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https://en.wikipedia.org/wiki/Adams%20operation | In mathematics, an Adams operation, denoted ψk for natural numbers k, is a cohomology operation in topological K-theory, or any allied operation in algebraic K-theory or other types of algebraic construction, defined on a pattern introduced by Frank Adams. The basic idea is to implement some fundamental identities in ... |
https://en.wikipedia.org/wiki/Cohomology%20operation | In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if F is a functor defining a cohomology theory, then a cohomology operation should be a natural transformation from F to itself. Through... |
https://en.wikipedia.org/wiki/Probabilistic%20argument | Probabilistic argument may refer to:
Probabilistic argument, any argument involving probability theory
Probabilistic method, a method of non-constructive existence proof in mathematics |
https://en.wikipedia.org/wiki/T-square%20%28fractal%29 | In mathematics, the T-square is a two-dimensional fractal. It has a boundary of infinite length bounding a finite area. Its name comes from the drawing instrument known as a T-square.
Algorithmic description
It can be generated from using this algorithm:
Image 1:
Start with a square. (The black square in the image... |
https://en.wikipedia.org/wiki/Manifold%20decomposition | In topology, a branch of mathematics, a manifold M may be decomposed or split by writing M as a combination of smaller pieces. When doing so, one must specify both what those pieces are and how they are put together to form M.
Manifold decomposition works in two directions: one can start with the smaller pieces and bu... |
https://en.wikipedia.org/wiki/Vaughan%20Jones | Sir Vaughan Frederick Randal Jones (31 December 19526 September 2020) was a New Zealand mathematician known for his work on von Neumann algebras and knot polynomials. He was awarded a Fields Medal in 1990.
Early life
Jones was born in Gisborne, New Zealand, on 31 December 1952. He was brought up in Cambridge, New Z... |
https://en.wikipedia.org/wiki/Asymmetric%20relation | In mathematics, an asymmetric relation is a binary relation on a set where for all if is related to then is not related to
Formal definition
A binary relation on is any subset of Given write if and only if which means that is shorthand for The expression is read as " is related to by " The binary re... |
https://en.wikipedia.org/wiki/Hyperbolic%20motion | In geometry, hyperbolic motions are isometric automorphisms of a hyperbolic space. Under composition of mappings, the hyperbolic motions form a continuous group. This group is said to characterize the hyperbolic space. Such an approach to geometry was cultivated by Felix Klein in his Erlangen program. The idea of reduc... |
https://en.wikipedia.org/wiki/SIAM%20Journal%20on%20Computing | The SIAM Journal on Computing is a scientific journal focusing on the mathematical and formal aspects of computer science. It is published by the Society for Industrial and Applied Mathematics (SIAM).
Although its official ISO abbreviation is SIAM J. Comput., its publisher and contributors frequently use the shorter a... |
https://en.wikipedia.org/wiki/Weighted%20geometric%20mean | In statistics, the weighted geometric mean is a generalization of the geometric mean using the weighted arithmetic mean.
Given a sample and weights , it is calculated as:
The second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual val... |
https://en.wikipedia.org/wiki/SKI%20combinator%20calculus | The SKI combinator calculus is a combinatory logic system and a computational system. It can be thought of as a computer programming language, though it is not convenient for writing software. Instead, it is important in the mathematical theory of algorithms because it is an extremely simple Turing complete language. I... |
https://en.wikipedia.org/wiki/Iterative%20Viterbi%20decoding | Iterative Viterbi decoding is an algorithm that spots the subsequence S of an observation O = {o1, ..., on} having the highest average probability (i.e., probability scaled by the length of S) of being generated by a given hidden Markov model M with m states. The algorithm uses a modified Viterbi algorithm as an inter... |
https://en.wikipedia.org/wiki/Augmented%20truncated%20cube | In geometry, the augmented truncated cube is one of the Johnson solids (). As its name suggests, it is created by attaching a square cupola () onto one octagonal face of a truncated cube.
