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https://en.wikipedia.org/wiki/Albanese%20variety
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In mathematics, the Albanese variety , named for Giacomo Albanese, is a generalization of the Jacobian variety of a curve.
Precise statement
The Albanese variety is the abelian variety generated by a variety taking a given point of to the identity of . In other words, there is a morphism from the variety to its Albanese variety , such that any morphism from to an abelian variety (taking the given point to the identity) factors uniquely through . For complex manifolds, defined the Albanese variety in a similar way, as a morphism from to a torus such that any morphism to a torus factors uniquely through this map. (It is an analytic variety in this case; it need not be algebraic.)
Properties
For compact Kähler manifolds the dimension of the Albanese variety is the Hodge number , the dimension of the space of differentials of the first kind on , which for surfaces is called the irregularity of a surface. In terms of differential forms, any holomorphic 1-form on is a pullback of translation-invariant 1-form on the Albanese variety, coming from the holomorphic cotangent space of at its identity element. Just as for the curve case, by choice of a base point on (from which to 'integrate'), an Albanese morphism
is defined, along which the 1-forms pull back. This morphism is unique up to a translation on the Albanese variety. For varieties over fields of positive characteristic, the dimension of the Albanese variety may be less than the Hodge numbers and (which need not
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https://en.wikipedia.org/wiki/Coherent%20duality
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In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory.
The historical roots of the theory lie in the idea of the adjoint linear system of a linear system of divisors in classical algebraic geometry. This was re-expressed, with the advent of sheaf theory, in a way that made an analogy with Poincaré duality more apparent. Then according to a general principle, Grothendieck's relative point of view, the theory of Jean-Pierre Serre was extended to a proper morphism; Serre duality was recovered as the case of the morphism of a non-singular projective variety (or complete variety) to a point. The resulting theory is now sometimes called Serre–Grothendieck–Verdier duality, and is a basic tool in algebraic geometry. A treatment of this theory, Residues and Duality (1966) by Robin Hartshorne, became a reference. One concrete spin-off was the Grothendieck residue.
To go beyond proper morphisms, as for the versions of Poincaré duality that are not for closed manifolds, requires some version of the compact support concept. This was addressed in SGA2 in terms of local cohomology, and Grothendieck local duality; and subsequently. The Greenlees–May duality, first formulated in 1976 by Ralf Strebel and in 1978 by Eben Matlis, is part of the continuing consideration of this area.
Adjoint funct
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https://en.wikipedia.org/wiki/Finalizer
|
In computer science, a finalizer or finalize method is a special method that performs finalization, generally some form of cleanup. A finalizer is executed during object destruction, prior to the object being deallocated, and is complementary to an initializer, which is executed during object creation, following allocation. Finalizers are strongly discouraged by some, due to difficulty in proper use and the complexity they add, and alternatives are suggested instead, mainly the dispose pattern (see problems with finalizers).
The term finalizer is mostly used in object-oriented and functional programming languages that use garbage collection, of which the archetype is Smalltalk. This is contrasted with a destructor, which is a method called for finalization in languages with deterministic object lifetimes, archetypically C++. These are generally exclusive: a language will have either finalizers (if automatically garbage collected) or destructors (if manually memory managed), but in rare cases a language may have both, as in C++/CLI and D, and in case of reference counting (instead of tracing garbage collection), terminology varies. In technical use, finalizer may also be used to refer to destructors, as these also perform finalization, and some subtler distinctions are drawn – see terminology. The term final also indicates a class that cannot be inherited; this is unrelated.
Terminology
The terminology of finalizer and finalization versus destructor and destruction varies be
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https://en.wikipedia.org/wiki/Disjunct
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The term disjunct can refer to:
disjunct (linguistics)
disjunct or quincunx in astrology, an aspect made when two planets are 150 degrees, or five signs apart
a disjunct distribution in biology, one in which two closely related taxa are widely separated geographically
disjunct (music), a melodic skip or leap
logical disjunction
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https://en.wikipedia.org/wiki/Symplectic
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The term "symplectic" is a calque of "complex" introduced by Hermann Weyl in 1939. In mathematics it may refer to:
Symplectic Clifford algebra, see Weyl algebra
Symplectic geometry
Symplectic group
Symplectic integrator
Symplectic manifold
Symplectic matrix
Symplectic representation
Symplectic vector space
It can also refer to:
Symplectic bone, a bone found in fish skulls
Symplectite, in reference to a mineral intergrowth texture
See also
Metaplectic group
Symplectomorphism
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https://en.wikipedia.org/wiki/High%20energy
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High energy may refer to:
High energy physics, a branch of physics dealing with subatomic particles and ionizing radiation
Hi-NRG, a kind of dance music
High Energy (The Supremes album), 1976
"High Energy" (The Supremes song), 1976
High Energy (Freddie Hubbard album), 1974
"High Energy" (Evelyn Thomas song), 1984
High Energy, a 1990s professional wrestling tag team consisting of Owen Hart and Koko B. Ware
See also
High Inergy
|
https://en.wikipedia.org/wiki/Differential%20algebra
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In mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators as algebraic objects in view of deriving properties of differential equations and operators without computing the solutions, similarly as polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras and Lie algebras may be considered as belonging to differential algebra.
More specifically, differential algebra refers to the theory introduced by Joseph Ritt in 1950, in which differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with finitely many derivations.
A natural example of a differential field is the field of rational functions in one variable over the complex numbers, where the derivation is differentiation with respect to More generally, every differential equation may be viewed as an element of a differential algebra over the differential field generated by the (known) functions appearing in the equation.
History
Joseph Ritt developed differential algebra because he viewed attempts to reduce systems of differential equations to various canonical forms as an unsatisfactory approach. However, the success of algebraic elimination methods and algebraic manifold theory motivated Ritt to consider a similar approach for differential equations. His efforts led to an initial pa
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https://en.wikipedia.org/wiki/Base%20change
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In mathematics, base change may mean:
Base change map in algebraic geometry
Fiber product of schemes in algebraic geometry
Change of base (disambiguation) in linear algebra or numeral systems
Base change lifting of automorphic forms
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https://en.wikipedia.org/wiki/Cavity
|
Cavity may refer to:
Biology and healthcare
Body cavity, a fluid-filled space in many animals where organs typically develop
Gastrovascular cavity, the primary organ of digestion and circulation in cnidarians and flatworms
Dental cavity or tooth decay, damage to the structure of a tooth
Lung cavity, an air-filled space within the lung
Nasal cavity, a large, air-filled space above and behind the nose in the middle of the face
Radio frequency resonance
Microwave cavity or RF cavity, a cavity resonator in the radio frequency range, for example used in particle accelerators
Optical cavity, the cavity resonator of a laser
Resonant cavity, a device designed to select for waves of particular wavelengths
Other uses
Cavity (band), a sludge metal band from Miami, Florida
Cavity method, a mathematical method to solve some mean field type of models
Cavity wall, a wall consisting of two skins with a cavity
See also
Cavitation, the phenomenon of partial vacuums forming in fluid, for example, in propellers
Cavitary pneumonia, a type of pneumonia in which a hole is formed in the lung
Cavity Search (disambiguation)
Hollow (disambiguation)
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https://en.wikipedia.org/wiki/Ron%20Kimmel
|
Ron Kimmel (, b. 1963) is a professor of Computer Science and Electrical and Computer Engineering (by courtesy) at the Technion Israel Institute of Technology. He holds a D.Sc. degree in electrical engineering (1995) from the Technion, and was a post-doc at UC Berkeley and Berkeley Labs, and a visiting professor at Stanford University. He has worked in various areas of image and shape analysis in computer vision, image processing, and computer graphics. Kimmel's interest in recent years has been non-rigid shape processing and analysis, medical imaging, computational biometry, deep learning, numerical optimization of problems with a geometric flavor, and applications of metric and differential geometry. Kimmel is an author of two books, an editor of one, and an author of numerous articles. He is the founder of the Geometric Image Processing Lab , and a founder and advisor of several successful image processing and analysis companies.
Kimmel's contributions include the development of fast marching methods for triangulated manifolds (together with James Sethian), the geodesic active contours algorithm for image segmentation, a geometric framework for image filtering (named Beltrami flow after the Italian mathematician Eugenio Beltrami), and the Generalized Multidimensional Scaling (together with his students the Bronstein brothers) with which he was able to compute the Gromov-Hausdorff distance between surfaces. He is one of the founders of the field of deep learning based com
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https://en.wikipedia.org/wiki/Transition%20function
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In mathematics, a transition function may refer to:
a transition map between two charts of an atlas of a manifold or other topological space
the function that defines the transitions of a state transition system in computing, which may refer more specifically to a
Turing machine,
finite-state machine, or
cellular automaton
a stochastic kernel In statistics and probability theory, the conditional probability distribution function controlling the transitions of a stochastic process
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https://en.wikipedia.org/wiki/Blowing%20up
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In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with all the directions pointing out of that subspace. For example, the blowup of a point in a plane replaces the point with the projectivized tangent space at that point. The metaphor is that of zooming in on a photograph to enlarge part of the picture, rather than referring to an explosion.
Blowups are the most fundamental transformation in birational geometry, because every birational morphism between projective varieties is a blowup. The weak factorization theorem says that every birational map can be factored as a composition of particularly simple blowups. The Cremona group, the group of birational automorphisms of the plane, is generated by blowups.
Besides their importance in describing birational transformations, blowups are also an important way of constructing new spaces. For instance, most procedures for resolution of singularities proceed by blowing up singularities until they become smooth. A consequence of this is that blowups can be used to resolve the singularities of birational maps.
Classically, blowups were defined extrinsically, by first defining the blowup on spaces such as projective space using an explicit construction in coordinates and then defining blowups on other spaces in terms of an embedding. This is reflected in some of the terminology, such as the classical term monoidal transformation. Contemporary algebraic geometry
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https://en.wikipedia.org/wiki/Hamiltonian%20vector%20field
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In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is a geometric manifestation of Hamilton's equations in classical mechanics. The integral curves of a Hamiltonian vector field represent solutions to the equations of motion in the Hamiltonian form. The diffeomorphisms of a symplectic manifold arising from the flow of a Hamiltonian vector field are known as canonical transformations in physics and (Hamiltonian) symplectomorphisms in mathematics.
Hamiltonian vector fields can be defined more generally on an arbitrary Poisson manifold. The Lie bracket of two Hamiltonian vector fields corresponding to functions f and g on the manifold is itself a Hamiltonian vector field, with the Hamiltonian given by the
Poisson bracket of f and g.
Definition
Suppose that is a symplectic manifold. Since the symplectic form is nondegenerate, it sets up a fiberwise-linear isomorphism
between the tangent bundle and the cotangent bundle , with the inverse
Therefore, one-forms on a symplectic manifold may be identified with vector fields and every differentiable function determines a unique vector field , called the Hamiltonian vector field with the Hamiltonian , by defining for every vector field on ,
Note: Some authors define the Hamiltonian vector field with the opposite sign. One has to
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https://en.wikipedia.org/wiki/Structural%20unit
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In polymer chemistry, a structural unit is a building block of a polymer chain. It is the result of a monomer which has been polymerized into a long chain.
There may be more than one structural unit in the repeat unit. When different monomers are polymerized, a copolymer is formed. It is a routine way of developing new properties for new materials.
Example
Consider the example of polyethylene terephthalate (PET or "polyester"). The monomers which could be used to create this polymer are ethylene glycol and terephthalic acid:
HO-CH2-CH2-OH
and
HOOC-C6H4-COOH
In the polymer, there are two structural units, which are
-O-CH2-CH2-O-
and
-CO-C6H4-CO-
The repeat unit is
-CH2-CH2-O-CO-C6H4-CO-O-
Functionality of structural units
The functionality of a monomeric structural unit is defined as the number of covalent bonds which it forms with other reactants. A structural unit in a linear polymer chain segment forms two bonds and is therefore bifunctional, as for the PET structural units above.
Other values of functionality exist. Unless the macromolecule is cyclic, it will have monovalent structural units at each end of the polymer chain. In branched polymers, there are trifunctional units at each branch point. For example, in the synthesis of PET, a small fraction of the ethylene glycol can be replaced by glycerol which has three alcohol groups. This trifunctional molecule inserts itself in the polymeric chain and bonds to three carboxylic acid groups forming a branch point.
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https://en.wikipedia.org/wiki/Reproductive%20biology
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Reproductive biology includes both sexual and asexual reproduction.
Reproductive biology includes a wide number of fields:
Reproductive systems
Endocrinology
Sexual development (Puberty)
Sexual maturity
Reproduction
Fertility
Human reproductive biology
Endocrinology
Human reproductive biology is primarily controlled through hormones, which send signals to the human reproductive structures to influence growth and maturation. These hormones are secreted by endocrine glands, and spread to different tissues in the human body. In humans, the pituitary gland synthesizes hormones used to control the activity of endocrine glands.
Reproductive systems
Internal and external organs are included in the reproductive system. There are two reproductive systems including the male and female, which contain different organs from one another. These systems work together in order to produce offspring.
Female reproductive system
The female reproductive system includes the structures involved in ovulation, fertilization, development of an embryo, and birth.
These structures include:
Ovaries
Oviducts
Uterus
Vagina
Mammary Glands
Estrogen is one of the sexual reproductive hormones that aid in the sexual reproductive system of the female.
Male reproductive system
The male reproductive system includes testes, rete testis, efferent ductules, epididymis, sex accessory glands, sex accessory ducts and external genitalia.
Testosterone, an androgen, although present in both males a
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https://en.wikipedia.org/wiki/Symplectic%20vector%20field
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In physics and mathematics, a symplectic vector field is one whose flow preserves a symplectic form. That is, if is a symplectic manifold with smooth manifold and symplectic form , then a vector field in the Lie algebra is symplectic if its flow preserves the symplectic structure. In other words, the Lie derivative of the vector field must vanish:
.
