• 충청수학회지
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• 제36권2호
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• pp.77-86
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• 2023

The purpose of this paper is to show that a certain finite dimensional representation of the rational Cherednik algebra of type A has a basis consisting of simultaneous eigenvectors for the actions of a certain family of commuting elements, which are introduced in the author's previous paper. To this end, we introduce a combinatorial object, which is called a restricted arrangement of colored beads, and consider an action of the affine symmetric group on the set of the arrangements.

• 대한기계학회논문집
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• 제17권9호
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• pp.2138-2144
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• 1993

An integral equation representation of cracks was presented which differs from well-known "dislocation layer" representation. In this new representation, the equations are written in terms of the displacement discontinuity across the crack surfaces rather than derivatives of the displacement-discontinuity. It was shown in that the new technique is well-suited to the treatment of kinked cracks. In the present paper, this integral equation representation is coupled to the direct boundary-element method for the treatment of finite bodies containing kinked cracks. The method is demonstrated for two-dimensional finite domains but extension to three-dimensional problems would appear to be possible. The resulting approach is shown to be simple, yet very accurate. accurate.

• Advances in Computational Design
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• 제5권3호
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• pp.277-289
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• 2020

This article describes the technology for constructing of a multiply-connected three-dimensional area's finite element representation. Representation of finite-element configuration of an area is described by a discrete set that consist of the number of nodes and elements of the finite-element grid, that are orderly set of nodes' coordinates and numbers of finite elements. Corresponding theorems are given, to prove the correctness of the solution method. The adequacy of multiply-connected area topology's finite element model is shown. The merging of subareas is based on the criterion of boundary nodes' coincidence by establishing a simple hierarchy of volumes, surfaces, lines and points. Renumbering nodes is carried out by the frontal method, where nodes located on the outer edges of the structure are used as the initial front.

• 전산구조공학
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• 제6권4호
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• pp.107-118
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• 1993

3차원적인 고체의 유한요소해석 결과를 컴퓨터 그래픽스를 이용하여 시각화하는 후처리 방법들을 고안하고, 유한요소해석 소프트웨어의 개발에 응용하여 그 실용성과 효율성을 검토하였다. 이 연구에서는 고체 구조물의 후처리에서 가장 어려운 문제인 입체 내부의 데이타를 표현하는 방법을 중점적으로 다루었으며, 이를 위하여 공간 내부의 절단면을 표시하는 방법, 입체를 절단하여 분리하는 방법, 등가곡면으로 데이타 값의 범위를 표시하는 방법을 제안하였다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1990년도 가을 학술발표회 논문집
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• pp.40-46
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• 1990

This paper introduces a geometric modelling system adopted in a newly developed preprocessor for finite element analysis of three dimensional structures. The formulation is characterized by hierarchical construction of structural model which consists of control points, curves, surfaces and solids. Various surface and solid modeling schemes based on blending functions and boundary representation are systematized for finite element mesh generation. The modeling system is integrated with model synthesis and operations which facilitate modelling of complex structures.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.213-222
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• 2021

In this paper we investigate the Baer-Kaplansky theorem for module classes on algebras of finite representation types over a field. To do this we construct finite dimensional quiver algebras over any field.

• 대한수학회보
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• 제56권1호
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• pp.187-200
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• 2019

Truncated Hankel operators are compressions of classical Hankel operators to model spaces. In this paper we describe matrix representations of truncated Hankel operators on finite-dimensional model spaces. We then show that the obtained descriptions hold also for some infinite-dimensional cases.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2005년도 학술발표회 논문집
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• pp.409-413
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• 2005

Even though the relative importance of length scale of flow system allow us to simplify three dimensional flow problem to one or two dimensional representation, many systems still require three dimensional analysis. The objective of this study is to develop an efficient and accurate finite element model for analyzing and predicting three dimensional flow features in natural rivers and to offend to model spreading of pollutants and transport of sediments in the future. Firstly, three dimensional Reynolds averaged Navier-Stokes equations with the hydrostatic pressure assumption in generalized curvilinear coordinates were combined with the kinematic free-surface condition. Secondly. to simulate realistic high Reynolds number flow, the model employed the Streamline Upwind/Petrov-Galerkin(SU/PG) scheme as a weighting function for the finite element method in conjunction with an appropriate turbulence model(Smagorinsky scheme for the horizontal plain and Mellor-Yamada scheme for the vertical direction). Several tests is performed for the purpose of validation and verification of the developed model. A simple rectangular channel, 5-shaped and U-shaped channel are used for tests and comparisons are made with RMA-10 model. Runs for each case is converged stably without a oscillation and calculated water-surface deformation, longitudinal and transversal velocities, and velocity vector fields are in good agreement with the results of RMA-10 model.

• 대한수학회지
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• 제37권1호
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• pp.55-72
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• 2000

In this paper, we develop the Grobner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Grobner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite dimensional irreducible representations of the simple tie algebra sl$_3$. Each of these monomial bases is in 1-1 correspondence with the set of semistandard Young tableaux with a given shape.

• Coupled systems mechanics
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• 제5권4호
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• pp.371-393
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• 2016

We propose a heat jet approach for a two-dimensional square lattice with nearest neighbouring harmonic interaction. First, we design a two-way matching boundary condition that linearly relates the displacement and velocity at atoms near the boundary, and a suitable input in terms of given incoming wave modes. Then a phonon representation for finite temperature lattice motion is adopted. The proposed approach is simple and compact. Numerical tests validate the effectiveness of the boundary condition in reflection suppression for outgoing waves. It maintains target temperature for the lattice, with expected kinetic energy distribution and heat flux. Moreover, its linear nature facilitates reliable finite temperature atomic simulations with a correct description for non-thermal motions.