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Choi, Junesang Chungcheong Mathematical Society 2013 충청수학회지 Vol.26 No.3
A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.
SOME GEOMETRIC INEQUALITIES OF MATHEMATICAL CONDUCTANCE
Chung, Bo-Hyun Chungcheong Mathematical Society 2013 충청수학회지 Vol.26 No.2
Let $D_0$, $D_1{\subset}\bar{R}^n$ be non-empty sets and let ${\Gamma}$ be the family of all closed curves which join $D_0$ to $D_1$. In this note, we introduce the concept of the mathematical conductance $C({\Gamma})$ of a curve family ${\Gamma}$ and examine some basic properties of mathematical conductance. And we obtain the inequalities in connection with capacity of condensers.
SOME APPLICATIONS OF MATHEMATICAL RESISTANCE
Chung, Bo-Hyun Chungcheong Mathematical Society 2013 충청수학회지 Vol.26 No.1
In this paper, we introduce the mathematical resistance and examine its properties and consider the applications of mathematical resistance to conformal mappings. We obtain the theorems in the connection with "the mathematical resistance zero" and "the fundamental sequences".
A DECOMPOSITION OF THE CURVATURE TENSOR ON SU(3)=T (k, l) WITH A SU(3)-INVARIANT METRIC
Son, Heui-Sang,Park, Joon-Sik,Pyo, Yong-Soo Chungcheong Mathematical Society 2015 충청수학회지 Vol.28 No.2
In this paper, we decompose the curvature tensor (field) on the homogeneous Riemannian manifold SU(3)=T (k, l) with an arbitrarily given SU(3)-invariant Riemannian metric into three curvature-like tensor fields, and investigate geometric properties.
BOUNDEDNESS IN PERTURBED NONLINEAR FUNCTIONAL DIFFERENTIAL SYSTEMS
Choi, Sang Il,Goo, Yoon Hoe Chungcheong Mathematical Society 2015 충청수학회지 Vol.28 No.2
In this paper, we investigate bounds for solutions of the perturbed nonlinear functional differential systems with a $t_{\infty}$-similarity condition using the notion of h-stability.
ASYMPTOTIC PROPERTY FOR NONLINEAR PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS
Im, Dong Man,Goo, Yoon Hoe Chungcheong Mathematical Society 2016 충청수학회지 Vol.29 No.1
This paper shows that the solutions to nonlinear perturbed functional differential system $$y^{\prime}=f(t,y)+{\int}^t_{t_0}g(s,y(s),Ty(s))ds+h(t,y(t))$$ have the asymptotic property by imposing conditions on the perturbed part ${\int}^t_{t_0}g(s,y(s),Ty(s))ds,h(t,y(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).
COMPUTATION OF NIELSEN NUMBERS FOR CERTAIN MAPS OF HYPERBOLIC SURFACES
Kim, Seung Won Chungcheong Mathematical Society 2015 충청수학회지 Vol.28 No.2
Let X be a closed surface for which the Euler characteristic $_{\mathcal{X}}(X)$ is negative, and let $f:X{\rightarrow}X$ be a self-map that is not surjective. In this short paper, we prove that we can compute the Nielsen number of f, N(f), under some algebraic conditions.
ON THE EXISTENCE OF p-ADIC ROOTS
Kim, Young-Hee,Choi, Jongsung Chungcheong Mathematical Society 2015 충청수학회지 Vol.28 No.2
In this paper, we give the condition for the existence of the q-th roots of p-adic numbers in $\mathbb{Q}_p$ with an integer $q{\geq}2$ and (p, q) = 1. We have the conditions for the existence of the fifth root and the seventh root of p-adic numbers in $\mathbb{Q}_p$, respectively.
Koh, Doowon Chungcheong Mathematical Society 2015 충청수학회지 Vol.28 No.2
Let $\mathbb{F}^d_q$ be a d-dimensional vector space over a finite field $\mathbb{F}^d_q$ with q elements. We endow the space $\mathbb{F}^d_q$ with a normalized counting measure dx. Let ${\sigma}$ be a normalized surface measure on an algebraic variety V contained in the space ($\mathbb{F}^d_q$, dx). We define the restricted averaging operator AV by $A_Vf(X)=f*{\sigma}(x)$ for $x{\in}V$, where $f:(\mathbb{F}^d_q,dx){\rightarrow}\mathbb{C}$: In this paper, we initially investigate $L^p{\rightarrow}L^r$ estimates of the restricted averaging operator AV. As a main result, we obtain the optimal results on this problem in the case when the varieties V are any nondegenerate algebraic curves in two dimensional vector spaces over finite fields. The Fourier restriction estimates for curves on $\mathbb{F}^2_q$ play a crucial role in proving our results.
MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEM WITH FINITE FRACTIONAL DIFFERENCE
He, Yansheng,Hou, Chengmin Chungcheong Mathematical Society 2015 충청수학회지 Vol.28 No.2
In this paper, we consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference. We transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.