References
Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contain... |
https://en.wikipedia.org/wiki/Biaugmented%20truncated%20cube | In geometry, the biaugmented truncated cube is one of the Johnson solids (). As its name suggests, it is created by attaching two square cupolas () onto two parallel octagonal faces of a truncated cube.
External links
Johnson solids |
https://en.wikipedia.org/wiki/Augmented%20truncated%20dodecahedron | In geometry, the augmented truncated dodecahedron is one of the Johnson solids (). As its name suggests, it is created by attaching a pentagonal cupola () onto one decagonal face of a truncated dodecahedron.
External links
Johnson solids |
https://en.wikipedia.org/wiki/Parabiaugmented%20truncated%20dodecahedron | In geometry, the parabiaugmented truncated dodecahedron is one of the Johnson solids (). As its name suggests, it is created by attaching two pentagonal cupolas () onto two parallel decagonal faces of a truncated dodecahedron.
External links
Johnson solids |
https://en.wikipedia.org/wiki/Metabiaugmented%20truncated%20dodecahedron | In geometry, the metabiaugmented truncated dodecahedron is one of the Johnson solids (). As its name suggests, it is created by attaching two pentagonal cupolas () onto two nonadjacent, nonparallel decagonal faces of a truncated dodecahedron.
External links
Johnson solids |
https://en.wikipedia.org/wiki/Triaugmented%20truncated%20dodecahedron | In geometry, the triaugmented truncated dodecahedron is one of the Johnson solids (); of them, it has the greatest volume in proportion to the cube of the side length. As its name suggests, it is created by attaching three pentagonal cupolas () onto three nonadjacent decagonal faces of a truncated dodecahedron.
Extern... |
https://en.wikipedia.org/wiki/Seifert%E2%80%93Weber%20space | In mathematics, Seifert–Weber space (introduced by Herbert Seifert and Constantin Weber) is a closed hyperbolic 3-manifold. It is also known as Seifert–Weber dodecahedral space and hyperbolic dodecahedral space. It is one of the first discovered examples of closed hyperbolic 3-manifolds.
It is constructed by gluing ... |
https://en.wikipedia.org/wiki/Erich%20Hecke | Erich Hecke (20 September 1887 – 13 February 1947) was a German mathematician known for his work in number theory and the theory of modular forms.
Biography
Hecke was born in Buk, Province of Posen, German Empire (now Poznań, Poland). He obtained his doctorate in Göttingen under the supervision of David Hilbert.
Kurt... |
https://en.wikipedia.org/wiki/MacTutor%20History%20of%20Mathematics%20Archive | The MacTutor History of Mathematics Archive is a website maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews in Scotland. It contains detailed biographies on many historical and contemporary mathematicians, as well as information on famous curves and various topics in the h... |
https://en.wikipedia.org/wiki/Dirichlet%20integral | In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the sinc function over the positive real line:
This integral is not absolutely convergent, meaning is not Lebesgue-integrable, because th... |
https://en.wikipedia.org/wiki/Projective%20hierarchy | In the mathematical field of descriptive set theory, a subset of a Polish space is projective if it is for some positive integer . Here is
if is analytic
if the complement of , , is
if there is a Polish space and a subset such that is the projection of onto ; that is,
The choice of the Polish space ... |
https://en.wikipedia.org/wiki/Nagata%E2%80%93Smirnov%20metrization%20theorem | In topology, the Nagata–Smirnov metrization theorem characterizes when a topological space is metrizable. The theorem states that a topological space is metrizable if and only if it is regular, Hausdorff and has a countably locally finite (that is, -locally finite) basis.
