• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.949-953
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• 2011

It is interesting to know the behavior of a network from its structure. One interesting topic is to find a relation between the existence of a positive equilibrium of the reaction network and its structure. One approach to study this topic is using the concept of deficiency. Another is using some conditions on nodes, which can apply to large-size networks compared to deficiency. In this work, we show the relation between deficiency and the conditions.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1545-1552
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• 2010

It is interesting to know the behavior of a network from its structure. One interesting topic is to find a relation between the existence of a positive equilibrium of the reaction network and its structure. One approach to study this topic is using the concept of deficiency. In this work, we develop an algorithm and show an elementary proof of the relation based on the algorithm and deficiency.

• 한국분말야금학회:학술대회논문집
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• 한국분말야금학회 2006년도 Extended Abstracts of 2006 POWDER METALLURGY World Congress Part 1
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• pp.60-61
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• 2006

In this contribution, we attempted a theoretical analysis on the validity of the widely-accepted idea that rough and singular surfaces can coexist in a crystal at equilibrium. By manipulating the Cahn and Hoffman capillarity vector, the conclusion that a crystal at equilibrium should be composed either of singular surfaces or of rough ones was reached.

• 대한수학회논문집
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• 제11권4호
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• pp.1175-1185
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• 1996

We study the computation of sparse null bases of equilibrium matrices in the context of structural optimization and incompressible fluid flow. In our approach we emphasize the parallel computatin and examine the applications. New block decomposition and node ordering schemes are suggested, and numerical examples are considered.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.365-380
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• 2012

Non-negative matrix factorization (NMF) is a very efficient method to explain the relationship between functions for finding basis information of multivariate nonnegative data. The multiplicative update (MU) algorithm is a popular approach to solve the NMF problem, but it fails to approach a stationary point and has inner iteration and zero divisor. So the elementwisely alternating projected gradient (eAPG) algorithm was proposed to overcome the defects. In this paper, we use the fact that the equilibrium point is stable to prove the convergence of the eAPG algorithm. By using a classic model, the equilibrium point is obtained and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the eAPG algorithm are obtained, which can accelerate the convergence. In addition, the conditions, which satisfy that the non-zero equilibrium point exists and is stable, can cause that the algorithm converges to different values. Both of them are confirmed in the experiments. And we give the mathematical proof that the eAPG algorithm can reach the appointed precision at the least iterations compared to the MU algorithm. Thus, we theoretically illustrate the advantages of the eAPG algorithm.

• Journal of Electrical Engineering and Technology
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• 제3권4호
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• pp.509-513
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• 2008

In this paper, we investigate how generators' ramp-rate constraints may influence their equilibrium strategy formulation. In the market model proposed in this study, the generators' ramp-rate constraints are explicitly represented. In order to fully characterize the inter-temporal nature of the ramp-rate constraints, a dynamic game model is presented. The subgame perfect Nash equilibrium is adopted as the solution of the game and the backward induction procedure for the solution of the game is designed in this paper. The inter-temporal nature of the ramp-rate constraints results in the Markov property of the game, and we have found that the Markov property of the game significantly simplifies the subgame perfect Nash equilibrium characterization. Finally, a simple electricity market numerical illustration is presented for the successful application of the approach proposed.

• 한국국방경영분석학회지
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• 제14권1호
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• pp.63-83
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• 1988

This study is concerned with the equilibrium bidding strategy and the optimal auction design of sequential auction with a reserve price and an entry fee. It is assumed that each bidder has a fixed reservation value and draws the reservation values of other bidders independently in the same distribution and may obtain at most one object to be sold. Under such assumptions, the sequential auction will be analyzed by the game theoretic approach. The purpose of this paper is, in the sequential auction, to find the equilibrium bidding strategy and to design the optimal auction under the equilibrium bidding strategy. The equilibrium bidding strategy and the optimal auction design are further analyzed with respect to change of the reserve price, the entry fee, and the number of bidders and objects. Specially, the auctioneer's expected revenue for each auction is obtained and analyzed.

• 한국국방경영분석학회지
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• 제13권2호
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• pp.63-83
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• 1987

This study is concerned with the equilibrium bidding strategy and the optimal auction design of sequential auction with a reserve price and an entry fee. It is assumed that each bidder has a fixed reservation value and draws the reservation values of other bidders independently in the same distribution and may obtain at most one object to be sold. Under such assumptions, the sequential auction will be analyzed by the game theoretic approach. The purpose of this paper is, in the sequential auction, to find the equilibrium bidding strategy and to design the optimal auction under the equilibrium bidding strategy. The equilibrium bidding strategy and the optimal auction design are further analyzed with respect to change of the reserve price, the entry fee, and the number of bidders and objects. Specially, the auctioneer's expected revenue for each auction is obtained and analyzed.

• Structural Engineering and Mechanics
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• 제7권2호
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• pp.159-180
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• 1999

The present paper shows a new non-tensorial approach to derive basic equations for various structural analyses. It can be used directly in numerical computation procedures. The aim of the paper is, however, to show that the approach serves as an excellent tool for analytical purposes also, working as a link between analytical and numerical techniques. The paper gives a method to derive, at first, expressions for strains in general beam and shell analyses, and secondly, the governing equilibrium equations. The approach is based on the utilization of local fixed Cartesian coordinate systems. Applying these, all the definitions required are the simple basic ones, well-known from the analyses in common global coordinates. In addition, the familiar principle of virtual work has been adopted. The method will be, apparently, most powerful in teaching the theories of curved beam and shell structures for students not familiar with tensor analysis. The final results obtained have no novelty value in themselves, but the procedure developed opens through its systematic and graphic progress a new standpoint to theoretical considerations.

• Wind and Structures
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• 제28권3호
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• pp.171-180
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• 2019

This paper presents a restart iterative approach for time-domain flutter analysis of long-span bridges using the commercial FE package ANSYS. This approach utilizes the recursive formats of impulse-response-function expressions for bridge's aeroelastic forces. Nonlinear dynamic equilibrium equations are iteratively solved by using the restart technique in ANSYS, which enable the equilibrium state of system to get back to last moment absolutely during iterations. The condition for the onset of flutter instability becomes that, at a certain wind velocity, the amplitude of vibration is invariant with time. A long-span suspension bridge was taken as a numerical example to verify the applicability and accuracy of the proposed method by comparing calculated results with wind tunnel tests. The proposed method enables the bridge designers and engineering practitioners to carry out time-domain flutter analysis of bridges in commercial FE package ANSYS.