• East Asian mathematical journal
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• 제36권5호
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• pp.555-560
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• 2020

We prove a new combination theorem for relatively hyperbolic groups by analyzing diagrams over HNN-extensions of relatively hyperbolic groups.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.621-640
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• 2022

The aim of this study is to establish some mean convergence theorems for double array of fuzzy random variables in metric space endowed with a convex combination operation under various assumptions.

• 논리연구
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• 제15권3호
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• pp.307-322
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• 2012

프리드먼에 의해 제안된 "크루스칼 정리의 소형화 정리"가 2차 페아노 공리체계의 부분 시스템인 $(\prod_{2}^{1}-BI)_0$에서 증명될 수 없음을 증명한다. 또한 위 증명이 크루스칼 정리와 관련된 기존의 연구에서 알려진 중요한 정리들을 잘 조합함으로 해서 가능함을 보인다.

• 한국수학교육학회지시리즈A:수학교육
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• 제43권4호
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• pp.391-398
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• 2004

It is well-known in the literature that the general term of a sequence can be represented by a linear combination of binomial coefficients. The theorem and its known proofs are not easy for highschool students to understand. In this paper we prove the theorem by a pictorial method and by a very short and easy inductive method to make the problem easy and accessible enough for highschool students.

• 충청수학회지
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• 제31권4호
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• pp.487-509
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• 2018

The Truncated Moment Problem (TMP) entails finding a positive Borel measure to represent all moments in a finite sequence as an integral; once the sequence admits one or more such measures, it is known that at least one of the measures must be finitely atomic with positive densities (equivalently, a linear combination of Dirac point masses with positive coefficients). On the contrary, there are more general moment problems for which we aim to find a "signed" measure to represent a sequence; that is, the measure may have some negative densities. This type of problem is referred to as the General Truncated Moment Problem (GTMP). The Jordan Decomposition Theorem states that any (signed) measure can be written as a difference of two positive measures, and hence, in the view of this theorem, we are able to apply results for TMP to study GTMP. In this note we observe differences between TMP and GTMP; for example, we cannot have an analogous to the Flat Extension Theorem for GTMP. We then present concrete solutions to lower-degree problems.

• 대한조선학회논문집
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• 제47권6호
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• pp.782-786
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• 2010

Thrust deduction related to the prediction of power performance of a ship is rather resistance increase, and as a preliminary study for it forces upon a circular cylinder in a uniform flow of ideal fluid due to singularities located behind it are investigated. The circle theorem is used to get the complex velocity potential for the flow field under consideration, and the Blasius theorem is applied to obtain forces upon the circular cylinder. As singularities sinks, point vortices and dipoles and their combinations are treated. $\varepsilon$, standing for the strength of a singularity, and $\delta$, representing the distance between the cylinder and the singularity, are important small parameters for the resistance and lateral forces. For sinks or point vortices it is shown that the dimensionless forces upon the cylinder is O($\epsilon$) if $\epsilon$= O($\delta$) is assumed, and the same holds for dipoles if $\epsilon$= O(${\delta}^3$) is supposed. Forces upon the cylinder by a symmetric pair of sinks are greater than a single sink located at the central plane since there is an additional term due to cross effects, and the same is also valid for the case of dipole. Combination of dipole and a point vortex is also considered and a few new aspects are clarified.

• 대한수학회보
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• 제59권1호
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• pp.227-239
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• 2022

In this paper, we consider Legendre trajectories of trans-S-manifolds. We obtain curvature characterizations of these curves and give a classification theorem. We also investigate Legendre curves whose Frenet frame fields are linearly dependent with certain combination of characteristic vector fields of the trans-S-manifold.

• 대한수학회논문집
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• 제16권4호
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• pp.679-690
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• 2001

Doubly stochastic matrices are n$\times$n nonnegative ma-trices whose row and column sums are all 1. Convex polytope $\Omega$$_{n}$ of doubly stochastic matrices and more generally (R,S), so called transportation polytopes, are important since they form the domains for the transportation problems. A theorem by Birkhoff classifies the extremal matrices of , $\Omega$$_{n}$ and extremal matrices of transporta-tion polytopes (R,S) were all classified combinatorially. In this article, we consider signed version of $\Omega$$_{n}$ and (R.S), obtain signed Birkhoff theorem; we define a new class of convex polytopes (R,S), calculate their dimensions, and classify their extremal matrices, Moreover, we suggest an algorithm to express a matrix in (R,S) as a convex combination of txtremal matrices. We also give an example that a polytope of signed matrices is used as a domain for a decision problem. In this context of finite reflection(Coxeter) group theory, our generalization may also be considered as a generalization from type $A_{*}$ n/ to type B$_{n}$ D$_{n}$. n/.

• 대한수학회논문집
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• 제9권4호
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• pp.951-959
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• 1994

A sequence ${X_j : j \geq 1}$ of random variables is said to be pairwise positive quadrant dependent (pairwise PQD) if for any real $r-i,r_j$ and $i \neq j$ $$ P{X_i > r_i,X_j > r_j} \geq P{X_i > r_i}P{X_j > r_j} $$ (see [8]) and a sequence ${X_j : j \geq 1}$ of random variables is said to be associated if for any finite collection ${X_{i(1)},...,X_{j(n)}}$ and any real coordinatewise nondecreasing functions f,g on $R^n$ $$ Cov(f(X_{i(1)},...,X_{j(n)}),g(X_{j(1)},...,X_{j(n)})) \geq 0, $$ whenever the covariance is defined (see [6]). Instead of association Cox and Grimmett's [4] original central limit theorem requires only that positively linear combination of random variables are PQD (cf. Theorem $A^*$).

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.697-710
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• 2010

In this paper, we prove existence of infinitely many positive and concave solutions, by means of a simple approach, to $3^{th}$ order three-point singular boundary value problem {$x^{\prime\prime\prime}(t)=\alpha(t)f(t,x(t))$, 0 < t < 1, $x(0)=x'(\eta)=x^{\prime\prime}(1)=0$, (1/2 < $\eta$ < 1). Moreover with respect to multiplicity of solutions, we don't assume any monotonicity on the nonlinearity. We rely on a combination of the analysis of the corresponding vector field on the phase-space along with Knesser's type properties of the solutions funnel and the well-known Krasnosel'ski$\breve{i}$'s fixed point theorem. The later is applied on a new very simple cone K, just on the plane $R^2$. These extensions justify the efficiency of our new approach compared to the commonly used one, where the cone $K\;{\subset}\;C$ ([0, 1], $\mathbb{R}$) and the existence of a positive Green's function is a necessity.