A topological space is called a regular spa... |
https://en.wikipedia.org/wiki/Pointed%20space | In mathematics, a pointed space or based space is a topological space with a distinguished point, the basepoint. The distinguished point is just simply one particular point, picked out from the space, and given a name, such as that remains unchanged during subsequent discussion, and is kept track of during all operati... |
https://en.wikipedia.org/wiki/Basepoint | Basepoint may refer to a point singled out in a:
Pointed set, or in a
Pointed space
See also
Origin (mathematics) |
https://en.wikipedia.org/wiki/Hyperbolic%203-manifold | In mathematics, more precisely in topology and differential geometry, a hyperbolic 3-manifold is a manifold of dimension 3 equipped with a hyperbolic metric, that is a Riemannian metric which has all its sectional curvatures equal to −1. It is generally required that this metric be also complete: in this case the manif... |
https://en.wikipedia.org/wiki/Matrix%20unit | In linear algebra, a matrix unit is a matrix with only one nonzero entry with value 1. The matrix unit with a 1 in the ith row and jth column is denoted as . For example, the 3 by 3 matrix unit with i = 1 and j = 2 is
A vector unit is a standard unit vector.
A single-entry matrix generalizes the matrix unit for matri... |
https://en.wikipedia.org/wiki/Abraham%20Wald | Abraham Wald (; , ; – ) was a Jewish Hungarian mathematician who contributed to decision theory, geometry and econometrics, and founded the field of sequential analysis. One of his well-known statistical works was written during World War II on how to minimize the damage to bomber aircraft and took into account the su... |
https://en.wikipedia.org/wiki/Eccentricity%20%28mathematics%29 | In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape.
One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular:
The eccentricity of a circle is 0.
The eccentricity of an ellipse which is ... |
https://en.wikipedia.org/wiki/Ellipse%20%28disambiguation%29 | In mathematics, an ellipse is a geometrical figure.
Ellipse may also refer to:
MacAdam ellipse, an area in a chromaticity diagram
Elliptic leaf shape
Superellipse, a geometric figure
As a name, it may also be:
The Ellipse, an area in Washington, D.C., United States
Ellipse Programmé, a French animation studio
Elips... |
https://en.wikipedia.org/wiki/Dirichlet%27s%20principle | In mathematics, and particularly in potential theory, Dirichlet's principle is the assumption that the minimizer of a certain energy functional is a solution to Poisson's equation.
Formal statement
Dirichlet's principle states that, if the function is the solution to Poisson's equation
on a domain of with boundar... |
https://en.wikipedia.org/wiki/Lickorish%E2%80%93Wallace%20theorem | In mathematics, the Lickorish–Wallace theorem in the theory of 3-manifolds states that any closed, orientable, connected 3-manifold may be obtained by performing Dehn surgery on a framed link in the 3-sphere with ±1 surgery coefficients. Furthermore, each component of the link can be assumed to be unknotted.
The the... |
https://en.wikipedia.org/wiki/Dehn%20surgery | In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a construction used to modify 3-manifolds. The process takes as input a 3-manifold together with a link. It is often conceptualized as two steps: drilling then filling.
Definitions
Given a 3-manifold and a link , the manifold drilled ... |
https://en.wikipedia.org/wiki/Adjunction%20space | In mathematics, an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another. Specifically, let X and Y be topological spaces, and let A be a subspace of Y. Let f : A → X be a continuous map (called the attaching map). One forms the adjunc... |
https://en.wikipedia.org/wiki/Atoroidal | In mathematics, an atoroidal 3-manifold is one that does not contain an essential torus.
There are two major variations in this terminology: an essential torus may be defined geometrically, as an embedded, non-boundary parallel, incompressible torus, or it may be defined algebraically, as a subgroup of its fundamenta... |
https://en.wikipedia.org/wiki/Boundary%20parallel | In mathematics, a closed n-manifold N embedded in an (n + 1)-manifold M is boundary parallel (or ∂-parallel, or peripheral) if there is an isotopy of N onto a boundary component of M.