An alternative definition is that a vector field is symplectic if its interior product with the symplectic form is closed. (The interior product gives a map from vector fields to 1-forms, which is an isomorphism due to the nondegeneracy of a symplectic 2-form.) The equivalence of the definitions follows from the closedness of the symplectic form and Cartan's magic formula for the Lie derivative in terms of the exterior derivative.
If the interior product of a vector field with the symplectic form is an exact form (and in particular, a closed form), then it is called a Hamiltonian vector field. If the first De Rham cohomology group of the manifold is trivial, all closed forms are exact, so all symplectic vector fields are Hamiltonian. That is, the obstruction to a symplectic vector field being Hamiltonian lives in . In particular, symplectic vector fields on simply connected manifolds are Hamiltonian.
The Lie bracket of two symplectic vector fields is Hamiltonian, and thus the collection of symplectic vector fields and the collection of Hamiltonian vector fields both form Lie algebras.
References
Symplectic geo
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https://en.wikipedia.org/wiki/Ric%20Holt
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Richard Craig Holt (February 13, 1941 – April 12, 2019) was an American-Canadian computer scientist.
Early life
Holt was born on in 1941 in Bartlesville, Oklahoma, to Vashti Young and C.P. Holt, but later moved to Toronto, Canada. As a teenager, he competed in track and field. He graduated from Cornell University in 1964 in engineering physics. He spent a year in the Peace Corps in Nigeria, and then worked for IBM. He went back to Cornell and obtained a PhD in computer science in 1970 under Alan Shaw.
Career
Holt joined the faculty at the University of Toronto in 1970. In 1997, he joined the faculty of the University of Waterloo, where he remained until his retirement in 2014.
Holt's main research areas were operating systems, programming languages and software engineering, contributing many seminal results to each. His work includes foundational work on deadlock, development of several compilers and compilation techniques. His Turing programming language was used in universities and high schools in Canada and internationally. He also participated in the development of the Grok, Euclid, SP/k, and S/SL programming languages.
For many years, he ran a software company, Holt Software Associates (HSA), which created the Ready to Program environment still widely used in Canadian High Schools to teach programming.
Holt served as president of Gravel Watch Ontario from 2003 until 2015.
In the fall of 2005, he was named #16 on Computing Canada's list of top 30 information tec
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https://en.wikipedia.org/wiki/Marine%20geology
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Marine geology or geological oceanography is the study of the history and structure of the ocean floor. It involves geophysical, geochemical, sedimentological and paleontological investigations of the ocean floor and coastal zone. Marine geology has strong ties to geophysics and to physical oceanography.
Marine geological studies were of extreme importance in providing the critical evidence for sea floor spreading and plate tectonics in the years following World War II. The deep ocean floor is the last essentially unexplored frontier and detailed mapping in support of both military (submarine) objectives and economic (petroleum and metal mining) objectives drives the research.–
Overview
The Ring of Fire around the Pacific Ocean with its attendant intense volcanism and seismic activity poses a major threat for disastrous earthquakes, tsunamis and volcanic eruptions. Any early warning systems for these disastrous events will require a more detailed understanding of marine geology of coastal and island arc environments.
The study of littoral and deep sea sedimentation and the precipitation and dissolution rates of calcium carbonate in various marine environments has important implications for global climate change.
The discovery and continued study of mid-ocean rift zone volcanism and hydrothermal vents, first in the Red Sea and later along the East Pacific Rise and the Mid-Atlantic Ridge systems were and continue to be important areas of marine geological research. The ext
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https://en.wikipedia.org/wiki/Final%20topology
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In general topology and related areas of mathematics, the final topology (or coinduced, strong, colimit, or inductive topology) on a set with respect to a family of functions from topological spaces into is the finest topology on that makes all those functions continuous.
The quotient topology on a quotient space is a final topology, with respect to a single surjective function, namely the quotient map. The disjoint union topology is the final topology with respect to the inclusion maps. The final topology is also the topology that every direct limit in the category of topological spaces is endowed with, and it is in the context of direct limits that the final topology often appears. A topology is coherent with some collection of subspaces if and only if it is the final topology induced by the natural inclusions.
The dual notion is the initial topology, which for a given family of functions from a set into topological spaces is the coarsest topology on that makes those functions continuous.
Definition
Given a set and an -indexed family of topological spaces with associated functions
the is the finest topology on such that
is continuous for each .
Explicitly, the final topology may be described as follows:
a subset of is open in the final topology (that is, ) if and only if is open in for each .
The closed subsets have an analogous characterization:
a subset of is closed in the final topology if and only if is closed in for each .
The family
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https://en.wikipedia.org/wiki/139%20%28number%29
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139 (one hundred [and] thirty-nine) is the natural number following 138 and preceding 140.
In mathematics
139 is the 34th prime number. It is a twin prime with 137. Because 141 is a semiprime, 139 is a Chen prime. 139 is the smallest prime before a prime gap of length 10.
This number is the sum of five consecutive prime numbers (19 + 23 + 29 + 31 + 37).
It is the smallest factor of 64079 which is the smallest Lucas number with prime index which is not prime. It is also the smallest factor of the first nine terms of the Euclid–Mullin sequence, making it the tenth term.
139 is a happy number and a strictly non-palindromic number.
In the military
RUM-139 VL-ASROC is a United States Navy ASROC anti-submarine missile
was a United States Navy Admirable-class minesweeper during World War II
was a United States Navy Haskell-class attack transport during World War II
was a United States Navy destroyer during World War II
was a United States Navy transport ship during World War I and World War II
was a tanker loaned to the Soviet Union during World War II, then returned to the United States in 1944
was a United States Navy cargo ship during World War II
was a United States Navy Des Moines-class heavy cruiser following World War II
was a United States Navy Wickes-class destroyer during World War II
In transportation
British Rail Class 139 is the TOPS classification assigned to the lightweight railcars by West Midlands Trains on the Stourbridge Town Branch Line
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https://en.wikipedia.org/wiki/146%20%28number%29
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146 (one hundred [and] forty-six) is the natural number following 145 and preceding 147.
In mathematics
146 is an octahedral number, the number of spheres that can be packed into in a regular octahedron with six spheres along each edge. For an octahedron with seven spheres along each edge, the number of spheres on the surface of the octahedron is again 146. It is also possible to arrange 146 disks in the plane into an irregular octagon with six disks on each side, making 146 an octo number.
There is no integer with exactly 146 coprimes less than it, so 146 is a nontotient. It is also never the difference between an integer and the total of coprimes below it, so it is a noncototient. And it is not the sum of proper divisors of any number, making it an untouchable number.
There are 146 connected partially ordered sets with four labeled elements.
See also
146 (disambiguation)
References
Integers
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https://en.wikipedia.org/wiki/Larry%20Fleinhardt
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Larry Fleinhardt, Ph.D., is a fictional character in the CBS crime drama Numb3rs, played by Peter MacNicol. He is the best friend and colleague of Charlie Eppes.
Dr. Lawrence Fleinhardt holds the Walter T. Merrick Chair of Theoretical Physics at the California Institute of Science, CalSci (a university based on Caltech and located in Los Angeles in the Numb3rs universe). He is portrayed as a brilliant theoretical physicist and cosmologist, who researches supersymmetry, string theory, 11-dimensional supergravity theory, doubly special relativity, black holes, Ly-alpha emitters, the cosmic microwave background, and gravitational waves, using LIGO to check predictions on quantum corrections. He may have even found a way to express Calabi–Yau manifolds in a way that goes beyond a nonvanishing harmonic spinor and, independent of Charlie, published a work of genius entitled Zero Point Energy and Quantum Cosmology, which could provide insight into the cosmological constant problem (episode 3x4, "The Mole").
Backstory
Larry Fleinhardt has always been fascinated with the stars. He had his first telescope at age three, was the president of the rocket club in the fifth grade, and worked as a docent at his local planetarium while in junior high school. Once a remarkable student comparable to Charlie, Larry graduated from college at the early age of 19. However, Fleinhardt had an addiction with card counting during his years as an undergraduate, which he feels ashamed about and has comp
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https://en.wikipedia.org/wiki/Grothendieck%20duality
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In mathematics, Grothendieck duality may refer to:
Coherent duality of coherent sheaves
Grothendieck local duality of modules over a local ring
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https://en.wikipedia.org/wiki/Duke%20Mathematical%20Journal
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Duke Mathematical Journal is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue included a paper by Solomon Lefschetz. Leonard Carlitz served on the editorial board for 35 years, from 1938 to 1973.
The current managing editor is Richard Hain (Duke University).
Impact
According to the journal homepage, the journal has a 2018 impact factor of 2.194, ranking it in the top ten mathematics journals in the world.
References
External links
Mathematics journals
Mathematical Journal
Academic journals established in 1935
Multilingual journals
English-language journals
French-language journals
Duke University Press academic journals
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https://en.wikipedia.org/wiki/Michael%20Nielsen
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Michael Aaron Nielsen (born January 4, 1974) is a quantum physicist, science writer, and computer programming researcher living in San Francisco.
Work
In 1998, Nielsen received his PhD in physics from the University of New Mexico. In 2004, he was recognized as Australia's "youngest academic" and was awarded a Federation Fellowship at the University of Queensland. During this fellowship, he worked at the Los Alamos National Laboratory, Caltech, and at the Perimeter Institute for Theoretical Physics.
Alongside Isaac Chuang, Nielsen co-authored a popular textbook on quantum computing, which has been cited more than 52,000 times as of July 2023.
In 2007, Nielsen shifted his focus from quantum information and computation to “the development of new tools for scientific collaboration and publication”, including the Polymath project with Timothy Gowers, which aims to facilitate "massively collaborative mathematics." Besides writing books and essays, he has also given talks about open science. He was a member of the Working Group on Open Data in Science at the Open Knowledge Foundation.
Nielsen is a strong advocate for open science and has written extensively on the subject, including in his book Reinventing Discovery, which was favorably reviewed in Nature and named one of the Financial Times' best books of 2011.
In 2015 Nielsen published the online textbook Neural Networks and Deep Learning, and joined the Recurse Center as a Research Fellow. He has also been a Research Fellow
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https://en.wikipedia.org/wiki/Fundamental%20solution
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In mathematics, a fundamental solution for a linear partial differential operator is a formulation in the language of distribution theory of the older idea of a Green's function (although unlike Green's functions, fundamental solutions do not address boundary conditions).
In terms of the Dirac delta "function" , a fundamental solution is a solution of the inhomogeneous equation
Here is a priori only assumed to be a distribution.
This concept has long been utilized for the Laplacian in two and three dimensions. It was investigated for all dimensions for the Laplacian by Marcel Riesz.
The existence of a fundamental solution for any operator with constant coefficients — the most important case, directly linked to the possibility of using convolution to solve an arbitrary right hand side — was shown by Bernard Malgrange and Leon Ehrenpreis. In the context of functional analysis, fundamental solutions are usually developed via the Fredholm alternative and explored in Fredholm theory.
Example
Consider the following differential equation with
The fundamental solutions can be obtained by solving , explicitly,
Since for the unit step function (also known as the Heaviside function) we have
there is a solution
Here is an arbitrary constant introduced by the integration. For convenience, set .
After integrating and choosing the new integration constant as zero, one has
Motivation
Once the fundamental solution is found, it is straightforward to find a solution of the or
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https://en.wikipedia.org/wiki/W%C5%82odzimierz%20Sto%C5%BCek
|
Włodzimierz Stożek (23 July 1883 – 3 or 4 July 1941) was a Polish mathematician of the Lwów School of Mathematics.
Head of the Mathematics Faculty on the Lwów University of Technology. He was arrested and murdered together with his two sons: the 29-year-old engineer Eustachy and 24-year-old Emanuel, graduate of the Institute of Technology by Nazis during the Second World War on 3 or 4 July in Lviv, during the Massacre of Lviv professors.
In December 1944, Stefan Banach wrote the following tribute to Stożek:
Professor Włodzimierz Stożek was an outstanding mathematician, the author of numerous papers on the theory of integral equations, potential theory, as well as on many other branches of mathematics. His work is widely known in Poland and also abroad. He had a very charming personality and was a distinguished scholar, beloved by his young students as someone with a very caring heart. He was always ready to assist anyone who asked for his help. He took little notice of nationality differences. Those of us who were close to him and knew him well now esteem even more highly his enlightened personality and great cultural contributions. He will be remembered as a great intellectual who loved all of humanity and served it faithfully.
References
Emilia Jakimowicz and Adam Miranowicz (2011) Stefan Banach: Remarkable Life, Brilliant Mathematics, 3rd edition, page 25, Gdańsk University Press, .
External links
1883 births
1941 deaths
Lwów School of Mathematics
Victims of the Ma
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https://en.wikipedia.org/wiki/Stanis%C5%82aw%20Ruziewicz
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Stanisław Ruziewicz (29 August 1889 – 12 July 1941) was a Polish mathematician and one of the founders of the Lwów School of Mathematics.
He was a former student of Wacław Sierpiński, earning his doctorate in 1913 from the University of Lwów; his thesis concerned continuous functions that are not differentiable. He became a professor at the same university (then named Jan Kazimierz University) and rector of the Academy of Foreign Trade in Lwów. During the Second World War, Ruziewicz's home city of Lwów was annexed by the
Ukrainian Soviet Socialist Republic, but then taken over by the General Government of German-occupied Poland in July 1941; Ruziewicz was arrested and murdered by the Gestapo on 12 July 1941 in Lwów, during the Massacre of Lwów professors.
