Encyclopedia - Coxeter Group: Encyclopedia Ii - Coxeter Group - Definition
Formally, a Coxeter group can be defined as a group with the presentation where mii = 1 and mij ≥ 2 for i ≠ j. The condi...   » Read the article

Encyclopedia - Convolution: Encyclopedia Ii - Convolution - Definition
The convolution of f and g is written f * g. It is defined as the integral of the product of the two functions after one is reversed and ...   » Read the article

Encyclopedia - Concrete Category: Encyclopedia Ii - Concrete Category - Definition
A concrete category is formally defined as follows: a category C a faithful functor F : C → Set The faithful functor F is typica...   » Read the article

Encyclopedia - Countable Set: Encyclopedia Ii - Countable Set - Definition
A set S is called countable if there exists an injective function If f is also bijective then S is called countably infinite or denume...   » Read the article

Dictionary - Enlightenment: Hindu - Hinduism Dictionary On Enlightenment
enlightenment: For Saiva monists, Self Realization, samadhi without seed (nirvikalpa samadhi); the ultimate attainment, sometimes re...   » Read the article

Encyclopedia - Veganism: Encyclopedia Ii - Veganism - Definition
The British Vegan Society defines veganism as "the practice of dispensing with all products derived wholly or partly from animals." [7] T...   » Read the article

Encyclopedia - Wicca: Encyclopedia Ii - Wicca - Definition
Gerald Gardner is credited with re-introducing the word 'Wicca' into the English language, although he himself used the spelling 'Wica' i...   » Read the article

Encyclopedia - Sephardi Jews: Encyclopedia Ii - Sephardi Jews - Definition
A Sephardi is a Jew originating in the Iberian Peninsula (Spain and Portugal: ספרד, Standard Hebrew Səfárad, Tiberian Hebrew Səp̄...   » Read the article

Encyclopedia - Affair: Encyclopedia Ii - Affair - Definition
1. A romantic relationship commonly of limited duration 2. Professional, personal, or public business. ... See also:Affair, Affair - De...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Definition
Two quantities are said to be in the golden ratio, if "the whole (i.e., the sum of the two parts) is to the larger part as the larger par...   » Read the article

Encyclopedia - Art In Ancient Greece: Encyclopedia Ii - Art In Ancient Greece - Definition
Art historians generally define Ancient Greek art as the art produced in the Greek-speaking world from about 1000 BC to about 100 BC. The...   » Read the article

Encyclopedia - New Woman: Encyclopedia Ii - New Woman - Definition
It was a reaction to the role, as characterized by the so-called Cult of Domesticity, ascribed to women in the Victorian era. Advocates o...   » Read the article

Encyclopedia - Phrase Structure Rules: Encyclopedia Ii - Phrase Structure Rules - Definition
Phrase structure rules are usually of the form , meaning that the constituent A is separated into the two subconstituents B and C. Some e...   » Read the article

Encyclopedia - Sieve Category Theory: Encyclopedia Ii - Sieve Category Theory - Definition
Let C be a category, and let c be an object of C. A sieve S on c is a subfunctor of Hom(−, c), i.e., for all objects c′ of C, S(c′)...   » Read the article

Encyclopedia - Betti Number: Encyclopedia Ii - Betti Number - Definition
The k-th Betti number bk(X) of the space X is defined as the rank of the abelian group Hk(X), the k-th homology group of X. Equivalen...   » Read the article

Encyclopedia - Bernstein Polynomial: Encyclopedia Ii - Bernstein Polynomial - Definition
The n + 1 Bernstein basis polynomials of degree n are defined as The Bernstein basis polynomials of degree n form a basis for the vect...   » Read the article

Encyclopedia - Automorphism: Encyclopedia Ii - Automorphism - Definition
The exact definition of an automorphism depends on the type of "mathematical object" in question and what, precisely, constitutes an "iso...   » Read the article