An example
Consider the annulus . Let π denote the projection map
If a circle S is embedded into the annulus so that π restricted to S... |
https://en.wikipedia.org/wiki/Comenius%20University%20Faculty%20of%20Mathematics%2C%20Physics%20and%20Informatics | The Faculty of Mathematics, Physics and Informatics (FMPH; ; ; colloquial: Matfyz) is one of 13 faculties of the Comenius University in Bratislava, the capital of Slovakia. The faculty provides higher education in mathematics, physics and informatics, as well as teacher training in subjects related to these branches of... |
https://en.wikipedia.org/wiki/Department%20of%20Computer%20Science%2C%20FMPI%2C%20Comenius%20University | The Department of Computer Science is a department of the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, the capital of Slovakia. It is headed by Prof. RNDr. Branislav Rovan, Phd.
Educational and scientific achievements
The first comprehensive computer science curriculum in... |
https://en.wikipedia.org/wiki/Pointed%20set | In mathematics, a pointed set (also based set or rooted set) is an ordered pair where is a set and is an element of called the base point, also spelled basepoint.
Maps between pointed sets and —called based maps, pointed maps, or point-preserving maps—are functions from to that map one basepoint to another, i.e... |
https://en.wikipedia.org/wiki/Projective%20differential%20geometry | In mathematics, projective differential geometry is the study of differential geometry, from the point of view of properties of mathematical objects such as functions, diffeomorphisms, and submanifolds, that are invariant under transformations of the projective group. This is a mixture of the approaches from Riemannian... |
https://en.wikipedia.org/wiki/Graphical%20Models | Graphical Models is an academic journal in computer graphics and geometry processing publisher by Elsevier. , its editor-in-chief is Bedrich Benes of the Purdue University.
History
This journal has gone through multiple names. Founded in 1972 as Computer Graphics and Image Processing by Azriel Rosenfeld, it became the... |
https://en.wikipedia.org/wiki/Hodge%20index%20theorem | In mathematics, the Hodge index theorem for an algebraic surface V determines the signature of the intersection pairing on the algebraic curves C on V. It says, roughly speaking, that the space spanned by such curves (up to linear equivalence) has a one-dimensional subspace on which it is positive definite (not uniquel... |
https://en.wikipedia.org/wiki/A%20Mathematician%27s%20Apology | A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy, which offers a defence of the pursuit of mathematics. Central to Hardy's "apology" – in the sense of a formal justification or defence (as in Plato's Apology of Socrates) – is an argument that mathematics has value independent of possible a... |
https://en.wikipedia.org/wiki/Thom%20space | In mathematics, the Thom space, Thom complex, or Pontryagin–Thom construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space.
Construction of the Thom space
One way to construct this space is a... |
https://en.wikipedia.org/wiki/Newton%27s%20method%20in%20optimization | In calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding the roots of a differentiable function , which are solutions to the equation . As such, Newton's method can be applied to the derivative of a twice-differentiable function to find the roots of the derivative (solutions to ), ... |
https://en.wikipedia.org/wiki/Algebra%20bundle | In mathematics, an algebra bundle is a fiber bundle whose fibers are algebras and local trivializations respect the algebra structure. It follows that the transition functions are algebra isomorphisms. Since algebras are also vector spaces, every algebra bundle is a vector bundle.
Examples include the tensor-algebra b... |
https://en.wikipedia.org/wiki/Moment%20problem | In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequence of moments
More generally, one may consider
for an arbitrary sequence of functions Mn.
Introduction
In the classical setting, μ is a measure on the real line, and M is the sequence { xn : n ... |
https://en.wikipedia.org/wiki/Fatness | Fatness may refer to:
Obesity, a medical condition where excess body fat has accumulated to the extent that it may have a negative impact on health
The property of a fat object, in geometry, referring to an object in two or more dimensions whose lengths in the different dimensions are similar |
https://en.wikipedia.org/wiki/List%20of%20metropolitan%20areas%20in%20Sweden | Sweden has three metropolitan areas consisting of the areas surrounding the three largest cities, Stockholm, Gothenburg and Malmö. The statistics have been retrieved from Statistics Sweden and the statistics released on 10 November 2014. The official land areas for each municipality have also been retrieved from Statis... |
https://en.wikipedia.org/wiki/Mandelbrot%20Competition | Named in honor of Benoit Mandelbrot, the Mandelbrot Competition was a mathematics competition founded by Sam Vandervelde, Richard Rusczyk and Sandor Lehoczky that operated from 1990 to 2019. It allowed high school students to compete individually and in four-person teams.
