Applications of Dirac's delta function in statistics. Int. J. Math. Educ. Sci. Technol., 35(2):185-195, 2004.Khuri, A.I., "Applications of Dirac's Delta Function in Statistics," International Journal of Mathematical Education in Science and Technology, Vol. 35, No. 2, pp. 185-195...
摘要: The evaluation of certain integrals is attained by use of ordinary linear differential equations having inputs that depend on the Dirac delta function. The method is illustrated by several examples.关键词: Dirac equation Differential equations ...
The previous chapter gathered together some general properties of the GFs and their companion, the Dirac delta function. This chapter considers the Green's functions for elliptic, parabolic, and hyperbolic equations that satisfy the BCs appropriate for each type of PDE....
2.12.TheDiracdeltafunction 325 2.13.Theconvolutionintegral 337 2.14.Afewwordsabouthigherorderequations 344 CHAPTER3.SYSTEMSOFFIRSTORDEREQUATIONS 3.1.Algebraicproperties,ofSolutionsof linearSystems 351 3.2.VectorSpaces 364 3.3.Dimensionofavectorspace 373 3.4.Applicationsoflinearalgebrato differentialequations 389...
The proposed technique leads to a myriad of novel integral representations for Dirac's delta function in one- and two dimensions, which are presented here for the first time. Since the derived integral representations are associated with physically realizable problems, they are problem-tailored, and...
of partial differential equations, as presented in the previous chapters, and then taking a suitable axial distribution of the Dirac delta function and its derivatives on a segment of the axis of symmetry of the body. This idea is extended to include distribution of these functions on arbitrary ...
F. Bagarello, Multiplication of distributions in one dimension: Possible approaches and applications to delta-function and its derivatives, J. Math. Anal. Appl. 196 (1995), 885-901.Bagarello, F., 1995. Multiplication of distribution in one dimension: possible approaches and applications to δ-...
where dðx ÀvtÞ is the Dirac delta function evaluated at the contact point, x ¼ vt; and the contact force f c ðtÞ is equal to the sum of the vehicle weight and the elastic force of the suspension system, i.e.
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where D is the diffusion constant and N(x, t = 0) = δ(x) is the Dirac delta function and lim x→±∞N(x, t) = 0. Then its fundamental solution is given by (14.2) Proof. In order to find a closed form representation of the solution in terms of the H-function, we use...