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 shifted. The integration range depends on the domain on which the functions are defined. While the symbol t is used above, it need not represent the time domain. In the case of a finite integration range, f and g are often considered to extend periodically in both directions ...

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Convolution, Convolution - Uses, Convolution - Definition, Convolution - Properties, Convolution - Commutativity, Convolution - Associativity, Convolution - Distributivity, Convolution - Associativity with scalar multiplication, Convolution - Convolution theorem, Convolution - Convolutions on groups

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Formally, a Coxeter group can be defined as a group with the presentation where mii = 1 and mij ≥ 2 for i ≠ j. The condition mij = ∞ means no relation of the form (ri rj)m should be imposed. The relation mii = 1 means that (ri)2 = 1 for all i (i.e. the generators are involutions). Under the condition that (ri)2See also:

Coxeter group, Coxeter group - Definition, Coxeter group - An example, Coxeter group - Finite Coxeter groups, Coxeter group - Symmetry groups of regular polytopes, Coxeter group - Affine Weyl groups, Coxeter group - Hyperbolic Coxeter groups

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A concrete category is formally defined as follows: a category C a faithful functor F : C → Set The faithful functor F is typically thought of as a forgetful functor, which assigns to every object of C its "underlying set", and to every morphism in C the corresponding function. Thus, a concrete category C consists not just of C itself, but of the category C and a corresponding forgetful functor F. In practice, the forgetful functor is usually clear, and we s ...

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Concrete category, Concrete category - Definition, Concrete category - Not all categories are concrete, Concrete category - Alternate definition

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A set S is called countable if there exists an injective function If f is also bijective then S is called countably infinite or denumerable. The terminology is not universal: some authors define denumerable to mean what we have called "countable"; some define countable to mean what we have called "countably infinite". The next result offers an alternative definition of a counta ...

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Countable set, Countable set - Definition, Countable set - Gentle introduction, Countable set - A more formal introduction, Countable set - Further theorems about uncountable sets

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enlightenment: For Saiva monists, Self Realization, samadhi without seed (nirvikalpa samadhi); the ultimate attainment, sometimes referred to as Paramatma darshana, or as atma darshana, "Self vision" (a term which appears in Patanjali's Yoga Sutras).

Enlightenment is the experience-nonexperience resulting in the realization of one's transcendent Self-Parasiva -which exists beyond time, form and space. Each tradition has its own understanding of enlightenment, often indicated by unique terms.

See: God Realization, kundalini, nirvikalpa samadhi, Self Realization, jivanmukta, jnana..

(See also: Enlightenment , Hinduism, Body Mind and Soul)

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Gerald Gardner is credited with re-introducing the word 'Wicca' into the English language, although he himself used the spelling 'Wica' in his published work of 1954. The spelling 'Wicca' is now used almost exclusively, (Seax-Wica being the only major use of the four-letter spelling). In Old English, wicca meant "A wizard, soothsayer, sorcerer, magician" (Bosworth, 1898 [1]). Its modern English descendant is the word witch, now used almost exclusively to describe women sorcerors, but formerly used for both sexes. Other ( ...

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Wicca, Wicca - Definition, Wicca - History of Wicca, Wicca - Origins, Wicca - Later developments, Wicca - Beliefs and practices, Wicca - Morality, Wicca - Discrimination and persecution of Wiccans, Wicca - United States, Wicca - Wiccan traditions, Wicca - Notes

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The British Vegan Society defines veganism as "the practice of dispensing with all products derived wholly or partly from animals." [7] The American Vegan Society also gives a similar definition. [8] The word vegan pronounced /ˈviːgən/ [vee-gun], was originally derived from vegetarian in 1944 when Elsie Shrigley and Donald Watson, frustrated that the term "vegetarianism" had come to include the eating of dairy products, founded the UK Vegan Society. " Vegan ...

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Veganism, Veganism - Definition, Veganism - Animal products, Veganism - Motivation, Veganism - Ethics, Veganism - Health, Veganism - Environmental considerations, Veganism - Sexual and feminist motives, Veganism - Vegan cuisine, Veganism - Similar diets and lifestyles, Veganism - Vegan nutrition, Veganism - Cultural aspects, Veganism - Criticism and controversy, Veganism - Ethical criticism, Veganism - Health criticism, Veganism - Notes

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A Sephardi is a Jew originating in the Iberian Peninsula (Spain and Portugal: ספרד, Standard Hebrew Səfárad, Tiberian Hebrew Səp̄áraḏ / Səp̄āraḏ), including those subject to expulsion from Spain by order of the Catholic Monarchs Ferdinand and Isabel (as codified in the Alhambra decree of 1492), or from Portugal by order of King Manuel I in 1497. Historically, Sephardim are those Jews associated with the Iberian peninsu ...

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Sephardi Jews, Sephardi Jews - Definition, Sephardi Jews - Distribution, Sephardi Jews - Language, Sephardi Jews - Early History, Sephardi Jews - Sephardim under Islam, Sephardi Jews - Later History and Culture, Sephardi Jews - Names, Sephardi Jews - Other Sephardic Pedigrees, Sephardi Jews - Congregations, Sephardi Jews - Relationship to other Jews, Sephardi Jews - Sephardic Chief Rabbis in Israel, Sephardi Jews - Medicine, Sephardi Jews - Notes

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1. A romantic relationship commonly of limited duration 2. Professional, personal, or public business. ...