Competition
The Mandelbrot was a "corresponden... |
https://en.wikipedia.org/wiki/Volume%20integral | In mathematics (particularly multivariable calculus), a volume integral (∭) refers to an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities, or to calculate mass f... |
https://en.wikipedia.org/wiki/Greater%20Hartford%20Academy%20of%20Mathematics%20and%20Science | The Academy of Aerospace and Engineering (also known as AAE, Aerospace, and Aerospace and Engineering) is a regional magnet high school located in Windsor, Connecticut. The school's half-day program operates as the Greater Hartford Academy of Mathematics And Science (also known as GHAMAS). The building houses a grade 6... |
https://en.wikipedia.org/wiki/Amsterdam%2C%20Saskatchewan | Amsterdam is a hamlet within the Rural Municipality of Buchanan No. 304, Saskatchewan, Canada. Listed as a designated place by Statistics Canada, the hamlet had a population of 25 in the Canada 2016 Census. The hamlet is located 63.9 km north of the city of Yorkton and 1.5 km west of Highway 9. The community was founde... |
https://en.wikipedia.org/wiki/William%20Chauvenet | William Chauvenet (24 May 1820 in Milford, Pennsylvania – 13 December 1870 in St. Paul, Minnesota) was a professor of mathematics, astronomy, navigation, and surveying who was instrumental in the establishment of the U.S. Naval Academy at Annapolis, Maryland, and later the second chancellor of Washington University in ... |
https://en.wikipedia.org/wiki/Hyperbolic%20link | In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry. A hyperbolic knot is a hyperbolic link with one component.
As a consequence of the work of William Thurston, it is known that every knot is p... |
https://en.wikipedia.org/wiki/Excision%20theorem | In algebraic topology, a branch of mathematics, the excision theorem is a theorem about relative homology and one of the Eilenberg–Steenrod axioms. Given a topological space and subspaces and such that is also a subspace of , the theorem says that under certain circumstances, we can cut out (excise) from both spac... |
https://en.wikipedia.org/wiki/Relative%20homology | In algebraic topology, a branch of mathematics, the (singular) homology of a topological space relative to a subspace is a construction in singular homology, for pairs of spaces. The relative homology is useful and important in several ways. Intuitively, it helps determine what part of an absolute homology group comes ... |
https://en.wikipedia.org/wiki/MSRI | MSRI may refer to:
Malaysian Social Research Institute, Kuala Lumpur, assists refugees
Mathematical Sciences Research Institute, California, undertakes research in mathematics |
https://en.wikipedia.org/wiki/Ideal%20theory | In mathematics, ideal theory is the theory of ideals in commutative rings. While the notion of an ideal exists also for non-commutative rings, a much more substantial theory exists only for commutative rings (and this article therefore only considers ideals in commutative rings.)
Throughout the articles, rings refer t... |
https://en.wikipedia.org/wiki/Computational%20topology | Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.
A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving problems ... |
https://en.wikipedia.org/wiki/Connected%20component | Connected component may refer to:
Connected component (graph theory), a set of vertices in a graph that are linked to each other by paths
Connected component (topology), a maximal subset of a topological space that cannot be covered by the union of two disjoint open sets
See also
Connected-component labeling, an algo... |
https://en.wikipedia.org/wiki/Supertrace | In the theory of superalgebras, if A is a commutative superalgebra, V is a free right A-supermodule and T is an endomorphism from V to itself, then the supertrace of T, str(T) is defined by the following trace diagram:
More concretely, if we write out T in block matrix form after the decomposition into even and odd su... |
https://en.wikipedia.org/wiki/Joachim%20Lambek | Joachim "Jim" Lambek (5 December 1922 – 23 June 2014) was a Canadian mathematician. He was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his PhD degree in 1950 with Hans Zassenhaus as advisor.