The Ruziewicz problem, asking whether the Lebesgue measure on the sphere may be characterized by certain of its properties, is named after him.
References
1889 births
1941 deaths
Lwów School of Mathematics
Victims of the Massacre of Lwów professors
People from the Kingdom of Galicia and Lodomeria
People from Kolomyia
Polish people executed by Nazi Germany
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https://en.wikipedia.org/wiki/Charles%20Parsons%20%28philosopher%29
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Charles Dacre Parsons (born April 13, 1933) is an American philosopher best known for his work in the philosophy of mathematics and the study of the philosophy of Immanuel Kant. He is professor emeritus at Harvard University.
Life and career
Parsons is a son of the famous Harvard sociologist Talcott Parsons. He earned his Ph.D. in philosophy at Harvard University in 1961, under the direction of Burton Dreben and Willard Van Orman Quine. He taught for many years at Columbia University before moving to Harvard University in 1989. He retired in 2005 as the Edgar Pierce professor of philosophy, a position formerly held by Quine.
He is an elected Fellow of the American Academy of Arts and Sciences and the Norwegian Academy of Science and Letters.
Among his former doctoral students are Michael Levin, James Higginbotham, Peter Ludlow, Gila Sher, Øystein Linnebo, Richard Tieszen, and Mark van Atten.
In 2017, Parsons held the Gödel Lecture titled Gödel and the universe of sets.
Philosophical work
In addition to his work in logic and the philosophy of mathematics, Parsons was an editor, with Solomon Feferman and others, of the posthumous works of Kurt Gödel. He has also written on historical figures, especially Immanuel Kant, Gottlob Frege, Kurt Gödel, and Willard Van Orman Quine.
Works
Books
1983. Mathematics in Philosophy: Selected Essays. Ithaca, N.Y.: Cornell Univ. Press.
2008. Mathematical Thought and its Objects. Cambridge Univ. Press.
2012. From Kant to Husse
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https://en.wikipedia.org/wiki/Specific%20rotation
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In chemistry, specific rotation ([α]) is a property of a chiral chemical compound. It is defined as the change in orientation of monochromatic plane-polarized light, per unit distance–concentration product, as the light passes through a sample of a compound in solution. Compounds which rotate the plane of polarization of a beam of plane polarized light clockwise are said to be dextrorotary, and correspond with positive specific rotation values, while compounds which rotate the plane of polarization of plane polarized light counterclockwise are said to be levorotary, and correspond with negative values. If a compound is able to rotate the plane of polarization of plane-polarized light, it is said to be “optically active”.
Specific rotation is an intensive property, distinguishing it from the more general phenomenon of optical rotation. As such, the observed rotation (α) of a sample of a compound can be used to quantify the enantiomeric excess of that compound, provided that the specific rotation ([α]) for the enantiopure compound is known. The variance of specific rotation with wavelength—a phenomenon known as optical rotatory dispersion—can be used to find the absolute configuration of a molecule. The concentration of bulk sugar solutions is sometimes determined by comparison of the observed optical rotation with the known specific rotation.
Definition
The CRC Handbook of Chemistry and Physics defines specific rotation as:
For an optically active substance, defined by [α]θ
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https://en.wikipedia.org/wiki/Enantiomeric%20excess
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In stereochemistry, enantiomeric excess (ee) is a measurement of purity used for chiral substances. It reflects the degree to which a sample contains one enantiomer in greater amounts than the other. A racemic mixture has an ee of 0%, while a single completely pure enantiomer has an ee of 100%. A sample with 70% of one enantiomer and 30% of the other has an ee of 40% (70% − 30%).
Definition
Enantiomeric excess is defined as the absolute difference between the mole fraction of each enantiomer:
where
In practice, it is most often expressed as a percent enantiomeric excess.
The enantiomeric excess can be determined in another way if we know the amount of each enantiomer produced. If one knows the moles of each enantiomer produced then:
Enantiomeric excess is used as one of the indicators of the success of an asymmetric synthesis. For mixtures of diastereomers, there are analogous definitions and uses for diastereomeric excess and percent diastereomeric excess.
As an example, a sample with 70 % of isomer and 30 % of will have a percent enantiomeric excess of 40. This can also be thought of as a mixture of 40 % pure with 60 % of a racemic mixture (which contributes half 30 % and the other half 30 % to the overall composition).
If given the enantiomeric excess of a mixture, the fraction of the main isomer, say , can be determined using and the lesser isomer .
A non-racemic mixture of two enantiomers will have a net optical rotation. It is possible to determine the sp
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https://en.wikipedia.org/wiki/John%20R.%20Kirtley
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John Robert Kirtley (born August 27, 1949) is an American condensed matter physicist and a consulting professor at the Center for Probing the Nanoscale in the department of applied physics at Stanford University. He shared the 1998 Oliver E. Buckley Prize of the American Physical Society, and is a Fellow of both the American Physical Society and the American Association for the Advancement of Sciences.
Early life and education
He received his BA in physics in 1971 and his PhD in physics in 1976, both from the University of California, Santa Barbara. His PhD topic was inelastic electron tunneling spectroscopy, with Paul Hansma as his thesis advisor. He was then a research assistant professor at the University of Pennsylvania from 1976 to 1978, working in the group of Donald N. Langenberg on non-equilibrium superconductivity. From 1978 to 2006 he was a research staff member at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York. Since 2006 he has worked at the University of Twente in the Netherlands, been an Alexander von Humboldt Foundation Forschungspreis winner at the University of Augsburg in Germany, a Jubileum Professor at Chalmers University of Technology in Sweden, and currently holds a Chaire d'Excellence from the NanoSciences Fondation in Grenoble, France.
Career
He has worked in the fields of Surface Enhanced Raman scattering, light emission from tunnel junctions and electron injection devices, noise in semiconducting devices, scanning tunnelin
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https://en.wikipedia.org/wiki/Carbohydrate%20acetalisation
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In carbohydrate chemistry carbohydrate acetalisation is an organic reaction and a very effective means of providing a protecting group. The example below depicts the acetalisation reaction of D-ribose 1. With acetone or 2,2-dimethoxypropane as the acetalisation reagent the reaction is under thermodynamic reaction control and results in the pentose 2. The latter reagent in itself is an acetal and therefore the reaction is actually a cross-acetalisation.
Kinetic reaction control results from 2-methoxypropene as the reagent. D-ribose in itself is a hemiacetal and in equilibrium with the pyranose 3. In aqueous solution ribose is 75% pyranose and 25% furanose and a different acetal 4 is formed.
Selective acetalization of carbohydrate and formation of acetals possessing atypical properties is achieved by using arylsulfonyl acetals. An example of arylsulfonyl acetals as carbohydrate-protective groups are phenylsulfonylethylidene acetals. These acetals are resistant to the acid hydrolysis and can be deprotected easily by classical reductive conditions.
References
Preparative Carbohydrate Chemistry Calinaud, P.; Gelas, J. in . Hanessian, S. Ed. Marcel Dekker, Inc.: New York, 1997.
External links
Organic reactions
Acetalisation
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https://en.wikipedia.org/wiki/Ivar%20Langen
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Ivar Langen (born December 21, 1942) was the rector at the University of Stavanger from 2003 to 2007. He was a central figure in the campaign to gain university status for Stavanger University College, which was awarded in 2005.
Langen has been a professor of Mechanical Engineering since 1994. In 1997, he founded the Centre for Maintenance and Asset Management, and from 2000 to 2003, he was the vice dean of the School of Science and Technology at Stavanger University College. Langen also serves on the board of directors of the International Society of Offshore and Polar Engineers and was president of the organisation from 2002 to 2003.
He is a fellow of the Norwegian Academy of Technological Sciences.
References
1942 births
Living people
Norwegian engineers
Academic staff of the University of Stavanger
Rectors of universities and colleges in Norway
Members of the Norwegian Academy of Technological Sciences
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https://en.wikipedia.org/wiki/Molecular%20neuroscience
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Molecular neuroscience is a branch of neuroscience that observes concepts in molecular biology applied to the nervous systems of animals. The scope of this subject covers topics such as molecular neuroanatomy, mechanisms of molecular signaling in the nervous system, the effects of genetics and epigenetics on neuronal development, and the molecular basis for neuroplasticity and neurodegenerative diseases. As with molecular biology, molecular neuroscience is a relatively new field that is considerably dynamic.
Locating neurotransmitters
In molecular biology, communication between neurons typically occurs by chemical transmission across gaps between the cells called synapses. The transmitted chemicals, known as neurotransmitters, regulate a significant fraction of vital body functions. It is possible to anatomically locate neurotransmitters by labeling techniques. It is possible to chemically identify certain neurotransmitters such as catecholamines by fixing neural tissue sections with formaldehyde. This can give rise to formaldehyde-induced fluorescence when exposed to ultraviolet light. Dopamine, a catecholamine, was identified in the nematode C. elegans by using this technique.
Immunocytochemistry, which involves raising antibodies against targeted chemical or biological entities, includes a few other techniques of interest. A targeted neurotransmitter could be specifically tagged by primary and secondary antibodies with radioactive labeling in order to identify the neuro
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https://en.wikipedia.org/wiki/Fisher%27s%20equation
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In mathematics, Fisher's equation (named after statistician and biologist Ronald Fisher) also known as the Kolmogorov–Petrovsky–Piskunov equation (named after Andrey Kolmogorov, Ivan Petrovsky, and Nikolai Piskunov), KPP equation or Fisher–KPP equation is the partial differential equation:It is a kind of reaction–diffusion system that can be used to model population growth and wave propagation.
Details
Fisher's equation belongs to the class of reaction-diffusion equations: in fact, it is one of the simplest semilinear reaction-diffusion equations, the one which has the inhomogeneous term
which can exhibit traveling wave solutions that switch between equilibrium states given by . Such equations occur, e.g., in ecology, physiology, combustion, crystallization, plasma physics, and in general phase transition problems.
Fisher proposed this equation in his 1937 paper The wave of advance of advantageous genes in the context of population dynamics to describe the spatial spread of an advantageous allele and explored its travelling wave solutions.
For every wave speed ( in dimensionless form) it admits travelling wave solutions of the form
where is increasing and
That is, the solution switches from the equilibrium state u = 0 to the equilibrium state u = 1. No such solution exists for c < 2. The wave shape for a given wave speed is unique. The travelling-wave solutions are stable against near-field perturbations, but not to far-field perturbations which can thicken the tail
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https://en.wikipedia.org/wiki/Steven%20Rudich
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Steven Rudich (born October 4, 1961) is a professor in the Carnegie Mellon School of Computer Science. In 1994, he and Alexander Razborov proved that a large class of combinatorial arguments, dubbed natural proofs, was unlikely to answer many of the important problems in computational complexity theory. For this work, they were awarded the Gödel Prize in 2007. He also co-authored a paper demonstrating that all currently known NP-complete problems remain NP-complete even under AC0 or NC0 reductions.
Amongst Carnegie Mellon students, he is best known as the teacher of the class "Great Theoretical Ideas in Computer Science" (formerly named "How to Think Like a Computer Scientist"), often considered one of the most difficult classes in the undergraduate computer science curriculum. He is an editor of the Journal of Cryptology, as well as an accomplished magician. His Erdős number is 2.
Leap@CMU
Rudich (and Merrick Furst, now a Distinguished Professor at the Georgia Institute of Technology) began the Leap@CMU (formerly called Andrew's Leap) summer enrichment program for high school (and occasionally, middle school) students in 1991. The summer enrichment program focuses mainly on theoretical aspects of Computer Science in the morning, followed by lunch recess, and then an elective—Robotics, Programming, or Mathematics Theory. The Programming elective is broken down into Intro Programming, Intermediate Programming, and Advanced Programming. As of 2017, the Math Theory Elective h
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https://en.wikipedia.org/wiki/Pacific%20Blue
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Pacific Blue may refer to:
Pacific Blue (company) (formerly Pacific Hydro), renewable energy company in Australia
Pacific Blue (TV series)
Pacific blue, a shade of azure manufactured by the Crayola company
Pacific Blue (dye), a dye used in cell biology
Virgin Australia Airlines (NZ) and Virgin Australia operated under brand Pacific Blue Airlines in New Zealand between 2003 and 2014
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https://en.wikipedia.org/wiki/Silverman%E2%80%93Toeplitz%20theorem
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In mathematics, the Silverman–Toeplitz theorem, first proved by Otto Toeplitz, is a result in summability theory characterizing matrix summability methods that are regular. A regular matrix summability method is a matrix transformation of a convergent sequence which preserves the limit.
An infinite matrix with complex-valued entries defines a regular summability method if and only if it satisfies all of the following properties:
An example is Cesaro summation, a matrix summability method with
References
Citations
Further reading
Toeplitz, Otto (1911) "Über allgemeine lineare Mittelbildungen." Prace mat.-fiz., 22, 113–118 (the original paper in German)
Silverman, Louis Lazarus (1913) "On the definition of the sum of a divergent series." University of Missouri Studies, Math. Series I, 1–96
, 43-48.
Theorems in analysis
Summability methods
Summability theory
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https://en.wikipedia.org/wiki/Edouard%20Van%20Beneden
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Édouard Joseph Louis Marie Van Beneden (5 March 1846 in Leuven – 28 April 1910 in Liège) was a Belgian embryologist, cytologist and marine biologist. He was professor of zoology at the University of Liège. He contributed to cytogenetics by his works on the roundworm Ascaris. In this work he discovered how chromosomes organized meiosis (the production of gametes).
He is son of Pierre-Joseph Van Beneden, a zoologist and paleontologist.
Van Beneden elucidated, together with Walther Flemming and Eduard Strasburger, the essential facts of mitosis, where, in contrast to meiosis, there is a qualitative and quantitative equality of chromosome distribution to daughter cells. (See karyotype).
