Scientiae Mathematicae Japonicae

NEURONAL MODELING IN THE PRESENCE OF RANDOM REFRACTORINESS

G. Esposito, V. Giorno, A.G. Nobile, L.M. Ricciardi, C. Valerio

2006 Volume 64 Issue 1 Pages 1-36
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_1

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Inclusion of refractoriness in a diffusion model for single neuron activity is the object of the present paper. An asymptotic analysis of the random process modeling the number of firings and the distribution of interspike intervals is performed under the approximation of exponentially distributed firings. In the cases of constant, uniform, exponential, Erlang, truncated normal and hyperexponential durations of refractory periods, asymptotic simple expressions are obtained and some numerical evaluations are performed

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FIXED POINT OF CONTRACTION AND EXPONENTIAL ATTRACTORS

Y. Takei, A. Yagi

2006 Volume 64 Issue 1 Pages 37-44
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_37

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The exponential attractor is known as one of useful notions of invariant attractors in the theory of infinite-dimensional dynamical systems. It is also known that, if the semigroup of a dynamical system satisfies a compact perturbation condition of contraction, then the dynamical system has exponential attractors. In this paper, we clarify the meaning of the compact perturbation condition of contraction and show that the exponential attractor is a natural generalization of the exponentially stable equilibrium

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WEAK AND STRONG SOLUTIONS OF ISOTROPIC VISCOELASTIC EQUATIONS WITH LONG NONLINEAR MEMORY

J-S. Hwang, S. Nakagiri

2006 Volume 64 Issue 1 Pages 45-60
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_45

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The equations of isotropic viscoelastic materials with long nonlinear memory are studied. The model equations are described by second order Volterra integrodifferential equation having nonlinear kernels. Based on the variational methods, we have proved the fundamental results on existence, uniqueness and regularity of weak and strong solutions for the equations

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TANGENT AND NORMAL VECTORS TO FEASIBLE REGIONS WITH GEOMETRICALLY DERIVABLE SETS

Yoshiyuki Sekiguchi, Wataru Takahashi

2006 Volume 64 Issue 1 Pages 61-71
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_61

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We give exact formulae for tangent cones and regular normal cones to feasible sets. We impose geometrical derivability on the sets used in constraint systems, which is weaker than Clarke regularity. Necessary optimality conditions with regular normal vectors can be stronger than those with general normal vectors. An example of the situation is given.

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COUNTEREXAMPLES ON GENERALIZED METRIC SPACES

Masami Sakai

2006 Volume 64 Issue 1 Pages 73-76
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_73

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In this paper, we give counterexamples of some questions on generalized metric spaces. First we show that there exists an open sequence-covering map of a countable g-second countable space onto the sequential fan Sω. This is a counterexample for a question posed by Y. Tanaka. Second we show that there exists a regular Fr´echet space Y satisfying the following conditions: (1) Y has a point-countable csnetwork and k-network of closed subsets; (2) every first countable closed subset of Y is countable; (3) Y is not locally separable and does not have any star-countable k-network. This is a counterexample for questions posed by S. Lin.

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A DUAL BASED HEURISTIC FOR A HUB-SPOKE AIR CARGO NETWORK DESIGN PROBLEM WITH HOP-COUNT CONSTRAINTS

Moon-Gil Yoon, Duk-Young Yoon, Sang-Heon Han

2006 Volume 64 Issue 1 Pages 77-90
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_77

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In this paper, we address a hub-spoke network design problem for air-cargo systems. To build such a network, three kinds of network costs should be considered: fixed costs for establishing a hub, fixed costs for operating air-cargo on each route and variable costs occurring on each route. With these kinds of costs, we develop an optimization model for designing a hub-spoke network in air-cargo systems, including the hop-count constraint being used effectively to deliver freights. We suggest a dual based heuristic algorithm to solve our problem. Computational experiments show that the proposed heuristic is satisfactory in both speed and the quality of the solutions generated.

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SEMIPRIME SKEW POLYNOMIAL RINGS

A. Moussavi, E Hashemi

2006 Volume 64 Issue 1 Pages 91-95
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_91

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ON POWERS OF P-POSINORMAL OPERATORS

Mi Young Lee, Sang Hun Lee

2006 Volume 64 Issue 1 Pages 97-101
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_97

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GRÖBNER BASES ON PATH ALGEBRAS AND THE HOCHSCHILD COHOMOLOGY ALGEBRAS

Yuji Kobayashi

2006 Volume 64 Issue 1 Pages 103-129
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_103

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We generalize the techniques developed in the previous paper [10] on free algebras and free bimodules to path algebras and projective bimodules. We develop the theory of Gröber bases on path algebras and their projective bimodules, and use it to construct projective resolutions of bimodules over a quotient algebra of a path algebra. It gives an effective way to calculate the Hochschild cohomology of algebras expressed as quotients of path algebras. We also give a formula for the cup product in the cohomology in terms of our resolution. It gives a way to determine the ring structure of the cohomology.

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CATEGORY OF HYPER BCK-ALGEBRAS

H. HARIZAVI, J. MACDONALD, R. A. BORZOOEI

2006 Volume 64 Issue 1 Pages 131-139
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_131

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In this paper we first define the category of hyper BCK-algebras. After that we show that the category of hyper BCK-algebras is connected, factorisable and has equalizers, coequalizers, products, coproducts, intersection and kernel. It is a consequence that this category is complete and cocomplete and hence has pullbacks and pushouts.

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KADISON’S SCHWARZ INEQUALITY AND FURUTA’S THEOREM

Masatoshi Fujii, Masahiro Nakamura, Yuki Seo

2006 Volume 64 Issue 1 Pages 141-145
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_141

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We make an interpretation of n-terms arithmetic-harmonic mean inequality via Kadison’s Schwarz inequality. It is inspired by a skillful proof of it due to T.Furuta. Certain allied topics are also discussed.

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DEGENERATE BOUNDARY-VALUE AND INITIAL BOUNDARY-VALUE PROBLEMS INCLUDING GENERAL WENTZELL BOUNDARY CONDITIONS

Angelo Favini, Yakov Yakubov

2006 Volume 64 Issue 1 Pages 147-162
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_147

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We study degenerate boundary-value problems for higher order ordinary differential equations with polynomial spectral parameter in both the equation and boundary conditions. An isomorphism and a coercive solvability of such problems have been established. We also treat initial boundary-value problems for higher order degenerate parabolic equations. Both studies include, in particular, second order equations with the general Wentzell boundary conditions. Moreover, the equation may contain a linear abstract operator and boundary conditions may contain linear functionals and values of an unknown functions and its derivatives in some inside points of the interval of the problem.

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EQUIVALENCE OF LINEAR CODES WITH THE SAME WEIGHT ENUMERATOR

E. J. Cheon

2006 Volume 64 Issue 1 Pages 163-172
Published: 2006
Released on J-STAGE: October 28, 2022

DOIhttps://doi.org/10.32219/isms.64.1_163

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Two equivalent linear codes have the same weight enumerator but the converse does not hold. We investigate which code is unique up to equivalence in view of the weight enumerator. The main purpose of this paper is to investigate the weight enumerators associated to the only one equivalent class of linear codes and to construct these codes. Furthermore, we construct non-equivalent linear codes with the same weight enumerator and give the generator matrices of these codes.

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