Biography
Lambek was born in Leipzig, Germany, where he attended a Gymnasium. H... |
https://en.wikipedia.org/wiki/Calculus%20of%20structures | The calculus of structures is a proof calculus with deep inference for studying the structural proof theory of noncommutative logic. The calculus has since been applied to study linear logic, classical logic, modal logic, and process calculi, and many benefits are claimed to follow in these investigations from the way ... |
https://en.wikipedia.org/wiki/Deep%20inference | Deep inference names a general idea in structural proof theory that breaks with the classical sequent calculus by generalising the notion of structure to permit inference to occur in contexts of high structural complexity. The term deep inference is generally reserved for proof calculi where the structural complexity ... |
https://en.wikipedia.org/wiki/Proof%20calculus | In mathematical logic, a proof calculus or a proof system is built to prove statements.
Overview
A proof system includes the components:
Formal language: The set L of formulas admitted by the system, for example, propositional logic or first-order logic.
Rules of inference: List of rules that can be employed to pro... |
https://en.wikipedia.org/wiki/Solid%20torus | In mathematics, a solid torus is the topological space formed by sweeping a disk around a circle. It is homeomorphic to the Cartesian product of the disk and the circle, endowed with the product topology.
A standard way to visualize a solid torus is as a toroid, embedded in 3-space. However, it should be distinguishe... |
https://en.wikipedia.org/wiki/Northeast%20Region%2C%20Brazil | The Northeast Region of Brazil (; ) is one of the five official and political regions of the country according to the Brazilian Institute of Geography and Statistics. Of Brazil's twenty-six states, it comprises nine: Maranhão, Piauí, Ceará, Rio Grande do Norte, Paraíba, Pernambuco, Alagoas, Sergipe and Bahia, along wit... |
https://en.wikipedia.org/wiki/Club%20set | In mathematics, particularly in mathematical logic and set theory, a club set is a subset of a limit ordinal that is closed under the order topology, and is unbounded (see below) relative to the limit ordinal. The name club is a contraction of "closed and unbounded".
Formal definition
Formally, if is a limit ordina... |
https://en.wikipedia.org/wiki/Mostowski%20collapse%20lemma | In mathematical logic, the Mostowski collapse lemma, also known as the Shepherdson–Mostowski collapse, is a theorem of set theory introduced by and .
Statement
Suppose that R is a binary relation on a class X such that
R is set-like: R−1[x] = {y : y R x} is a set for every x,
R is well-founded: every nonempty subset ... |
https://en.wikipedia.org/wiki/Suspension%20%28topology%29 | In topology, a branch of mathematics, the suspension of a topological space X is intuitively obtained by stretching X into a cylinder and then collapsing both end faces to points. One views X as "suspended" between these end points. The suspension of X is denoted by SX or susp(X).
There is a variation of the suspensi... |
https://en.wikipedia.org/wiki/Nemmers%20Prize%20in%20Mathematics | The Frederic Esser Nemmers Prize in Mathematics is awarded biennially from Northwestern University. It was initially endowed along with a companion prize, the Erwin Plein Nemmers Prize in Economics, as part of a $14 million donation from the Nemmers brothers. They envisioned creating an award that would be as prestigio... |
https://en.wikipedia.org/wiki/Leroy%20P.%20Steele%20Prize | The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
The prizes have been given since 1970, from a bequest of Leroy P. Steele, and were set up ... |
https://en.wikipedia.org/wiki/Induced%20metric | In mathematics and theoretical physics, the induced metric is the metric tensor defined on a submanifold that is induced from the metric tensor on a manifold into which the submanifold is embedded, through the pullback. It may be determined using the following formula (using the Einstein summation convention), which is... |
https://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt%20equation | The Wheeler–DeWitt equation for theoretical physics and applied mathematics, is a field equation attributed to John Archibald Wheeler and Bryce DeWitt. The equation attempts to mathematically combine the ideas of quantum mechanics and general relativity, a step towards a theory of quantum gravity.