Encyclopedia - Baire Space: Encyclopedia Ii - Baire Space - Definition
The precise definition of a Baire space has undergone slight changes throughout history, mostly due to prevailing needs and viewpoints. F...   » Read the article

Encyclopedia - Curvature Form: Encyclopedia Ii - Curvature Form - Definition
Let G be a Lie group and be a principal G-bundle. Let us denote the Lie algebra of G by g. Let ω denote the connection form on E (which...   » Read the article

Encyclopedia - Bubble Tea: Encyclopedia Ii - Bubble Tea - Definition
Bubble tea consists of a mixture of sweetened tea, iced or hot, and milk and possibly other flavorings. Black gummy balls made of tapioca...   » Read the article

Encyclopedia - Bounded Set: Encyclopedia Ii - Bounded Set - Definition
A set S of real numbers is called bounded above if there is a real number k such that k ≥ s for all s in S. The number k is called an u...   » Read the article

Encyclopedia - Biproduct: Encyclopedia Ii - Biproduct - Definition
Let C be a preadditive category. In particular, morphisms in C can be added. Given objects A1,...,An in C, suppose that we have: another...   » Read the article

Encyclopedia - Bilinear Operator: Encyclopedia Ii - Bilinear Operator - Definition
For a formal definition, given three vector spaces V, W and X over the same base field F, a bilinear operator is a function B : V �...   » Read the article

Encyclopedia - Associative Algebra: Encyclopedia Ii - Associative Algebra - Definition
An associative algebra A over a field K is defined to be a vector space over K together with a K-bilinear multiplication A x A → A (whe...   » Read the article

Encyclopedia - Betweenness: Encyclopedia Ii - Betweenness - Definition
For a graph G: = (V,E) with n vertices, the betweenness CB(v) for vertex v is: where σst is the number of shortest geodesic paths fro...   » Read the article

Encyclopedia - Abel's Identity: Encyclopedia Ii - Abel's Identity - Definition
Given a homogeneous linear second-order ordinary differential equation Abel's identity can be written as where W(x) is the Wronskia...   » Read the article

Encyclopedia - Analog Hole: Encyclopedia Ii - Analog Hole - Definition
The analog hole (sometimes analog reconversion problem or analog reconversion issue) is a fundamental, and inevitable vulnerability in co...   » Read the article

Encyclopedia - Almost Disjoint Sets: Encyclopedia Ii - Almost Disjoint Sets - Definition
The most common choice is to take "small" to mean finite. In this case, two sets are almost disjoint if their intersection is finite, i.e...   » Read the article

Encyclopedia - Admittance Matrix: Encyclopedia Ii - Admittance Matrix - Definition
The admittance matrix of a graph G is defined as L: = D − A with D the degree matrix of G and A the adjacency matrix of G. More expli...   » Read the article

Encyclopedia - Algebraic Connectivity: Encyclopedia Ii - Algebraic Connectivity - Definition
The algebraic connectivity of a graph G is the the second smallest eigenvalue of the Laplacian matrix of G. This eigenvalue is greater th...   » Read the article

Encyclopedia - Character Actor: Encyclopedia Ii - Character Actor - Definition
Typically, character actors lack some of the stereotypical physical attributes associated with stars. A character actor may be very short...   » Read the article

Encyclopedia - Angstrom: Encyclopedia Ii - Angstrom - Definition
1 ångström (Å) = 10–10 metres = 0.1 nm For comparison, the average diameter of an atom, calculated from its empirical radius, ranges...   » Read the article

Encyclopedia - Software Agent: Encyclopedia Ii - Software Agent - Definition
The term "agent" describes a software abstraction, an idea, or a concept, similar to OOP terms such as methods, functions, and objects. T...   » Read the article

Encyclopedia - Algebraic Space: Encyclopedia Ii - Algebraic Space - Definition
An algebraic space X is comprised of an affine scheme U and a closed subscheme R ⊂ U × U satisfying the following two conditions: 1. ...   » Read the article