Publications
Recherches sur la composition et la signification de l'œuf 1868 Full text available from Archive.org PDF
La maturation de l'oeuf, la fecondation, et les premieres phases du développement embryonnaire des mammifères, d'aprés des recherches faites chez le lapin : communication préliminaire in Bulletins de l'Académie royale de Belgique. 2me.série ; 40(12) 1875
Family
Van Beneden's father, Pierre-Joseph van Beneden (18091894) was also a well-known biologist. He introduced two important terms into evolutionary biology and ecology: mutualism and commensalism.
References
Sources
Hamoir, Gabriel. "La révolution évolutionniste en Belgique: du fixiste Pierre-Joseph Van Beneden à son fils darwiniste Édouard", Presses Universitaires de Liège, 2001.
Belgian zoologists
Academic staff of
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https://en.wikipedia.org/wiki/Social%20parasitism
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Social parasitism or social parasite may refer to the following:
Parasitism (social offense), a label for those deemed to contribute insufficiently to human society
Social parasitism (biology), interspecies relationship based on exploiting interactions between members of a social species
"Social Parasite", a song by Alice in Chains from the album Music Bank
See also
Parasite (disambiguation)
Social science disambiguation pages
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https://en.wikipedia.org/wiki/End%20group
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End groups are an important aspect of polymer synthesis and characterization. In polymer chemistry, they are functional groups that are at the very ends of a macromolecule or oligomer (IUPAC). In polymer synthesis, like condensation polymerization and free-radical types of polymerization, end-groups are commonly used and can be analyzed by nuclear magnetic resonance (NMR) to determine the average length of the polymer. Other methods for characterization of polymers where end-groups are used are mass spectrometry and vibrational spectrometry, like infrared and raman spectroscopy. These groups are important for the analysis of polymers and for grafting to and from a polymer chain to create a new copolymer. One example of an end group is in the polymer poly(ethylene glycol) diacrylate where the end-groups are circled.
End groups in polymer synthesis
End groups are seen on all polymers and the functionality of those end groups can be important in determining the application of polymers. Each type of polymerization (free radical, condensation or etc.) has end groups that are typical for the polymerization, and knowledge of these can help to identify the type of polymerization method used to form the polymer.
Step-growth polymerization
Step-growth polymerization involves two monomers with bi- or multifunctionality to form polymer chains. Many polymers are synthesized via step-growth polymerization and include polyesters, polyamides, and polyurethanes. A sub-class of step-growth p
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https://en.wikipedia.org/wiki/Martinsried
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Martinsried is one of Munich's two science suburbs. It is a section of Planegg municipality in the district of Munich in Bavaria, Germany.
Martinsried is best known as the location of the Max Planck Institute of Biochemistry, the Max Planck Institute of Neurobiology and the
accompanying biotechnology campus, which actually straddles the Munich/Planegg border. The campus is adjacent to the Großhadern hospital campus, housing most of the Faculty of Medicine of the Ludwig Maximilian University of Munich. The Faculty of Chemistry and a part of the Biology Faculty of the university also relocated to this new campus in 1999 and 2005.
Munich's other "science suburb" is Garching, situated to the north on the opposite end of the U6 subway, with a large part of the Technische Universität München and several Max Planck Institutes.
Geography
Martinsried is located in the "Münchner Schotterebene" and borders directly the urban area of Munich near Großhadern. The village center lies about 2.5 km from the centre of Planegg and about 15 km southwest of Munich's city centre.
Infrastructure
North of Martinsried, state road 2343 goes from Gräfelfing to Munich. To the south, state road 2344 goes from Planegg to the junction with the Munich-Fürstenried A95 motorway.
The Martinsried research campus can be reached by the Munich subway line U6 from the Großhadern (change to bus 266) or Klinikum Großhadern stations (15 min. walk). Planning is now underway for a possible future extension of th
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https://en.wikipedia.org/wiki/Max%20Planck%20Institute%20of%20Biochemistry
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The Max Planck Institute of Biochemistry (MPIB) is a research institute of the Max Planck Society located in Martinsried, a suburb of Munich. The institute was founded in 1973 by the merger of three formerly independent institutes: the Max Planck Institute of Biochemistry, the Max Planck Institute of Protein and Leather Research (founded 1954 in Regensburg), and the Max Planck Institute of Cell Chemistry (founded 1956 in Munich).
With 800 employees in currently seven research departments and about 26 research groups, the MPIB is one of the largest biologically medically oriented institutes of the Max Planck Society.
Departments
There are seven departments currently in the institute.
Cellular Biochemistry (Franz-Ulrich Hartl)
Cellular and Molecular Biophysics (Petra Schwille)
Molecular Machines and Signaling (Brenda Schulman)
Molecular Medicine (Reinhard Fässler)
Molecular Structural Biology (Wolfgang Baumeister)
Proteomics and Signal Transduction (Matthias Mann)
Structural Cell Biology (Elena Conti)
Research groups
There are 26 research groups currently based at the MPIB, including 3 emeritus research groups:
Molecular Structural Biology (Wolfgang Baumeister / Cryo-Electron Tomography, Electron Microscopical Structure Research, Protein and Cell Structure, Protein Degradation)
Molecular Mechanisms of DNA Repair (Christian Biertümpfel / Structural Biology, DNA Repair, DNA Replication, DNA Recombination, Protein-DNA-Interactions)
Systems Biology of Membrane Traff
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https://en.wikipedia.org/wiki/Survival%20%28disambiguation%29
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Survival is the act of surviving; to stay living
Survival may also refer to:
Biology
Self-preservation, behavior that ensures the survival of an organism
Survival of the fittest
Medicine and statistics
Survival analysis, a statistical technique to analyze longevity
Survival rate, the percentage of people who are alive for a given period of time
People
Survival Tobita (born 1970), a Japanese professional wrestler
Arts, entertainment, and media
Gaming
Games
Science Horizons Survival, or Survival, a video game for the ZX Spectrum
Survival: The Ultimate Challenge, a 2001 PC strategy game by Techland
Other uses in gaming
Survival game, a genre
Survival mode, a game mode
Genres
Survival film, a film genre
Survival horror, a genre
Literature
Survival!, a 1984 collection of short stories by Gordon R. Dickson
Survival: A Thematic Guide to Canadian Literature, a 1972 book by Margaret Atwood
"Survival", a short story by John Wyndham which appears in the collection The Seeds of Time
Survival (manhwa) (살아남기; Saranamgi), a Korean manhwa comic book
Music
Albums
Survival (Bob Marley and the Wailers album), or the title song
Survival (Born from Pain album), 2008
Survival (Dave East album), 2019
Survival (Grand Funk Railroad album), 1971
Survival (The O'Jays album), or the title song
Songs
"Survival" (Drake song), 2018
"Survival" (Eminem song), 2013
"Survival" (Muse song), 2012
"Survival," by Glay from Heavy Gauge
"Survival," by Madonna from Bedtime
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https://en.wikipedia.org/wiki/Instance%20%28computer%20science%29
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When a computer system creates a new context based on a pre-existing model or scheme, the model is said to have been instantiated. The encapsulated context that results from this instantiation process is referred to as an instance of the model or scheme. This general concept applies specifically across computer science in several ways.
Object-oriented programming
Typically, OOP object instances share a data layout scheme in common with numerous other runtime instances—particularly those of the same or similar data type. In order to ensure that the values stored in each instance are kept separate for the duration of their lifetimes, the system must allocate—and privately associate with each respective new context—a distinct copy of this layout image. This prevents the values in one instance from interfering with the values in any other.
Machine identity
A computer instance can be a software state which exposes an operating system or other hosting environment. Available resources in this virtual machine typically include access to storage, a CPU, and GPU, for example.
Computer graphics
In computer graphics, a polygonal model can be instantiated in order to be drawn several times in different locations in a scene.
This is a technique that can be used to improve the performance of rendering, since a portion of the work needed to display each instance is reused.
Operating systems
In the context of POSIX-oriented operating systems, the term "(program) instance" typically
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https://en.wikipedia.org/wiki/Subclass%20%28set%20theory%29
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In set theory and its applications throughout mathematics, a subclass is a class contained in some other class in the same way that a subset is a set contained in some other set.
That is, given classes A and B, A is a subclass of B if and only if every member of A is also a member of B.
If A and B are sets, then of course A is also a subset of B.
In fact, when using a definition of classes that requires them to be first-order definable, it is enough that B be a set; the axiom of specification essentially says that A must then also be a set.
As with subsets, the empty set is a subclass of every class, and any class is a subclass of itself. But additionally, every class is a subclass of the class of all sets. Accordingly, the subclass relation makes the collection of all classes into a Boolean lattice, which the subset relation does not do for the collection of all sets. Instead, the collection of all sets is an ideal in the collection of all classes. (Of course, the collection of all classes is something larger than even a class!)
References
Set theory
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https://en.wikipedia.org/wiki/Vernon%20Benjamin%20Mountcastle
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Vernon Benjamin Mountcastle (July 15, 1918 – January 11, 2015) was an American neurophysiologist and Professor Emeritus of Neuroscience at Johns Hopkins University. He discovered and characterized the columnar organization of the cerebral cortex in the 1950s. This discovery was a turning point in investigations of the cerebral cortex, as nearly all cortical studies of sensory function after Mountcastle's 1957 paper, on the somatosensory cortex, used columnar organization as their basis.
Early life and education
Vernon Benjamin Mountcastle was born on July 15, 1918, in Shelbyville, Kentucky as the third of five children into a family of "farmers, industrial entrepreneurs, or builders of railroads".
In 1921 his family moved to Roanoke, Virginia where he went to elementary and junior high school and was "an enthusiastic Boy Scout".
Because his mother, a former teacher, had taught him to read and write when he was 4 years old, he immediately moved ahead two grades when entering the public school system and graduated high school at the age of 16.
He entered Roanoke College in Salem, Virginia in 1935, in the midst of the Great Depression, where he majored in chemistry and finished in 3 years. While at Roanoke, he played tennis and was a member of the Sigma Chi Fraternity.
In 1938 he started medical school at Johns Hopkins University where his teachers included William Mansfield Clark, Philip Bard, Adolf Meyer, Arnold Rice Rich, Maxwell Wintrobe, and Warfield Longcope. During his s
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https://en.wikipedia.org/wiki/Beta-dual%20space
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In functional analysis and related areas of mathematics, the beta-dual or -dual is a certain linear subspace of the algebraic dual of a sequence space.
Definition
Given a sequence space the -dual of is defined as
If is an FK-space then each in defines a continuous linear form on
Examples
Properties
The beta-dual of an FK-space is a linear subspace of the continuous dual of . If is an FK-AK space then the beta dual is linear isomorphic to the continuous dual.
Functional analysis
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https://en.wikipedia.org/wiki/Bijection%2C%20injection%20and%20surjection
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In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other.
A function maps elements from its domain to elements in its codomain. Given a function :
The function is injective, or one-to-one, if each element of the codomain is mapped to by at most one element of the domain, or equivalently, if distinct elements of the domain map to distinct elements in the codomain. An injective function is also called an injection. Notationally:
or, equivalently (using logical transposition),
The function is surjective, or onto, if each element of the codomain is mapped to by at least one element of the domain. That is, the image and the codomain of the function are equal. A surjective function is a surjection. Notationally:
The function is bijective (one-to-one and onto, one-to-one correspondence, or invertible) if each element of the codomain is mapped to by exactly one element of the domain. That is, the function is both injective and surjective. A bijective function is also called a bijection. That is, combining the definitions of injective and surjective,
where means "there exists exactly one ".
In any case (for any function), the following holds:
An injective function need not be surjective (not all elements of the codomain may be associated with arguments), and a surjective function need no
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https://en.wikipedia.org/wiki/Domenico%20Comparetti
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Domenico Comparetti (27 June 183520 January 1927) was an Italian scholar. He was born in Rome and died in Florence.
Life
He studied at the University of Rome La Sapienza, took his degree in 1855 in natural science and mathematics, and entered his uncle's pharmacy as an assistant. His scanty leisure was, however, given to study. He learned Greek by himself, and gained facility in the modern language by conversing with the Greek students at the university. In spite of all disadvantages, he not only mastered the language but became one of the chief classical scholars of Italy.
In 1857 he published, in the Rheinisches Museum, a translation of some recently discovered fragments of Hypereides, with a dissertation on that orator. This was followed by a notice of the annalist Granius Licinianus, and one on the oration of Hypereides on the Lamian War. In 1859 he was appointed professor of Greek at Pisa on the recommendation of the duke of Sermoneta. A few years later he was called to a similar post at Florence, remaining emeritus professor at Pisa also. He subsequently took up his residence in Rome as lecturer on Greek antiquities and greatly interested himself in the Roman Forum excavations. He was a member of the governing bodies of the academies of Milan, Venice, Naples and Turin. He was appointed senator in 1891.
In Pisa, in 1863, he met Leone Raffalovich, a businessman from Odessa. After a short engagement, he married Leone's daughter Elena on 13 August, and in 1865 their dau
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https://en.wikipedia.org/wiki/Robert%20Watson%20%28computer%20scientist%29
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Robert Nicholas Maxwell Watson (born 3 May 1977) is a FreeBSD developer, and founder of the TrustedBSD Project. He is currently employed as a Professor of Systems, Security, and Architecture in the Security Research Group at the University of Cambridge Computer Laboratory.
Education
Watson graduated in computer science from Carnegie Mellon University and has attained a PhD from University of Cambridge. As well as Cambridge, he has worked at the National Institutes of Health, Carnegie Mellon University, Trusted Information Systems, Network Associates, McAfee, and SPARTA. He obtained a PhD in computer security from the University of Cambridge Computer Laboratory, supervised by Ross Anderson and sponsored by Google.
