Singular Integral

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singular integral

[′siŋ·gyə·lər ¦int·ə·grəl əv ə ‚dif·ə′ren·chəl i′kwā·zhən]
(mathematics)

Singular Integral

 

(1) A method of representing functions. A singular integral is an integral of the form

which, when certain conditions on ∫ are fulfilled, converges to its generating function f(x) as n → ∞. The function Kn is called the kernel of the singular integral. For example,

and

are the singular integrals of Dirichlet and Vallée Poussin, respectively. The systematic investigation of singular integrals was begun by H. Lebesgue in 1909. Singular integrals attracted attention in connection with the problem of representing and approximating functions of various classes by simpler functions, such as smooth functions and polynomials.

(2) An improper integral. [23–1231–]

References in periodicals archive ?
By his singular measure of success, a planet with 120 billion extravagant consumers, living 150 years each should be a stunningly better place for all (all humans, that is).
In the singular measure case, a speed cannot be defined, and we are forced to introduce the intermittency function [beta] of the moment order [alpha].
singular measures, Fourier transform, orthogonal polynomials, almost periodic Jacobi matrices, Fourier-Bessel functions, quantum intermittency, Julia sets, iterated function systems, generalized dimensions, potential theory
These moments are of interest when completing the analogy with theory of the generalized dimension of singular measures.
As it happens, for the singular measures that we are interested in, the asymptotic behavior of the position moments [v.
com, a website providing information on the "eco-performance" of all 2006 vehicle models based on each car's Green Score -- "a singular measure incorporating unhealthy tailpipe emissions, fuel consumption and the emissions of gases that cause global warming.
Because the IT "factor" is based on a singular measure, the path from CAT to IT measures the extent to which IT covaries with the other motorically based elementary tasks.
If the goal is to build theories bridging the gap between "simple" and "complex" cognitive tasks, multiple measurement is necessary at each level so that it is possible to examine the relationship among latent factors, as opposed to comparing singular measures of IT to latent psychometric group and general factors.
The creation of the sense of humor, and its elevation as the sine qua non of personality, seems to arrive in the middle of a broad period in which anger was under attack, jealousy censored, and romantic love eased from its status as the singular measure of intimate relationships.
There is in fact, so increasing numbers of scholars affirm, no singular measure of literacy; rather, there are many literacies.
For the Green Book Online, ACEEE noted that vehicles are analyzed on the basis of a Green Score, "a singular measure that incorporates unhealthy tailpipe emissions, fuel consumption and the emissions of gases that cause global warming.
According to ACEEE, the natural gas-powered Honda Civic GX is the "greenest" vehicle available this model year based on it's "green score," a singular measure that incorporates unhealthy tailpipe emissions, fuel consumption and emissions of greenhouse gases.