A problem of synthesizing an optimal file transfer on a file transmission net N is to consider how to distribute, with a minimum total cost, copies of a file J with some information from source vertex set S to all vertices of N by the respective vertices' copy demand numbers. The case of |S| =1 has been studied so far. This paper deals with N such that |S|1, where a forest-type file transfer is defined. This paper proposes a polynomial time algorithm to synthesize an optimal forest-type file transfer on such N satisfying SM U, where M and U are mother vertex set and positive demand vertex set of N, respectively.

A problem of obtaining an optimal file transfer on a file transmission net N is to consider how to distribute, with a minimum total cost, copies of a file with some information from a vertex of N to all vertices of N by the respective vertices' copy demand numbers (i.i., needed numbers of copies). The maximum number of copies of file which can be made at a vertex is called the copying number of the vertex. In this paper, we consider as N an arborescence-net with constraints on copying numbers, and give a necessary and sufficient condition for a file transfer to be optimal on N, and furthermore propose an O(n2) algorithm for obtaining an optimal file transfer on N, where n is the number of vertices of N.

A vertex-capacitated network is a graph whose edges and vertices have infinite positive capacities and finite positive capacities, respectively. Such a network is a model of a communication system in which capacities of links are much larger than those of stations. This paper considers a problem of realizing a flow-saturation in an undirected vertex-capacitated network by adding the least number of edges. By defining a set of influenced vertex pairs by adding edges, we show the follwing results.(1) It suffices to add the least number of edges to unsaturated vertex pairs for realizing flow-saturation.(2) An associated graph of a flow-unsaturated network defined in this paper gives us a sufficient condition that flow-saturation is realized by adding a single edge.

This paper presents and effective acceleration technique for the homotopy method using a rectangular subdivision (which will be called the rectangular algorithm" in this paper). The rectangular algorithm is an efficient solution algorithm that is globally convergent for a large class of nonlinear resistive networks. In the rectangular algorithm, the restart technique is usually used in order to improve the accuracy of the solution. In this paper, we show that certain realization of the restart technique achieves local quadratic convergence. In other words, if we determine the grid size of the rectangular subdivision pertinently in each restart, the sequence of the approximate solutions generated by the algorithm converges to the exact solution quadratically. And in this case, the computational work involved in each restart is almost identical to that of Newton's method. Therefore, our algorithm becomes as efficient as Newton's method when it reaches sufficiently close to the solution.

Recently, a fail-safe principle in wide sense was proposed by one of the authors, in order to accomplish the flexible security against accidents or failures. This new principle is established by the following idea: i.e., if the tolerable range of the deviated output response as a behavior of system is definitely estimated, in advance, and if the response can be found in this range, we can always use this response as available. Even if the deviation range of the output response extends far from the tolerable one, it is sufficient that the system itself has a methodology to find the available response in the tolerable range, and the system behaves by this response. This new concept of an extended type of the fail-safe principle is a significant application of the mathematical theory of nondeterministic fluctuations of systems which was presented by the authors. In this paper, the foundation is given to this principle by developing its mathematical theory, in detail.

In this letter, a constructive simplified Newton method is presented for calculating solutions of infinite dimensional nonlinear equations, which uses a projection scheme from an infinite dimensional space to finite dimensional subspaces. A convergence theorem of the method is shown based on Urabe's theorem.

We analyze the nonlinear dynamics of PLL from the "complex" singularity structure by introducing the complex time. The most important results which we have obtained in this work are as follow: (1) From the psi-series expansion of the solution, the local behavior in the neighbourhood of a movable singularity is mapped onto an integrable differential equation: the Ricatti equation. (2) From the movable pole of the Ricatti equation, a set of infinitly clustered singularities about a movable singularity is shown to exist for the equation of PLL by the multivalued mapping. The above results are interesting because the clustering and/or the fractal distribution of singularities is known to be a characteristic feature of the non-integrability or chaos. By using the method in this letter, we can present a circumstantial evidence for chaotic dynamics without assuming any small parameters in the equation of PLL.

In this paper, we shall describe about a fuzzy estimation theory based on the concept of set-valued operators, suitable for available operation of extremely complicated large-scale network systems. Fundamental conditions for availability of system behaviors of such network systems are clarified in a form of β-level fixed point theorem for system of fuzzy-set-valued operators. Here, the proof of this theorem is accomplished in a weak topology introduced into the Banach space.

A 2-switch node network is one of the most fundamental structure among communication nets such as telephone networks and local area networks etc. In this letter, we prove that a problem of designing a 2-switch node network satisfying capacity conditions of switch nodes and their link, which we call 2-switch node network problem, is NP-complete.

Let us introduce n ( ≥ 2) mappings fi (i=1,,n ≡ 0) defined on reflexive real Banach spaces Xi-1 and let fi:Xi-1 → Yi be completely continuous on bounded convex closed subsets Xi-1(0) ⊂ Xi-1. Moreover, let us introduce n set-valued mappings Fi : Xi-1 Yi → Fc(Xi) (the family of all non-empty compact subsets of Xi), (i=1,,n ≡ 0). Here, we have a fixed point theorem in weak topology on the successively recurrent system of set-valued mapping equations:xi ∈ Fi(xi-1, fi(xi-1)), (i=1,,n ≡ 0). This theorem can be applied immediately to analysis of the availability of system of circular networks of channels undergone by uncertain fluctuations and to evaluation of the tolerability of behaviors of those systems.