• 대한수학회지
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• 제41권1호
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• pp.77-94
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• 2004

This paper is an expository presentation of a large part of the results, about zeros of real polynomials on Banach spaces, that have been obtained in recent years. Also new results, for or-thogonally additive polynomials on $L_p$ spaces, are given.

• 제어로봇시스템학회논문지
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• 제15권7호
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• pp.671-674
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• 2009

Determining the Schur stability of a polynomial is one of fundamental steps in many engineering problems including digital control system design or digital filter design. Due to its importance a variety of techniques have been reported in the literature for checking the Schur stability of a given polynomial. However most of them focus on real polynomials, and few results are available for complex polynomials. This paper concerns the Schur stability of complex polynomials. A simplified Jury's table for real polynomials is extended to complex polynomials.

• 대한수학회보
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• 제36권1호
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• pp.161-169
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• 1999

Generalized nonnegative trigonometric polynomials are defined as the products of nonnegative trigonometric polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We improve and extend the large sieve involving pth powers of trigonometric polynomials so that it holds for generalized trigonometric polynomials.

• 대한수학회논문집
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• 제25권2호
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• pp.215-224
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• 2010

Generalized nonnegative polynomials are defined as products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. In this paper we extend quadrature sums involving pth powers of polynomials to those for generalized polynomials.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.49-58
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• 2005

In this paper we observe the structure of the roots of q-Bernoulli polynomials, ${\beta}_n(w,h{\mid}q)$, using numerical investigation. By numerical experiments, we demonstrate a remarkably regular structure of the real roots of ${\beta}_n(w,h{\mid}q)$ for $-{\frac{1}{5}},-{\frac{1}{2}}$. Finally, we give a table for numbers of real and complex zeros of ${\beta}_n(w,h{\mid}q)$.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.881-883
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• 1989

Aperiodicity of interval polynomials is studied. Aperiodicity is normally defined as a property such that all the roots are simple and negative real, while interval polynomials are referred to as polynomials with coefficients lying within specified closed intervals on the real axis. Several conditions for aperiodicity, including an exact one, are derived. Comments on them are given in contrast to the work by Soh and Berger, who also considered the problem with a modified definition of aperiodicity.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1277-1284
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• 2010

One purpose of this paper is to consider the reflection symmetries of the q-Genocchi polynomials $G^*_{n,q}(x)$. We also observe the structure of the roots of q-Genocchi polynomials, $G^*_{n,q}(x)$, using numerical investigation. By numerical experiments, we demonstrate a remarkably regular structure of the real roots of $G^*_{n,q}(x)$.

• 대한수학회논문집
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• 제24권2호
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• pp.239-245
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• 2009

We estimate the positive real zeros of certain trinomial equations and then deduce zeros bounds of some lacunary polynomials.

• 호남수학학술지
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• 제32권4호
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• pp.563-579
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• 2010

In this paper we introduce the new analogs of Genocchi numbers and polynomials. Finally, we investigate the zeros of the twisted (h,q)-extension of Genocchi polynomials ${G_{n,q,w}^{(h)}}$(x).

• East Asian mathematical journal
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• 제26권3호
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• pp.351-363
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• 2010

We introduce a special class of real recurrent polynomials $f_m$$($m{\geq}1$) of degree m+1, with positive roots $s_m$, which are decreasing as m increases. The first root $s_1$, as well as the last one denoted by $s_{\infty}$ are expressed in closed form, and enclose all $s_m$ (m > 1). This technique is also used to find weaker than before [6] sufficient convergence conditions for some popular iterative processes converging to solutions of equations.