Updated on 2024/12/19

写真a

 
KOSUGI Nobuko
 
Organization
Faculty of Economics Professor
Contact information
The inquiry by e-mail is 《here》
External link

Degree

  • 博士（理学） ( お茶の水女子大学 )

Education

  • 1998.3
     

    Ochanomizu University   Graduate School, Doctral Research Course in Human Culture   doctor course   withdrawn before completion

  • 1996.3
     

    Ochanomizu University   Graduate School, Division of Natural Science   master course   completed

  • 1990.3
     

    Ochanomizu University   Faculty of Science   graduated

Research History

  • 2013.4 - 　

    中央大学経済学部 教授

  • 2012.4 - 2013.3

    東京海洋大学大学院海洋科学技術研究科 准教授

  • 2007.4 - 2012.3

    東京海洋大学海洋工学部 准教授

  • 2003.10 - 2007.3

    東京海洋大学海洋工学部 助教授

  • 2003.4 - 2003.9

    東京商船大学商船学部 助教授

  • 2002.4 - 2003.3

    東京商船大学商船学部 専任講師

  • 1998.4 - 2002.3

    お茶の水女子大学理学部 助手

  • 1990.4 - 1992.11

    日本銀行

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Professional Memberships

  • Mathematics Education Society of Japan

  • 電子情報通信学会

  • 日本数学会

Research Interests

  • 確率論

Research Areas

  • Natural Science / Applied mathematics and statistics  / 数学基礎・応用数学

  • Natural Science / Basic analysis  / Basic analysis

  • Natural Science / Basic mathematics  / 数学基礎・応用数学

Papers

  • A note on the correlation matrix of fractional Brownian motion Reviewed

    Nobuko Kosugi

    International Mathematical Forum   14 ( 2 )   69 - 72   2019.3

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    Language：Japanese   Publisher：Hikari Ltd.  

    DOI： 10.12988/imf.2019.917

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  • A new approach to Bezout equations derived from multivariate polynomial matrices and real entire functions Reviewed

    Koichi Suyama, Nobuko Kosugi

    LINEAR & MULTILINEAR ALGEBRA   63 ( 11 )   2318 - 2331   2015.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：TAYLOR & FRANCIS LTD  

    This paper focuses on Bezout equations derived from multivariate polynomial matrices in which relationships between one primary variable and other variables are described by real entire functions. We propose a method for obtaining a solution belonging to a set of multivariate rational function matrices in which all entries are real entire functions with respect to the primary variable. The proposed method is based on a new approach that overcomes the constraints and difficulties due to many variables by expanding a class of solutions to multivariate rational function matrices.

    DOI： 10.1080/03081087.2015.1008969

    Web of Science

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  • Bezout equations over bivariate polynomial matrices related by an entire function Reviewed

    Koichi Suyama, Nobuko Kosugi

    LINEAR & MULTILINEAR ALGEBRA   63 ( 6 )   1138 - 1153   2015.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：TAYLOR & FRANCIS LTD  

    This study addresses Bezout equations over bivariate polynomial matrices, where the relationship between two variables is described by a real entire function. This paper proposes a solution method that makes optimal use of minor primeness to reduce such Bezout equations to simple equations over univariate scalar polynomials. The proposed solution method requires only matrix calculations, thus making it very useful, especially in the absence of modern computer algebra systems.

    DOI： 10.1080/03081087.2014.922968

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  • Digital redesign of infinite-dimensional controllers based on numerical integration of new representation Reviewed

    Nobuko Kosugi, Koichi Suyama

    SYSTEMS & CONTROL LETTERS   62 ( 7 )   531 - 538   2013.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    Continuous-time infinite-dimensional controllers that include Laplace transforms of time functions with compact support are indispensable for the advanced control of delay systems. However, no study has yet been conducted on digital redesign for obtaining digital controllers that are used in sampled-data control systems from predesigned continuous-time infinite-dimensional controllers. We introduce a new representational form to describe the continuous-time input-output relation of linear time-invariant systems, called "finite interval integral representation". Using numerical integration, we approximate the continuous-time input-output relation of a predesigned infinite-dimensional controller in the finite interval integral representation to obtain a digital controller. (c) 2013 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.sysconle.2013.03.007

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  • Continuous-time Markov analysis for risk evaluation Reviewed

    Koichi Suyama, Nobuko Kosugi, Kyoko Kaneoka

    International Journal of Contemporary Mathematical Sciences   8   381 - 399   2013.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Hikari Ltd  

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  • Integrator reset strategy based on L2 gain analysis Reviewed

