Search for "Generalized functions" in article titles:

1. Generalized almost-periodic functions: Classes of functions that are various generalizations of almost-periodic functions. Each of them generalizes some aspects of Bohr and Bochner almost-periodic functions (cf. (Mathematics) [100%] 2023-10-11
2. Generalized functions, space of: distribution space The space dual to the space of test (sufficiently good) functions. The Fréchet–Schwartz spaces (cf. (Mathematics) [100%] 2023-10-12
3. Generalized functions, product of: The product $ a f = f a $ of a generalized function $ f $ in $ D ^ \prime ( O) $ and a function $ a \in C ^ \infty ( O) $ is defined by the equation $$ ( a f , \phi ) = ( f , a \phi ) ,\ \ \phi \in D ( O) . $$ Here $ a ... (Mathematics) [100%] 2023-10-12

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1. Generalized function: A mathematical concept generalizing the classical concept of a function. The need for such a generalization arises in many problems in engineering, physics and mathematics. (Mathematics) [100%] 2023-10-01 [Functional analysis]
2. Generalized function: In mathematics, generalized functions are objects extending the notion of functions on real or complex numbers. There is more than one recognized theory, for example the theory of distributions. (Objects extending the notion of functions) [100%] 2024-11-24 [Generalized functions]
3. Generalized function algebras: Let $\Omega$ be an open subset of ${\bf R} ^ { n }$. A generalized function algebra is an associative, commutative differential algebra $\mathcal{A} ( \Omega )$ containing the space of distributions $\mathcal{D} ^ { \prime } ( \Omega )$ or other distribution spaces as a linear subspace ... (Mathematics) [81%] 2023-09-03
4. Generalized analytic function: A function $ w ( z) = u ( x , y ) + i v ( x , y ) $ satisfying a system $$ \tag{1 } \frac{\partial u }{\partial x } - \frac{\partial v }{\partial y } + a u + b v = 0 ,\ \ \frac{\partial u }{\partial y } + \frac{\partial v }{\partial ... (Mathematics) [81%] 2023-10-17
5. Generalised logistic function: The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. [77%] 2024-07-29 [Mathematical modeling]
6. Egorov generalized function algebra: Given an open subset $\Omega$ of ${\bf R} ^ { n }$, Yu.V. Egorov defined the generalized function algebra $\mathcal{A} ( \Omega )$ as the factor algebra of $( \mathcal{C} ^ { \infty } ( \Omega ) ) ^ { \mathbf{N} }$ modulo the ideal of sequences $( u_j )_{ j \in ... (Mathematics) [70%] 2023-10-21
7. Colombeau generalized function algebras: Let $\Omega$ be an open subset of ${\bf R} ^ { n }$, and let $\mathcal{D} ( \Omega )$ be the algebra of compactly supported smooth functions. In the original definition, J.F. (Mathematics) [70%] 2023-10-22
8. Functions (mathematics): This page is about mathematical functions. For functions in the context of computer programming, see functions. (Mathematics) [68%] 2024-01-03 [Pre-Calculus]
9. Generalized functional linear model: The generalized functional linear model (GFLM) is an extension of the generalized linear model (GLM) that allows one to regress univariate responses of various types (continuous or discrete) on functional predictors, which are mostly random trajectories generated by a square ... (Mathematical model for stochastic processes) [67%] 2023-12-28 [Generalized linear models]
10. Generalized functional linear model: The generalized functional linear model (GFLM) is an extension of the generalized linear model (GLM) that allows one to regress univariate responses of various types (continuous or discrete) on functional predictors, which are mostly random trajectories generated by a square ... (Mathematical model for stochastic processes) [67%] 2023-12-30 [Generalized linear models]
11. Generalized function, derivative of a: A weak extension of the operation of ordinary differentiation. Let $ f $ be a generalized function, $ f \in \mathcal D ^ \prime ( O) $. (Mathematics) [63%] 2023-09-07
12. Generalized pencil-of-function method: Generalized pencil-of-function method (GPOF), also known as matrix pencil method, is a signal processing technique for estimating a signal or extracting information with complex exponentials. Being similar to Prony and original pencil-of-function methods, it is generally ... [63%] 2022-06-27 [Signal processing] [Computational electromagnetics]...
13. Support of a generalized function: The set of those (and only those) points such that in any neighbourhood of them the generalized function does not vanish. A generalized function $f$ in $\mathcal D^\prime(O)$ vanishes in an open set $O^\prime \subset O$ if ... (Mathematics) [63%] 2023-10-13
14. Function (engineering): In engineering, a function is interpreted as a specific process, action or task that a system is able to perform. In the lifecycle of engineering projects, there are usually distinguished subsequently: Requirements and Functional specification documents. (Engineering) [59%] 2023-11-04 [Engineering concepts]
15. Function (computer programming): In computer programming, a function or subroutine is a sequence of program instructions that performs a specific task, packaged as a unit. This unit can then be used in programs wherever that particular task should be performed. (Computer programming) [59%] 2023-11-04 [Source code] [Programming constructs]...
16. Function: A function "f" is a fixed method for calculating a unique output "f(x)" for every given input "x". For example, the polynomial function takes numbers as inputs and outputs their squares. [59%] 2023-02-05 [Mathematics]
17. Function: Function,1 in mathematics, a variable number the value of which depends upon the values of one or more other variable numbers. The theory of functions is conveniently divided into (I. Functions of Real Variables, wherein real, and only real ... [59%] 2022-09-02