the REME Museum.
Previously, the site was RAF Lyneham which closed on 31 December 2012.
History
RAF Lyneham
RAF Lyneham was built in 1939, necessitating the demolition of Lyneham Court manor house, the buildings of Cranley Farm and the village's tennis courts. The airfield itself was initially a grass landing area although the RAF always planned to lay hard runways. Hangars and other buildings were dispersed around the site to avoid creating one large target for an aerial enemy.
The station was opened on 18 May 1940 as No. 33 Maintenance Unit (33MU), with no ceremony and few personnel. During the war the station's squadrons operated regular transport schedules to Gibraltar
With the increase in air transport operations in the RAF, as opposed to ferrying, Transport Command was formed in March 1943. Lyneham, in No. 46 Group RAF, was its main airfield in the south, and as well as sending its own aircraft overseas, acted as the clearance airfield for planning, diplomatic clearance, customs and briefing purposes for transport aeroplanes from other stations flying abroad. It also provided
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https://en.wikipedia.org/wiki/Giovanni%20Alfonso%20Borelli
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Giovanni Alfonso Borelli (; 28 January 1608 – 31 December 1679) was a Renaissance Italian physiologist, physicist, and mathematician. He contributed to the modern principle of scientific investigation by continuing Galileo's practice of testing hypotheses against observation. Trained in mathematics, Borelli also made extensive studies of Jupiter's moons, the mechanics of animal locomotion and, in microscopy, of the constituents of blood. He also used microscopy to investigate the stomatal movement of plants, and undertook studies in medicine and geology. During his career, he enjoyed the patronage of Queen Christina of Sweden.
Biography
Giovanni Borelli was born on 28 January 1608 in the district of Castel Nuovo, in Naples. He was the son of Spanish infantryman Miguel Alfonso and a local woman named Laura Porello (alternately Porelli or Borelli.)
Borelli eventually traveled to Rome where he studied under Benedetto Castelli, matriculating in mathematics at Sapienza University of Rome. Sometime before 1640 he was appointed Professor of Mathematics at Messina. In the early 1640s, he met Galileo Galilei in Florence. While it is likely that they remained acquaintances, Galileo rejected considerations to nominate Borelli as head of Mathematics at the University of Pisa when he left the post himself. Borelli would attain this post in 1656. It was there that he first met the Italian anatomist Marcello Malpighi.
Borelli and Malpighi were both founder-members of the short-lived Acca
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https://en.wikipedia.org/wiki/Abram%20Ioffe
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Abram Fedorovich Ioffe (; – 14 October 1960) was a prominent Soviet physicist. He received the Stalin Prize (1942), the Lenin Prize (1960) (posthumously), and the Hero of Socialist Labor (1955). Ioffe was an expert in various areas of solid state physics and electromagnetism. He established research laboratories for radioactivity, superconductivity, and nuclear physics, many of which became independent institutes.
Biography
Ioffe was born into a middle-class Ukrainian Jewish family in the small town of Romny, Russian Empire (now in Sumy Oblast, Ukraine). After graduating from Saint Petersburg State Institute of Technology in 1902, he spent two years as an assistant to Wilhelm Röntgen in his Munich laboratory. Ioffe completed his Ph.D. at Munich University in 1905. His dissertation studied the electrical conductivity/electrical stress of dielectric crystals.
After 1906, Ioffe worked in the Saint Petersburg (from 1924 Leningrad) Polytechnical Institute where he eventually became a professor. In 1911 he (independently of Millikan) determined the charge of an electron. In this experiment, the microparticles of zinc metal were irradiated with ultraviolet light to eject the electrons. The charged microparticles were then balanced in an electric field against gravity so that their charges could be determined (published in 1913). In 1911 Ioffe converted from Judaism to Lutheranism and married a non-Jewish woman. In 1913 he attained the title of Magister of Philosophy and in 1915
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https://en.wikipedia.org/wiki/Yakov%20Zeldovich
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Yakov Borisovich Zeldovich (, ; 8 March 1914 – 2 December 1987), also known as YaB, was a leading Soviet physicist of Belarusian origin, who is known for his prolific contributions in physical cosmology, physics of thermonuclear reactions, combustion, and hydrodynamical phenomena.
From 1943, Zeldovich, a self-taught physicist, started his career by playing a crucial role in the development of the former Soviet program of nuclear weapons. In 1963, he returned to academia to embark on pioneering contributions on the fundamental understanding of the thermodynamics of black holes and expanding the scope of physical cosmology.
Biography
Early life and education
Yakov Zeldovich was born into a Belarusian Jewish family in his grandfather's house in Minsk. However, in mid-1914, the Zeldovich family moved to Saint Petersburg. They resided there until August 1941, when the family was evacuated together with the faculty of the Institute of Chemical Physics to Kazan to avoid the Axis Invasion of the Soviet Union. They remained in Kazan until the summer of 1943, when Zeldovich moved to Moscow.
His father, Boris Naumovich Zeldovich, was a lawyer; his mother, Anna Petrovna Zeldovich (née Kiveliovich), a translator from French to Russian, was a member of the Writer's Union. Despite being born into a devoted and religious Jewish family, Zeldovich was an "absolute atheist".
Zeldovich was an autodidact. He was regarded as having a remarkably versatile intellect, and during his life he e
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https://en.wikipedia.org/wiki/Symbol%20table
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In computer science, a symbol table is a data structure used by a language translator such as a compiler or interpreter, where each identifier (or symbol), constant, procedure and function in a program's source code is associated with information relating to its declaration or appearance in the source. In other words, the entries of a symbol table store the information related to the entry's corresponding symbol.
Background
A symbol table may only exist in memory during the translation process, or it may be embedded in the output of the translation, such as in an ABI object file for later use. For example, it might be used during an interactive debugging session, or as a resource for formatting a diagnostic report during or after execution of a program.
Description
The minimum information contained in a symbol table used by a translator and intermediate representation (IR) includes the symbol's name and its location or address. For a compiler targeting a platform with a concept of relocatability, it will also contain relocatability attributes (absolute, relocatable, etc.) and needed relocation information for relocatable symbols. Symbol tables for high-level programming languages may store the symbol's type: string, integer, floating-point, etc., its size, and its dimensions and its bounds. Not all of this information is included in the output file, but may be provided for use in debugging. In many cases, the symbol's cross-reference information is stored with or linked to
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https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock%20method
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In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.