Research
Watson's work has been supported by DARPA, Apple Computer, the Navy, and other US government agencies. His main research interests are network security and operating system security. His main open source software contributions include his work in developing the multi-threaded and multi-processor FreeBSD network stack, the TrustedBSD project, and OpenBSM. His writing has been featured in forums such as ACM's Queue Magazine, the USENIX Annual Technical Conference, BSDCon, and a Slashdot interview. He was also a FreeBSD Core Team member from 2000 to 2012. Watson is coauthor of the standard textbook The Design and Implementation of the FreeBSD Operating System (2nd ed., 2015) by Marshall Kirk McKusick.
References
Free software programmers
Living people
Free
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https://en.wikipedia.org/wiki/Hendricus%20Stoof
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Hendricus Theodorus Christiaan "Henk" Stoof (born 1962) is a professor in theoretical physics at Utrecht University in the Netherlands. His main interests are atomic physics, condensed matter physics and many-body physics. He is a Fellow of the American Physical Society.
During the last ten years, the group of H.T.C. Stoof has been involved in the study of various aspects of the physics of ultracold atomic gases. In addition, they performed research on skyrmion lattices in the quantum Hall effect and collective modes in supersolid 4He. Below the results obtained from the study of degenerate Fermi gases are briefly summarized.
Already in 1996 they predicted that an atomic gas of 6Li (a fermionic isotope of lithium) becomes a Bardeen-Cooper-Schrieffer (BCS) superfluid at experimentally obtainable temperatures. They have also performed a detailed study of the superfluid behaviour of this gas below the critical temperature. Motivated by this work, at least six experimental groups from around the world, including the groups of R. Grimm, R.G. Hulet, D.S. Jin, and W. Ketterle, started trying to achieve the necessary conditions for the BCS transition in 6Li.
In the last seven years the study of superfluidity in Fermi gases has been at the center of attention of the ultracold atoms community. It is fair to say that the very successful experiments, that ultimately have led to the creation of the superconductor with, as a fraction of the Fermi energy, the highest critical temperature
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https://en.wikipedia.org/wiki/Superhelix
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A superhelix is a molecular structure in which a helix is itself coiled into a helix. This is significant to both proteins and genetic material, such as overwound circular DNA.
The earliest significant reference in molecular biology is from 1971, by F. B. Fuller:
A geometric invariant of a space curve, the writhing number, is defined and studied. For the central curve of a twisted cord the writhing number measures the extent to which coiling of the central curve has relieved local twisting of the cord. This study originated in response to questions that arise in the study of supercoiled double-stranded DNA rings.</blockquote>
About the writhing number, mathematician W. F. Pohl says:
<blockquote>It is well known that the writhing number is a standard measure of the global geometry of a closed space curve.
Contrary to intuition, a topological property, the linking number, arises from the geometric properties twist and writhe according to the following relationship:
Lk= T + W,
where Lk is the linking number, W is the writhe and T is the twist of the coil.
The linking number refers to the number of times that one strand wraps around the other. In DNA this property does not change and can only be modified by specialized enzymes called topoisomerases.
See also
DNA supercoil (superhelical DNA)
Knot theory
References
External links
DNA Structure and Topology at Molecular Biochemistry II: The Bello Lectures.
Helices
Molecular biology
Molecular topology
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https://en.wikipedia.org/wiki/Ben%20Shneiderman
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Ben Shneiderman (born August 21, 1947) is an American computer scientist, a Distinguished University Professor in the University of Maryland Department of Computer Science, which is part of the University of Maryland College of Computer, Mathematical, and Natural Sciences at the University of Maryland, College Park, and the founding director (1983-2000) of the University of Maryland Human-Computer Interaction Lab. He conducted fundamental research in the field of human–computer interaction, developing new ideas, methods, and tools such as the direct manipulation interface, and his eight rules of design.
Early life and education
Born in New York, Shneiderman, attended the Bronx High School of Science, and received a BS in Mathematics and Physics from the City College of New York in 1968. He then went on to study at the State University of New York at Stony Brook, where he received an MS in Computer Science in 1972 and graduated with a PhD in 1973.
Career
Shneiderman started his academic career at the State University of New York at Farmingdale in 1968 as instructor at the Department of Data Processing. In the last year before his graduation he was an instructor at the Department of Computer Science of Stony Brook University (then called State University of New York at Stony Brook). In 1973 he was appointed assistant professor at the Indiana University, Department of Computer Science. In 1976 he moved to the University of Maryland. He started out as assistant professor in
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https://en.wikipedia.org/wiki/Load%20factor
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Load factor may refer to:
Load factor (aeronautics), the ratio of the lift of an aircraft to its weight
Load factor (computer science), the ratio of the number of records to the number of addresses within a data structure
Load factor (electrical), the average power divided by the peak power over a period of time
Capacity factor, the ratio of actual energy output to the theoretical maximum possible in a power station
Passenger load factor, the ratio of revenue passenger miles to available seat miles of a particular transportation operation (e.g. a flight)
Factor loadings in statistics, the exposure to specific factors or components in Factor Analysis or Principal Component Analysis
See also
Add-on factor - sometimes called load factor
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https://en.wikipedia.org/wiki/NUS%20High%20School%20of%20Math%20and%20Science
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The NUS High School of Math and Science, also known as NUS High School or NUSH, is a specialised independent high school in Singapore offering a six-year Integrated Programme (IP) leading to the NUS High School Diploma. Its parent university is the National University of Singapore.
The school offers an accelerated mathematics and science curriculum integrated with language, arts, humanities, and sports, in a modular system. Over 70% of its graduates have pursued Science, Technology, Engineering and Medicine-related courses in university.
Curriculum
Academic curriculum
NUS High School is an Integrated Programme school, which allows students to bypass the GCE O Levels. However, unlike other Integrated Programme schools, it does not offer GCE A Level or International Baccalaureate programmes. Instead, it offers an NUS High School Diploma, which is recognized by all universities in Singapore, as well as by universities worldwide.
The diploma's curriculum is based on a modular system similar to its parent university NUS. Core modules are compulsory, elective modules help deepen the student's knowledge and may be compulsory for a major in a particular subject, and enrichment modules are purely for the student's interests. The school uses the cumulative average point (CAP) system, a 5-point system similar to the grade point average used in the United States. This is unlike most other schools in Singapore, where subjects are graded according to the British GCSE System.
The schoo
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https://en.wikipedia.org/wiki/Differential-algebraic%20system%20of%20equations
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In electrical engineering, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system.
In mathematics these are examples of differential algebraic varieties and correspond to ideals in differential polynomial rings (see the article on differential algebra for the algebraic setup).
We can write these differential equations for a dependent vector of variables x in one independent variable t, as
When considering these symbols as functions of a real variable (as is the case in applications in electrical engineering or control theory) we look at as a vector of dependent variables and the system has as many equations, which we consider as functions .
They are distinct from ordinary differential equation (ODE) in that a DAE is not completely solvable for the derivatives of all components of the function x because these may not all appear (i.e. some equations are algebraic); technically the distinction between an implicit ODE system [that may be rendered explicit] and a DAE system is that the Jacobian matrix is a singular matrix for a DAE system. This distinction between ODEs and DAEs is made because DAEs have different characteristics and are generally more difficult to solve.
In practical terms, the distinction between DAEs and ODEs is often that the solution of a DAE system depends on the derivatives of the input signal and not just the signal itself as i
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https://en.wikipedia.org/wiki/Dr%20Tatiana%27s%20Sex%20Advice%20to%20All%20Creation
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Dr Tatiana's Sex Advice to All Creation: The Definitive Guide to the Evolutionary Biology of Sex is a 2002 popular science book by the British evolutionary biologist Olivia Judson written in the role of her alter ego, agony aunt Dr Tatiana. Dr Tatiana receives letters from various creatures about their sex lives, and responds by explaining the biology of sex to creatures concerned.
The book grew out of the article "Sex Is War!" she had written for the Economist in 1997. It became an international best-seller and was nominated for the Samuel Johnson Prize for Non-Fiction in 2003. It was later turned into a musical of the same name, shown on Channel 4 in 2005.
References
(UK edition)
(US edition)
External links
Dr Tatiana's Sex Advice to All Creation, Google Books
2002 non-fiction books
Books about evolution
Non-fiction books about sexuality
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https://en.wikipedia.org/wiki/Bruno%20Pontecorvo
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Bruno Pontecorvo (; , Bruno Maksimovich Pontecorvo; 22 August 1913 – 24 September 1993) was an Italian and Soviet nuclear physicist, an early assistant of Enrico Fermi and the author of numerous studies in high energy physics, especially on neutrinos. A convinced communist, he defected to the Soviet Union in 1950, where he continued his research on the decay of the muon and on neutrinos. The prestigious Pontecorvo Prize was instituted in his memory in 1995.
The fourth of eight children of a wealthy Jewish-Italian family, Pontecorvo studied physics at the University of Rome La Sapienza, under Fermi, becoming the youngest of his Via Panisperna boys. In 1934 he participated in Fermi's famous experiment showing the properties of slow neutrons that led the way to the discovery of nuclear fission. He moved to Paris in 1936, where he conducted research under Irène and Frédéric Joliot-Curie. Influenced by his cousin, Emilio Sereni, he joined the Italian Communist Party, whose leader were in Paris as refugees, and as did his sisters Giuliana and Laura and brother Gillo. The Italian Fascist regime's 1938 racial laws against Jews caused his family members to leave Italy for Britain, France and the United States.
When the German Army closed in on Paris during the Second World War, Pontecorvo, his brother Gillo, cousin Emilio Sereni and Salvador Luria fled the city on bicycles. He eventually made his way to Tulsa, Oklahoma, where he applied his knowledge of nuclear physics to prospecti
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https://en.wikipedia.org/wiki/IFM
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IFM may refer to:
Organisations
IFM Therapeutics, a US-based pharmaceutical company
Institute of Fisheries Management, a UK non-profit organisation
(Malaysian: 'Malaysian Physics Institute'), a Malaysian professional body
Institute for Media and Communication Policy, a German research institution
Intergalactic FM, an online radio station based in the Netherlands
(French: 'French Institute of Fashion'), a French higher-education institution
iFM is a station of Radio Mindanao Network in the Philippines
Science and technology
Immunofluorescence microscopy, a technique used for light microscopy
Incremental funding methodology, an approach to software development
Forest fire weather index, () a risk estimate
Interaction-free measurement, in quantum mechanics
Other
Independent forest monitoring, in forest law enforcement
International Formula Master, a form of Motor Racing
IFM Investors, an Australian investment management company
See also
International Falcon Movement – Socialist Educational International, a federation of international progressive youth education organisations
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https://en.wikipedia.org/wiki/Exact%20Equation
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In mathematics, the term exact equation can refer either of the following:
Exact differential equation
Exact differential form
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https://en.wikipedia.org/wiki/Nakayama%27s%20lemma
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In mathematics, more specifically abstract algebra and commutative algebra, Nakayama's lemma — also known as the Krull–Azumaya theorem — governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field. It is an important tool in algebraic geometry, because it allows local data on algebraic varieties, in the form of modules over local rings, to be studied pointwise as vector spaces over the residue field of the ring.
The lemma is named after the Japanese mathematician Tadashi Nakayama and introduced in its present form in , although it was first discovered in the special case of ideals in a commutative ring by Wolfgang Krull and then in general by Goro Azumaya (1951). In the commutative case, the lemma is a simple consequence of a generalized form of the Cayley–Hamilton theorem, an observation made by Michael Atiyah (1969). The special case of the noncommutative version of the lemma for right ideals appears in Nathan Jacobson (1945), and so the noncommutative Nakayama lemma is sometimes known as the Jacobson–Azumaya theorem. The latter has various applications in the theory of Jacobson radicals.
Statement
Let be a commutative ring with identity 1. The following is Nakayama's lemma, as stated in :
Statement 1: Let be an ideal in , and a finitely gener
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https://en.wikipedia.org/wiki/Jack%20Lewis%2C%20Baron%20Lewis%20of%20Newnham
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Jack Lewis, Baron Lewis of Newnham, FRS, HonFRSC (13 February 1928 – 17 July 2014) was an English chemist working mainly in the area of inorganic chemistry.
Education and personal life
Educated at Barrow Grammar School, he graduated in 1949 with a bachelor's degree in chemistry from the University of London, after which he moved to the University of Nottingham where he obtained his Ph.D.
In 1951 he married Elfreida "Freddie" Lamb (1928-2023). They had one son and one daughter.
Professional career
In 1953 he was appointed lecturer at the University of Sheffield before returning to London in 1956 as a lecturer at Imperial College London. He was Professor of Chemistry at the University of Manchester from 1961 to 1967, University College London from 1967 to 1970, and the University of Cambridge from 1970 to 1995. He was also the first Warden of Robinson College, the newest of the Cambridge colleges, from its foundation in 1977 until 2001.
He was elected a Fellow of the Royal Society (FRS) in 1973 and was awarded their Davy Medal in 1985, and their Royal Medal in 2004. He was also an Honorary Fellow of the Royal Society of Chemistry, and its president from 1986 to 1988. He was a member of the American Academy of Arts and Sciences, the National Academy of Sciences, and the American Philosophical Society.
He was knighted in 1982 and created Baron Lewis of Newnham of Newnham in the County of Cambridgeshire on 8 February 1989. He was a member of the House of Lords, where he sat
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https://en.wikipedia.org/wiki/Teichm%C3%BCller%20space
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In mathematics, the Teichmüller space of a (real) topological (or differential) surface is a space that parametrizes complex structures on up to the action of homeomorphisms that are isotopic to the identity homeomorphism. Teichmüller spaces are named after Oswald Teichmüller.