Encyclopedia - Archimedean Group: Encyclopedia Ii - Archimedean Group - Definition
In the subsequent, we use the notation na (where n is in the set N of natural numbers) for the sum of a with itself n times. An Archimede...   » Read the article

Encyclopedia - Diamondsuit: Encyclopedia Ii - Diamondsuit - Definition
For a given cardinal number κ and a stationary set S ⊆ κ, ◊S is the statement that there is a sequence such that every Aδ is a s...   » Read the article

Encyclopedia - Cone Linear Algebra: Encyclopedia Ii - Cone Linear Algebra - Definition
A subset C of a real vector space V is a (linear) cone iff λx belongs to C for any x in C and any positive scalar λ of V. The condition...   » Read the article

Encyclopedia - Darboux Integral: Encyclopedia Ii - Darboux Integral - Definition
A partition of an interval [a,b] is a finite sequence Each [xi − 1,xi] is called a subinterval of the partition. A refinement of the...   » Read the article

Encyclopedia - Cylinder Set: Encyclopedia Ii - Cylinder Set - Definition
Let be a finite set, containing n objects or letters. The collection of all bi-infinite strings in these letters is denoted by where ...   » Read the article

Encyclopedia - Cup Product: Encyclopedia Ii - Cup Product - Definition
In cohomology theory, the cup product is a construction giving a product on the graded cohomology ring H∗(X) of an object X. In the sin...   » Read the article

Encyclopedia - Covering Graph Theory: Encyclopedia Ii - Covering Graph Theory - Definition
A vertex covering for a graph G is a set of vertices V so that every edge of G is adjacent to at least one vertex in V. The minimum verte...   » Read the article

Encyclopedia - Silver Ratio: Encyclopedia Ii - Silver Ratio - Definition
Silver ratio - Definition as . The silver ratio (δS) is defined as the irrational number formed from the sum of 1 and the square root ...   » Read the article

Encyclopedia - Decision Problem: Encyclopedia Ii - Decision Problem - Definition
A decision problem is a countable set S and a function . Let A be the preimage of f for 1. The problem is called decidable if A is a...   » Read the article

Encyclopedia - Differentiable Manifold: Encyclopedia Ii - Differentiable Manifold - Definition
A differentiable manifold is a topological manifold (with or without boundary) whose transition maps are all differentiable. A topologica...   » Read the article

Encyclopedia - Diffeology: Encyclopedia Ii - Diffeology - Definition
If X is a set, a diffeology on X is a set of maps, called plots, from open subsets of Rn (n ≥ 0) to X such that the following hold: Ev...   » Read the article

Encyclopedia - Dicyclic Group: Encyclopedia Ii - Dicyclic Group - Definition
For each integer n > 1, the dicyclic group Dicn can be defined as the subgroup of the unit quaternions generated by More abstractl...   » Read the article

Encyclopedia - Degree Matrix: Encyclopedia Ii - Degree Matrix - Definition
Given a graph G = (V,E) with the degree matrix D for G is a square matrix defined as ... See also:Degree matrix, Degree matrix - ...   » Read the article

Encyclopedia - Coupling Probability: Encyclopedia Ii - Coupling Probability - Definition
Using the standard formalism of probability, let X1 and X2 be two random variables defined on probability spaces (Ω1,F1,P1) and (Ω2,F2,...   » Read the article

Encyclopedia - Comma Category: Encyclopedia Ii - Comma Category - Definition
The most general comma category construction involves two converging functors. Typically, one of these will be a "selection" or "constant...   » Read the article

Encyclopedia - Computable Function: Encyclopedia Ii - Computable Function - Definition
A partial function is called computable if the graph of f is a recursively enumerable set. The set of partial computable functions wit...   » Read the article

Encyclopedia - Compassionate Conservatism: Encyclopedia Ii - Compassionate Conservatism - Definition
Compassionate conservatism is a political philosophy that was invented by Marvin Olasky, who went on to memorialize it in his 2000 book C...   » Read the article

