• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1171-1187
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• 2011

Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.293-307
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• 1997

In this paper we present the $L^2$-estimation for the kernel $K_n$ of the remaider term for the Gaussian quadrature with respect to one of four Chebyshev weight functions and the error bound of the type on the contour $$ $\mid$R_n(f)$\mid$ \leq \frac{2\pi}{\sqrt{l(\Gamma)}} max_{z\in\Gamma}$\mid$f(z)$\mid$ (\smallint_\Gamma $\mid$K_n(z)$\mid$^2$\mid$dz$\mid$)^\frac{2}{1}, $$ where $l(\Gamma)$ denotes the length of the contour $\Gamma$.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.159-167
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• 2006

The transform domain characterization of cyclic codes over finite fields using Discrete Fourier Transform(DFT) over an appropriate extension field is well known. In this paper, we extend this transform domain characterization for cyclic codes over $F_p + uF_p +... + u^{k-l}F_p$. We give a way to characterize cyclic codes over $F_p + uF_p +... + u^{k-l}F_p$ by Mattson-Solomon polynomials and multiple defining sets.

• Proceedings of the KIEE Conference
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• 1998.07a
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• pp.241-243
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• 1998

This paper describes a new method for the faster shape optimization of the electromagnetic devices. In a conventional iterative method of shape design optimization using design sensitivity based on a finite element method, meshes for a new shape of the model are generated and a discretized system equation is solved using the meshes in each iteration. They cause much design time. To save this time, a polynomial approximation of the finite element solution with respect to the geometric design parameters using Taylor expansion is constructed. This approximate state variable expressed explicitly in terms of design parameters is employed in a gradient-based optimization method. The proposed method is applied to the shape design of quadrupole magnet.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.867-877
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• 2024

The objective of this article is to acquire analogs for the degree of best one-sided approximation to investigate some Jackson's well-known theorems for best one-sided approximations in weighted L_p,α-spaces. In addition, some operators that are used to approximate unbounded functions have been introduced as be algebraic polynomials in the same weighted spaces. Our main results are given in terms of degree of the best one-sided approximation in terms of averaged modulus of smoothness.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.13-33
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• 2015

In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.135-151
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• 2005

In this paper, we obtain some properties of the sequences $U^{q}_n\;and\;V^{q}_n$ introduced in [6]. We find polynomial representations and formulas of them. For q = 5, $U^{5}_n$ is the Fibonacci sequence $F_n\;and\;V^{5}_n$ is the Lucas sequence $L_n$.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.417-426
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• 2017

We explicitly determine fundamental units and regulators of an infinite family of cyclic quartic function fields $L_h$ of unit rank 3 with a parameter h in a polynomial ring $\mathbb{F}_q[t]$, where $\mathbb{F}_q$ is the finite field of order q with characteristic not equal to 2. This result resolves the second part of Lehmer's project for the function field case.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.179-188
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• 1999

In this paper we find some classes of operators for which Weyl`s theorem holds. The main result is as follows. If T$\in$L(\ulcorner) satisfies the following: (ⅰ) Either T or T\ulcorner is reduced by each of its eigenspaces; (ⅱ) Weyl`s theorem holds for T; (ⅲ) T is isoloid, then for every polynomial p, Weyl`s theorem holds for p(T).

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1247-1256
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• 2008

Based on two real and invertible $d{\times}d$ matrices Band C such that the norm $||C^T\;B||$ is sufficiently small, we provide a construction of tight Gabor frames $\{E_{Bm}T_{Cn}g\}_{m,n{\in}{\mathbb{Z}^d}$ with explicitly given and compactly supported generators. The generators can be chosen with arbitrary polynomial decay in the frequency domain.