Each point in a Teichmüller space may be regarded as an isomorphism class of "marked" Riemann surfaces, where a "marking" is an isotopy class of homeomorphisms from to itself. It can be viewed as a moduli space for marked hyperbolic structure on the surface, and this endows it with a natural topology for which it is homeomorphic to a ball of dimension for a surface of genus . In this way Teichmüller space can be viewed as the universal covering orbifold of the Riemann moduli space.
The Teichmüller space has a canonical complex manifold structure and a wealth of natural metrics. The study of geometric features of these various structures is an active body of research.
The sub-field of mathematics that studies the Teichmüller space is called Teichmüller theory.
History
Moduli spaces for Riemann surfaces and related Fuchsian groups have been studied since the work of Bernhard Riemann (1826-1866), who knew that parameters were needed to describe the variations of complex structures on a surface of genus . The early study of Teichmüller space, in the late nineteenth–early twentieth century, was geometric and founded on the interpretation of Riemann surfaces as hyperbolic surfaces. Among the main
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https://en.wikipedia.org/wiki/Riesz%E2%80%93Fischer%20theorem
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In mathematics, the Riesz–Fischer theorem in real analysis is any of a number of closely related results concerning the properties of the space L2 of square integrable functions. The theorem was proven independently in 1907 by Frigyes Riesz and Ernst Sigismund Fischer.
For many authors, the Riesz–Fischer theorem refers to the fact that the Lp spaces from Lebesgue integration theory are complete.
Modern forms of the theorem
The most common form of the theorem states that a measurable function on is square integrable if and only if the corresponding Fourier series converges in the Lp space This means that if the Nth partial sum of the Fourier series corresponding to a square-integrable function f is given by
where the nth Fourier coefficient, is given by
then
where is the -norm.
Conversely, if is a two-sided sequence of complex numbers (that is, its indices range from negative infinity to positive infinity) such that
then there exists a function f such that f is square-integrable and the values are the Fourier coefficients of f.
This form of the Riesz–Fischer theorem is a stronger form of Bessel's inequality, and can be used to prove Parseval's identity for Fourier series.
Other results are often called the Riesz–Fischer theorem . Among them is the theorem that, if A is an orthonormal set in a Hilbert space H, and then
for all but countably many and
Furthermore, if A is an orthonormal basis for H and x an arbitrary vector, the series
converges (or ) to
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https://en.wikipedia.org/wiki/AD-mix
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In organic chemistry, AD-mix is a commercially available mixture of reagents that acts as an asymmetric catalyst for various chemical reactions, including the Sharpless asymmetric dihydroxylation of alkenes. The two letters AD, stand for asymmetric dihydroxylation. The mix is available in two variations, "AD-mix α" and "AD-mix β" following ingredient lists published by Barry Sharpless.
The mixes contain:
Potassium osmate K2OsO2(OH)4 as the source of Osmium tetroxide
Potassium ferricyanide K3Fe(CN)6, which is the re-oxidant in the catalytic cycle
Potassium carbonate
A chiral ligand:
AD-mix α contains (DHQ)2PHAL, the phthalazine adduct with dihydroquinine
AD-mix β contains (DHQD)2PHAL, the phthalazine adduct with dihydroquinidine
References
External links
Catalytic Asymmetric Dihydroxylation of Alkenes at Imperial College London Link
Reagents for organic chemistry
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https://en.wikipedia.org/wiki/Sparse%20conditional%20constant%20propagation
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In computer science, sparse conditional constant propagation (SCCP) is an optimization frequently applied in compilers after conversion to static single assignment form (SSA). It simultaneously removes some kinds of dead code and propagates constants throughout a program. Moreover, it can find more constant values, and thus more opportunities for improvement, than separately applying dead code elimination and constant propagation in any order or any number of repetitions.
The algorithm operates by performing abstract interpretation of the code in SSA form. During abstract interpretation, it typically uses a flat lattice of constants for values and a global environment mapping SSA variables to values in this lattice. The crux of the algorithm comes in how it handles the interpretation of branch instructions. When encountered, the condition for a branch is evaluated as best possible given the precision of the abstract values bound to variables in the condition. It may be the case that the values are perfectly precise (neither top nor bottom) and hence, abstract execution can decide in which direction to branch. If the values are not constant, or a variable in the condition is undefined, then both branch directions must be taken to remain conservative.
Upon completion of the abstract interpretation, instructions which were never reached are marked as dead code. SSA variables found to have constant values may then be inlined at (propagated to) their point of use.
Note
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https://en.wikipedia.org/wiki/Autodynamics
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Autodynamics was a physics theory proposed by Ricardo Carezani (1921–2016.) In the early, 1940s as a replacement for Einstein's theories of special relativity and general relativity. Autodynamics never gained status as a viable alternative model within the physics community, and today is wholly rejected by mainstream science.
Main tenets of autodynamics
The primary claim of autodynamics is that the equations of the Lorentz transformation are incorrectly formulated to describe relativistic effects, which would invalidate special relativity, general relativity, and Maxwell's equations. The effect of the revised equations proposed in autodynamics is to cause particle mass to decrease with particle velocity, being exchanged with kinetic energy (with mass being zero and kinetic energy being equal to the rest mass at c). This exchange between mass and energy is the proposed mechanism underlying most of the derived conclusions of autodynamics.
Ancillary predictions of autodynamics include:
the nonexistence of the neutrino,
the existence of additional particles that have not been observed by mainstream physicists (including the "picograviton" and the "electromuon"),
the existence of additional decay modes for muons and interaction modes for energetic atomic nuclei.
Status of autodynamics
Autodynamics is wholly rejected by the mainstream scientific community. Since Carezani's original publication, no papers on autodynamics have appeared in the scientific literature, except fo
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https://en.wikipedia.org/wiki/Dobi%C5%84ski%27s%20formula
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In combinatorial mathematics, Dobiński's formula states that the n-th Bell number Bn (i.e., the number of partitions of a set of size n) equals
where denotes Euler's number.
The formula is named after G. Dobiński, who published it in 1877.
Probabilistic content
In the setting of probability theory, Dobiński's formula represents the nth moment of the Poisson distribution with mean 1. Sometimes Dobiński's formula is stated as saying that the number of partitions of a set of size n equals the nth moment of that distribution.
Reduced formula
The computation of the sum of Dobiński's series can be reduced to a finite sum of terms, taking into account the information that is an integer. Precisely one has, for any integer
provided (a condition that of course implies , but that is satisfied by some of size ). Indeed, since , one has
Therefore for all
so that the tail is dominated by the series , which implies , whence the reduced formula.
Generalization
Dobiński's formula can be seen as a particular case, for , of the more general relation:
and for in this formula for Touchard polynomials
Proof
One proof relies on a formula for the generating function for Bell numbers,
The power series for the exponential gives
so
The coefficient of in this power series must be , so
Another style of proof was given by Rota. Recall that if x and n are nonnegative integers then the number of one-to-one functions that map a size-n set into a size-x set is the falling f
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https://en.wikipedia.org/wiki/Loop%20dependence%20analysis
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In computer science, loop dependence analysis is a process which can be used to find dependencies within iterations of a loop with the goal of determining different relationships between statements. These dependent relationships are tied to the order in which different statements access memory locations. Using the analysis of these relationships, execution of the loop can be organized to allow multiple processors to work on different portions of the loop in parallel. This is known as parallel processing. In general, loops can consume a lot of processing time when executed as serial code. Through parallel processing, it is possible to reduce the total execution time of a program through sharing the processing load among multiple processors.
The process of organizing statements to allow multiple processors to work on different portions of a loop is often referred to as parallelization. In order to see how we can exploit parallelization, we have to first analyze the dependencies within individual loops. These dependencies will help determine which statements in the loop need to be completed before other statements can start, and which statements in the loop can be executed in parallel with respect to the other statements in the loop. Two general categories of dependencies that will be analyzed in the loop are data dependencies and control dependencies.
Description
Loop dependence analysis occur on a normalized loop of the form:
for i1 until U1 do
for i2 until U2 do
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https://en.wikipedia.org/wiki/Record-oriented%20filesystem
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In computer science, a record-oriented filesystem is a file system where data is stored as collections of records. This is in contrast to a byte-oriented filesystem, where the data is treated as an unformatted stream of bytes. There are several different possible record formats; the details vary depending on the particular system. In general the formats can be fixed-length or variable length, with different physical organizations or padding mechanisms; metadata may be associated with the file records to define the record length, or the data may be part of the record. Different access methods for records may be provided, for example records may be retrieved in sequential order, by key, or by record number.
Origin and characteristics
Record-oriented filesystems are frequently associated with mainframe operating systems, such as OS/360 and successors and DOS/360 and successors, and midrange operating systems, such as RSX-11 and VMS. However, they originated earlier in software such as Input/Output Control System (IOCS). Records, sometimes called logical records, are often written together in blocks, sometimes called physical records; this is the norm for direct access and tape devices, but files on unit record devices are normally unblocked, i.e., there is only one record per block.
Record-oriented filesystems can be supported on media other than direct access devices. A deck of punched cards can be considered a record-oriented file. A magnetic tape is an example of a mediu
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https://en.wikipedia.org/wiki/List%20of%20plasma%20physicists
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This is a list of physicists who have worked in or made notable contributions to the field of plasma physics.
See also
Whistler (radio) waves
Langmuir waves
Plasma physicists
Plasma physicists
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https://en.wikipedia.org/wiki/Complete%20Boolean%20algebra
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In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to construct Boolean-valued models of set theory in the theory of forcing. Every Boolean algebra A has an essentially unique completion, which is a complete Boolean algebra containing A such that every element is the supremum of some subset of A. As a partially ordered set, this completion of A is the Dedekind–MacNeille completion.
More generally, if κ is a cardinal then a Boolean algebra is called κ-complete if every subset of cardinality less than κ has a supremum.
Examples
Complete Boolean algebras
Every finite Boolean algebra is complete.
The algebra of subsets of a given set is a complete Boolean algebra.
The regular open sets of any topological space form a complete Boolean algebra. This example is of particular importance because every forcing poset can be considered as a topological space (a base for the topology consisting of sets that are the set of all elements less than or equal to a given element). The corresponding regular open algebra can be used to form Boolean-valued models which are then equivalent to generic extensions by the given forcing poset.
The algebra of all measurable subsets of a σ-finite measure space, modulo null sets, is a complete Boolean algebra. When the measure space is the unit interval with the σ-algebra of Lebesgue measurable sets, the Boolean algebra is called the random algeb
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https://en.wikipedia.org/wiki/Stephen%20Epstein%20%28cardiologist%29
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Stephen E. Epstein is the Head of Translational and Vascular Biology Research at the MedStar Heart and Vascular Institute, MedStar Washington Hospital Center and Clinical Professor of Medicine at the Georgetown University School of Medicine.
Early Education
After graduating summa cum laude from Columbia College and elected to Phi Beta Kappa, Epstein took his medical training at Cornell University Medical College. He was elected to AOA, the medical honor society. Epstein interned at the New York Hospital, New York, NY.
Career
Epstein served for over 30 years as Chief of the Cardiology Branch of the NHLBI at the National Institutes of Health in Bethesda, MD. He then served as Executive Director of the Cardiovascular Research Institute and Director of Vascular Biology Research, at the MedStar Health Research Institute, Washington Hospital Center. He currently serves as Head of Translational Research at the MedStar Heart and Vascular Institute, MedStar Washington Hospital Center.
With more than 500 publications in peer‐reviewed medical journals, Epstein is a recognized international authority on angiogenesis and on the application of stem cell strategies for cardiovascular therapeutics. His recent work on stem cell therapy has demonstrated that mesenchymal stem cells (MSCs) when administered intravenously to mice with acute myocardial infarction and to mice with ischemic cardiomyopathy, markedly attenuate the progressive development of adverse left ventricular remodeling an
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https://en.wikipedia.org/wiki/Crypton%20%28particle%29
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In particle physics, the crypton is a hypothetical superheavy particle, thought to exist in a hidden sector of string theory. It has been proposed as a candidate particle to explain the dark matter content of the universe. Cryptons arising in the hidden sector of a superstring-derived flipped SU(5) GUT model have been shown to be metastable with a lifetime exceeding the age of the universe. Their slow decays may provide a source for the ultra-high-energy cosmic rays (UHECR).
References
Hypothetical elementary particles
String theory
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https://en.wikipedia.org/wiki/Solomon%20Marcus
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Solomon Marcus (; 1 March 1925 – 17 March 2016) was a Romanian mathematician, member of the Mathematical Section of the Romanian Academy (full member from 2001) and emeritus professor of the University of Bucharest's Faculty of Mathematics.
His main research was in the fields of mathematical analysis, mathematical and computational linguistics and computer science. He also published numerous papers on various cultural topics: poetics, linguistics, semiotics, philosophy, and history of science and education.
Early life and education
He was born in Bacău, Romania, to Sima and Alter Marcus, a Jewish family of tailors. From an early age he had to live through dictatorships, war, infringements on free speech and free thinking as well as anti-Semitism. At the age of 16 or 17 he started tutoring younger pupils in order to help his family financially.
He graduated from Ferdinand I High School in 1944, and completed his studies at the University of Bucharest's Faculty of Science, Department of Mathematics, in 1949. He continued tutoring throughout college and later recounted in an interview that he had to endure hunger during those years and that till the age of 20 he only wore hand-me-downs from his older brothers.