Encyclopedia - Collective Trade Marks: Encyclopedia Ii - Collective Trade Marks - Definition
Collective trade marks are trade marks owned by an organisation (such as an association), whose members use them to identify themselves w...   » Read the article

Encyclopedia - Coequalizer: Encyclopedia Ii - Coequalizer - Definition
The coequalizer is a special kind of colimit in category theory. Specifically it is the colimit of the diagram consisting of two objects ...   » Read the article

Encyclopedia - Conditional Quantum Entropy: Encyclopedia Ii - Conditional Quantum Entropy - Definition
Given two quantum states ρ and σ, the von Neumann entropies are S(ρ) and S(σ). The von Neumann entropy measures how uncertain we are ...   » Read the article

Encyclopedia - Riesz-thorin Theorem: Encyclopedia Ii - Riesz-thorin Theorem - Definition
A slightly informal version of the theorem can be stated as follows: Theorem: Assume T is a bounded linear operator from Lp to Lp and at ...   » Read the article

Encyclopedia - Coordinate Space: Encyclopedia Ii - Coordinate Space - Definition
Let F denote an arbitrary field (such as the real numbers R or the complex numbers C). For any positive integer n, the space of all n-tup...   » Read the article

Encyclopedia - Slew Rate: Encyclopedia Ii - Slew Rate - Definition
The slew-rate of an op-amp is defined as the maximum rate of change of the output voltage for all possible input signals. Slew rate is...   » Read the article

Encyclopedia - Convex Cone: Encyclopedia Ii - Convex Cone - Definition
A subset C of a vector space V is a convex cone iff αx + βy belongs to C, for any positive scalars α, β of V, and any x, y in C. The ...   » Read the article

Encyclopedia - Closeness Mathematics: Encyclopedia Ii - Closeness Mathematics - Definition
Given a metric space (X,d) we call a point p close to a set A if d(p,A) = 0 Similarly a set B is called close to a set A if    » Read the article

Encyclopedia - Quaternion: Encyclopedia Ii - Quaternion - Definition
While the complex numbers are obtained by adding the element i to the real numbers which satisfies i2 = −1, the quaternions are obtaine...   » Read the article

Encyclopedia - Permatemp: Encyclopedia Ii - Permatemp - Definition
The normal practice of temporary employment is one in which the employee has a close relationship with the agency from which they receive...   » Read the article

Encyclopedia - Perverse Effects Of Vaccination: Encyclopedia Ii - Perverse Effects Of Vaccination - Definition
There is a critical threshold value (denoted qc) at which enough people are immune to the disease that its spread through the population ...   » Read the article

Encyclopedia - Paraphilia: Encyclopedia Ii - Paraphilia - Definition
The word is used differently by different groups. As used in psychology or sexology it is simply a neutral umbrella term used to cover a ...   » Read the article

Encyclopedia - Ph: Encyclopedia Ii - Ph - Definition
Though a pH value has no unit, it is not an arbitrary scale; the number arises from a definition based on the activity of hydrogen ions i...   » Read the article

Encyclopedia - Octonion: Encyclopedia Ii - Octonion - Definition
The octonions can be thought of as octets (or 8-tuples) of real numbers. Every octonion is a real linear combination of the unit octonion...   » Read the article

Encyclopedia - Phase Matter: Encyclopedia Ii - Phase Matter - Definition
Even though the concept of phases is widely-used in the physical sciences, it is not easy to define precisely. Before presenting the gene...   » Read the article

Encyclopedia - Spectral Density: Encyclopedia Ii - Spectral Density - Definition
The power spectral density, PSD, describes how the power (or variance) of a time series is distributed with frequency. If f(t) is a signa...   » Read the article