In this approach, ti... |
https://en.wikipedia.org/wiki/Growth%20curve | Growth curve can refer to:
Growth curve (statistics), an empirical model of the evolution of a quantity over time.
Growth curve (biology), a statistical growth curve used to model a biological quantity.
Curve of growth (astronomy), the relation between the equivalent width and the optical depth. |
https://en.wikipedia.org/wiki/Taut%20foliation | In mathematics, tautness is a rigidity property of foliations. A taut foliation is a codimension 1 foliation of a closed manifold with the property that every leaf meets a transverse circle. By transverse circle, is meant a closed loop that is always transverse to the tangent field of the foliation.
If the foliated ma... |
https://en.wikipedia.org/wiki/Pseudogroup | In mathematics, a pseudogroup is a set of diffeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation of the concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of... |
https://en.wikipedia.org/wiki/Direct%20integral | In mathematics and functional analysis a direct integral or Hilbert integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was introduced in 1949 by John von Neumann in one of the papers in ... |
https://en.wikipedia.org/wiki/San%20Rafael%20Department | San Rafael is one of the departments of Mendoza Province, Argentina. The seat of the department is in the city of San Rafael.
Statistics
Geographical location: 34° 15´ to 36° southern latitude and 70° 10´ to 66° 55´ eastern longitude.
Area: 31,235 km² (20.82% of the provincial area)
Extension: 204 km from north to sou... |
https://en.wikipedia.org/wiki/Zeno%20machine | In mathematics and computer science, Zeno machines (abbreviated ZM, and also called accelerated Turing machine, ATM) are a hypothetical computational model related to Turing machines that are capable of carrying out computations involving a countably infinite number of algorithmic steps. These machines are ruled out i... |
https://en.wikipedia.org/wiki/Scott%20core%20theorem | In mathematics, the Scott core theorem is a theorem about the finite presentability of fundamental groups of 3-manifolds due to G. Peter Scott, . The precise statement is as follows:
Given a 3-manifold (not necessarily compact) with finitely generated fundamental group, there is a compact three-dimensional submanifol... |
https://en.wikipedia.org/wiki/BTI | BTI or Bti may refer to:
Acronyms
Bacillus thuringiensis israelensis (Bti), a bacterium
Barisan Tani Indonesia
Baron Tornado Index of tornado probability
Before the Impact, an American TV series
Beverage Testing Institute
Bicycle Technologies International, Santa Fe, New Mexico, US
Boston Theological Institute
... |
https://en.wikipedia.org/wiki/Zeitschrift%20f%C3%BCr%20Angewandte%20Mathematik%20und%20Physik | The Zeitschrift für Angewandte Mathematik und Physik (English: Journal of Applied Mathematics and Physics) is a bimonthly peer-reviewed scientific journal published by Birkhäuser Verlag. The editor-in-chief is Kaspar Nipp (ETH Zurich). It was established in 1950 and covers the fields of theoretical and applied mechanic... |
https://en.wikipedia.org/wiki/Alexander%20McAulay | Alexander McAulay (9 December 1863 – 6 July 1931) was the first professor of mathematics and physics at the University of Tasmania, Hobart, Tasmania. He was also a proponent of dual quaternions, which he termed "octonions" or "Clifford biquaternions".
McAulay was born on 9 December 1863 and attended Kingswood School i... |
https://en.wikipedia.org/wiki/Vector%20algebra | In mathematics, vector algebra may mean:
Linear algebra, specifically the basic algebraic operations of vector addition and scalar multiplication; see vector space.