Academic career
Marcus obtained his PhD in Mathematics in 1956, with a thesis on the Monotonic functions of two variables, written under the direction of Miron Nicolescu. He was appointed Lecturer in 1955, Associate Professor in 1964, and became a Professor in 1966 (Em
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https://en.wikipedia.org/wiki/Via%20Panisperna%20boys
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Via Panisperna boys (Italian: I ragazzi di Via Panisperna) is the name given to a group of young Italian scientists led by Enrico Fermi, who worked at the Royal Physics Institute of the University of Rome La Sapienza. In 1934 they made the famous discovery of slow neutrons, which later made possible the nuclear reactor and then the construction of the first atomic bomb.
The nickname of the group comes from the address of the Institute, located in a street of Rione Monti in the city centre, which got its name from a nearby monastery, San Lorenzo in Panisperna.
The other members of the group were Edoardo Amaldi, Oscar D'Agostino, Ettore Majorana, Bruno Pontecorvo, Franco Rasetti and Emilio Segrè. All were physicists, except for D'Agostino, who was a chemist.
The growth of the group
The group grew under the supervision of the physicist, minister, senator and director of the Institute of Physics Orso Mario Corbino. Corbino recognized the qualities of Enrico Fermi and led the commission which appointed him in 1926 to one of the first three professorships in Theoretical Physics in Italy. From 1929, Fermi and Corbino dedicated themselves to the transformation of the institute into a modern research centre.
Rasetti and Fermi were contemporaries, who had met as undergraduates at Pisa, and worked together in Florence. The first of the Boys to join them was Segrè, who had been studying engineering. Segrè had got to know Rasetti through mountaineering and then been drawn into physic
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https://en.wikipedia.org/wiki/Neutron%20interferometer
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In physics, a neutron interferometer is an interferometer capable of diffracting neutrons, allowing the wave-like nature of neutrons, and other related phenomena, to be explored.
Interferometry
Interferometry inherently depends on the wave nature of the object. As pointed out by de Broglie in his PhD thesis, particles, including neutrons, can behave like waves (the so-called wave–particle duality, now explained in the general framework of quantum mechanics). The wave functions of the individual interferometer paths are created and recombined coherently which needs the application of dynamical theory of diffraction. Neutron interferometers are the counterpart of X-ray interferometers and are used to study quantities or benefits related to thermal neutron radiation.
Applications
In 1975 Werner and Overhauser demonstrated quantum phase shifts on neutron matter waves due to gravity. The interferometer was oriented such that two paths are at different heights in Earth's gravitational field. The interferometer was sufficiently sensitive to detected the phase shift due to different acceleration. The phase shift originates from time-dilation differences along the two paths.
Construction
Like X-ray interferometers, neutron interferometers are typically made from a single large crystal of silicon, often 10 to 30 or more centimeters in diameter and 20 to 60 cm or more in length. Modern semiconductor technology allows large single-crystal silicon boules to be easily grown. Since the b
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https://en.wikipedia.org/wiki/Genetic%20fuzzy%20systems
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In computer science and operations research, Genetic fuzzy systems are fuzzy systems constructed by using genetic algorithms or genetic programming, which mimic the process of natural evolution, to identify its structure and parameter.
When it comes to automatically identifying and building a fuzzy system, given the high degree of nonlinearity of the output, traditional linear optimization tools have several limitations. Therefore, in the framework of soft computing, genetic algorithms (GAs) and genetic programming (GP) methods have been used successfully to identify structure and parameters of fuzzy systems.
Fuzzy systems
Fuzzy systems are fundamental methodologies to represent and process linguistic information, with mechanisms to deal with uncertainty and imprecision. For instance, the task of modeling a driver parking a car involves greater difficulty in writing down a concise mathematical model as the description becomes more detailed. However, the level of difficulty is not so much using simple linguistic rules, which are themselves fuzzy. With such remarkable attributes, fuzzy systems have been widely and successfully applied to control, classification and modeling problems (Mamdani, 1974) (Klir and Yuan, 1995) (Pedrycz and Gomide, 1998).
Although simplistic in its design, the identification of a fuzzy system is a rather complex task that comprises the identification
of (a) the input and output variables, (b) the rule base (knowledge base), (c) the membership func
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https://en.wikipedia.org/wiki/S-TEC
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S-TEC may refer to:
S-TEC Corporation, a US corporation and manufacturer of flight control systems
Daewoo S-TEC engine, low-displacement engine codeveloped by Suzuki and Daewoo Motors
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https://en.wikipedia.org/wiki/Power%20closed
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In mathematics a p-group is called power closed if for every section of the product of powers is again a th power.
Regular p-groups are an example of power closed groups. On the other hand, powerful p-groups, for which the product of powers is again a th power are not power closed, as this property does not hold for all sections of powerful p-groups.
The power closed 2-groups of exponent at least eight are described in .
References
Group theory
P-groups
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https://en.wikipedia.org/wiki/Romer%27s%20gap
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Romer's gap is an example of an apparent gap in the tetrapod fossil record used in the study of evolutionary biology. Such gaps represent periods from which excavators have not yet found relevant fossils. Romer's gap is named after paleontologist Alfred Romer, who first recognised it. Recent discoveries in Scotland are beginning to close this gap in palaeontological knowledge.
Age
Romer's gap ran from approximately 360 to 345 million years ago, corresponding to the first 15 million years of the Carboniferous, the early Mississippian (starting with the Tournaisian and moving into the Visean). The gap forms a discontinuity between the primitive forests and high diversity of fishes in the end Devonian and more modern aquatic and terrestrial assemblages of the early Carboniferous.
Mechanism behind the gap
There has been long debate as to why there are so few fossils from this time period. Some have suggested the problem was of fossilization itself, suggesting that there may have been differences in the geochemistry of the time that did not favour fossil formation. Also, excavators simply may not have dug in the right places. The existence of a true low point in vertebrate diversity has been supported by independent lines of evidence, however recent finds in five new locations in Scotland have yielded multiple fossils of early tetrapods and amphibians. They have also allowed the most accurate logging of the geology of this period. This new evidence suggests that - at least loc
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https://en.wikipedia.org/wiki/Outline%20of%20energy
|
The following outline is provided as an overview of and topical guide to energy:
Energy – in physics, this is an indirectly observed quantity often understood as the ability of a physical system to do work on other physical systems. Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert force (a pull or a push) against an object that is moving along a definite path of certain length.
Forms of energy
Chemical energy – energy contained in molecules
Electrical energy – energy from electric fields
Electro-centric energy – energy sustaining the continuous motion of free electrons.
Gravitational energy – energy from gravitational fields
Ionization energy – energy that binds an electron to its atom or molecule
Kinetic energy – (), energy of the motion of a body
Magnetic energy – energy from magnetic fields
Mechanical energy – The sum of (usually macroscopic) kinetic and potential energies
Mechanical wave – (), a form of mechanical energy propagated by a material's oscillations
Nuclear binding energy – energy that binds nucleons to form the atomic nucleus
Potential energy – energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors.
Elastic energy – energy of deformation of a material (or its container) exhibiting a restorative force
Gravitational energy – potential energy associated with a gravitational field.
Nuclear
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https://en.wikipedia.org/wiki/Powerful%20p-group
|
In mathematics, in the field of group theory, especially in the study of p-groups and pro-p-groups, the concept of powerful p-groups plays an important role. They were introduced in , where a number of applications are given, including results on Schur multipliers. Powerful p-groups are used in the study of automorphisms of p-groups , the solution of the restricted Burnside problem , the classification of finite p-groups via the coclass conjectures , and provided an excellent method of understanding analytic pro-p-groups .
Formal definition
A finite p-group is called powerful if the commutator subgroup is contained in the subgroup for odd , or if is contained in the subgroup for .
Properties of powerful p-groups
Powerful p-groups have many properties similar to abelian groups, and thus provide a good basis for studying p-groups. Every finite p-group can be expressed as a section of a powerful p-group.
Powerful p-groups are also useful in the study of pro-p groups as it provides a simple means for characterising p-adic analytic groups (groups that are manifolds over the p-adic numbers): A finitely generated pro-p group is p-adic analytic if and only if it contains an open normal subgroup that is powerful: this is a special case of a deep result of Michel Lazard (1965).
Some properties similar to abelian p-groups are: if is a powerful p-group then:
The Frattini subgroup of has the property
for all That is, the group generated by th powers is precisely the s
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https://en.wikipedia.org/wiki/Cartan%27s%20equivalence%20method
|
In mathematics, Cartan's equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism. For example, if M and N are two Riemannian manifolds with metrics g and h, respectively,
when is there a diffeomorphism
such that
?
Although the answer to this particular question was known in dimension 2 to Gauss and in higher dimensions to Christoffel and perhaps Riemann as well, Élie Cartan and his intellectual heirs developed a technique for answering similar questions for radically different geometric structures. (For example see the Cartan–Karlhede algorithm.)
Cartan successfully applied his equivalence method to many such structures, including projective structures, CR structures, and complex structures, as well as ostensibly non-geometrical structures such as the equivalence of Lagrangians and ordinary differential equations. (His techniques were later developed more fully by many others, such as D. C. Spencer and Shiing-Shen Chern.)
The equivalence method is an essentially algorithmic procedure for determining when two geometric structures are identical. For Cartan, the primary geometrical information was expressed in a coframe or collection of coframes on a differentiable manifold. See method of moving frames.
Overview
Specifically, suppose that M and N are a pair of manifolds each carrying a G-structure for a structure group G. This amounts to giving a special class of coframes on M a
|
https://en.wikipedia.org/wiki/Rebecca%20Twigg
|
Rebecca Twigg (born March 26, 1963) is an American former racing cyclist.
Cycling career
An academic prodigy, she enrolled at the University of Washington in Seattle at the age of 14 and rode for the school's team. US national team coach Eddie Borysewicz saw her and invited her to join his team when she was 17. She earned degrees in biology and computer science from UW.
Twigg won six world track cycling championships in the individual pursuit. She also won 16 US championships (the first – the individual time trial – when she was 18) and two Olympic medals, the silver medal in the 1984 road race in Los Angeles, and a bronze medal in the pursuit in Barcelona in 1992.
She won the first three editions of the Women's Challenge on the road.
Twigg was a three-time Olympian (1984, 1992, and 1996). However, her final Olympic appearance, in Atlanta in 1996, ended in controversy when she quit the team in a disagreement with the coach Chris Carmichael and the U.S. Cycling Federation. The federation had invested in the development of the so-called SuperBike. Twigg, after using the bike earlier in the Games, refused to ride it, citing poor individual fit and claiming that pressure from the staff on her to use the SuperBike and their refusal to grant accreditation to her personal coach, Eddie Borysewicz, left her defocused.
Twigg married Mark Whitehead – a fellow member of the 1984 US Olympic cycling team – in 1985, but the marriage only lasted a couple of years.
Post-cycling life
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https://en.wikipedia.org/wiki/IUPAC%20nomenclature%20for%20organic%20transformations
|
The IUPAC Nomenclature for Transformations is a methodology for naming a chemical reaction. Traditionally, most chemical reactions, especially in organic chemistry, are named after their inventors, the so-called name reactions, such as Knoevenagel condensation, Wittig reaction, Claisen-Schmidt condensation, Schotten–Baumann reaction, and Diels-Alder reaction. A lot of reactions derive their name from the reagent involved like bromination or acylation. On rare occasions, the reaction is named after the company responsible like in the Wacker process or the name only hints at the process involved like in the halogen dance rearrangement. The related IUPAC nomenclature is designed for naming organic compounds themselves.
The IUPAC Nomenclature for Transformations was developed in 1981 and presents a clear-cut methodology for naming an organic reaction. It incorporates the reactant and product in a chemical transformation together with one of three transformation types:
substitutions have the infix -de-. For example: methoxy-de-bromination for the chemical reaction of a bromo-alkane to an alkoxy-alkane
additions end with -addition. For example: hydro-bromo-addition for the hydrobromination of an alkene
eliminations. end with -elimination. For example: dibromo-elimination.
Notes and references
Chemical nomenclature
Chemical reactions
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https://en.wikipedia.org/wiki/Pro-p%20group
|
In mathematics, a pro-p group (for some prime number p) is a profinite group such that for any open normal subgroup the quotient group is a p-group. Note that, as profinite groups are compact, the open subgroups are exactly the closed subgroups of finite index, so that the discrete quotient group is always finite.
Alternatively, one can define a pro-p group to be the inverse limit of an inverse system of discrete finite p-groups.
The best-understood (and historically most important) class of pro-p groups is the p-adic analytic groups: groups with the structure of an analytic manifold over such that group multiplication and inversion are both analytic functions.
The work of Lubotzky and Mann, combined with Michel Lazard's solution to Hilbert's fifth problem over the p-adic numbers, shows that a pro-p group is p-adic analytic if and only if it has finite rank, i.e. there exists a positive integer such that any closed subgroup has a topological generating set with no more than elements. More generally it was shown that a finitely generated profinite group is a compact p-adic Lie group if and only if it has an open subgroup that is a uniformly powerful pro-p-group.
The Coclass Theorems have been proved in 1994 by A. Shalev and independently by C. R. Leedham-Green. Theorem D is one of these theorems and asserts that, for any prime number p and any positive integer r, there exist only finitely many pro-p groups of coclass r. This finiteness result is fundamental for the cl
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https://en.wikipedia.org/wiki/Hans%20Kramers
|
Hendrik Anthony "Hans" Kramers (17 December 1894 – 24 April 1952) was a Dutch physicist who worked with Niels Bohr to understand how electromagnetic waves interact with matter and made important contributions to quantum mechanics and statistical physics.
Background and education
Hans Kramers was born on 17 December 1894 in Rotterdam. the son of Hendrik Kramers, a physician, and Jeanne Susanne Breukelman.
