Spectral Distribution of the Weber Operator Perturbed by the Dirac Delta Function

2021 ◽  
Vol 57 (8) ◽  
pp. 1003-1009
Author(s):  
A. S. Pechentsov
2020 ◽  
Author(s):  
Matheus Pereira Lobo

I present a finite result for the Dirac delta "function."


2001 ◽  
Vol 694 ◽  
Author(s):  
Fredy R Zypman ◽  
Gabriel Cwilich

AbstractWe obtain the statistics of the intensity, transmission and conductance for scalar electromagnetic waves propagating through a disordered collection of scatterers. Our results show that the probability distribution for these quantities x, follow a universal form, YU(x) = xne−xμ. This family of functions includes the Rayleigh distribution (when α=0, μ=1) and the Dirac delta function (α →+ ∞), which are the expressions for intensity and transmission in the diffusive regime neglecting correlations. Finally, we find simple analytical expressions for the nth moment of the distributions and for to the ratio of the moments of the intensity and transmission, which generalizes the n! result valid in the previous case.


Resonance ◽  
2003 ◽  
Vol 8 (8) ◽  
pp. 48-58 ◽  
Author(s):  
V Balakrishnan

2020 ◽  
Vol 6 (2) ◽  
pp. 158-163
Author(s):  
B. B. Dhanuk ◽  
K. Pudasainee ◽  
H. P. Lamichhane ◽  
R. P. Adhikari

One of revealing and widely used concepts in Physics and mathematics is the Dirac delta function. The Dirac delta function is a distribution on real lines which is zero everywhere except at a single point, where it is infinite. Dirac delta function has vital role in solving inhomogeneous differential equations. In addition, the Dirac delta functions can be used to explore harmonic information’s imbedded in the physical signals, various forms of Dirac delta function and can be constructed from the closure relation of orthonormal basis functions of functional space. Among many special functions, we have chosen the set of eigen functions of the Hamiltonian operator of harmonic oscillator and angular momentum operators for orthonormal basis. The closure relation of orthonormal functions  used to construct the generator of Dirac delta function which is used to expand analytic functions log(x + 2),exp(-x2) and x within the valid region of arguments.


1971 ◽  
Vol 38 (4) ◽  
pp. 906-910 ◽  
Author(s):  
G. L. Agrawal ◽  
W. G. Gottenberg

The axisymmetric problem of a line load acting along the axis of a semi-infinite elastic solid is solved using Hankel transforms. In this solution the line load is interpreted as a body force loading and by assuming the line load to be of the form of a Dirac delta function the solution of Mindlin’s problem of a point load within the interior of the half space is obtained. Solutions of this problem presented in the literature have been obtained using semi-inverse techniques whereas the solution given here is obtained in a systematic step-by-step manner.


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