The algebraic operations in vector calculus, namely the specific additional structure of vectors in 3-dimensional Euclidean space of dot product and esp... |
https://en.wikipedia.org/wiki/Hyperbolic%20coordinates | In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane
.
Hyperbolic coordinates take values in the hyperbolic plane defined as:
.
These coordinates in HP are useful for studying logarithmic comparisons of direct proportion in Q and measuring deviations from direc... |
https://en.wikipedia.org/wiki/Normal%20map | Normal map may refer to:
Normal mapping in 3D computer graphics
Normal invariants in mathematical surgery theory
Normal matrix in linear algebra
Normal operator in functional analysis |
https://en.wikipedia.org/wiki/Community%20areas%20in%20Chicago | The city of Chicago is divided into 77 community areas for statistical and planning purposes. Census data and other statistics are tied to the areas, which serve as the basis for a variety of urban planning initiatives on both the local and regional levels. The areas' boundaries do not generally change, allowing compar... |
https://en.wikipedia.org/wiki/Prime%20Obsession | Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications.
The book was awarded the Mathematical Association of America's in... |
https://en.wikipedia.org/wiki/Cayley%27s%20formula | In mathematics, Cayley's formula is a result in graph theory named after Arthur Cayley. It states that for every positive integer , the number of trees on labeled vertices is .
The formula equivalently counts the number of spanning trees of a complete graph with labeled vertices .
Proof
Many proofs of Cayley's tree... |
https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Hopf%20theorem | In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used in differential topology. It is named after Henri Poincaré and Heinz Hopf.
The Poincaré–Hopf theorem is often
illustrated by the special ca... |
https://en.wikipedia.org/wiki/Regions%20of%20Brazil | Brazil is geopolitically divided into five regions (also called macroregions), by the Brazilian Institute of Geography and Statistics, which are formed by the federative units of Brazil. Although officially recognized, the division is merely academic, considering geographic, social and economic factors, among others, a... |
https://en.wikipedia.org/wiki/Northrop%20Tacit%20Blue | The Northrop Tacit Blue was a technology demonstrator aircraft created to demonstrate that a low-observable stealth surveillance aircraft with a low-probability-of-intercept radar (LPIR) and other sensors could operate close to the forward line of battle with a high degree of survivability.
Development
Unveiled by the... |
https://en.wikipedia.org/wiki/Hankel%20contour | In mathematics, a Hankel contour is a path in the complex plane which extends from
(+∞,δ), around the origin counter clockwise and back to
(+∞,−δ), where δ is an arbitrarily small positive number. The contour thus remains arbitrarily close to the real axis but without crossing the real axis except for negative values ... |
https://en.wikipedia.org/wiki/Function%20of%20a%20real%20variable | In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers , or a subset of that contains an interval of positive length. Most real functions that are considered and studied are differentia... |
https://en.wikipedia.org/wiki/Legendre%20chi%20function | In mathematics, the Legendre chi function is a special function whose Taylor series is also a Dirichlet series, given by
As such, it resembles the Dirichlet series for the polylogarithm, and, indeed, is trivially expressible in terms of the polylogarithm as
The Legendre chi function appears as the discrete Fourier tr... |
https://en.wikipedia.org/wiki/Robert%20Gunning | Robert Gunning may refer to:
Sir Robert Gunning, 1st Baronet (1731–1816), British diplomat
Robert C. Gunning, professor of mathematics at Princeton University
Robert Halliday Gunning (1818–1900), Scottish physician
Robert Gunning, American businessman, creator of the Gunning fog index of readability
Robert Gunnin... |
https://en.wikipedia.org/wiki/MuMATH | muMATH is a computer algebra system (CAS), which was developed in the late 1970s and early eighties by Albert D. Rich and David Stoutemyer of Soft Warehouse in Honolulu, Hawaii. It was implemented in the muSIMP programming language which was built on top of a LISP dialect called . Platforms supported were CP/M and TRS-... |
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