The Hartree–Fock method often assumes that the exact N-body wave function of the system can be approximated by a single Slater determinant (in the case where the particles are fermions) or by a single permanent (in the case of bosons) of N spin-orbitals. By invoking the variational method, one can derive a set of N-coupled equations for the N spin orbitals. A solution of these equations yields the Hartree–Fock wave function and energy of the system. Hartree–Fock approximation is an instance of mean-field theory, where neglecting higher-order fluctuations in order parameter allows replacing interaction terms with quadratic terms, obtaining exactly solvable Hamiltonian.
Especially in the older literature, the Hartree–Fock method is also called the self-consistent field method (SCF). In deriving what is now called the Hartree equation as an approximate solution of the Schrödinger equation, Hartree required the final field as computed from the charge distribution to be "self-consistent" with the assumed initial field. Thus, self-consistency was a requirement of the solution. The solutions to the non-linear Hartree–Fock equations also behave as if each particle is subjected to the mean field created by all other particles (see the Fock operator below), and hence the termino
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https://en.wikipedia.org/wiki/Particle%20Physics%20and%20Astronomy%20Research%20Council
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The Particle Physics and Astronomy Research Council (PPARC) was one of a number of research councils in the United Kingdom. It directed, coordinated and funded research in particle physics and astronomy for the people of the UK. Its head office was at Polaris House in Swindon, Wiltshire, but it also operated three scientific sites: the UK Astronomy Technology Centre (UK ATC) in Edinburgh, the Isaac Newton Group of Telescopes (ING) in La Palma and the Joint Astronomy Centre (JAC) in Hawaii. It published the Frontiers magazine three times a year, containing news and highlights of the research and outreach programmes it supports.
The PPARC was formed in April 1994 when the Science and Engineering Research Council was split into several organizations; other products of the split included the Engineering and Physical Sciences Research Council (EPSRC) and the Biotechnology and Biological Sciences Research Council (BBSRC). In April 2007, it merged with the Council for the Central Laboratory of the Research Councils (CCLRC) and the nuclear physics portion of the EPSRC to form the new Science and Technology Facilities Council (STFC).
Frontiers magazine
PPARC previously published a magazine called Frontiers, .
See also
List of astronomical societies
References
External links
PPARC website archive (2007)
Frontiers magazine website archive (2007)
Research Councils UK
British astronomy organisations
Research councils
Scientific organizations established in 1994
Scientific org
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https://en.wikipedia.org/wiki/Oscillation%20%28mathematics%29
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In mathematics, the oscillation of a function or a sequence is a number that quantifies how much that sequence or function varies between its extreme values as it approaches infinity or a point. As is the case with limits, there are several definitions that put the intuitive concept into a form suitable for a mathematical treatment: oscillation of a sequence of real numbers, oscillation of a real-valued function at a point, and oscillation of a function on an interval (or open set).
Definitions
Oscillation of a sequence
Let be a sequence of real numbers. The oscillation of that sequence is defined as the difference (possibly infinite) between the limit superior and limit inferior of :
.
The oscillation is zero if and only if the sequence converges. It is undefined if and are both equal to +∞ or both equal to −∞, that is, if the sequence tends to +∞ or −∞.
Oscillation of a function on an open set
Let be a real-valued function of a real variable. The oscillation of on an interval in its domain is the difference between the supremum and infimum of :
More generally, if is a function on a topological space (such as a metric space), then the oscillation of on an open set is
Oscillation of a function at a point
The oscillation of a function of a real variable at a point is defined as the limit as of the oscillation of on an -neighborhood of :
This is the same as the difference between the limit superior and limit inferior of the function at , provided the poi
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https://en.wikipedia.org/wiki/Carlo%20Matteucci
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Carlo Matteucci (20 or 21 June 1811 – 25 June 1868) was an Italian physicist and neurophysiologist who was a pioneer in the study of bioelectricity.
Biography
Carlo Matteucci was born at Forlì, in the province of Romagna, to Vincenzo Matteucci, a physician, and Chiara Folfi. He studied mathematics at the University of Bologna from 1825 to 1828, receiving his doctorate in 1829. From 1829 to 1831, he studied at the École Polytechnique in Paris, France. Upon returning to Italy, Matteucci studied at Bologna (1832), Florence, Ravenna (1837) and Pisa. He established himself as the head of the laboratory of the Hospital of Ravenna and became a professor of physics at the local college. In 1840, by recommendation of François Arago (1786–1853), his teacher at the École Polytechnique, to the Grand-Duke of Tuscany, Matteucci accepted a post of professor of physics at the University of Pisa.
Instigated by the work of Luigi Galvani (1737–1798) on bioelectricity, Matteucci began in 1830 a series of experiments which he pursued until his death in 1865. Using a sensitive galvanometer of Leopoldo Nobili, he was able to prove that injured excitable biological tissues generated direct electrical currents, and that they could be summed up by adding elements in series, like in Alessandro Volta’s (1745-1827) electric pile. Thus, Mateucci was able to develop what he called a "rheoscopic frog", by using the cut nerve of a frog's leg and its attached muscle as a kind of sensitive electricity detec
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https://en.wikipedia.org/wiki/Heinrich%20Gustav%20Magnus
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Heinrich Gustav Magnus (; 2 May 1802 – 4 April 1870) was a notable German experimental scientist. His training was mostly in chemistry but his later research was mostly in physics. He spent the great bulk of his career at the University of Berlin, where he is remembered for his laboratory teaching as much as for his original research. He did not use his first given name, and was known throughout his life as Gustav Magnus.
Education
Magnus was born in Berlin to a Jewish family, his father a wealthy merchant. In his youth he received private instruction in mathematics and natural science. At the University of Berlin he studied chemistry and physics, 1822–27, and obtained a doctorate for a dissertation on tellurium in 1827. His doctoral adviser was Eilhard Mitscherlich. He then went to Stockholm for a year as a visiting research fellow at the laboratory of Jöns Jakob Berzelius (who was a personal friend of Mitscherlich). That was followed by a year in Paris at the laboratory of Joseph Louis Gay-Lussac and Louis Jacques Thénard. Therefore, he had a first-rate education in experimental science when in 1831 he was appointed lecturer in physics and technology at the University of Berlin. In 1834 he became assistant professor, and in 1845 was appointed full professor, and later he was elected the dean of the faculty.
