• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2149-2154
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• 2017

In this paper, we obtain a simple lower bound for the number of positive (resp. negative) crossings in oriented link diagrams in terms of the maximal (resp. minimal) degree of the Jones polynomial.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.171-177
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• 2019

We associate a positive integer n and a subgroup H of the group G(n) with a polynomial $J_{n,H}(x)$, which is called the Galois polynomial. It turns out that $J_{n,H}(x)$ is a polynomial with integer coefficients for any n and H. In this paper, we provide an equivalent condition for a subgroup H to provide the Galois polynomial which is irreducible over ${\mathbb{Q}}$.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.1
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• pp.115-123
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• 1997

In this paper we present a polynomial matrix decomposition algorithm that determines a polynomial matix M(z) which satisfies the relation V(z)=M(z) for a given polynomial matrix V(z) which is paraconjugate hermitian matrix with normal rank r and is positive semidenfinite on the unit circle of z-plane. All the decomposition procedures in this proposed method are performed in the digitral domain. We also discuss how to apply the polynomial matirx decomposition in realizing MIMO LBR two-pairs.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.169-180
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• 2006

We study convergence of multisplitting method associated with a block diagonal conformable multisplitting for solving a linear system whose coefficient matrix is a symmetric positive definite matrix which is not an H-matrix. Next, we study the validity of m-step multisplitting polynomial preconditioners which will be used in the preconditioned conjugate gradient method.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.423-438
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• 1996

Let L be a linear functional on the vector space of polynomials in x. Let $\omega(x)$ be a polynomial in x of degree d, for some positive integer d. We consider two sets of polynomials, ${R_n (x)}_{n \geq 0}, {S_n(x)}_{n \geq 0}$, such that $R_n(x)$ is a polynomial in x of degree n and $S_n(x)$ is a polynomial in $\omega(x)$ of degree n. (So $S_n(x)$ is a polynomial in x of degree dn.)

• Honam Mathematical Journal
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• v.40 no.2
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• pp.281-291
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• 2018

We associate a positive integer n and a subgroup H of the group $({\mathbb{Z}}/n{\mathbb{Z}})^{\times}$ with a polynomial $J_n,H(x)$, which is called the Galois polynomial. It turns out that $J_n,H(x)$ is a polynomial with integer coefficients for any n and H. In this paper, we provide an equivalent condition for a subgroup H to provide the Galois polynomial which is irreducible over ${\mathbb{Q}}$ in the case of $n=p^{e_1}_1{\cdots}p^{e_r}_r$ (prime decomposition) with all $e_i{\geq}2$.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.899-927
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• 2019

In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1311-1322
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• 2008

The Fifteen Theorem proved by Conway and Schneeberger is a criterion for positive definite quadratic forms over the rational integer ring to be universal. In this paper, we give a proof of an analogy of the Fifteen Theorem for definite quadratic forms over polynomial rings, which is known as the Four Conjecture proposed by Gerstein.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.661-667
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• 2003

In this paper, we show, for a positive integer m and a large odd integer n, the polynomial equation (equation omitted) has a real zero on $((n+1)^{1+\frac{1}{m}},{\;}(n+1)^{1+\frac{1}{m}}+{\frac{1}{2}})$ and $((n+1)^{1+\frac{1}{m}}+{\frac{1}{2}},{\;}(n+2)^{1+\frac{1}{m}})$ respectively.