• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.223-232
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• 2017

We classify the extreme and exposed symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms. We also show that every extreme symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms is exposed.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.659-670
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• 2008

We denote by $\mathcal{Q}$(A) the set of all real matrices with the same sign pattern as a real matrix A. A matrix A is an SN-matrix provided there exists a set S of sign pattern such that the set of sign patterns of vectors in the -space of $\tilde{A}$ is S, for each ${\tilde{A}}{\in}\mathcal{Q}(A)$. Some properties of SN-matrices arc investigated.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.549-557
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• 2004

In this paper, we prove the product property and the existence of an extremal analytic disc relative to the higher order Kobayashi metric. Also by making use of the upper semicontinuity of the higher order Kobayashi metric, we introduce a pseudodistance and investigate some properties of that pseudodistance related to the usual Kobayashi metric.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.137-150
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• 2016

We introduce a new approach that allows us to solve, algorithmically, the contractive completion problem. In this article, we provide concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size $4{\times}4$ using a Moore-Penrose inverse of a matrix.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.235-240
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• 1998

Given a Unimodular polynomial P of degree N$\geq$1, the exteremal problem for ${\gamma}$ =max{｜P(eit)｜:0 $\leq$t$\leq$2$\pi$} satisfies ${\gamma}$$\leq$C{{{{ SQRT { N+1} where C is a universal constant. Here we show that C < 2+{{{{ whenever N is fixed and P has the coefficients of a Rudin-Shapiro polynomial.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.201-209
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• 2020

We introduce and study some basic properties of rough I-convergent of triple sequence spaces and also study the set of all rough I-limits of a triple sequence spaces.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1123-1139
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• 2014

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < ${\alpha}$ < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.641-653
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• 2020

To extend the well-known extremal characterization of the geometric mean of two n × n positive definite matrices A and B, we solve the following problem: $${\max}\{X:X=X^*,\;\(\array{A&V&X\\V&B&W\\X&W&C}\){\geq}0\}$$. We find an explicit expression of the maximum value with respect to the matrix geometric mean of Schur complements.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.249-258
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• 2006

The weakened forms of the (${\theta},s$)-continuous function are introduced and their basic properties are investigated in concern with the other weakened continuous function. The open property of a function and the extremal disconnectedness of the spaces are crucial tools for the survey of these functions.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.29-33
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• 1994

There are various aspects of the solution of boundary-value problems for second-order linear elliptic equations in two independent variables. One useful method of solving such boundary-value problems for Laplace's equation is by means of suitable integral representations of solutions and these representations are obtained most directly in terms of particular singular solutions, termed Green's functions.(omitted)