• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권3호
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• pp.225-242
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• 2016

The phase-type representation is strongly connected with the positive realization in positive system. We attempt to transform phase-type representation into sparse mono-cyclic positive representation with as low order as possible. Because equivalent positive representations of a given phase-type distribution are non-unique, it is important to find a simple sparse positive representation with lower order that leads to more effective use in applications. A Hypo-Feedback-Coxian Block (HFCB) representation is a good candidate for a simple sparse representation. Our objective is to find an HFCB representation with possibly lower order, including all the eigenvalues of the original generator. We introduce an efficient nonlinear optimization method for computing an HFCB representation from a given phase-type representation. We discuss numerical problems encountered when finding efficiently a stable solution of the nonlinear constrained optimization problem. Numerical simulations are performed to show the effectiveness of the proposed algorithm.

• 호남수학학술지
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• 제26권4호
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• pp.483-507
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• 2004

In this paper the left regular representation and the reduced $C^*$-algebra for a commutative separative semigroup is defined. The universal representation, the reduced $C^*$-algebra and the full $C^*$-algebra for the additive semigroup $N^+$ are given. Also it is proved that $C*_r(N^+){\ncong}C^*(N^+)$.

• 한국지반공학회지:지반
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• 제10권1호
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• pp.7-18
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• 1994

본 연구에서는 단조하중과 반복하중에 대한 점토지반의 거동을 표현할 수 있는 새로운 구성모델을 제안하였다. 제안된 모델은 과압밀상태에서의 응력-변형률 관계를 쌍곡선식으로 가정하고 한계상태이론과 결합시켜 비배수 응력경로를 예측한다. 에너지분산식을 이용하여 개발된 이 구성모델은 단조하중 작용시에 미약한 과압밀상태 및 과다한 과압밀상태의 점성토거동을 표현할 수 있다. 또한 반복하중하에서의 거동을 나타내기 위하여 단조하중에 대하여 개발된 구성모델에 비배수 경로간격비 이동함수를 도입하였다. 이를 위하여 한개의 추가적인 모델계수가 필요하며 그 값은 합리적 방법으로 실험결과로부터 산정될 수 있다. 본 구성모델은 비교적 쉽고 정확하게 반복하중을 받는 점성토지반의 비배수 거동에 대한 실험결과를 예측한다.

• Earthquakes and Structures
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• 제14권6호
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• pp.551-565
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• 2018

Experimental testing is considered the most realistic approach to obtain a detailed representation of the nonlinear behaviour of masonry-infilled reinforced concrete (RC) structures. Among other applications, these tests can be used to calibrate the properties of numerical models such as simplified macro-models (e.g., strut-type models) representing the masonry infill behaviour. Since the significant cost of experimental tests limits their widespread use, alternative approaches need to be established to obtain adequate data to validate the referred simplified models. The proposed paper introduces a detailed finite element modelling strategy that can be used as an alternative to experimental tests to represent the behaviour of masonry-infilled RC frames under earthquake loading. Several examples of RC infilled frames with different infill configurations and properties subjected to cyclic loading are analysed using the proposed modelling approach. The comparison between numerical and experimental results shows that the numerical models capture the overall nonlinear behaviour of the physical specimens with adequate accuracy, predicting their monotonic stiffness, strength and several failure mechanisms.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.1-28
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• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• 대한수학회논문집
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• 제9권4호
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• pp.927-931
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• 1994

Let G be a cyclic group of order 2 and let $S^1$ denote the unit circle in $R^2$ with the standard metric. We consider smooth G-vector bundles over $S^1$ when G acts on $S^1$ by reflection. Then the fixed point set of G on $S^1$ is two points ${z_0, z_1}$. Let $E$\mid$_{z_0} and E$\mid$_{z_1}$ be the fiber G-representation spaces at $z_0$ and $z_1$ respectively. We associate an orthogonal G-representation $\rho_i : G \to O(n)$ to $E$\mid$_{z_i}, i = 0, 1$. Let det $p\rho_i(g), g \neq 1$, be denoted by det $E$\mid$_{z_i}$ since det $\rho_i(g)$ is independent of choice of $\rho_i$.

• 대한수학회보
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• 제45권1호
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• pp.33-37
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• 2008

Let G be a compact abelian Lie group, and M an odd-dimensional closed smooth G-manifold. If the fixed point set $M^G\neq\emptyset$ and dim $M^G=0$, then G has a subgroup H with $G/H{\cong}\mathbb{Z}_2$, the cyclic group of order 2. The tangential representation $\tau_x$(M) of G at $x{\in}M^G$ is also regarded as a representation of H by restricted action. We show that the number of fixed points is even, and that the tangential representations at fixed points are pairwise isomorphic as representations of H.

• Steel and Composite Structures
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• 제28권2호
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• pp.123-138
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• 2018

Eccentrically braced frames (EBF) represent an optimal structural solution for seismic prone areas, being able to provide high dissipative capacity and good elastic stiffness, to withstand strong seismic events without significant loss of bearing capacity and to avoid damage to non-structural elements in case of low and moderate earthquakes. The accurate knowledge of the cyclic behaviour of the dissipative links, characterizing the whole performance of EBFs, is required to optimize the structural properties and to refine the design techniques adopted for multi-storey buildings' analysis. Reliable numerical models for the links, at the same time requiring a limited computational effort, are then needed. The present work shows the results of a wide experimental test campaign executed on real-scale one storey/one bay frames with horizontal and vertical links, together with the elaboration of a simple semi-analytical model for the quick representation of the cyclic behaviour of shear links.

• 충청수학회지
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• 제27권2호
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• pp.287-295
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• 2014

In this paper, we prove that the image of the representation of the automorphism group of a supersingular K3 surface of Artin-invariant 1 over odd characteristic p on the global two forms is a finite cyclic group of order p + 1. Using this result, we deduce, for such a K3 surface, there exists an automorphism which cannot be lifted over a field of characteristic 0.

• 한국전자거래학회지
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• 제8권1호
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• pp.113-119
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• 2003

This paper proposes a new multiplicative inverse algorithm for the Galois field GF (2/sup m/) whose elements are represented by optimal normal basis type Ⅱ. One advantage of the normal basis is that the squaring of an element is computed by a cyclic shift of the binary representation. A normal basis element is always possible to rewrite canonical basis form. The proposed algorithm combines normal basis and canonical basis. The new algorithm is more suitable for implementation than conventional algorithm.