Teaching
As a teacher at the University of Berlin his success was rapid and extraordinary. His lucid style and the perfection of his experimental demonstrations drew t
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https://en.wikipedia.org/wiki/Jean-Antoine%20Chaptal
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Jean-Antoine Chaptal, comte de Chanteloup (5 June 1756 – 29 July 1832) was a French chemist, physician, agronomist, industrialist, statesman, educator and philanthropist. His multifaceted career unfolded during one of the most brilliant periods in French science. In chemistry it was the time of Antoine Lavoisier, Claude-Louis Berthollet, Louis Guyton de Morveau, Antoine-François Fourcroy and Joseph Gay-Lussac. Chaptal made his way into this elite company in Paris beginning in the 1780s, and established his credentials as a serious scientist most definitely with the publication of his first major scientific treatise, the Ėléments de chimie (3 vols, Montpellier, 1790). His treatise brought the term "nitrogen" into the revolutionary new chemical nomenclature developed by Lavoisier. By 1795, at the newly established École Polytechnique in Paris, Chaptal shared the teaching of courses in pure and applied chemistry with Claude-Louis Berthollet, the doyen of the science. In 1798, Chaptal was elected a member of the prestigious Chemistry Section of the Institut de France. He became president of the section in 1802 soon after Napoleon appointed him Minister of Interior (6 November 1800). Chaptal was a key figure in the early industrialization in France under Napoleon and during the Bourbon Restoration. He was a founder and first president in 1801 of the important Society for the Encouragement of National Industry and a key organizer of industrial expositions held in Paris in 1801 and
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https://en.wikipedia.org/wiki/Fluid%20parcel
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In fluid dynamics, a fluid parcel, also known as a fluid element or material element, is an infinitesimal volume of fluid, identifiable throughout its dynamic history while moving with the fluid flow. As it moves, the mass of a fluid parcel remains constant, while—in a compressible flow—its volume may change, and its shape changes due to distortion by the flow. In an incompressible flow, the volume of the fluid parcel is also a constant (isochoric flow).
Material surfaces and material lines are the corresponding notions for surfaces and lines, respectively.
The mathematical concept of a fluid parcel is closely related to the description of fluid motion—its kinematics and dynamics—in a Lagrangian frame of reference. In this reference frame, fluid parcels are labelled and followed through space and time. But also in the Eulerian frame of reference the notion of fluid parcels can be advantageous, for instance in defining the material derivative, streamlines, streaklines, and pathlines; or for determining the Stokes drift.
The fluid parcels, as used in continuum mechanics, are to be distinguished from microscopic particles (molecules and atoms) in physics. Fluid parcels describe the average velocity and other properties of fluid particles, averaged over a length scale which is large compared to the mean free path, but small compared to the typical length scales of the specific flow under consideration. This requires the Knudsen number to be small, as is also a pre-requisite fo
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https://en.wikipedia.org/wiki/Ekman%20number
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The Ekman number (Ek) is a dimensionless number used in fluid dynamics to describe the ratio of viscous forces to Coriolis forces. It is frequently used in describing geophysical phenomena in the oceans and atmosphere in order to characterise the ratio of viscous forces to the Coriolis forces arising from planetary rotation. It is named after the Swedish oceanographer Vagn Walfrid Ekman.
When the Ekman number is small, disturbances are able to propagate before decaying owing to low frictional effects. The Ekman number also describes the order of magnitude for the thickness of an Ekman layer, a boundary layer in which viscous diffusion is balanced by Coriolis effects, rather than the usual convective inertia.
Definitions
It is defined as:
- where D is a characteristic (usually vertical) length scale of a phenomenon; ν, the kinematic eddy viscosity; Ω, the angular velocity of planetary rotation; and φ, the latitude. The term 2 Ω sin φ is the Coriolis frequency.
It is given in terms of the kinematic viscosity, ν; the angular velocity, Ω; and a characteristic length scale, L.
There do appear to be some differing conventions in the literature.
Tritton gives:
In contrast, the NRL Plasma Formulary gives:
where Ro is the Rossby number and Re is the Reynolds number.
These equations can generally not be used in oceanography. An estimation of the viscous terms of Navier-Stokes equation (with eventually the Eddy Viscosity) and of the Coriolis terms needs to be done.
References
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https://en.wikipedia.org/wiki/Vagn%20Walfrid%20Ekman
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Vagn Walfrid Ekman (3 May 1874 – 9 March 1954) was a Swedish oceanographer.
Born in Stockholm to Fredrik Laurentz Ekman, himself an oceanographer, he became committed to oceanography while studying physics at the University of Uppsala and, in particular, on hearing Vilhelm Bjerknes lecture on fluid dynamics.
During the expedition of the Fram, Fridtjof Nansen had observed that icebergs tend to drift not in the direction of the prevailing wind but at an angle of 20°-40° to the right. Bjerknes invited Ekman, still a student, to investigate the problem. Later, in 1905, Ekman published his theory of the Ekman spiral which explains the phenomenon in terms of the balance between frictional effects in the ocean and the Coriolis force, which arises from moving objects in a rotating environment, like planetary rotation.
On completing his doctorate in Uppsala in 1902, Ekman joined the International Laboratory for Oceanographic Research, Oslo where he worked for seven years, not only extending his theoretical work but also developing experimental techniques and instruments such as the Ekman current meter and Ekman water bottle.
From 1910 to 1939 he continued his theoretical and experimental work at the University of Lund, where he was professor of mechanics and mathematical physics. He was elected a member of the Royal Swedish Academy of Sciences in 1935.
A gifted amateur bass singer, pianist, and composer, he continued working right up to his death in Gostad, near Stockaryd, Sweden
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https://en.wikipedia.org/wiki/Contact%20geometry
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In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently, such a distribution may be given (at least locally) as the kernel of a differential one-form, and the non-integrability condition translates into a maximal non-degeneracy condition on the form. These conditions are opposite to two equivalent conditions for 'complete integrability' of a hyperplane distribution, i.e. that it be tangent to a codimension one foliation on the manifold, whose equivalence is the content of the Frobenius theorem.
Contact geometry is in many ways an odd-dimensional counterpart of symplectic geometry, a structure on certain even-dimensional manifolds. Both contact and symplectic geometry are motivated by the mathematical formalism of classical mechanics, where one can consider either the even-dimensional phase space of a mechanical system or constant-energy hypersurface, which, being codimension one, has odd dimension.
