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  • Author: Devendra Kumar x
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Abstract

We study the growth of functions which are harmonic in any number of variables. The results are expressed in terms of spherical harmonic coefficients as well as by the approximation error of the harmonic function with (𝑝, 𝑞)-growth.

Abstract

In this paper, we obtain the distribution of mixed sum of two independent random variables with different probability density functions. One with probability density function defined in finite range and the other with probability density function defined in infinite range and associated with product of Srivastava's polynomials and H-function. We use the Laplace transform and its inverse to obtain our main result. The result obtained here is quite general in nature and is capable of yielding a large number of corresponding new and known results merely by specializing the parameters involved therein. To illustrate, some special cases of our main result are also given.

Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics Equation

In this paper, we apply a combined form of the Laplace transform method with the homotopy perturbation method to obtain the solution of nonlinear gas dynamics equation. This method is called the homotopy perturbation transform method (HPTM). This technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that this scheme solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method. The results reveal that the homotopy perturbation transform method (HPTM) is very efficient, simple and can be applied to other nonlinear problems.

Abstract

In this paper we consider general class of distribution. Recurrence relations satisfied by the quotient moments and conditional quotient moments of lower generalized order statistics for a general class of distribution are derived. Further the results are deduced for quotient moments of order statistics and lower records and characterization of this distribution by considering the recurrence relation of conditional expectation for general class of distribution satisfied by the quotient moment of the lower generalized order statistics.

Abstract

In this paper we consider the equation ∇2 φ + A(r 2)X · ∇φ + C(r 2)φ = 0 for X ∈ ℝN whose coefficients are entire functions of the variable r = |X|. Corresponding to a specified axially symmetric solution φ and set C n of (n + 1) circles, an axially symmetric solution Λn*(x, η;C n) and Λn(x, η;C n) are found that interpolates to φ(x, η) on the C n and converges uniformly to φ(x, η) on certain axially symmetric domains. The main results are the characterization of growth parameters order and type in terms of axially symmetric harmonic polynomial approximation errors and Lagrange polynomial interpolation errors using the method developed in [MARDEN, M.: Axisymmetric harmonic interpolation polynomials in ℝN, Trans. Amer. Math. Soc. 196 (1974), 385–402] and [MARDEN, M.: Value distribution of harmonic polynomials in several real variables, Trans. Amer. math. Soc. 159 (1971), 137–154].

Abstract.

In this paper, we study the Chebyshev polynomial approximation of entire solutions of Helmholtz equations in in Banach spaces ( space, Hardy space and Bergman space). Some bounds on generalized order of entire solutions of Helmholtz equations of slow growth have been obtained in terms of the coefficients and approximation errors using function theoretic methods.

Abstract

In the present paper, the coefficients characterizations of generalized type Tm(f;α,α) of entire transcendental functions f of several complex variables m (m2) for slow growth have been obtained in terms of the sequence of best polynomial approximations of f in the Hardy Banach spaces Hq(Um) and in the Banach spaces Bm(p,q,λ). The presented work is the extension and refinement of the corresponding assertions made by Vakarchuk and Zhir [, , , , , ], Gol’dberg [] and Sheremeta [, ] to the multidimensional case.

Abstract

The aim of the present work is to propose a user friendly approach based on homotopy analysis method combined with Sumudu transform method to drive analytical and numerical solutions of the fractional Newell-Whitehead-Segel amplitude equation which describes the appearance of the stripe patterns in 2-dimensional systems. The coupling of homotopy analysis method with Sumudu transform algorithm makes the calculation very easy. The proposed technique gives an analytic solution in the form of series which converge very fastly. The analytical and numerical results reveal that the coupling of homotopy analysis technique with Sumudu transform algorithm is very easy to apply and highly accuratewhen apply to non-linear differential equation of fractional order.

Abstract

All-optical arithmetic and logic unit is an integral part of contemporary optical data processing network. Accordingly, in this paper a method to develop all-optical arithmetic unit has been proposed. The proposed logic unit consists of semiconductor optical amplifier (SOA) whose fast non-linear characteristics have been utilized for the execution of numerous binary logic operations such as AND, OR, NAND, NOR, EXOR, buffer etc., as well as arithmetic operations, for instance half-addition and half-subtraction, etc. Numerical simulations for the various logic operations have been realized and output verified for the 100 Gbps data rate. Numerical executions have been also done for the crucial key parameters as the bias voltage, confinement factor, and laser power, yielded with good extinction ratio more than 10 dB. The proposed design consists of SOA with benefits of design as rapid switching speed, consumes low power and avoids optoelectronic translation. The design is having with good prospect for impending all optical complex computing networks.