• Structural Engineering and Mechanics
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• 제21권2호
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• pp.205-220
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• 2005

This paper presents the possibilities of adapting artificial neural networks (ANNs) to predict the dimensionless parameters related to the maximum contact pressures of an elasticity problem. The plane symmetric double receding contact problem for a rigid stamp and two elastic strips having different elastic constants and heights is considered. The external load is applied to the upper elastic strip by means of a rigid stamp and the lower elastic strip is bonded to a rigid support. The problem is solved under the assumptions that the contact between two elastic strips also between the rigid stamp and the upper elastic strip are frictionless, the effect of gravity force is neglected and only compressive normal tractions can be transmitted through the interfaces. A three layered ANN with backpropagation (BP) algorithm is utilized for prediction of the dimensionless parameters related to the maximum contact pressures. Training and testing patterns are formed by using the theory of elasticity with integral transformation technique. ANN predictions and theoretical solutions are compared and seen that ANN predictions are quite close to the theoretical solutions. It is demonstrated that ANNs is a suitable numerical tool and if properly used, can reduce time consumed.

• 대한수학회논문집
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• 제24권3호
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• pp.425-432
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• 2009

This paper introduces a local non-positivity of two set-valued mappings (F,Q) and considers the existences and properties of solutions for set-valued mixed vector FQ-implicit variational inequality problems and set-valued mixed vector FQ-complementarity problems in the neighborhood of a point belonging to an underlined domain K of the set-valued mappings, where the neighborhood is contained in K. This paper generalizes and extends many results in [1, 3-7].

• 대한기계학회논문집
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• 제6권2호
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• pp.169-175
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• 1982

원주체의 전단스피닝 가공에서 가공물의 반경과 두께 방향의 상대 위치가 변화하지 않는다는 조건 아래서 흐름 함수에 의하여 속도장을 구하고, 접촉계수에 대하여 변형에너지의 국소치를 구함으로써 상당히 낮은 상계치를 얻었으며, 이를 A1-1100-1, A1-1100-H14, A1-6061-0 등 여러 가지 재료에 대한 실험치와 비교한 결과, 정량적으로 일치하였다.

• 대한수학회지
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• 제32권4호
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• pp.761-773
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• 1995

The nonlinear boundary value problem $$ y" = f(x, y, y') = -\frac{x}{3}y' - \frac{y^2}{g(x)}, 0 < x < 1, $$ $$ (1.1) y'(0) = 0, and either (H) : y(1) = \lambda > 0 $$ $$ or (S) : y'(1) + (1 - \upsilon)y(1) = 0, 1 - \upsilon > 0, $$ $$g \in C[0, 1], k \leq g(x) \leq K on [0, 1] for some k, K > 0 $$ arises in the nonlinear circular membrane under normal pressure [2, 3]., 3].

• Korean Journal of Mathematics
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• 제16권3호
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• pp.259-269
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• 2008

The non-existence and existence of the positive solution for the generalized cooperation biological model for two species of animals $${\Delta}u+u(a-bu+g(v))=0\;in\;{\Omega}\\{\Delta}v+v(d+h(u)-cv)=0\;in\;{\Omega}\\u=v=0\;on\;{\partial}{\Omega}$$ are investigated. The techniques used in this paper are elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

• 호남수학학술지
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• 제31권2호
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• pp.247-258
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• 2009

This paper introduces new mixed vector FQ-implicit variational inequality problems and corresponding mixed vector FQ-implicit complementarity problems for set-valued mappings, and studies the equivalence between them under certain assumptions in Banach spaces. It also derives some new existence theorems of solutions for them with examples under suitable assumptions without monotonicity. This paper generalizes and extends many results in [8, 10, 19-22].

• 한국경영과학회지
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• 제22권3호
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• pp.59-80
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• 1997

Designing highly survivable interoffice telecommunication networks is considered. The problem is formulated as a minimum-cost network design problem with three node connectivity constraints. These valid and facet-defining inequalities for the convex hull of the solution are presented. A branch and cut algorithm is proposed based on the inequalities to obtain the optimal solution. With the lower bound by the cutting plane algorithm, a delete-ink heuristic is proposed to otain a good upper bound in the branch and bound procedure. The effeciveness of the branch and cut algorithm is demonstrated with computational results for a variety of problem sets : different lower bounds, two types of link costs and large number of links. The cutting plane procedure based on the three inequalities provides excellent lower bounds to the optimal solutions.

• 대한산업공학회지
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• 제9권2호
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• pp.3-8
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• 1983

The multiple choice knapsack problem is modified. To solve this modified multiple choice knapsack problem, Lagrangian relaxation is used, and to take advantage of the special structure of subproblems obtained by decomposing this relaxed Lagrangian problem, a modified ranking algorithm is used. The K best rank order solutions obtained from each subproblem as a result of applying modified ranking algorithm are used to formulate restricted problems of the original problem. The optimality for the original problem of solutions obtained from the restricted problems is judged from the upper bound and lower bounds calculated iteratively from the relaxed problem and restricted problems, respectively.

• Structural Engineering and Mechanics
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• 제27권5호
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• pp.609-623
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• 2007

The problem of a semi-infinite magneto-electro-elastically impermeable mode-III crack in a magneto-electro-elastic material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane shear impacts, electric displacement and magnetic induction impacts are exerted symmetrically on the upper and lower surfaces of the crack, the magneto-electro-elastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors and dynamic energy density factor are obtained. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into three simultaneous dual integral equations, one of which is converted into an Abel's integral equation and the others into a singular integral equation with Cauchy kernel. Based on the obtained fundamental solutions of point impact loads, the solutions of two kinds of different loading cases are evaluated by integration. For some particular cases, the present results reduce to the previous results.

• Korean Journal of Mathematics
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• 제12권1호
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• pp.77-90
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• 2004

The purpose of this paper is to give a sufficient condition for the existence, nonexistence and uniqueness of coexistence of positive solutions to a rather general type of elliptic competition system of the Dirichlet problem on the bounded domain ${\Omega}$ in $R^n$. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations. This result yields an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.