Applications
Like symplectic geometry, contact geometry has broad applications in physics, e.g. geometrical optics, classical mechanics, thermodynamics, geometric quantization, integrable systems and to control theory. Contact geometry also has applications to low-dimensional topology; for example, it has been used by Kronheimer and Mrowka to prove the property P conjecture, by Michael Hutchings to define an invar
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https://en.wikipedia.org/wiki/Georg%20Christoph%20Lichtenberg
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Georg Christoph Lichtenberg (1 July 1742 – 24 February 1799) was a German physicist, satirist, and Anglophile. As a scientist, he was the first to hold a professorship explicitly dedicated to experimental physics in Germany. He is remembered for his posthumously published notebooks, which he himself called , a description modelled on the English bookkeeping term "waste books" or "scrapbooks", and for his discovery of tree-like electrical discharge patterns now called Lichtenberg figures.
Life
Georg Christoph Lichtenberg was born in Ober-Ramstadt near Darmstadt, Landgraviate of Hesse-Darmstadt, the youngest of 17 children. His father, Johann Conrad Lichtenberg, was a pastor ascending through the ranks of the church hierarchy, who eventually became superintendent for Darmstadt. Unusually for a clergyman in those times, he seems to have possessed a fair amount of scientific knowledge. Lichtenberg was educated at his parents' house until 10 years old, when he joined the Lateinschule in Darmstadt. His intelligence became obvious at a very early age. He wanted to study mathematics, but his family could not afford to pay for lessons. In 1762, his mother applied to Ludwig VIII, Landgrave of Hesse-Darmstadt, who granted sufficient funds. In 1763, Lichtenberg entered the University of Göttingen.
In 1769 he became extraordinary professor of physics, and six years later ordinary professor. He held this post till his death. Invited by his students, he visited England twice, from Easter
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https://en.wikipedia.org/wiki/1634%20in%20science
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The year 1634 in science and technology involved some significant events.
Astronomy
Johannes Kepler's fictional account of the view from the Moon Somnium (written 1608) is published posthumously by his son.
Botany
Thomas Johnson begins publishing Mercurius Botanicus, including a list of indigenous British plants.
Mathematics
Gilles de Roberval shows that the area under a cycloid is three times the area of its generating circle.
Medicine
Louise Bourgeois Boursier publishes her Collection of Secrets on obstetrics in Paris, including techniques such as podalic version.
Zoology
Publication of Insectorum sive Minimorum Animalium Theatrum in London, compiled posthumously from the work of Edward Wotton, Conrad Gesner and Thomas Penny by Thomas Muffet and prepared for publication by Théodore de Mayerne.
Institutions
The Académie Française is formed by Cardinal Richelieu (it will be formally established in 1635).
Births
Deaths
February 15 – Wilhelm Fabry, German-born surgeon (born 1560)
June 26 – Nikolaus Ager, French botanist (born 1568)
Marin le Bourgeoys, French inventor and artist (born c. 1550) (approximate date)
Martin Llewellyn, British cartographer (born 1565?)
References
17th century in science
1630s in science
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https://en.wikipedia.org/wiki/1636%20in%20science
|
The year 1636 in science and technology involved some significant events.
Mathematics
Pierre de Fermat begins to circulate his work in analytic geometry in manuscript.
Muhammad Baqir Yazdi and René Descartes independently discover the pair of amicable numbers 9,363,584 and 9,437,056.
Physics
Marin Mersenne publishes his Traité de l'harmonie universelle, containing Mersenne's laws describing the frequency of oscillation of a stretched string.
Publications
Daniel Schwenter publishes Delicia Physic-Mathematicae, including a description of a quill pen with an ink reservoir.
Births
Father Jacques Marquette, French explorer (died 1675)
December 26 – Justine Siegemund, German midwife (died 1705)
Deaths
February 22 – Sanctorius, Italian physiologist (born 1561)
Louise Bourgeois Boursier, French Royal midwife (born 1563)
Michal Sedziwój, Polish alchemist (born 1566)
References
17th century in science
1630s in science
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https://en.wikipedia.org/wiki/1653%20in%20science
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The year 1653 in science and technology involved some significant events.
Biology
Jan van Kessel paints a series of pictures of insects and fruit.
Mathematics
Blaise Pascal publishes his Traité du triangle arithmétique in which he describes a convenient tabular presentation for binomial coefficients, now called Pascal's triangle.
Physics
Blaise Pascal publishes his Treatise on the Equilibrium of Liquids in which he explains his law of pressure.
Births
January 16 – Johann Conrad Brunner, Swiss anatomist (died 1727)
March 24 – Joseph Sauveur, French mathematician and acoustician (died 1716)
Deaths
Jan Stampioen, Dutch mathematician (born 1610) (gunpowder explosion)
References
17th century in science
1650s in science
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https://en.wikipedia.org/wiki/1649%20in%20science
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The year 1649 in science and technology involved some significant events.
Biology
Publication of John Jonston's Historiae naturalis in Frankfurt begins with De piscibus et cetis.
Technology
Johann Schröder publishes two methods for the production of elemental Arsenic.
Mathematics
Frans van Schooten publishes the first Latin version of René Descartes' La Géométrie. His commentary makes the work understandable to the broader mathematical community. The Latin version also includes Florimond de Beaune's Notes brièves, the first important introduction to Descartes' cartesian geometry.
Events
The semi-formal Oxford Philosophical Club of natural philosophers begins to meet; it is a predecessor of the Royal Society of London.
Births
March 3 – John Floyer, English physician (died 1734)
Deaths
September 6 – Robert Dudley, English-born navigator (born 1574)
References
17th century in science
1640s in science
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https://en.wikipedia.org/wiki/Frank%20Rowlett
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Frank Byron Rowlett (May 2, 1908 – June 29, 1998) was an American cryptologist.
Life and career
Rowlett was born in Rose Hill, Lee County, Virginia and attended Emory & Henry College in Emory, Virginia. In 1929 he received a bachelor's degree in mathematics and chemistry. He was hired by William Friedman as a "junior cryptanalyst" for the Signals Intelligence Service (SIS) on April Fools' Day 1930; shortly after, he was followed into SIS by Abraham Sinkov and Solomon Kullback.
During the 1930s, after a lengthy period of training, Rowlett and his colleagues compiled codes and ciphers for use by the U.S. Army and began solving a number of foreign, notably Japanese, systems. In the mid-1930s, they solved the first Japanese machine for encipherment of diplomatic communications, known to the Americans as RED. In 1939–40, Rowlett led the SIS effort that solved a more sophisticated Japanese diplomatic machine cipher, codenamed PURPLE by the U.S. Once, when asked what his greatest contribution to that effort had been, Rowlett said, "I was the one who believed it could be done." Rowlett supervised cryptanalyst Virginia Dare Aderholdt, who decrypted the Japanese surrender message, August 14, 1945.
