• Journal of Advanced Navigation Technology
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• v.15 no.4
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• pp.543-548
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• 2011

In this paper, H-polarized electromagnetic scattering problems by a resistive strip grating over a grounded dielectric plane according to the strip width and grating period, the relative permittivity and thickness of a dielectric layer, and incident angles of a TE (transverse electric) plane wave are analyzed by applying the FGMM (Fourier-Galerkin Moment Method). The tapered resistivity of resistive strips in this paper varies from finite resistivity at one edge to zero resistivity at the other edge, then the induced surface current density on the resistive strip is expanded in a series of Jacobi polynomials of the order ${\alpha}=1$, ${\beta}=0$ as a kind of orthogonal polynomials. The numerical results of the normalized reflected power show in good agreement with those of existing papers.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.465-471
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• 2016

In this paper, we establish certain integrals involving Srivastava's Polynomials [5] and Aleph Function ([8], [10]). On account of general nature of the functions and polynomials involved in the integrals, our results provide interesting unifications and generalizations of a large number of new and known results, which may find useful applications in the field of science and engineering. To illustrate, we have recorded some special cases of our main results which are also sufficiently general and unified in nature and are of interest in themselves.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.827-844
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• 2016

Here, in this paper, we aim at establishing some new unified integral and differential formulas associated with the $\bar{H}$-function. Each of these formula involves a product of the $\bar{H}$-function and Srivastava polynomials with essentially arbitrary coefficients and the results are obtained in terms of two variables $\bar{H}$-function. By assigning suitably special values to these coefficients, the main results can be reduced to the corresponding integral formulas involving the classical orthogonal polynomials including, for example, Hermite, Jacobi, Legendre and Laguerre polynomials. Furthermore, the $\bar{H}$-function occurring in each of main results can be reduced, under various special cases.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.527-534
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• 2013

We first aim at proving an interesting easily derivable summation formula. Then it is easily seen that this formula immediately yields a hypergeometric summation theorem recently added to the literature by Qureshi et al. Moreover we apply the main formulas to present some interesting summation formulas, whose special cases are also seen to yield the earlier known results.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.935-950
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• 1997

When $\tau$ is a quasi-definite moment functional on P, the vector space of all real polynomials, we consider a symmetric bilinear form $\phi(\cdot,\cdot)$ on $P \times P$ defined by $$ \phi(p,q) = \lambad p(a)q(a) + \mu p(b)q(b) + <\tau,p'q'>, $$ where $\lambda,\mu,a$, and b are real numbers. We first find a necessary and sufficient condition for $\phi(\cdot,\cdot)$ and show that such orthogonal polynomials satisfy a fifth order differential equation with polynomial coefficients.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.895-904
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• 2000

The contact problem of two elastic bodies of arbitrary shape with a general kernel form, investigated from Hertz problem, is reduced to an integral equation of the second kind with Cauchy kernel. A numerical method is adapted to determine the unknown potential function between the two surfaces under certain conditions. Many cases are derived and discussed from the work.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.205-228
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• 2005

Let I(f) be the integral defined by : $I(f) = \int\limits_{a}^{b} f(x)w(x)dx$ with f a given function, w a nonclassical weight function and [a, b] an interval of IR (of finite or infinite length). We propose to calculate the approximate value of I(f) by using a new scheme for deriving a non-linear system, satisfied by the three-term recurrence coefficients of semi-classical orthogonal polynomials. Finally we studies the Stability and complexity of this scheme.

• Journal of the Korean Mathematical Society
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• v.8 no.1
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• pp.25-30
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• 1971

Put ($$^*$$) $$G[x,y]={\sum}\limits^{p+q=n}_{p,q=0}[-n]_{p+q}c_{p,q}x^py^q$$, where $[{\lambda}]_m$ is the Pocbhammer symbol and the $c_{p,q}$ are arbitrary constants. Making use of the specialized forms of some of his earlier results (see [8] and [9] the author derives here bilateral generating functions of the type ($$^{**}$$) $${\sum}\limits^{\infty}_{n=0}{\frac{[\lambda]_n}{n!}}_2F_1[\array{{\rho}-n,\;{\alpha};\\{\lambda}+{\rho};}x]\;G[y,z]t^n$$ where ${\alpha}$, ${\rho}$ and ${\lambda}$ are arbitrary complex numbers. In particular, it is shown that when G[y, z] is a double hypergeometric polynomial, the right-band member of ($^{**}$) belongs to a class of general triple hypergeometric functions introduced by the author [7]. An interesting special case of ($^{**}$) when ${\rho}=-m,\;m$ being a nonnegative integer, yields a class of bilateral generating functions for the Jacobi polynomials $\{P_n{^{{\alpha},{\beta}}}(x)\}$ in the form ($$^{***}$$) $${\sum\limits^{\infty}_{n=0}}\(\array{m+n\\n}\)P{^{({\alpha}-n,{\beta}-n)}_{m+n}(x)\;G[y,z]{\frac{t^n}{n!}}$$, which provides a unification of several known results. Further extensions of ($^{**}$) and ($^{***}$) with G[y, z] replaced by an analogous multiple sum $H\[y_1,{\cdots},y_m\]$ are also discussed.

• The Journal of Information Technology
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• v.8 no.2
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• pp.77-84
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• 2005

In this paper, electromagnetic scattering problems by a resistive strip grating with tapered resistivity on a grounded dielectric plane according to strip width and spacing, relative permittivity and thickness of dielectric layers, and incident angles of a electric wave are analyzed by applying the Fourier-Galerkin Moment Method known as a numerical procedure. The boundary conditions are applied to obtain the unknown field coefficients and the resistive boundary condition is used for the relationship between the tangential electric field and the electric current density on the strip. The resistivity of resistive strips in this paper varies from zeroes at one edge to infinite at the other edge, then the induced surface current density on the resistive strip is expanded in a series of Jacobi polynomials of the order ${\alpha}=0.2,\;{\beta}=-0.2$ as a orthogonal polynomials. The numerical results of the geometrically normalized reflected power in this paper are compared with those for the existing perfectly conducting strip. The numerical results of the normalized reflected power for conductive strips case with zero resistivity in this paper show in good agreement with those of existing papers.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.267-280
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• 2009

In this paper we investigate a simple two-level additive Schwarz preconditioner for the P1 symmetric interior penalty Galerkin method of the Poisson equation on rectangular meshes. The construction is based on the decomposition of the global space of piecewise linear polynomials into the sum of local subspaces, each of which corresponds to an element of the underlying mesh, and the global coarse subspace consisting of piecewise constants. This preconditioner is a direct combination of the block Jacobi iteration and the cell-centered finite difference method, and thus very easy to implement. Explicit upper and lower bounds for the maximum and minimum eigenvalues of the preconditioned matrix system are derived and confirmed by some numerical experiments.