    Koichi Suyama, Nobuko Kosugi

    International Journal of Contemporary Mathematical Sciences   7 ( 39 )   1947 - 1962   2012.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Hikari Ltd  

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  • Safety assessment of control laws using Markov analysis Reviewed

    Koichi Suyama, Nobuko Kosugi

    Applied Mathematical Sciences   6 ( 95 )   4737 - 4762   2012.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Hikari Ltd  

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  • Digital redesign of infinite-dimensional controllers based on numerical integration Reviewed

    Nobuko Kosugi, Koichi Suyama

    Applied Mathematical Sciences   6 ( 77 )   3801 - 3819   2012.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Hikari Ltd  

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  • A new method for solving Bezout equations over 2-D polynomial matrices from delay systems Reviewed

    Nobuko Kosugi, Koichi Suyama

    Systems & Control Letters   61 ( 6 )   723 - 729   2012.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevie  

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  • An efficient calculation algorithm in continuous-time Markov analysis using large-scale numerical calculation Reviewed

    Nobuko Kosugi, Koichi Suyama

    International Mathematical Forum   7 ( 10 )   455 - 467   2012.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Hikari Ltd  

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  • Finite spectrum assignment of multi-input systems with non-commensurate delays Reviewed

    Nobuko Kosugi, Koichi Suyama

    INTERNATIONAL JOURNAL OF CONTROL   85 ( 9 )   1197 - 1208   2012

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：TAYLOR & FRANCIS LTD  

    We present a new framework for finite spectrum assignment for multi-input systems with non-commensurate delays using an algebraic approach over multidimensional polynomial matrices. By focusing on the solvability of a Bezout equation over multidimensional polynomial matrices, we derive a necessary and sufficient condition for finite spectrum assignability under which a finite number of spectra can be assigned by a control law using a ring of entire functions, i.e. Laplace transforms of all exponential time functions with compact support. Furthermore, using a solution to the Bezout equation, we present a design method for a controller that achieves finite spectrum assignment.

    DOI： 10.1080/00207179.2012.679974

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  • The d-OR gate problem in dynamic fault trees and its solution in Markov analysis Reviewed

    Nobuko Kosugi, Koichi Suyama

    International Mathematical Forum   6 ( 56 )   2771 - 2793   2011.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Hikari Ltd  

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  • New coprimeness over multivariable polynomial matrices and its application to control of delay systems Reviewed

    Nobuko Kosugi, Koichi Suyama

    Systems & Control Letters   60 ( 6 )   414 - 419   2011.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier  

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  • Non-coherence in safety of switching control systems and its Markov analysis Reviewed

    Nobuko Kosugi, Koichi Suyama

    INTERNATIONAL JOURNAL OF CONTROL   84 ( 11 )   1796 - 1806   2011

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：TAYLOR & FRANCIS LTD  

    This article appropriately describes the safety dynamics of switching control systems under the most realistic and popular failure mode of a switching unit, 'locking', by introducing a new idea of situation-dependent basic events in dynamic fault trees with restorable basic events. As a result, possible non-coherence in the safety dynamics is pointed out for the first time. This article also presents a safety analysis framework based on the Markov analysis in order to address the non-coherence correctly.

    DOI： 10.1080/00207179.2011.626456

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  • Finite spectrum assignment of systems with general delays Reviewed

    Nobuko Kosugi, Koichi Suyama

    INTERNATIONAL JOURNAL OF CONTROL   84 ( 12 )   1983 - 1995   2011

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：TAYLOR & FRANCIS LTD  

    This article presents a new framework for dealing with pure and distributed delays simultaneously and impartially as general delays in algebraic finite spectrum assignment. The framework based on an important property common to general delays gives a sufficient condition for finite spectrum assignability of scalar systems with several general delays and a design method of a controller achieving finite spectrum assignment. Especially in algebraic control theory for delay systems, pure and distributed delays have never been dealt with simultaneously and impartially. The framework is significantly important also for multidimensional system theory because its potential applicability to the discussion on systems with general delays, i.e. the possibility that especially distributed delay operators are used as variables for describing multidimensional systems, is clarified for the first time.

