• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.81-85
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• 1983

It is the purpose of this paper to give some remarks on finite fields. We shall show that the little theorem of Fermat, Euler's criterion for quadratic residue mod p, and other few theorems in the number theory can be derived from the theorems in theory of finite field K=GF(p), where p is a prime. The forms of some irreducible ploynomials over K-GF(p) will be given explicitly.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.807-816
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• 2015

Let $P(z)={\limits\sum_{j=0}^{n}}a_jz^j$ be a polynomial of degree n and Re $a_j={\alpha}_j$, Im $a_j=B_j$. In this paper, we have obtained a zero-free region for polynomials in terms of ${\alpha}_j$ and ${\beta}_j$ and also obtain the bound for number of zeros that can lie in a prescribed region.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.67-75
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• 2004

Paul Turan observed that the Legendre polynomials satisfy the inequality $P_n(x)^2-P_{n-1}(x)P_{n+1}(x)$ > 0, $-1{\leq}x{\leq}1$. And G. Gasper(ref. [6], ref. [7]) proved such an inequality for Jacobi polynomials and J. Bustoz and N. Savage (ref. [2]) proved $P^{\alpha}_n(x)P^{\beta}_{n+1}(x)-P^{\alpha}_{n+1}(x)P{\beta}_n(x)$ > 0, $\frac{1}{2}{\leq}{\alpha}$ < ${\beta}{\leq}{\alpha}+2.0$ < $x$ < 1, for the ultraspherical polynomials (respectively, Laguerre ploynomials). The Bustoz-Savage inequalities hold for Laguerre and ultraspherical polynomials which are symmetric. In this paper, we prove some similar inequalities for non-symmetric Jacobi polynomials.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.6 no.1
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• pp.10-16
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• 1995

The E-polarized scattering problems by a perfect conductor strip grating are analyzed by the method of moments. For an E-polarization the induced surface current density is expected to blow up at the strip both edges. Then the induced surface current density on the strip is expanded in a series of multiplication of Ultraspherical ploynomials with zeroth order and functions with appropriate edge boundary condition. The numerical results for current density and reflection cofficient are compared with other functions, it is shown that numerical results better improves the convergence of the moment method soulutions with general incident angles than the existing several other functions. The sharp variation points in the magnitude of geometric-optical reflection coefficient can be moved by varying the incident angle, strip width, and strip spacing.

• Journal of Advanced Navigation Technology
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• v.15 no.3
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• pp.349-354
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• 2011

In this paper, H-polarized scattering problems by a resistive strip grating with zero resistivity at strip-edges 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 transverse electric (TE) plane wave are analyzed by applying the Fourier-Galerkin Moment Method (FGMM). The tapered resistivity of resistive strips has zero resistivity at strip edges, then the induced surface current density on the resistive strip is expanded in a series of Chebyshev polynomials of the second kind as a orthogonal ploynomials. The sharp variations of the reflected power are due to resonance effects were previously called wood's anomallies, the numerical results for the reflected power are compared with those of uniform resistivity in the existing papers.