Silver ratio - Definition as . The silver ratio (δS) is defined as the irrational number formed from the sum of 1 and the square root of 2. That is: It follows from this definition that: (δS − 1)2 = 2. Silver ratio - Definition as . The silver ratio can also be defined by the simple continued fract ...

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Silver ratio, Silver ratio - Definition, Silver ratio - Definition as, Silver ratio - Definition as, Silver ratio - Properties, Silver ratio - Silver means, Silver ratio - External link

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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 recursive set. It is called partially decidable, solvable or provable if A is a recursively enumerable set. Otherwise, the problem is called undecidable. We can give an alternati ...

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Decision problem, Decision problem - Definition, Decision problem - Notes, Decision problem - Examples, Decision problem - History

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A differentiable manifold is a topological manifold (with or without boundary) whose transition maps are all differentiable. A topological manifold without boundary is a topological space which is locally homeomorphic to Euclidean space, by homeomorphisms called charts. By composing two charts we can get a real function, called a transition map. A Ck n-manifold is a topological n-manifold for which all transition maps are Ck(Rn). Thus a CSee also:

Differentiable manifold, Differentiable manifold - History, Differentiable manifold - Definition, Differentiable manifold - Atlas, Differentiable manifold - Sheaf, Differentiable manifold - Differentiable functions, Differentiable manifold - Algebra of scalars, Differentiable manifold - Tangent bundle, Differentiable manifold - Cotangent bundle, Differentiable manifold - Jet bundle, Differentiable manifold - Tensor bundle, Differentiable manifold - Exterior calculus, Differentiable manifold - Exterior derivative, Differentiable manifold - Interior product, Differentiable manifold - Lie derivative, Differentiable manifold - Classification, Differentiable manifold - Subtypes, Differentiable manifold - Smooth manifolds, Differentiable manifold - Analytic manifolds, Differentiable manifold - pseudo-Riemannian manifolds, Differentiable manifold - Symplectic manifolds, Differentiable manifold - Lie groups, Differentiable manifold - Generalizations

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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: Every constant map is a plot. For a given map, if every point in the domain has a neighborhood such that restricting the map to this neighborhood is a plot, then the map itself is a plot. If p is a plot, and f is a smooth function from an open subset of some real vector space into the domain of p, then the composit ...

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Diffeology, Diffeology - Definition, Diffeology - Smooth manifolds, Diffeology - Examples, Diffeology - External link

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For each integer n > 1, the dicyclic group Dicn can be defined as the subgroup of the unit quaternions generated by More abstractly, one can define the dicyclic group Dicn as any group having the presentation Some things to note which follow from this definition: x4 = 1 x2ak = ak+n = ak< ...

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Dicyclic group, Dicyclic group - Definition, Dicyclic group - Properties, Dicyclic group - Generalizations

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Given a graph G = (V,E) with the degree matrix D for G is a square matrix defined as ...

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Degree matrix, Degree matrix - Definition, Degree matrix - Examples

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Using the standard formalism of probability, let X1 and X2 be two random variables defined on probability spaces (Ω1,F1,P1) and (Ω2,F2,P2). Then a coupling of X1 and X2 is a new probability space See also:

Coupling probability, Coupling probability - Definition, Coupling probability - Examples

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The most general comma category construction involves two converging functors. Typically, one of these will be a "selection" or "constant" functor: many accounts of category theory consider these special cases only, but the term is actually much more general. (A selection functor maps every object in the domain category to the same, fixed object in the codomain category, and every domain morphism to the identity morphism of that fixed object. Often, the choice of domain category is not relevant; typically, the discrete category having only one object is used.) See also:

Comma category, Comma category - Definition, Comma category - General form, Comma category - Category of objects under A, Comma category - Category of objects over A, Comma category - Other variations, Comma category - Examples of use, Comma category - Some notable categories, Comma category - Limits and universal morphisms, Comma category - Adjunctions

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A partial function is called computable if the graph of f is a recursively enumerable set. The set of partial computable functions with one parameter is usually denoted or if the number of parameters is clear from the context. A total function is called computable if the graph of f is a recursive set. The set of total computable fun ...

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Computable function, Computable function - Definition, Computable function - Remarks, Computable function - Examples, Computable function - Properties

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Compassionate conservatism is a political philosophy that was invented by Marvin Olasky, who went on to memorialize it in his 2000 book Compassionate Conservatism: What it is, What it Does, and How it Can Transform America, and Myron Magnet of the Manhattan Institute. Olasky has been called the "godfather of compassionate conservatism". The phrase was popularized when George W. Bush adopted it as one of his key sloga ...

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Compassionate conservatism, Compassionate conservatism - Definition, Compassionate conservatism - 1980s uses of the term

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Collective trade marks are trade marks owned by an organisation (such as an association), whose members use them to identify themselves with a level of quality or accuracy, geographical origin, or other characteristics set by the organisation. Collective trade marks ( frequently referred to as collective marks) are exceptions to the underlying principle of trade marks in that most trade marks serve as "badges of origin" - they indicate the individual source of the goods or services. A collective trade mark, however, can be used by a variety of traders, rather than just one individual concern, ...

