In the topological sum of pairwise disjoint topological spaces, we inves- tigate topological properties of the following generalized closed sets: preclosed sets, semi-closed sets, α-closed sets, g-closed sets, sg-closed sets, gs-closed sets, gp-closed sets. Moreover, we have a characterization of some generalized compact topological sum. The results are proved by using a unified concept in the sense of [23] [13] [22] (eg., [17]) (cf. Section 2 and Section 3 below); we have generalized versions of main results.

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A simple boundary value problem for a n-th order linear ordinary differential equation which appears typically in the theory of Heaviside cable and Thomson cable is treated. Output-input voltage relation is investigated. We found the best constant of Sobolev-type inequality, which estimates the square of supremum of absolute value of output voltage from above by the power of input voltage. The best constant is a rational function of the characteristic roots and also a rational function of the characteristic coefficients. The second formula for the best constant is very important because even for small number of n it is difficult to obtain the exact value of characteristic roots but in some cases it is easy to know the coefficients of characteristic polynomial. Giambelli’s formula which appears in the theory of representation of finite groups plays an important role.

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The present paper is devoted to giving the existence and uniqueness theorem on disintegrations of operator valued weights by applying Sutherland’s theorem on disintegrations of weights on a von Neumann algebra. To do so, we study the measurability and the integration of a field of operator valued weights. The results obtained here are expected to be useful for discussing reductions of inclusion relations of von Neumann subalgebras.

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In this paper, the matching of center lines from stereo tree images is con- sidered, and formulated as a combinatorial optimization problem. Marr and Poggio showed that the Hopfield network, a kind of artificial neural network model, can be applied to reconstruct 3D structure from random dot stereogram. Their method con- sists of the following five steps; 1.form matching candidates, 2.allocate candidates on units of network, 3.determine connection weights among units from the characteristics of images, 4.converge to a stable state and 5.reconstruct 3D structure from the state of network. This paper proposes a new formation of connection weights in the stereo line matching algorithm.

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In recent years, particle swarm optimization (PSO) proposed by Kennedy et al. has been widely used as a general approximate solution method for optimization problems. The authors proposed a revised PSO (rPSO) method incorporating the homomorphous mapping and the multiple stretching technique in order to cope with shortcomings of PSO and showed its efficiency for nonlinear programming problems. In this paper, we construct an interactive fuzzy satisficing method for multiobjective nonlinear programming problems based on the rPSO. In order to obtain better solutions in consideration of the property of multiobjective programming problems, we incorporate the direction to nondominated solutions into the rPSO. Furthermore, the efficiency of the proposed method (MOrPSO) is shown through applications to numerical examples.

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This paper proposes a 0-1 knapsack problem considering both the maximization of the total return including randomness and minimization of available budget, simultaneously. For the flexibility of setting each goal, the satisfaction function is introduced and the model maximizing minimum aspiration levels is proposed. Since this problem is not a well-defined problem due to including randomness and fuzziness, chance constraints are introduced, and a main problem is transformed into a nonlinear 0-1 programming problem. In previous researches, the solution method using a parametric dynamic programming approach is constructed. However, this solution method is not efficient due to using dynamic programming repeatedly. Therefore, in this paper, the efficient solution method is constructed. This means that the number of using dynamic programming is as small as possible.

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In this paper, we address a network optimization problem for supply chain network systems. Supply chain management (scm) has been drawing much attention for most companies. Among other factors, the reconfiguration of the existing supply chain network (scn) is essential to retain competitive edge. We suggest a meta heuristic algorithm to solve this problem. It has been implemented to evaluate several recon- figuration alternatives for warehouses distributed all nationwide, especially focusing on the warehouses in specific region of Japan, of a major household appliances com- pany. We simulated two cases by using actual data to confirm the effectiveness of the proposed algorithm. Computational experiments show that the proposed heuristic is satisfactory in both speed and the quality of the solutions generated.

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