Rowlett also played a crucial role in protecting American communications during World War II, making fundamental and innovative contributions to the design of the SIGABA cipher machine. Its security was an important factor in saving American lives in combat. In 1964, Congress awarded Rowle
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https://en.wikipedia.org/wiki/Abraham%20Sinkov
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Abraham Sinkov (August 22, 1907 – January 19, 1998) was a US cryptanalyst. An early employee of the U.S. Army's Signals Intelligence Service, he held several leadership positions during World War II, transitioning to the new National Security Agency after the war, where he became a deputy director. After retiring in 1962, he taught mathematics at Arizona State University.
Biography
Sinkov was the son of Jewish immigrants Morris (Mordechai Eliezer) and Ethel (née Etel Constantinowsky) from Alexandria, Russia, which is now Oleksandriya, Kirovohrad Oblast, Ukraine. Sinkov was born in Philadelphia, but grew up in Brooklyn. After graduating from Boys High School he took his B.S. in mathematics from City College of New York. (By coincidence, one of his close friends at Boys High and CCNY was Solomon Kullback). Mr. Sinkov taught in New York City schools but was unhappy with the working conditions and anxious to use his mathematics knowledge in practical ways.
Early career
The opportunity for a career change came in 1930. Sinkov and Kullback took the Civil Service examination and placed high. Both received mysterious letters from Washington asking about their knowledge of foreign languages. Sinkov knew French and Kullback, Spanish. This was acceptable to their prospective employer, and they were offered positions as junior cryptanalysts. Although neither was quite certain what a cryptanalyst did, they accepted.
The small Signals Intelligence Service (SIS) organization (Sinkov an
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https://en.wikipedia.org/wiki/Radiant%20energy
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In physics, and in particular as measured by radiometry, radiant energy is the energy of electromagnetic and gravitational radiation. As energy, its SI unit is the joule (J). The quantity of radiant energy may be calculated by integrating radiant flux (or power) with respect to time. The symbol Qe is often used throughout literature to denote radiant energy ("e" for "energetic", to avoid confusion with photometric quantities). In branches of physics other than radiometry, electromagnetic energy is referred to using E or W. The term is used particularly when electromagnetic radiation is emitted by a source into the surrounding environment. This radiation may be visible or invisible to the human eye.
Terminology use and history
The term "radiant energy" is most commonly used in the fields of radiometry, solar energy, heating and lighting, but is also sometimes used in other fields (such as telecommunications). In modern applications involving transmission of power from one location to another, "radiant energy" is sometimes used to refer to the electromagnetic waves themselves, rather than their energy (a property of the waves). In the past, the term "electro-radiant energy" has also been used.
The term "radiant energy" also applies to gravitational radiation. For example, the first gravitational waves ever observed were produced by a black hole collision that emitted about 5.3 joules of gravitational-wave energy.
Analysis
Because electromagnetic (EM) radiation can be concep
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https://en.wikipedia.org/wiki/CAG
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CAG or cag may refer to:
Cagoule, a lightweight weatherproof raincoat or anorak with a hood
CAG promoter, used in molecular biology
CAG, a codon for the amino acid glutamine
Cagliari–Elmas Airport (IATA airport code: CAG) in Cagliari, Sardinia, Italy
Canadian Association of Geographers
Chassis Air Guide, in computers is Intel's thermal solution to PC chassis
Cheap Ass Gamer, an online BBS community
China National Aviation Corporation (ICAO airline designator: CAG)
Chinese Academy of Governance, a training center for middle and senior government officials of the Chinese government
Civil Affairs Group, an acronym for United States Marine Corps Civil Affairs Groups
Closed angle glaucoma, a type of eye disease
Colegio Americano de Guatemala (American School of Guatemala)
Combat Applications Group, an abbreviation of the former official name of Delta Force, a United States Army Special Operations Command military unit
Commander, Air Group, the informal name for the senior US Navy officer of a carrier air wing
Commentaria in Aristotelem Graeca, a series of original-language texts of ancient and Byzantine commentaries on Aristotle
Communication Arts Guild, an organisation dedicated to the Indian advertising industry
Comptroller and Auditor General, a senior civil servant charged with improving government accountability
Computer-assisted gaming, used for example for PnP role-playing games
ConAgra Foods Inc., stock ticker on New York Stock Exchange
Consensus audi
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https://en.wikipedia.org/wiki/Expressed%20sequence%20tag
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In genetics, an expressed sequence tag (EST) is a short sub-sequence of a cDNA sequence. ESTs may be used to identify gene transcripts, and were instrumental in gene discovery and in gene-sequence determination. The identification of ESTs has proceeded rapidly, with approximately 74.2 million ESTs now available in public databases (e.g. GenBank 1 January 2013, all species). EST approaches have largely been superseded by whole genome and transcriptome sequencing and metagenome sequencing.
An EST results from one-shot sequencing of a cloned cDNA. The cDNAs used for EST generation are typically individual clones from a cDNA library. The resulting sequence is a relatively low-quality fragment whose length is limited by current technology to approximately 500 to 800 nucleotides. Because these clones consist of DNA that is complementary to mRNA, the ESTs represent portions of expressed genes. They may be represented in databases as either cDNA/mRNA sequence or as the reverse complement of the mRNA, the template strand.
One can map ESTs to specific chromosome locations using physical mapping techniques, such as radiation hybrid mapping, HAPPY mapping, or FISH. Alternatively, if the genome of the organism that originated the EST has been sequenced, one can align the EST sequence to that genome using a computer.
The current understanding of the human set of genes () includes the existence of thousands of genes based solely on EST evidence. In this respect, ESTs have become a tool t
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https://en.wikipedia.org/wiki/Nick%20Pippenger
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Nicholas John Pippenger is a researcher in computer science. He has produced a number of fundamental results many of which are being widely used in the field of theoretical computer science, database processing and compiler optimization. He has also achieved the rank of IBM Fellow at Almaden IBM Research Center in San Jose, California. He has taught at the University of British Columbia in Vancouver, British Columbia, Canada and at Princeton University in the US. In the Fall of 2006 Pippenger joined the faculty of Harvey Mudd College.
Pippenger holds a B.S. in Natural Sciences from Shimer College and a PhD from the Massachusetts Institute of Technology. He is married to Maria Klawe, President of Harvey Mudd College. In 1997 he was inducted as a Fellow of the Association for Computing Machinery. In 2013 he became a fellow of the American Mathematical Society.
The complexity class, Nick's Class (NC), of problems quickly solvable on a parallel computer, was named by Stephen Cook after Nick Pippenger for his research on circuits with polylogarithmic depth and polynomial size.