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Collective trade marks, Collective trade marks - Definition, Collective trade marks - The regulations concerning the use of the mark, Collective trade marks - International treaties and collective trademarks, Collective trade marks - Examples, Collective trade marks - Cases involving collective trade marks

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The coequalizer is a special kind of colimit in category theory. Specifically it is the colimit of the diagram consisting of two objects X and Y and two parallel morphisms f, g : X → Y. More explicity, the coequalizer can be defined as an object Q and a morphism q : Y → Q such that q O f = q O g. Moreover, the pair (Q, q) must be universal in the sense that given any other such pair (Q′, q′) there exists a unique morphism u : Q → Q′ ...

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Coequalizer, Coequalizer - Definition, Coequalizer - Examples, Coequalizer - Special cases

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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 about the value of the state; how much the state is a mixed state. The joint quantum entropy S(ρ,σ) measures our uncertainty about the joint system which contains both states. By analogy with the classical conditional ...

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Conditional quantum entropy, Conditional quantum entropy - Definition, Conditional quantum entropy - Properties

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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 the same time from Lq to Lq. Then it is also a bounded operator from Lr to L< ...

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Riesz-Thorin theorem, Riesz-Thorin theorem - Definition, Riesz-Thorin theorem - Application examples, Riesz-Thorin theorem - Convolution operators, Riesz-Thorin theorem - Thorin's contribution

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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-tuples of elements of F forms an n-dimensional vector space over F called coordinate space and denoted Fn. An element of Fn is written where each xi is an element of F. The operations on Fn are defined by T ...

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Coordinate space, Coordinate space - Definition, Coordinate space - Matrix notation, Coordinate space - Standard basis, Coordinate space - Discussion

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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 typically expressed in units of V/µs. ...

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Slew rate, Slew rate - Definition, Slew rate - Origin of slew rate limiting

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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 defining condition can be written more succintly as "αC + βC = C for any positive scalars α, β of V. The concept is meaningful for any vector space that allows the concept of "positive" scalar, such as spaces over the rational, algeb ...

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Convex cone, Convex cone - Definition, Convex cone - Convex cones are linear cones, Convex cone - Alternative definitions, Convex cone - Blunt and pointed cones, Convex cone - Half-spaces, Convex cone - Salient convex cones and perfect half-spaces, Convex cone - Cross-sections and projections of a convex set, Convex cone - Flat section, Convex cone - Spherical section, Convex cone - Partial order defined by a convex cone, Convex cone - Proper convex cone

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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 See also:

Closeness mathematics, Closeness mathematics - Definition, Closeness mathematics - Properties, Closeness mathematics - Closeness relation between a point and a set, Closeness mathematics - Closeness relation between two sets, Closeness mathematics - Generalized definition

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While the complex numbers are obtained by adding the element i to the real numbers which satisfies i2 = −1, the quaternions are obtained by adding the elements i, j and k to the real numbers which satisfy the following relations. If the multiplication is assumed to be associative (as indeed it is), the following relations follow directly: (these are derived in detail below). Every quaternion is a real linear combination of the basis qua ...

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Quaternion, Quaternion - Definition, Quaternion - Example, Quaternion - Arithmetic, Quaternion - Fundamental formula, Quaternion - Profile, Quaternion - Rotation group, Quaternion - Representing quaternions by matrices, Quaternion - Quaternion operations, Quaternion - Addition and products, Quaternion - Functions of a quaternion variable, Quaternion - Exponentials and logarithms, Quaternion - Trigonometry, Quaternion - Hyperbolic, Quaternion - Inverse hyperbolic functions, Quaternion - Inverse trigonometric functions, Quaternion - Construction of quaternions from complex numbers, Quaternion - Generalizations, Quaternion - History, Quaternion - Use controversy, Quaternion - Recent years, Quaternion - Quotes about quaternions, Quaternion - External articles and resources

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The normal practice of temporary employment is one in which the employee has a close relationship with the agency from which they receive their pay. Their work may range from day labor to high-priced consulting. The employee may work for one or several companies, and the working periods may be for days or months at a time, but the working periods come about regularly. Temporary agencies may or may not provide benefits (such as subsidized he ...

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Permatemp, Permatemp - Definition, Permatemp - Legal issues, Permatemp - Vizcaino v. Microsoft, Permatemp - IRS tax rulings, Permatemp - Changes, Permatemp - Permatemp job stability, Permatemp - Permatemp culture, Permatemp - Notes

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There is a critical threshold value (denoted qc) at which enough people are immune to the disease that its spread through the population (even to unvaccinated susceptible individuals) is stopped. This effect is commonly known as herd immunity. If a vaccination programme does not attain qc, its effect is not to prevent the spread of the disease across the unvaccinated poupulation; instead it delays the spread and so increases the average age at which individuals are infected. In some diseases that ha ...

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Perverse effects of vaccination, Perverse effects of vaccination - Definition, Perverse effects of vaccination - Examples, Perverse effects of vaccination - Diseases

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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 wide variety of atypical sexual interests. There are eight types of paraphilias, and according to the Diagnostic and Statistical Manual of Mental Disorders, the activity must be the sole means of sexual gratification for a period of six (6) months, and cause "marked distress or interpersonal difficulty". Exhibitionism is the recurrent urge or behavior to expose one's genitals t ...

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Paraphilia, Paraphilia - Definition, Paraphilia - Behavioral imprinting, Paraphilia - History of the term, Paraphilia - Common paraphilias, Paraphilia - Paraphilias which relate to illegal activities, Paraphilia - Other paraphilias, Paraphilia - Controversy, Paraphilia - Religious views of paraphilia

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