• Journal of applied mathematics & informatics
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• v.30 no.3_4
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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 Biosystems Engineering
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• v.3 no.2
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• pp.62-68
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• 1978

Equilibrium moisture content of rough rice is an important factor because it has a close relationship to storage and drying problems. Determination of the EMC for 10 different varieties of rough rice were made in atmospheres of various constant humidities at three different constant temperatures. In addition , some physical properties were also measured for two different levels of moisture content of the samples. The results may be summarized as follows ; 1. Several physical properties of ten different varieties of rough were measured. Significant difference of the properties was appeared between the varieties in which the difference was pronounced in the dimensions of the varieties. Also, all the dimensions were increased as the moisture content of the rough rice was increased from 14 % to 16%. 2. Significant difference of the equilibrium moisture content was also appeared between some of the varieties in which the equilibrium moisture content of Josaengtongil and Minehikari was 24.26% while that of the others was in the range between 18 to 19% at the conditions of relative humidity of 84% and temperature of 47℃ , respectively. Similar pattern was also observed in other conditions. 3. The values of the constant of Henderson's equation were calculated from the data obtained but they are believed to be useful until more precise and complete data are obtained. There was a good agreement between the calculated and experimental results.

• 연구논문집
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• s.27
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• pp.183-200
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• 1997

We have calculated the energy of three distinct grain configurations, namely completely connected, partially connected and unconnected configurations, evolving during a spheroidization of polycrystalline thin film by extending a geometrical model due to Miller et al. to the case of spheroidization at both the surface and film-substrate interface. "Stabilitl" diagram defining a stable region of each grain configuration has been established in terms of the ratio of grain size to film thickness vs. equilibrium wetting or dihedral angles at various interface energy conditions. The occurrence of spheroidization at the film-substrate interface significantly enlarges the stable region of unconnected grain configuration thereby greatly facilitating the occurrence of agglomeration. Complete separation of grain boundary is increasingly difficult with a reduction of equilibrium wetting angle. The condition for the occurrence of agglomeration differs depending on the equilibrium wetting or dihedral angles. The agglomeration occurs, at low equilibrium angles, via partially connected configuration containing stable holes centered at grain boundary vertices, whereas it occurs directly via completely connected configuration at large equilibrium angles except for the case having small surface and/or film-substrate interface energy. The initiation condition of agglomeration is defined by the equilibrium boundary condition between the partially connected and unconnected configurations for the former case, whereas it can, for the latter case, largely deviate from the equilibrium boundary condition between the completely connected and unconnected configurations because of the presence of a finite energy barrier to overcome to reach the unconnected grain configuration.

• Structural Engineering and Mechanics
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• v.60 no.1
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• pp.111-130
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• 2016

Two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations. The first element is formulated for the infinite ratio of beam radius to thickness. In the second one, theory of the thick beam is used. Advantage of these elements is that by utilizing only one element, the exact solution will be obtained. Due to incorporating equilibrium conditions in the presented formulations, both proposed elements gave the precise internal forces. By solving some numerical tests, the high performance of the recommended formulations and also, interaction effects of the bending and axial forces will be demonstrated. While the second element has less error than the first one in thick regimes, the first element can be used for all regimes due to simplicity and good convergence. Based on static responses, it can be deduced that the first element is efficient for all the range of structural characteristics. The free vibration analysis will be performed using the first element. The results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.61-68
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• 2000

In general, the design of membrane structures takes three steps. The first is shape finding analysis which is determination of initial equilibrium geometry with uniform stresses. The second step involve the computation of the stress-deformation to get completed membrane under various load conditions. The third step is to divide the membrane structures into several plan strips from the initial equilibrium states. This procedure is needed because of the initial shape has usually undevelopable curved surface and is called as "cutting patterns generation". By introducing this work, the deformation due to the initial stress is removed and approximate cutting patterns are generated. In this approach, however, material properties is not considered, therefore the error between the design stresses and actual stresses during the fabrication of plan strips should be occurred. In this paper, actual equilibrium shape analysis procedure for HP shape models is presented. The deviations of stresses between the design stresses and actual stresses are estimated.

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1529-1536
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• 2004

A structure is broken down into a number of substructures by means of the finite element method and the substructures are synthesized for the complete structure. The divided substructures take two types: fixed-free and free-free elements. The flexibility and stiffness matrices of the free-free elements are the Moore-Penrose inverse of each other. Thus, it is not easy to determine the equilibrium equations of the complete structure composed of two mixed types of substructures. This study provides the general form of equilibrium equation of the entire structure through the process of assembling the equilibrium equations of substructures with end conditions of mixed types. Applications demonstrate that the proposed method is effective in the structural analysis of geometrically complicated structures.

• Textile Coloration and Finishing
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• v.18 no.5 s.90
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• pp.48-52
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• 2006

A mixed adsorbent prepared by pyrolysing a mixture of carbon and flyash in 1:1 ratio was tested for its deceleration ability for three different classes of dyes, namely Astrazone Blue FRR(C.I. Basic Blue 69), Teflon Blue ANL(C.I. Acid Slue 125) and Verofix Red(Reactive Red 3GL). Equilibrium investigations were carried out at the optimum conditions obtained in the previous studies. The equilibrium data fitted reasonably well to both the Freundlich and Langmuir adsorption models. However the Langmuir model was more appropriate to describe the adsorption behavior of the dyes to the hybrid absorbent system compared with the Freundlich model. The mixed adsorbent cm be an low-cost alternative to activated carbons.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.112-117
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• 2000

A numerical study on natural convection in a vertical square cavity filled with a porous medium is carried out with Brinkman-Forchheimer-extended Darcy flow model, and the validity of local thermodynamic equilibrium assumption is studied. The local thermodynamic equilibrium refers to the state in which a single temperature can be used to describe a heat transfer process in a multiphase system. With this assumption, the analysis is greatly simplified because only one equation is needed to describe the heat transfer process. But prior to using this assumption, it is necessary to know in what conditions the assumption can be used. The numerical results of this study reveal that large temperature difference between fluid phase and solid phase exists near wall region, paticularily when the convection becomes dominant over conduction. And the influence of flow parameters such as fluid Rayleigh number, fluid Prandtl number, dimensionless particle diameter and conductivity ratio are investigated.

• Journal of the Korean Operations Research and Management Science Society
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• v.24 no.1
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• pp.13-25
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• 1999

This paper presents a model of competitive positioning and pricing of new products in a multi-segmented market. The segments in the market are located on a multi-dimensional discrete attribute space with fixed demands. Firms launch products sequentially on the attribute space, incurring fixed and variable costs, and then decide on their product prices. Each firm acts to maximize its profit. Market share of a firm is determined by the position and price of Its product. We provide sufficient conditions for the existence and uniqueness of Nash equilibrium Another equilibrium concept is Introduced and related to the Nash equilibrium. A heuristic algorithm based on genetic algorithms is designed to obtain the Nash equilibrium.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.4
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• pp.379-389
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• 2002

In this paper, we study the competition between two kinds of suppliers, a bricks and mortars(B&M) and a clicks and mortars(C&M). Using the circular spatial market model, we derive and analyze the Nash and Stackelberg equilibria as a function of offline market share and efficiency of online channel of the C&M supplier. The result can be summarized as follows: (1) Stackelberg equilibrium is always superior to the Nash equilibrium, (2) Under certain conditions, the price of online channel can be higher than that of offline channel, (3) It is impossible for the C&M supplier to encroach on all of the B&M supplier's market, (4) In some cases, the C&M supplier has incentive to lower the efficiency of its online channel for more profit.