• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.221-229
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• 2005

In this paper we consider the decompositions of subdirect sums and direct sums in bounded BCK-algebras. The main results are as follows. Given a bounded BCK-algebra X, if X can be decomposed as the subdirect sum $\bar{\bigoplus}_{i{\in}I}A_i$ of a nonzero ideal family $\{A_i\;{\mid}\;i{\in}I\}$ of X, then I is finite, every $A_i$ is bounded, and X is embeddable in the direct sum $\bar{\bigoplus}_{i{\in}I}A_i$ ; if X is with condition (S), then it can be decomposed as the subdirect sum $\bar{\bigoplus}_{i{\in}I}A_i$ if and only if it can be decomposed as the direct sum $\bar{\bigoplus}_{i{\in}I}A_i$ ; if X can be decomposed as the direct sum $\bar{\bigoplus}_{i{\in}I}A_i$, then it is isomorphic to the direct product $\prod_{i{\in}I}A_i$.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.291-299
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• 2009

For $G_{\phi}$-sequences ${\phi}_i$ and ${\kappa}$-functions ${\kappa}_i$(i = 1,2,3) we obtain the most general $H{\ddot{o}}lder$ type inequalities on the functions of $G_{\kappa}G_{\phi}$-bounded variations.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1573-1590
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• 2020

In this paper, we classify all solutions bounded from below to uniformly elliptic equations of second order in the form of Lu(x) = a_ij(x)D_iju(x) + b_i(x)D_iu(x) + c(x)u(x) = f(x) or Lu(x) = D_i(a_ij(x)D_ju(x)) + b_i(x)D_iu(x) + c(x)u(x) = f(x) in unbounded cylinders. After establishing that the Aleksandrov maximum principle and boundary Harnack inequality hold for bounded solutions, we show that all solutions bounded from below are linear comb_inations of solutions, which are sums of two special solutions that exponential growth at one end and exponential decay at the another end, and a bounded solution that corresponds to the inhomogeneous term f of the equation.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.535-539
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• 2007

Given operators X and Y acting on a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX=Y. In this article, we show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $X=(x_{ij})\;and\;Y=(y_{ij})$ be operators in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that AX=Y. (2) There is a bounded sequence $\{\alpha_n\}\;in\;\mathbb{C}$ such that $y_{ij}=\alpha_jx_{ij}\;for\;i,\;j\;{\in}\;\mathbb{N}$. Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax=y. We show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $x=(x_i)\;and\;y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that Ax=y. (2) There is a bounded sequence $\{\alpha_n\}$ in $\mathbb{C}$ such that $y_i=\alpha_ix_i\;for\;i{\in}\mathbb{N}$.

• Honam Mathematical Journal
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• v.7 no.1
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• pp.1-6
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• 1985

Bounded linear operators defined from a space with vector norm into (LF)-complete vector lattice are represented by Hellinger integration.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1101-1110
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• 2023

At the present paper, we investigate bounded approximately local derivations of ℓ¹-Munn algebra 𝕄_I(𝒜), where I is an arbitrary non-empty set and 𝒜 is an approximately locally unital Banach algebra. Indeed, we show that if _𝒜B(𝒜, 𝒜^*) and B_𝒜(𝒜, 𝒜^*) are reflexive, then every bounded approximately local derivation from 𝕄_I(𝒜) into any Banach 𝕄_I(𝒜)-bimodule X is a derivation. Finally, we apply this result to study bounded approximately local derivations of the semigroup algebra ℓ¹(S), where S is a uniformly locally finite inverse semigroup.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.487-498
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• 2010

For some $\phi$-sequences $\phi_1$, $\phi_2$ and $\phi_3$, and $\kappa$-function $\kappa_1$, $\kappa_2$ and $\kappa_3$ with $\kappa_1^{-1}(x)\kappa_2^{-1}(x)\;{\geq}\;\kappa_3^{-1}(x)$ for $x\;{\geq}\;0$, the Luxemburg norm is lower semi-continuous on ${\kappa}{\phi}BV_0$, and some specialized equivalent conditions are considered.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.499-518
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• 1995

In this paper we consider more systematically the centralizer C(S) of the set $S = {f_a $\mid$ f_a : X \to X ; x \longmapsto x * a, a \in X}$ with respect to the semigroup End(X) of all endomorphisms of an implicative BCK-algebra X with the condition (S). We obtain a series of interesting results. The main results are stated as follows : (1) C(S) with repect to a binary operation * defined in a certain way forms a bounded implicative BCK-algebra with the condition (S). (2) X can be imbedded in C(S) such that X is an ideal of C(S)/ (3) If X is not bounded, it can be imbedded in a bounded subalgebra T of C(S) such that X is a maximal ideal of T. (4) If $X (\neq {0})$ is semisimple, C(S) is BCK-isomorphic to $\prod_{i \in I}{A_i}$ in which ${A_i}_{i \in I}$ is simple ideal family of X.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.59-78
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• 2004

This paper is devoted to illustrate some numerical procedures to solve the boundary equilibrium problems of three-dimensional solids that are subjected to thermal strains. The constitutive equations take into account the bounded tensile strength of the material and they are presented in the framework of non-linear elasticity and small strains. The associated equilibrium problem is solved numerically by means of the finite element method and the numerical techniques, i.e. the Newton-Raphson method and the secant method, are revised in order to assure the solution convergence of the discretized problem. Some numerical examples are illustrated.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.1-22
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• 1997

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.