generalized function

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generalized function

[′jen·rə‚līzd ′fəŋk·shən]

(industrial engineering)

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For a general d, Zhao [12] proved the analytic continuation of [zeta]([s.sub.1], ..., [s.sub.d]) as a function of d variables using the theory of generalized function and Akiyama, Egami and Tanigawa [1] proved the same result by applying the classical Euler-Maclaurin formula to the index of the summation [n.sub.d].

Analytic continuation of the multiple Fibonacci zeta functions

A synchronization is generalized function projective synchronization, which is a more general definition of chaotic synchronization, it encompasses function projective synchronization.

Hybrid generalized function projective delay synchronization in complex dynamical networks via feedback control

qualifies as a representative for a random generalized function. We obtain an imbedding [mathematical expression not reproducible].

Some Nonlinear Stochastic Cauchy Problems with Generalized Stochastic Processes

For the Dirac delta function, as a singular generalized function, there are different types of approximation (see, e.g., [19, 20, 23]).

Computing the electric and magnetic matrix green's functions in a rectangular parallelepiped with a perfect conducting boundary

Hartley, "Generalized function for the fractional calculus," Tech.

Fractional calculus of the generalized Mittag-Leffler type function

Among the topics are quantifying soil-root interactions, nitrogen management effects of root systems, characterizing root length density distribution in wheat using a generalized function, modeling Lolium perenne L.

Enhancing understanding and quantification of soil-root growth interactions

In higher dimensions we need to define it as a random generalized function. Let [C.sup.1.sub.0](D) be the set of test functions on D, i.e.

The Gaussian free field and strict plane partitions

The gamma, generalized gamma, Weibull and another type of gamma incomplete distribution are obtained as particular cases of the density generalized function. Some properties associated with the density function and other frequently used functions such as the k-th moment, risk function, life time are derived.

Una distribucion generalizada tipo gamma que involucra la funcion hipergeometrica confluente de segunda clase

A method based on the theory of the generalized function of the Fourier transformation is used for solving the matrix equation (2) [1]:

Radiation of electric and magnetic dipole antennas in magnetically anisotropic media/Apibendrinto funkciju metodo taikymas elektrodinamikos magnetines anizotropines erdves uzdaviniuose

In section 4 we give a mild generalization of this mock theta function and show this generalized function belongs to the family of [F.sub.q] -functions.

On a second order mock theta functions *

With the help of this function we can define the Laplace transform L of a generalized function [PHI] [member of] [F's.ub.[theta]] (N') by

Large deviations properties of solutions of nonlinear stochastic convolution equations

Finally, as for the usual Dirac delta as a generalized function, we show how to express a mean geometric density [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in terms of a suitable approximating sequence of classical functions.

On mean densities of inhomogeneous geometric processes arising in material science and medicine