Pippenger became one of the most recent mathematicians to write a technical article in Latin, when he published a brief derivation of a new formula for e, whereby the Wallis product for is modified by taking roots of its terms:
References
External links
Pippenger's web page at HMC
Harvey Mudd College faculty
IBM Fellows
Fellows of the Association for Computing Machinery
Fellows of the American Mathem
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https://en.wikipedia.org/wiki/Metabolite
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In biochemistry, a metabolite is an intermediate or end product of metabolism.
The term is usually used for small molecules. Metabolites have various functions, including fuel, structure, signaling, stimulatory and inhibitory effects on enzymes, catalytic activity of their own (usually as a cofactor to an enzyme), defense, and interactions with other organisms (e.g. pigments, odorants, and pheromones).
A primary metabolite is directly involved in normal "growth", development, and reproduction. Ethylene exemplifies a primary metabolite produced large-scale by industrial microbiology.
A secondary metabolite is not directly involved in those processes, but usually has an important ecological function. Examples include antibiotics and pigments such as resins and terpenes etc.
Some antibiotics use primary metabolites as precursors, such as actinomycin, which is created from the primary metabolite tryptophan. Some sugars are metabolites, such as fructose or glucose, which are both present in the metabolic pathways.
Examples of primary metabolites produced by industrial microbiology include:
The metabolome forms a large network of metabolic reactions, where outputs from one enzymatic chemical reaction are inputs to other chemical reactions.
Metabolites from chemical compounds, whether inherent or pharmaceutical, form as part of the natural biochemical process of degrading and eliminating the compounds.
The rate of degradation of a compound is an important determinant of the du
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https://en.wikipedia.org/wiki/Omics
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The branches of science known informally as omics are various disciplines in biology whose names end in the suffix -omics, such as genomics, proteomics, metabolomics, metagenomics, phenomics and transcriptomics. Omics aims at the collective characterization and quantification of pools of biological molecules that translate into the structure, function, and dynamics of an organism or organisms.
The related suffix -ome is used to address the objects of study of such fields, such as the genome, proteome or metabolome respectively. The suffix -ome as used in molecular biology refers to a totality of some sort; it is an example of a "neo-suffix" formed by abstraction from various Greek terms in , a sequence that does not form an identifiable suffix in Greek.
Functional genomics aims at identifying the functions of as many genes as possible of a given organism. It combines
different -omics techniques such as transcriptomics and proteomics with saturated mutant collections.
Origin
The Oxford English Dictionary (OED) distinguishes three different fields of application for the -ome suffix:
in medicine, forming nouns with the sense "swelling, tumour"
in botany or zoology, forming nouns in the sense "a part of an animal or plant with a specified structure"
in cellular and molecular biology, forming nouns with the sense "all constituents considered collectively"
The -ome suffix originated as a variant of -oma, and became productive in the last quarter of the 19th century. It origi
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https://en.wikipedia.org/wiki/Louis%20W.%20Tordella
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Louis William Tordella (May 1, 1911 – January 9, 1996) was the longest serving deputy director of the National Security Agency.
Biography
Tordella was born in Garrett, Indiana, on May 1, 1911 and grew up in the Chicago environs. He displayed an early affinity for mathematics, and obtained bachelors, masters, and doctoral degrees in the 1930s. The outbreak of World War II found him teaching mathematics at Chicago's Loyola University. He joined the US Navy, immediately made contacts in the service, and was brought aboard as a lieutenant junior grade in 1942. He went directly into cryptologic work for the Navy's codebreaking organization, OP-20-G. He finished the war at OP-20-G collection stations on the West Coast, at Bainbridge Island, Washington, and Skaggs Island Naval Communication Station.
After the war Tordella stayed on with the Navy, and in 1949 joined the newly created Armed Forces Security Agency (AFSA), an early attempt to achieve service unity in the business of cryptology. He was a key figure in devising policy for the new agency, and for its successor, the National Security Agency, which emerged in 1952 to replace AFSA.
His career at NSA brought him to the very front rank of cryptologists. He was an early advocate of the use of computers for cryptologic work, and helped to cement a close working relationship with American industry. His grasp of computer technology and the associated engineering concepts, coupled with his understanding of cryptanalysis, led Tord
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https://en.wikipedia.org/wiki/Whitney%20embedding%20theorem
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In mathematics, particularly in differential topology, there are two Whitney embedding theorems, named after Hassler Whitney:
The strong Whitney embedding theorem states that any smooth real -dimensional manifold (required also to be Hausdorff and second-countable) can be smoothly embedded in the real -space, if . This is the best linear bound on the smallest-dimensional Euclidean space that all -dimensional manifolds embed in, as the real projective spaces of dimension cannot be embedded into real -space if is a power of two (as can be seen from a characteristic class argument, also due to Whitney).
The weak Whitney embedding theorem states that any continuous function from an -dimensional manifold to an -dimensional manifold may be approximated by a smooth embedding provided . Whitney similarly proved that such a map could be approximated by an immersion provided . This last result is sometimes called the Whitney immersion theorem.
A little about the proof
The general outline of the proof is to start with an immersion with transverse self-intersections. These are known to exist from Whitney's earlier work on the weak immersion theorem. Transversality of the double points follows from a general-position argument. The idea is to then somehow remove all the self-intersections. If has boundary, one can remove the self-intersections simply by isotoping into itself (the isotopy being in the domain of ), to a submanifold of that does not contain the double-points. Th
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https://en.wikipedia.org/wiki/Small%20molecule
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In molecular biology and pharmacology, a small molecule or micromolecule is a low molecular weight (≤ 1000 daltons) organic compound that may regulate a biological process, with a size on the order of 1 nm. Many drugs are small molecules; the terms are equivalent in the literature. Larger structures such as nucleic acids and proteins, and many polysaccharides are not small molecules, although their constituent monomers (ribo- or deoxyribonucleotides, amino acids, and monosaccharides, respectively) are often considered small molecules. Small molecules may be used as research tools to probe biological function as well as leads in the development of new therapeutic agents. Some can inhibit a specific function of a protein or disrupt protein–protein interactions.
Pharmacology usually restricts the term "small molecule" to molecules that bind specific biological macromolecules and act as an effector, altering the activity or function of the target. Small molecules can have a variety of biological functions or applications, serving as cell signaling molecules, drugs in medicine, pesticides in farming, and in many other roles. These compounds can be natural (such as secondary metabolites) or artificial (such as antiviral drugs); they may have a beneficial effect against a disease (such as drugs) or may be detrimental (such as teratogens and carcinogens).