Encyclopedia - Viswanath's Constant: Encyclopedia Ii - Viswanath's Constant - Definition
The constant is defined as the exponential rate at which the average absolute value of a random Fibonacci sequence increases. A "random F...   » Read the article

Encyclopedia - Voronoi Diagram: Encyclopedia Ii - Voronoi Diagram - Definition
For any (topologically) discrete set S of points in Euclidean space and for almost any point x, there is one point of S to which x is clo...   » Read the article

Encyclopedia - Product Topology: Encyclopedia Ii - Product Topology - Definition
Let I be a (possibly infinite) index set and suppose Xi is a topological space for every i in I. Set X = Π Xi, the Cartesian product of ...   » Read the article

Encyclopedia - Probable Cause: Encyclopedia Ii - Probable Cause - Definition
The most widely held common definition is "a reasonable belief that a crime has been committed". An alternative definition has been propo...   » Read the article

Encyclopedia - Null Set: Encyclopedia Ii - Null Set - Definition
Let X be a measurable space, let μ be a measure on X, and let N be a measurable set in X. If μ is a positive measure, then N is null if...   » Read the article

Encyclopedia - Nitrite: Encyclopedia Ii - Nitrite - Definition
The nitrite ion is NO2-. A nitrite compound is one that contains this group, either an ionic compound, or an analogous covalent one. Thes...   » Read the article

Encyclopedia - Model Theory: Encyclopedia Ii - Model Theory - Definition
A model is formally defined in the context of some language L, which consists of a set of constant symbols, a set of relation symbols eac...   » Read the article

Encyclopedia - Minimum Message Length: Encyclopedia Ii - Minimum Message Length - Definition
From Shannon's Mathematical Theory of Communication (1949) we know that in an optimal code, the message length (in binary) of an event E,...   » Read the article

Encyclopedia - Metric Space: Encyclopedia Ii - Metric Space - Definition
A metric space is a 2-tuple (X,d) where X is a set and d is a metric on X, that is, a function d : X × X → R such that d(x, y)...   » Read the article

Encyclopedia - Megabyte: Encyclopedia Ii - Megabyte - Definition
Because of inconsistencies in the use of SI-derived prefixes such as kilo- and mega-, the exact number can be any one of the following: ...   » Read the article

Encyclopedia - Morphism: Encyclopedia Ii - Morphism - Definition
A category C is given by two pieces of data: a class of objects and a class of morphisms. There are two operations defined on every morph...   » Read the article

Encyclopedia - Multiplication: Encyclopedia Ii - Multiplication - Definition
As for what multiplication means, the product of two whole numbers n and m is: This is just a shorthand for saying, "Add m to itself n...   » Read the article

Encyclopedia - Nitride: Encyclopedia Ii - Nitride - Definition
The nitride ion is N3- (a nitrogen atom plus three electrons). A nitride (compound) is a compound that has nitrogen with more electroposi...   » Read the article

Encyclopedia - Neighbourhood Mathematics: Encyclopedia Ii - Neighbourhood Mathematics - Definition
If X is a topological space and p is a point in X, a neighbourhood of p is a set V, which contains an open set U containing p. Note th...   » Read the article

Encyclopedia - Mythology: Encyclopedia Ii - Mythology - Definition
In order to consider mythology, it is first necessary to consider what is meant by the term myth. Myths are generally narratives passed d...   » Read the article

Encyclopedia - Muslim Politicians: Encyclopedia Ii - Muslim Politicians - Definition
There is a wide range of Muslim politicians, from male dictators like Saddam Hussain to female democratic leaders like Benazir Bhutto or ...   » Read the article

Encyclopedia - Urbanized Area: Encyclopedia Ii - Urbanized Area - Definition
The US Census Bureau defines an urbanized area as: "Core census block groups or blocks that have a population density of at least 1,000 p...   » Read the article

Encyclopedia - Unix Time: Encyclopedia Ii - Unix Time - Definition
There are two layers of encoding that make up Unix time, and they can be usefully separated. The first layer encodes a point in time as a...   » Read the article