In 1912 Hans finished secondary education (HBS) in Rotterdam, and studied mathematics and physics at the University of Leiden, where he obtained a master's degree in 1916. Kramers wanted to obtain foreign experience during his doctoral research, but his first choice of supervisor, Max Born in Göttingen, was not reachable because of the First World War. Because Denmark was neutral in this war, as was the Netherlands, he travelled (by ship, overland was impossible) to Copenhagen, where he visited unannounced the then still relatively unknown Niels Bohr. Bohr took him on as a Ph.D. candidate and Kramers prepared his dissertation under Bohr's direction. Although Kramers did most of his doctoral research (on intensities of atomic transitions) in Copenhagen, he obtained his formal Ph.D. under Ehrenfest in Leiden, on 8 May 1919.
Kramers enjoyed music, and played cello and piano.
Academic career
He worked for almost ten years in Bohr's group, becoming an associate professor at the University of Copenhagen. He played a role in the ill-fated BKS theory of 1924-5. Kramers left Denm
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https://en.wikipedia.org/wiki/Latency
|
Latency or latent may refer to:
Science and technology
Latent heat, energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process
Latent variable, a variable that is not directly observed but inferred in statistics
Biology and medicine
Latency period or latent period, the time between development of a disease or exposure to a pathogen, chemical, or radiation and when symptoms first become apparent (e.g. latent tumor) or when the disease becomes infectious (e.g. infectious disease)
Latent homosexuality, a term proposed by Sigmund Freud
Sleep onset latency, the time it takes a person to fall asleep
Virus latency, the ability of a virus to remain dormant
Engineering
Latency (engineering), a measure of the time delay experienced by a system
Latency (audio), the delay between the moment an audio signal is triggered and the moment it is produced or received
CAS latency, computer memory latency
Network latency or network delay, a measure of the time delay required for information to travel across a network
Rotational latency, the delay waiting for the rotation of the disk to bring the required disk sector under the read-write head
Mechanical latency
Other uses
Latency stage, a term coined by Sigmund Freud for a stage in a child's psychosexual development
Latent Recordings, an independent Canadian record label
Nuclear latency, the condition of a country capable of developing nuclear weapons but not yet possessing them
|
https://en.wikipedia.org/wiki/Jane%20Reece
|
Jane B. Reece (born 15 April 1944) is an American scientist and textbook author. Along with American biologist Neil Campbell, she wrote the widely used Campbell/Reece Biology textbooks.
Reece received an A.B. in Biology from Harvard University, an M.S. in microbiology from Rutgers University, and a Ph.D. in bacteriology from the University of California, Berkeley. Her doctoral thesis was entitled 'The RecE pathway of genetic combination in Escherichia Coli'. Having completed her Ph.D., she stayed at UC Berkeley for a while as a postdoctoral researcher, before accepting tenure at Stanford University as a researcher. Her research mainly focused on genetic recombination in bacteria.
Reece has taught at various colleges, including Middlesex County College (New Jersey) and Queensborough Community College (New York City). She is the author or co-author of several textbooks at Benjamin Cummings, at which place she has served as an editor since she joined in 1978.
Notable among her works is The World of the Cell, third edition, which she co-authored with W.M. Becker and M.F. Poesie.
In 2017 she was awarded an honorary doctorate from Uppsala University, Sweden.
References
1944 births
Living people
American geneticists
American science writers
American textbook writers
Women textbook writers
Science teachers
Harvard University alumni
Rutgers University alumni
University of California, Berkeley alumni
Queensborough Community College faculty
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https://en.wikipedia.org/wiki/Andrew%20Harman
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Andrew Harman (born 1964) is an author from the United Kingdom known for writing pun-filled and farcical fantasy fiction.
Life
Andrew Harman studied biochemistry at the University of York, being a member of Wentworth College.
Since 2000, Harman has moved on from writing to create YAY Games, a UK independent publisher of board and card games. This award-winning company released Frankenstein's Bodies in 2014 – inspired by the works of Iain Lowson in his RPG Dark Harvest: The Legacy of Frankenstein. This was followed in 2015 by the family friendly hit Sandcastles and 2016 sees the launch of Ominoes the brand new 6,000 year old game.
Writing career
Harman rose to prominence in the 1990s as a writer of farcical fantasies and "tales of the absurd" after the success of Terry Pratchett's novels. Harman novels feature extremely convoluted plots and lots of puns and silly names. His first four novels are set in the kingdoms of Rhyngill and Cranachan, and feature recurring characters. Other of his novels are set in the fictional UK town of Camford, which is a hybridisation of the two university towns of Oxford and Cambridge.
Each of Harman's novels bear titles that pun on other famous works. His books are published under the Orbit imprint in the UK.
Critical reception
The St. James Guide to Fantasy Writers described Harman's fiction as "sometimes clever and occasionally very amusing, but it consists of many jokes for the sake of jokes and is a little way removed from the conve
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https://en.wikipedia.org/wiki/Nutritional%20genomics
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Nutritional genomics, also known as nutrigenomics, is a science studying the relationship between human genome, human nutrition and health. People in the field work toward developing an understanding of how the whole body responds to a food via systems biology, as well as single gene/single food compound relationships. Nutritional genomics or Nutrigenomics is the relation between food and inherited genes, it was first expressed in 2001.
Introduction
The term "nutritional genomics" is an umbrella term including several subcategories, such as nutrigenetics, nutrigenomics, and nutritional epigenetics. Each of these subcategories explain some aspect of how genes react to nutrients and express specific phenotypes, like disease risk. There are several applications for nutritional genomics, for example how much nutritional intervention and therapy can successfully be used for disease prevention and treatment.
Background and preventive health
Nutritional science originally emerged as a field that studied individuals lacking certain nutrients and the subsequent effects, such as the disease scurvy which results from a lack of vitamin C. As other diseases closely related to diet (but not deficiency), such as obesity, became more prevalent, nutritional science expanded to cover these topics as well. Nutritional research typically focuses on preventative measure, trying to identify what nutrients or foods will raise or lower risks of diseases and damage to the human body.
For example
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https://en.wikipedia.org/wiki/Peter%20Woit
|
Peter Woit (; born September 11, 1957) is an American theoretical physicist. He is a senior lecturer in the Mathematics department at Columbia University. Woit, a critic of string theory, has published a book Not Even Wrong (2006) and writes a blog of the same name.
Career
Woit graduated in 1979 from Harvard University with bachelor's and master's degrees in physics. He obtained his PhD in particle physics from Princeton University in 1985, followed by postdoctoral work in theoretical physics at State University of New York at Stony Brook and mathematics at the Mathematical Sciences Research Institute (MSRI) in Berkeley. He spent four years as an assistant professor at Columbia. He now holds a permanent position in the mathematics department, as senior lecturer and as departmental computer administrator.
Woit is a U.S. citizen and also has a Latvian passport. His father was born in Riga and became exiled with his own parents at the beginning of the Soviet occupation of Latvia.
Criticism of string theory
He is critical of string theory on the grounds that it lacks testable predictions and is promoted with public money despite its failures so far, and has authored both scientific papers and popular polemics on this topic. His writings claim that excessive media attention and funding of this one particular mainstream endeavour, which he considers speculative, risks undermining public faith in the freedom of scientific research. His moderated weblog on string theory and ot
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https://en.wikipedia.org/wiki/Gregory%20Winter
|
Sir Gregory Paul Winter (born 14 April 1951) is a Nobel Prize-winning English molecular biologist best known for his work on the therapeutic use of monoclonal antibodies. His research career has been based almost entirely at the MRC Laboratory of Molecular Biology and the MRC Centre for Protein Engineering, in Cambridge, England.
He is credited with having invented techniques to both humanize (1986) and, later, to fully humanize using phage display, antibodies for therapeutic uses. Previously, antibodies had been derived from mice, which made them difficult to use in human therapeutics because the human immune system had anti-mouse reactions to them. For these developments Winter was awarded the 2018 Nobel Prize in Chemistry along with George Smith and Frances Arnold.
He is a Fellow of Trinity College, Cambridge and was appointed Master of Trinity College, Cambridge on 2 October 2012, remaining in office until 2019. From 2006 to 2011, he was Deputy Director of the Laboratory of Molecular Biology, Medical Research Council, acting Director from 2007 to 2008 and Head of the Division of Protein and Nucleic Acids Chemistry from 1994 to 2006. He was also Deputy Director of the MRC Centre for Protein Engineering from 1990 to its closure in 2010.
Education
Winter was educated at the Royal Grammar School, Newcastle upon Tyne. He went on to study Natural Sciences at the University of Cambridge graduating from Trinity College, Cambridge in 1973. He was awarded a PhD degree, from the
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https://en.wikipedia.org/wiki/Locally%20compact%20quantum%20group
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In mathematics and theoretical physics, a locally compact quantum group is a relatively new C*-algebraic approach toward quantum groups that generalizes the Kac algebra, compact-quantum-group and Hopf-algebra approaches. Earlier attempts at a unifying definition of quantum groups using, for example, multiplicative unitaries have enjoyed some success but have also encountered several technical problems.
One of the main features distinguishing this new approach from its predecessors is the axiomatic existence of left and right invariant weights. This gives a noncommutative analogue of left and right Haar measures on a locally compact Hausdorff group.
Definitions
Before we can even begin to properly define a locally compact quantum group, we first need to define a number of preliminary concepts and also state a few theorems.
Definition (weight). Let be a C*-algebra, and let denote the set of positive elements of . A weight on is a function such that
for all , and
for all and .
Some notation for weights. Let be a weight on a C*-algebra . We use the following notation:
, which is called the set of all positive -integrable elements of .
, which is called the set of all -square-integrable elements of .
, which is called the set of all -integrable elements of .
Types of weights. Let be a weight on a C*-algebra .
We say that is faithful if and only if for each non-zero .
We say that is lower semi-continuous if and only if the set is a closed subset of for ev
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https://en.wikipedia.org/wiki/Tom%20Kibble
|
Sir Thomas Walter Bannerman Kibble (; 23 December 1932 – 2 June 2016) was a British theoretical physicist, senior research investigator at the Blackett Laboratory and Emeritus Professor of Theoretical Physics at Imperial College London. His research interests were in quantum field theory, especially the interface between high-energy particle physics and cosmology. He is best known as one of the first to describe the Higgs mechanism, and for his research on topological defects. From the 1950s he was concerned about the nuclear arms race and from 1970 took leading roles in promoting the social responsibility of the scientist.
Early life and education
Kibble was born in Madras, in the Madras Presidency of British India, on 23 December 1932. He was the son of the statistician Walter F. Kibble, and the grandson of William Bannerman, an officer in the Indian Medical Service, and the author Helen Bannerman. His father was a mathematics professor at Madras Christian College, and Kibble grew up playing on the grounds of the college and solving mathematics puzzles his father gave him. He was educated at Doveton Corrie School in Madras and then in Edinburgh, Scotland, at Melville College and at the University of Edinburgh. He graduated from the University of Edinburgh with a BSc in 1955, MA in 1956 and a PhD in 1958.
Career
Kibble worked on mechanisms of symmetry breaking, phase transitions and the topological defects (monopoles, cosmic strings or domain walls) that can be formed.
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https://en.wikipedia.org/wiki/Charles%20Hellaby
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Charles William Hellaby is a South African mathematician who is an associate professor of applied mathematics at the University of Cape Town, South Africa, working in the field of cosmology. He is a member of the International Astronomical Union and a member of the Baháʼí Faith.
Life
Hellaby was born to Rev. William Allen Meldrum Hellaby and Emily Madeline Hellaby. His twin brother, Mark Edwin Hellaby, pursued a career in literature while his younger brother, Julian Meldrum Hellaby, took to music as a career. He obtained a BSc (Physics & Astronomy) at the University of St Andrews, Scotland in 1977. He completed his MSc (Relativity) at Queen's University, Kingston, Ontario in 1981 and his PhD (Relativity) at Queen's University in 1985.
From 1985 to 1988 he was a Post Doctoral Researcher at the University of Cape Town under George Ellis. In 1989 he was appointed a lecturer at the University of Cape Town.
Hellaby is a member of the International Astronomical Union (Division J Galaxies and Cosmology), having previously been a member of Division VIII Galaxies & the Universe and subsequently Commission 47 Cosmology.
Research
His research interests include:
Inhomogeneous cosmology. Standard cosmology assumes a smooth homogeneous universe, but the real universe is very lumpy
Inhomogeneous cosmological models - their evolution, geometry and singularities
Non-linear structure formation in the universe
Extracting the geometry of the cosmos from observations
The Lemaitre–Tol
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https://en.wikipedia.org/wiki/616%20%28number%29
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616 (six hundred [and] sixteen) is the natural number following 615 and preceding 617.
While 666 is called the "number of the beast" in most manuscripts of Revelation , a fragment of the earliest papyrus 115 gives the number as 616.
In mathematics
616 is a member of the Padovan sequence, coming after 265, 351, 465 (it is the sum of the first two of these). 616 is a polygonal number in four different ways: it is a heptagonal number, as well as 13-, 31- and 104-gonal.
It is also the sum of the squares of the factorials of 2,3,4: (2!)² + (3!)² + (4!)² = 4+36+576=616.
The 616th harmonic number is the first to exceed seven.
Number of the beast
666 is generally believed to have been the original Number of the Beast in the Book of Revelation in the Christian Bible. In 2005, however, a fragment of papyrus 115 was revealed, containing the earliest known version of that part of the Book of Revelation discussing the Number of the Beast. It gave the number as 616, suggesting that this may have been the original. One possible explanation for the two different numbers is that they reflect two different spellings of Emperor Nero/Neron's name, for which (according to this theory) this number is believed to be a code.
In other fields
Earth-616 is the name used to identify the primary continuity in which most Marvel Comics' titles take place.
616 film, a medium film format.
Area code 616, an area code in Michigan.
References
Integers
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