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Affair, Affair - Definition, Affair - Famous affairs, Affair - Major, Affair - Minor

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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 part is to the smaller part", i.e. if where a is the larger part and b is the smaller part. Equivalently, they are in the golden ratio if the ratio of the larger one to the smaller one equals the ratio of the smaller one to their difference, i.e. if After multiplying the first equation with a/b or the second equation with (a − b)/b, both of these equations are se ...

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Golden ratio, Golden ratio - Definition, Golden ratio - History, Golden ratio - A startlingly quick proof of irrationality, Golden ratio - Alternate forms, Golden ratio - Mathematical uses, Golden ratio - Aesthetic uses, Golden ratio - Decimal expansion

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Art historians generally define Ancient Greek art as the art produced in the Greek-speaking world from about 1000 BC to about 100 BC. They generally exclude the art of the Mycenaean and Minoan civilisations, which flourished from about 1500 to about 1200 BC. Despite the fact that these were Greek-speaking cultures, there is little or no continuity between the art of these civilisations and later Greek art. At the other end of the time-scale, art historians generally hold that Ancient Greek art as a distinct culture ended with the esta ...

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Art in Ancient Greece, Art in Ancient Greece - Definition, Art in Ancient Greece - Periods, Art in Ancient Greece - Survivals, Art in Ancient Greece - Pottery, Art in Ancient Greece - Sculpture, Art in Ancient Greece - Architecture, Art in Ancient Greece - Coin design

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It was a reaction to the role, as characterized by the so-called Cult of Domesticity, ascribed to women in the Victorian era. Advocates of the New Woman ideal were found among novelists, playwrights, journalists, pamphleteers, political thinkers and suffragettes. Men who favoured the new cause gathered, for example, in the Fabian Society. The supporters' common aim was to encourage women to liberate themselves from male domination, manage their own lives, and leave behind anything that might restrict their pursuit of happiness and their self ...

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New Woman, New Woman - Definition, New Woman - Quotation, New Woman - External link, New Woman - Other uses

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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′) ⊆ Hom(−, c), and for all arrows f:c″→c′, S(f) is the restriction of Hom(f, c), the pullback by f, to S(c′). Put another way, a sieve is a collection S of arrows with a common codomain which satisfies the functoriality condition, ...

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Sieve category theory, Sieve category theory - Definition, Sieve category theory - Pullback of sieves, Sieve category theory - Properties of sieves

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The n + 1 Bernstein basis polynomials of degree n are defined as The Bernstein basis polynomials of degree n form a basis for the vector space Πn of polynomials of degree n. A linear combination of Bernstein basis polynomials is called a Bernstein polynomial or polynomial in Bernstein form of degree n. The coefficients βν are called Bernste ...

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Bernstein polynomial, Bernstein polynomial - Definition, Bernstein polynomial - Notes, Bernstein polynomial - Example, Bernstein polynomial - Approximating continuous functions, Bernstein polynomial - Proof

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The precise definition of a Baire space has undergone slight changes throughout history, mostly due to prevailing needs and viewpoints. First, we give the usual modern definition, and then we give a historical definition which is closer to the definition originally given by Baire. Baire space - Modern definition. A topological space is called a Baire space if the countable union of any collection of closed se ...

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Baire space, Baire space - Motivation, Baire space - Definition, Baire space - Modern definition, Baire space - Historical definition, Baire space - Examples, Baire space - Baire category theorem, Baire space - Properties

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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 (where the image of (x,y) is written as xy) such that the associative law holds: (x y) z = x (y z) for all x, y and z in A. The bilinearity of the multiplication can be expressed as (x + y) z = x z + y z  
...

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Associative algebra, Associative algebra - Definition, Associative algebra - Examples, Associative algebra - Algebra homomorphisms, Associative algebra - Index-free notation, Associative algebra - Generalizations, Associative algebra - Coalgebras, Associative algebra - Representations, Associative algebra - Motivation for a Hopf algebra, Associative algebra - Motivation for a Lie algebra

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The exact definition of an automorphism depends on the type of "mathematical object" in question and what, precisely, constitutes an "isomorphism" of that object. The most general setting in which these words have meaning is an abstract branch of mathematics called category theory. Category theory deals with abstract objects and morphisms between those objects. In category theory, an automorphism is an endomorphism (i.e. a morphism from an object to itself) which is also an isomorph ...

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Automorphism, Automorphism - Definition, Automorphism - Automorphism group, Automorphism - Examples, Automorphism - Inner and outer automorphisms, Automorphism - Reference

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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 from s to t, and σst(v) the number of shortest geodesic paths from s to t that pass through a vertex v. This may be normalised by dividing through by See also:

Betweenness, Betweenness - Definition

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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 object A1 ⊕ ··· ⊕ An in C (the biproduct); morphisms pk: A1 ⊕ ··· ⊕ An → Ak in C (the projection morphisms); and morphisms i< ...

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Biproduct, Biproduct - Definition, Biproduct - Examples, Biproduct - Properties

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Bubble tea consists of a mixture of sweetened tea, iced or hot, and milk and possibly other flavorings. Black gummy balls made of tapioca, called "pearls" or "bubbles" or Boba, sit at the bottom of the cup. The pearls are much larger than those found in tapioca pudding, with a diameter of at least 6 millimeters (smaller balls are occasionally used). They are sucked through a wide straw along with the drink, pro ...

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Bubble tea, Bubble tea - Definition, Bubble tea - Origin, Bubble tea - Variations, Bubble tea - Names, Bubble tea - Availability, Bubble tea - Trivia, Bubble tea - Related topic, Bubble tea - Bubble tea vendors

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