• Smart Structures and Systems
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• 제18권1호
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• pp.117-138
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• 2016

In this paper a different formulation for the response of structural systems controlled by Tuned Liquid Column Damper (TLCD) devices is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it has been demonstrated that existing model may lead to inaccurate prediction of liquid motion, thus reflecting in a possible imprecise description of the structural response. For this reason the recently proposed fractional formulation introduced to model liquid displacements in TLCD devices, is here extended to deal with TLCD controlled structures under base excitations. As demonstrated through an extensive experimental analysis, the proposed model can accurately capture structural responses both in time and in frequency domain. Further, the proposed fractional formulation is linear, hence making identification of the involved parameters extremely easier.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제17권1호
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• pp.15-27
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• 2013

Division of fractions is always a difficult topic for primary school students. Most of the presentations in teaching the topic in textbooks are procedural, asking students to invert the second fraction and multiply it with the first one, that is, $$\frac{a}{b}{\div}\frac{c}{d}=\frac{a}{b}{\times}\frac{d}{c}$$. Such procedural approach in teaching diminishes both the understanding of structure in mathematics and the interest in learning the subject. This paper discussed the formulation of teaching the division of fractions, which based on research lessons in some primary five classrooms. The formulated lessons started with an analogy to division of integers and working with division of fractions with equal denominators and then extended to division of fractions in general. It is found that the using of analogy helps students to invent their procedure in working the division problem. Some procedures found by students are discussed, with the focus on the development of their invention and mathematical thinking.

• 대한수학회논문집
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• 제20권3호
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• pp.589-602
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• 2005

We present the numerical algorithm for the model for high-strain rate deformation in hyperelastic-viscoplastic materials based on a fully conservative Eulerian formulation by Plohr and Sharp. We use a hyperelastic equation of state and the modified Steinberg and Lund's rate dependent plasticity model for plasticity. A two-dimensional approximate Riemann solver is constructed in an unsplit manner to resolve the complex wave structure and combined with the second order TVD flux. Numerical results are also presented.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1409-1420
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• 2011

In this paper we present an operational method for solving linear Volterra-Fredholm integral equations (VFIE). The method is con- structed based on three matrices with simple structures which lead to a simple and high accurate algorithm. We also present an error estimation and demonstrate accuracy of the method by numerical examples.

• 대한수학회논문집
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• 제12권3호
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• pp.813-827
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• 1997

Multigrid methods for two first-order system least squares (FOSLS) using bilinear finite elements are developed for the pure traction problem of planar linear elasticity. They are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. In this paper, concentration is given on solving for the gradients of displacement only. Numerical results show that the convergences are uniform even as the material becomes nearly incompressible. Computations for convergence rates are included.

• 대한산업공학회지
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• 제16권2호
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• pp.119-127
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• 1990

This paper deals with the production scheduling problems of a dedicated Flexible Manufacturing System. In this work, a new mathematical formulation is proposed and two heuristic algorithms which can generate real-time schedules are suggested. Example problems to demonstrate the good performance and the validity of these two proposed algorithms are also included.

• 대한수학회논문집
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• 제17권1호
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• pp.71-80
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• 2002

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

• 대한수학회논문집
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• 제33권2호
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• pp.651-669
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• 2018

The article is themed to classify new (fully) degenerate Hermite-Bernoulli polynomials with formulation in terms of p-adic fermionic integrals on $\mathbb{Z}_p$. The entire paper is designed to illustrate new properties in association with Daehee polynomials in a consolidated and generalized form.

• 대한수학회보
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• 제47권2호
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• pp.275-286
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• 2010

The algebraic structure of the natural integral cohomology operations is explored by means of examples. We decompose the generators of the groups $H^m(\mathbb{Z},\;n)$ with $2\;{\leq}\;n\;{\leq}\;7$ and $2\;{\leq}\;m\;{\leq}\;13$ into the operations of cup products, cross-cap products and compositions. Examination of these decompositions and comparison with other possible generators demonstrates the existence of relations between integral operations that have withheld formulation. The calculated groups and generators are collected in a table for practical reference.

• 대한수학회논문집
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• 제11권3호
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• pp.867-880
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• 1996

Numerical approximations to the linear elasticity are traditionally based on the finite element method. In this paper we propose a new formulation based on the cubic spline collocation method for linear elastic problem on the unit square. We present several numerical results for the eigenvalues of the matrix represented by cubic collocation method and preconditioner matrix which is preconditioned by FEM and FDM. Finally we present the numerical solution for some example equation.