• 대한수학회논문집
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• 제13권1호
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• pp.1-6
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• 1998

The paper refers to ordered semigroups in which $x^2 (x \in S)$ are left ideal elements. We mainly show that this $po$-semigroup is left regular if and only if S is a union of left simple subsemigroups of S.

• Korean Journal of Mathematics
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• 제15권2호
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• pp.115-119
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• 2007

Let R be a Krull ring with the unique regular maximal ideal M. We show that R has a regular prime element and reg-$dimR=1{\Leftrightarrow}R$ is a factorial ring and reg-$dim(R)=1{\Rightarrow}M$ is invertible ${\Leftrightarrow}R{\varsubsetneq}[R:M]{\Leftrightarrow}M$ is divisorial ${\Leftrightarrow}$ reg-$htM=1{\Rightarrow}R$ is a rank one discrete valuation ring. We also show that if M is generated by regular elements, then R is a rank one discrete valuation ring ${\Rightarrow}$ R is a factorial ring and reg-dim(R)=1.

• 대한수학회보
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• 제61권1호
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• pp.117-133
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• 2024

Let 𝓟 = {X_i : i ∈ I} be a partition of a set X. We say that a transformation f : X → X preserves 𝓟 if for every X_i ∈ 𝓟, there exists X_j ∈ 𝓟 such that X_if ⊆ X_j. Consider the semigroup 𝓑(X, 𝓟) of all transformations f of X such that f preserves 𝓟 and the character (map) χ^(f): I → I defined by i_χ^(f) = j whenever X_if ⊆ X_j is bijective. We describe Green's relations on 𝓑(X, 𝓟), and prove that 𝒟 = 𝒥 on 𝓑(X, 𝓟) if 𝓟 is finite. We give a necessary and sufficient condition for 𝒟 = 𝒥 on 𝓑(X, 𝓟). We characterize unit-regular elements in 𝓑(X, 𝓟), and determine when 𝓑(X, 𝓟) is a unit-regular semigroup. We alternatively prove that 𝓑(X, 𝓟) is a regular semigroup. We end the paper with a conjecture.

• 전산구조공학
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• 제5권2호
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• pp.105-118
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• 1992

Static performance was compared for the triangular plate elements through some numerical experiments. Four Kirchhoff elements and six Mindlin elements were selected for the comparison. Numerical tests were executed for the problems of rectangular plates with regular and distorted meshes, rhombic plates, circular plates and cantilever plates. Among the Kirchhoff 9 DOF elements, the discrete Kirchhoff theory element was the best. Element distortion and the aspect ratio were shown to have negligible effects on the displacement behaviour. The Specht's element resulted in better results than the Bergan's but it was sensitive to the aspect ratio. The element based on the hybrid stress method also resulted in good results but it assumed to be less reliable. Among the linear Mindlin elements, the discrete shear triangle was the best in view of reliability, accuracy and convergence. Since the thin plate behaviour of it was as good as the DKT element, it can be used effectively in the finite element code regardless of the thickness. As a quadratic Mindlin element, the MITC7 element resulted in best results in almost all cases considered. The results were at least as good as those of doubly refined meshes of linear elements.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권4호
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• pp.253-274
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• 2005

An additive regular Semiring S is left inversive if the Set E+ (S) of all additive idempotents is left regular. The set LC(S) of all left inversive semiring congruences on an additive regular semiring S is a lattice. The relations $\theta$ and k (resp.), induced by tr. and ker (resp.), are congruences on LC(S) and each $\theta$-class p$\theta$ (resp. each k-class pk) is a complete modular sublattice with $p_{min}$ and $p_{max}$ (resp. With $p^{min}$ and $p^{max}$), as the least and greatest elements. $p_{min},\;p_{max},\;p^{min}$ and $p^{max}$, in particular ${\epsilon}_{max}$, the maximum additive idempotent separating congruence has been characterized explicitly. A semiring is quasi-inversive if and only if it is a subdirect product of a left inversive and a right inversive semiring.

• 대한수학회보
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• 제59권3호
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• pp.617-642
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• 2022

For positive integers n and d with d < n, an n × n array A based on 𝒳 = {0, 1, …, nd} is called a sparse anti-magic square of order n with density d, denoted by SAMS(n, d), if each non-zero element of X occurs exactly once in A, and its row-sums, column-sums and two main diagonal-sums constitute a set of 2n + 2 consecutive integers. An SAMS(n, d) is called regular if there are exactly d non-zero elements in each row, each column and each main diagonal. In this paper, we investigate the existence of regular sparse anti-magic squares of order n ≡ 1, 5 (mod 6), and prove that there exists a regular SAMS(n, d) for any n ≥ 5, n ≡ 1, 5 (mod 6) and d with 2 ≤ d ≤ n - 1.

• 대한수학회보
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• 제59권5호
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• pp.1177-1190
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• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α₁, …, α_p and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and Ann_R(α^m) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (αⁿ, bⁿ) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.515-530
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• 2015

We say that (R, f, g) is an additive (m, n)-semihyperring if R is a non-empty set, f is an m-ary associative hyperoperation, g is an n-ary associative operation and g is distributive with respect to f. In this paper, we describe a number of characterizations of additive (m, n)-semihyperrings which generalize well-known results. Also, we consider distinguished elements, hyperideals, Rees factors and regular relations. Later, we give a natural method to derive the quotient (m, n)-semihyperring.

• Structural Engineering and Mechanics
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• 제52권5호
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• pp.919-935
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• 2014

In this study, the control of the shape of pre-stressed cable structures and the effective control element were examined. The process of deriving the displacement control equations using the force method was explained, and the concurrent control scheme (CCS) and the sequence control scheme (SCS) were proposed. To explain the control scheme process, the quadrilateral cable net model was adopted and classified into a regular model and an irregular model for the analysis of the control results. In the control analysis of the regular model, the CCS and SCS analysis results proved reliable. For the SCS, the errors occur in the control stage and varied according to the control sequence. In the control analysis of the irregular model, the CCS analysis result also proved relatively reliable, and the SCS analysis result with the correction of errors in each stage was found nearly consistent with the target shape after the control. Finally, to investigate an effective control element, the Geiger cable dome was adopted. A set of non-redundant elements was evaluated in the reduced row echelon form of a coefficient matrix of control equations. Important elements for shape control were also evaluated using overlapping elements in the element sets, which were selected based on cable adjustments.

• Structural Engineering and Mechanics
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• 제14권5호
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• pp.595-610
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• 2002

This paper presents an efficiency of various non-conforming (NC) modes in development of a series of new finite elements with the special emphasis on 4-node quadrilateral elements. The NC modes have been used as a key scheme to improve the behaviors of various types of new finite elements, i.e., Mindlin plate bending elements, membrane elements with drilling degrees of freedom, flat shell elements. The NC modes are classified into three groups according to the 'correction constants' of 'Direct Modification Method'. The first group is 'basic NC modes', which have been widely used by a number of researchers in the finite element communities. The basic NC modes are effective to improve the behaviors of regular shaped elements. The second group is 'hierarchical NC modes' which improve the behaviors of distorted elements effectively. The last group is 'higher order NC modes' which improve the behaviors of plate-bending elements. When the basic NC modes are combined with hierarchical or higher order NC modes, the elements become insensitive to mesh distortions. When the membrane component of a flat shell has 'hierarchical NC modes', the membrane locking can be suppressed. A number of numerical tests are carried out to show the positive effect of aforementioned various NC modes incorporated into various types of finite elements.