Encyclopedia - Siemens Unit: Encyclopedia Ii - Siemens Unit - Definition
For a device with electrical resistance R, the conductance G is defined as where G is the conductance, R is the resistance, I is the cu...   » Read the article

Encyclopedia - Set Of Uniqueness: Encyclopedia Ii - Set Of Uniqueness - Definition
A subset E of the circle is called a set of uniqueness, or a U-set, if any trigonometric expansion which converges to zero outside E i...   » Read the article

Encyclopedia - Zeta Function Regularization: Encyclopedia Ii - Zeta Function Regularization - Definition
An example of zeta function regularization is the calculation of the vacuum expectation value of the energy. The unregulated value is giv...   » Read the article

Encyclopedia - Radiance: Encyclopedia Ii - Radiance - Definition
Radiance is defined by where the approximation holds for small A and Ω, L is the radiance (W·m-2·sr-1), Φ is the radiant flux or ...   » Read the article

Encyclopedia - Spline Mathematics: Encyclopedia Ii - Spline Mathematics - Definition
A one-dimensional polynomial spline, S(t), is an example of a piecewise function. In its most general form a polynomial spline, defined o...   » Read the article

Encyclopedia - Scalar Field: Encyclopedia Ii - Scalar Field - Definition
A scalar field is a function from Rn to R. That is, it is a function defined on the n-dimensional Euclidean space with real values. Often...   » Read the article

Encyclopedia - Graph Homomorphism: Encyclopedia Ii - Graph Homomorphism - Definition
A graph homomorphism f from a graph G: = (V,E) to a graph G': = (V',E'), written is a mapping from the vertex set of G to the vertex se...   » Read the article

Encyclopedia - Relation Mathematics: Encyclopedia Ii - Relation Mathematics - Definition
A relation over the sets X1, ..., Xn is an (n + 1)-tuple R=(X1, ..., Xn, G(R)) where G(R) is a subset of X1 × ... × Xn (the Cartesian p...   » Read the article

Encyclopedia - Reichsführer-ss: Encyclopedia Ii - Reichsführer-ss - Definition
Reichsführer-SS was both a title and a rank. The title of Reichsführer was first created in 1926 by Joseph Berchtold. Berchtold's prede...   » Read the article

Encyclopedia - Recursive Function: Encyclopedia Ii - Recursive Function - Definition
Take as axioms the axioms of the primitive recursive functions, but extend the definitions so as to allow for partial functions. Add one ...   » Read the article

Encyclopedia - Quotient Space: Encyclopedia Ii - Quotient Space - Definition
Suppose X is a topological space and ~ is an equivalence relation on X. We define a topology on the quotient set X/~ (the set consisting ...   » Read the article

Encyclopedia - Split-complex Number: Encyclopedia Ii - Split-complex Number - Definition
A split-complex number is one of the form z = x + j y = e (jw) where x and y are real numbers and the quantity j satisfies j2 = +1. T...   » Read the article

Encyclopedia - Stochastic Process: Encyclopedia Ii - Stochastic Process - Definition
A stochastic process is a random function, that is a random variable X defined on a probability space (Ω , Pr) with values in a space of...   » Read the article

Encyclopedia - Triumphalism: Encyclopedia Ii - Triumphalism - Definition
The term is sometimes used to refer to relatively inconsequential behavior, such as excessively demonstrative glee at the defeat or failu...   » Read the article

Encyclopedia - Turing Machine: Encyclopedia Ii - Turing Machine - Definition
Turing machine - Informal description. The concept of the Turing machine is based on the idea of a person executing a well-defined proc...   » Read the article

Encyclopedia - Unique Selling Proposition: Encyclopedia Ii - Unique Selling Proposition - Definition
In his book Reality in Advertising, Rosser Reeves (Chairman of the Board at Ted Bates & Company) gives the precise definition as it w...   » Read the article