Molecular weight cutoff
The upper molecular-weight limit for a small molecule is approximately 900 daltons, which allows for th
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https://en.wikipedia.org/wiki/Triangle%20Fraternity
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Triangle is a fraternity for male students majoring in engineering, architecture, and the physical, mathematical, biological, and computer sciences. It is the only member of the North American Interfraternity Conference to limit its membership recruitment to these majors.
Triangle Fraternity organized at the University of Illinois at Urbana–Champaign in the fall of 1906 and was incorporated by the state of Illinois on 15 April 1907, which is celebrated each year as Founders' Day.
As of February 2020 there are 39 chapters and six colonies of Triangle Fraternity active in the U.S. The headquarters is located in Plainfield, Indiana in a historic building erected as a Carnegie library in 1912.
Triangle Fraternity is one of three active national fraternities not to use Greek letters for its name, the others being Acacia and FarmHouse.
History
Triangle was formed in the fall of 1906 by sixteen civil engineering juniors at the University of Illinois. It was formally incorporated on 15 April 1907. The date of incorporation has been designated as Founders' Day, and Triangle celebrates it every year at each chapter.
Triangle's mission statement reads, "The purpose of Triangle shall be to maintain a fraternity of engineers, architects and scientists. It shall carry out its purpose by establishing chapters that develop balanced men who cultivate high moral character, foster lifelong friendships, and live their lives with integrity."
Symbols
Colors: Old Rose and Gray
Coat of Arm
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https://en.wikipedia.org/wiki/Fraction%20%28disambiguation%29
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A fraction is one or more equal parts of something.
Fraction may also refer to:
Fraction (chemistry), a quantity of a substance collected by fractionation
Fraction (floating point number), an (ambiguous) term sometimes used to specify a part of a floating point number
Fraction (politics), a subgroup within a parliamentary party
Fraction (radiation therapy), one unit of treatment of the total radiation dose of radiation therapy that is split into multiple treatment sessions
Fraction (religion), the ceremonial act of breaking the bread during Christian Communion
People with the surname
Matt Fraction, a comic book author
See also
Algebraic fraction, an indicated division in which the divisor, or both dividend and divisor, are algebraic expressions
Irrational fraction, a type of algebraic fraction
Faction (disambiguation)
Frazione, a type of administrative division of an Italian commune
Free and Independent Fraction, a Romanian political party
Part (disambiguation)
Ratio
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https://en.wikipedia.org/wiki/2520%20%28number%29
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2520 (two thousand five hundred twenty) is the natural number following 2519 and preceding 2521.
In mathematics
2520 is:
the smallest number divisible by all integers from one to ten, i.e., it is their least common multiple.
half of 7! (5040), meaning 7 factorial, or .
the product of five consecutive numbers, namely .
a superior highly composite number.
a colossally abundant number.
the last highly composite number that is half of the next highly composite number.
the last highly composite number that is a divisor of all following highly composite numbers.
palindromic in undecimal (199111) and a repdigit in bases 55, 59, and 62.
a Harshad number in all bases between binary and hexadecimal.
the aliquot sum of 1080.
part of the 53-aliquot tree. The complete aliquot sequence starting at 1080 is 1080, 2520, 6840, 16560, 41472, 82311, 27441, 12209, 451, 53, 1, 0.
Factors
The factors, also called divisors, of 2520 are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520.
References
Integers
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https://en.wikipedia.org/wiki/MOP
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A mop is an implement for mopping floors
MOP, mop or MoP may refer to:
Computer science
Maintenance Operations Protocol, in computer networks
Metaobject protocol, a technique that allows a computer programmer to extend or alter the semantics of a language
Multiple Online Programming – see MINIMOP
Government and organizations
Macanese pataca, the currency of Macau, by ISO 4217 code
Ministry of Public Works (Chile)
United Nations Messengers of Peace
Messengers of Peace (Scouting)
Places
Manila Ocean Park, an aquarium in the Philippines
Mount Pleasant Municipal Airport (Michigan) (IATA: MOP), in Mount Pleasant, Michigan
Science
mu opioid peptide (MOP) receptor, also referred to as mu Opioid receptor
MOP Flippase, Multidrug/Oligosaccharidyl-lipid/Polysaccharide (MOP) Flippase superfamily of transport proteins
Muriate of potash, see potassium chloride
Mathematical Olympiad Program, held at Carnegie Mellon University to train team members for the International Mathematical Olympiad
Sports
Major Opportunity Point, tennis terminology used to describe the point 0-30
Most Outstanding Player, see also Most Valuable Player
NCAA basketball tournament Most Outstanding Player in the NCAA basketball tournaments
List of NCAA Division I Ice Hockey Tournament Most Outstanding Player in NCAA ice hockey tournaments
Other
GBU-57A/B MOP, or Massive Ordnance Penetrator, a bomb used by the United States Air Force
Manual of Practice, or Project Resource Manual, published by t
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https://en.wikipedia.org/wiki/Bert%20Sutherland
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William Robert Sutherland (May 10, 1936 – February 18, 2020) was an American computer scientist who was the longtime manager of three prominent research laboratories, including Sun Microsystems Laboratories (1992–1998), the Systems Science Laboratory at Xerox PARC (1975–1981), and the Computer Science Division of Bolt, Beranek and Newman, Inc. which helped develop the ARPANET.
In these roles, Sutherland participated in the creation of the personal computer, the technology of advanced microprocessors, the Smalltalk programming language, the Java programming language and the Internet.
Unlike traditional corporate research managers, Sutherland added individuals from fields like psychology, cognitive science, and anthropology to enhance the work of his technology staff. He also directed his scientists to take their research, like the Xerox Alto "personal" computer, outside of the laboratory to allow people to use it in a corporate setting and to observe their interaction with it.
In addition, Sutherland fostered a collaboration between the researchers at California Institute of Technology developing techniques of very large scale integrated circuits (VLSI) — his brother Ivan and Carver Mead — and Lynn Conway of his PARC staff. With PARC resources made available by Sutherland, Mead and Conway developed a textbook and university syllabus that helped expedite the development and distribution of a technology whose effect is now immeasurable.
Sutherland said that a research lab is
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https://en.wikipedia.org/wiki/Algebraically%20compact%20module
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In mathematics, algebraically compact modules, also called pure-injective modules, are modules that have a certain "nice" property which allows the solution of infinite systems of equations in the module by finitary means. The solutions to these systems allow the extension of certain kinds of module homomorphisms. These algebraically compact modules are analogous to injective modules, where one can extend all module homomorphisms. All injective modules are algebraically compact, and the analogy between the two is made quite precise by a category embedding.
