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Continuous
Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous game, a generalization of games used in game theory ** Law of Continuity, a heuristic principle of Gottfried Leibniz * Continuous function, in particular: ** Continuity (topology), a generalization to functions between topological spaces ** Scott continuity, for functions between posets ** Continuity (set theory), for functions between ordinals ** Continuity (category theory), for functors ** Graph continuity, for payoff functions in game theory * Continuity theorem may refer to one of two results: ** Lévy's continuity theorem, on random variables ** Kolmogorov continuity theorem, on stochastic processes * In geometry: ** Parametric continuity, for parametrised curves ** Geometric continuity, a concept primarily applied to the conic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Function
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as '' discontinuities''. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is . Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity. Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuity (topology)
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as '' discontinuities''. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is . Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity. Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous And Progressive Aspects
The continuous and progressive aspects (abbreviated and ) are grammatical aspects that express incomplete action ("to do") or state ("to be") in progress at a specific time: they are non-habitual, imperfective aspects. In the grammars of many languages the two terms are used interchangeably. This is also the case with English: a construction such as ''"He is washing"'' may be described either as ''present continuous'' or as ''present progressive''. However, there are certain languages for which two different aspects are distinguished. In Chinese, for example, ''progressive'' aspect denotes a current action, as in "he is getting dressed", while ''continuous'' aspect denotes a current state, as in "he is wearing fine clothes". As with other grammatical categories, the precise semantics of the aspects vary from language to language, and from grammarian to grammarian. For example, some grammars of Turkish count the -iyor form as a present tense; some as a progressive tense; and som ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Continuity
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or C^ function). Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an open set U on the real line and a function f defined on U with real values. Let ''k'' be a non-negative integer. The function f is said to be of differentiability class ''C^k'' if the derivatives f',f'',\dots,f^ exist and are continuous on U. If f is k-differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Continuity
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or C^ function). Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an open set U on the real line and a function f defined on U with real values. Let ''k'' be a non-negative integer. The function f is said to be of differentiability class ''C^k'' if the derivatives f',f'',\dots,f^ exist and are continuous on U. If f is k-di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuity (mathematics)
In mathematics, the terms continuity, continuous, and continuum are used in a variety of related ways. Continuity of functions and measures * Continuous function * Absolutely continuous function * Absolute continuity of a measure with respect to another measure * Continuous probability distribution: Sometimes this term is used to mean a probability distribution whose cumulative distribution function (c.d.f.) is (simply) continuous. Sometimes it has a less inclusive meaning: a distribution whose c.d.f. is absolutely continuous with respect to Lebesgue measure. This less inclusive sense is equivalent to the condition that every set whose Lebesgue measure is 0 has probability 0. * Geometric continuity * Parametric continuity Continuum * Continuum (set theory), the real line or the corresponding cardinal number * Linear continuum, any ordered set that shares certain properties of the real line * Continuum (topology), a nonempty compact connected metric space (sometimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Wave
A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particle accelerator having a continuous output, as opposed to a pulsed output. Continuous wave is also the name given to an early method of radio transmission, in which a sinusoidal carrier wave is switched on and off. Information is carried in the varying duration of the on and off periods of the signal, for example by Morse code in early radio. In early wireless telegraphy radio transmission, CW waves were also known as "undamped waves", to distinguish this method from damped wave signals produced by earlier ''spark gap'' type transmitters. Radio Transmissions before CW Very early radio transmitters used a spark gap to produce radio-frequency oscillations in the transmitting antenna. The signals produced by these spark-gap transmitters c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Business Continuity
Business continuity may be defined as "the capability of an organization to continue the delivery of products or services at pre-defined acceptable levels following a disruptive incident", and business continuity planning (or business continuity and resiliency planning) is the process of creating systems of prevention and recovery to deal with potential threats to a company. In addition to prevention, the goal is to enable ongoing operations before and during execution of disaster recovery. Business continuity is the intended outcome of proper execution of both business continuity planning and disaster recovery. Several business continuity standards have been published by various standards bodies to assist in check listing ongoing planning tasks. An organization's resistance to failure is "the ability ... to withstand changes in its environment and still function". Often called resilience, it is a capability that enables organizations to either endure environmental changes witho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuity Editing
Continuity editing is the process, in film and video creation, of combining more-or-less related shots, or different components cut from a single shot, into a sequence to direct the viewer's attention to a pre-existing consistency of story across both time and physical location. Often used in feature films, continuity editing, or "cutting to continuity", can be contrasted with approaches such as montage, with which the editor aims to generate, in the mind of the viewer, new associations among the various shots that can then be of entirely different subjects, or at least of subjects less closely related than would be required for the continuity approach. When discussed in reference to classical Hollywood cinema, it may also be referred to as classical continuity. Common techniques of continuity editing Continuity editing can be divided into two categories: temporal continuity and spatial continuity. Within each category, specific techniques will work against a sense of continuity. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Stochastic Process
In probability theory, a continuous stochastic process is a type of stochastic process that may be said to be "continuous" as a function of its "time" or index parameter. Continuity is a nice property for (the sample paths of) a process to have, since it implies that they are well-behaved in some sense, and, therefore, much easier to analyze. It is implicit here that the index of the stochastic process is a continuous variable. Some authorsDodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', OUP. (Entry for "continuous process") define a "continuous (stochastic) process" as only requiring that the index variable be continuous, without continuity of sample paths: in some terminology, this would be a continuous-time stochastic process, in parallel to a "discrete-time process". Given the possible confusion, caution is needed. Definitions Let (Ω, Σ, P) be a probability space, let ''T'' be some interval of time, and let ''X'' : ''T'' ×&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum (other)
Continuum may refer to: * Continuum (measurement), theories or models that explain gradual transitions from one condition to another without abrupt changes Mathematics * Continuum (set theory), the real line or the corresponding cardinal number * Linear continuum, any ordered set that shares certain properties of the real line * Continuum (topology), a nonempty compact connected metric space (sometimes Hausdorff space) * Continuum hypothesis, the hypothesis that no infinite sets are larger than the integers but smaller than the real numbers * Cardinality of the continuum, a cardinal number that represents the size of the set of real numbers Science * Continuum morphology, in plant morphology, underlining the continuum between morphological categories * Continuum concept, in psychology * Continuum mechanics, in physics, deals with continuous matter * Space-time continuum, any mathematical model that combines space and time into a single continuum * Continuum theory of specific he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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