Definitions
Let be a ring, and a left -module. Consider a system of infinitely many linear equations
where both sets and may be infinite, and for each the number of nonzero is finite.
The goal is to decide whether such a system has a solution, that is whether there exist elements of such that all the equations of the system are simultaneously satisfied. (It is not required that only finitely many are non-zero.)
The module M is algebraically compact if, for all such systems, if every subsystem formed by a finite number of the equations has a solution, then the whole system has a solution. (The solutions to the various subsystems may be different.)
On the other hand, a module homomorphism is a pure embedding if the induced homomorphism between the tensor products is injective for every right -module . The module is pure-injective if any pure injective homomorphism splits (that is, there exists with ).
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https://en.wikipedia.org/wiki/Particle%20detector
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In experimental and applied particle physics, nuclear physics, and nuclear engineering, a particle detector, also known as a radiation detector, is a device used to detect, track, and/or identify ionizing particles, such as those produced by nuclear decay, cosmic radiation, or reactions in a particle accelerator. Detectors can measure the particle energy and other attributes such as momentum, spin, charge, particle type, in addition to merely registering the presence of the particle.
Examples and types
Many of the detectors invented and used so far are ionization detectors (of which gaseous ionization detectors and semiconductor detectors are most typical) and scintillation detectors; but other, completely different principles have also been applied, like Čerenkov light and transition radiation.
Historical examples
Bubble chamber
Wilson cloud chamber (diffusion chamber)
Photographic plate
Detectors for radiation protection
The following types of particle detector are widely used for radiation protection, and are commercially produced in large quantities for general use within the nuclear, medical, and environmental fields.
Dosimeter
Electroscope (when used as a portable dosimeter)
Gaseous ionization detector
Geiger counter
Ionization chamber
Proportional counter
Scintillation counter
Semiconductor detector
Commonly used detectors for particle and nuclear physics
Gaseous ionization detector
Ionization chamber
Proportional counter
Multiwire proportional chamber
Drift cha
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https://en.wikipedia.org/wiki/Low-discrepancy%20sequence
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In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x1, ..., xN has a low discrepancy.
Roughly speaking, the discrepancy of a sequence is low if the proportion of points in the sequence falling into an arbitrary set B is close to proportional to the measure of B, as would happen on average (but not for particular samples) in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice of B (hyperspheres, hypercubes, etc.) and how the discrepancy for every B is computed (usually normalized) and combined (usually by taking the worst value).
Low-discrepancy sequences are also called quasirandom sequences, due to their common use as a replacement of uniformly distributed random numbers.
The "quasi" modifier is used to denote more clearly that the values of a low-discrepancy sequence are neither random nor pseudorandom, but such sequences share some properties of random variables and in certain applications such as the quasi-Monte Carlo method their lower discrepancy is an important advantage.
Applications
Quasirandom numbers have an advantage over pure random numbers in that they cover the domain of interest quickly and evenly.
Two useful applications are in finding the characteristic function of a probability density function, and in finding the derivative function of a deterministic function with a small amount of noise. Quasirandom numbers allow higher-order moment
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https://en.wikipedia.org/wiki/Janice%20E.%20Voss
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Janice Elaine Voss (October 8, 1956 – February 6, 2012) was an American engineer and a NASA astronaut. Voss received her B.S. in engineering science from Purdue University, her M.S. in electrical engineering from MIT, and her PhD in aeronautics and astronautics from MIT. She flew in space five times, jointly holding the record for American women. Voss died in Arizona on February 6, 2012, from breast cancer.
Education
Voss was born in South Bend, Indiana in 1956 and grew up in Rockford, Illinois where she received her kindergarten-6th grade education from Maud E. Johnson Elementary School and Guilford Center School. In 1972, Voss graduated from Minnechaug Regional High School in Wilbraham, Massachusetts. After high school, Voss went on to earn her Bachelor of Science in engineering science from Purdue University in 1975. During her time at Purdue, she was a member of Alpha Phi Omega. Voss continued her education at MIT, earning her Master of Science degree in electrical engineering in 1977, completing her thesis on Kalman filtering techniques. From 1973 to 1975, Voss took correspondence courses at the University of Oklahoma. From 1977 to 1978, she completed work in space physics at Rice University. In 1983, Voss became a Draper Fellow while continuing her graduate studies in the Draper Laboratory at MIT. As a Draper Laboratory Fellow, she worked on developing software for the space shuttle program. Voss earned her Doctor of Philosophy in aeronautics and astronautics from MIT
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https://en.wikipedia.org/wiki/Three-address%20code
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In computer science, three-address code (often abbreviated to TAC or 3AC) is an intermediate code used by optimizing compilers to aid in the implementation of code-improving transformations. Each TAC instruction has at most three operands and is typically a combination of assignment and a binary operator. For example, t1 := t2 + t3. The name derives from the use of three operands in these statements even though instructions with fewer operands may occur.
Since three-address code is used as an intermediate language within compilers, the operands will most likely not be concrete memory addresses or processor registers, but rather symbolic addresses that will be translated into actual addresses during register allocation. It is also not uncommon that operand names are numbered sequentially since three-address code is typically generated by the compiler.
A refinement of three-address code is A-normal form (ANF).
Examples
In three-address code, this would be broken down into several separate instructions. These instructions translate more easily to assembly language. It is also easier to detect common sub-expressions for shortening the code. In the following example, one calculation is composed of several smaller ones:
# Calculate one solution to the [[Quadratic equation]].
x = (-b + sqrt(b^2 - 4*a*c)) / (2*a)
t1 := b * b
t2 := 4 * a
t3 := t2 * c
t4 := t1 - t3
t5 := sqrt(t4)
t6 := 0 - b
t7 := t5 + t6
t8 := 2 * a
t9 := t7 / t8
x := t9
Three-address code may have conditional
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https://en.wikipedia.org/wiki/Center%20for%20Complex%20Quantum%20Systems
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The Center for Complex Quantum Systems is a research institute within the Department of Physics of The University of Texas at Austin in the United States.
The center, founded in 1967 by Ilya Prigogine, is dedicated to the theoretical and computational research of complex systems, statistical mechanics and chaos theory.
The current research staff includes William C. Schieve and Linda Reichl, the center's director.
Notes
External links
The Center for Complex Quantum Systems
University of Texas at Austin
Systems science institutes
Research institutes in Texas
Physics research institutes
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