    DOI： 10.1080/00207179.2011.631150

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  • 数理モデルによる物流施設の立地の説明可能性に関する研究

    松下修, 小杉のぶ子, 苦瀬博仁, 延東晃

    東京海洋大学研究報告   6   33 - 45   2010.3

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    Language：Japanese   Publisher：東京海洋大学  

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  • Remarks on Tauberian theorem of exponential type and Fenchel-Legendre transform Reviewed

    Y Kasahara, N Kosugi

    OSAKA JOURNAL OF MATHEMATICS   39 ( 3 )   613 - 619   2002.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：OSAKA JOURNAL OF MATHEMATICS  

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  • A remark on the covariance matrix of fractional Brownian motion Reviewed

    Yuji Kasahara, Norio Kono, Nobuko Kosugi

    Natural Science Report of Ochanomizu University   52 ( 1 )   13 - 19   2001.10

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：お茶の水女子大学  

    Let X^H(t) be a fractional Brownian motion with index H (0<H&le;1/2), and let D_n(t_0, t_1, ... t_n) (0&le;t_0<t_1<...<t_n) denote the correlation matrix of {X^H(t_<k+1>)-X^H(t_k): k=1, ..., n-1}. In this paper the asymptotic behaviour of (1/n) log det D_n as n tends to ∞ is studied.

    CiNii Books

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    Other Link： http://hdl.handle.net/10083/2349

  • Large deviation around the origin for sums of nonnegative i.i.d. random variables Reviewed

    Yuji Kasahara, Nobuko Kosugi

    Natural Science Report of Ochanomizu University   51 ( 1 )   27 - 31   2000.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：お茶の水女子大学  

    Let X_1, X_2,... be nonnegative independent random variables with a common distribution attracted to the stable law G_α, and put S_n=X_1+X_2+…+X_n. That is for some monotone increasing function σ(n), P[S_n/σ(n)&le;x]→G_α(x), for every x>0 as n→∞. The aim of the present paper is to study the asymptotic behaviour of P[S_n/σ(n)&le;x_n], where x_n is a positive sequence such that x_n→0 as n→∞.

    CiNii Books

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    Other Link： http://hdl.handle.net/10083/867

  • Tauberian theorem of exponential type on limits of oscillation Reviewed

    N Kosugi

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY   39 ( 4 )   783 - 792   1999.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

    Web of Science

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  • Tauberian theorem of exponential type and its application to multiple convolution Reviewed

    N Kosugi

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY   39 ( 2 )   331 - 346   1999.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

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  • Functional limit theorem for occupation times of Gaussian processes - non-critical case Reviewed

    N Kosugi

    OSAKA JOURNAL OF MATHEMATICS   36 ( 1 )   149 - 155   1999.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：OSAKA JOURNAL OF MATHEMATICS  

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  • A limit theorem for occupation times of fractional Brownian motion Reviewed

    Y Kasahara, N Kosugi

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   67 ( 2 )   161 - 175   1997.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    Recently, N. Kono gave a limit theorem for occupation times of fractional Brownian motion, which result generalizes the well-known Kallianpur-Robbins law for two-dimensional Brownian motion. This paper studies a functional limit theorem for Kono's result. It is proved that, under a suitable normalization, the limiting process is the inverse of an extremal process.

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Books

  • 経済学部生のための数学 ー高校数学から偏微分までー

    小杉, のぶ子（ Role： Sole author）

    コロナ社  2023.10  （ ISBN:9784339061284 ）

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    Total pages：ix, 211p   Language：Japanese  

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  • はじめての確率論

    小杉のぶ子, 久保幹雄（ Role： Joint author）

    近代科学社  2011.6 

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    Language：Japanese   Book type：Scholarly book

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Research Projects

  • Study of fractional Brownian motion

    Grant number：10640107  1998 - 2000

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Ochanomizu University

    KASAHARA Yuji, KOSUGI Nobuko, MAEJIMA Makoto, KANEKO Akira

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    Grant amount： \2900000 （ Direct Cost: \2900000 ）

    1. Fractional Brownian motions are Gaussian processes having self-similarity. We studied the relationship between the Hearst index and the asymptotic behavior of the tail probabilities of their local times. In relation to this problem we studied the order of infinitesimal of the determinant of the covariance matrix as the dimension goes to infinity. We proved that it decreases exponentially and we found the relation between the exponent and the Hearst index. We also generalized the above results for more general Gaussian processes.
    2. When we studied the above problem we noticed that Tauberian theorems of exponential types are essential, and we obtained some useful theorems on this subject. As an application we studied the distribution function of the sums of independent random variables which are positive and identically distributed.
    3. We studied on some properties of self-similar processes.
    4. It is well known that the amount of time that a Brownian motion spends on the half line obeys the arc-sine law. We tried to find similar results for fractional Brownian motions but failed. Instead, however, we obtained an interesting result for linear diffusions : We found a relation between the so-called speed measure of the diffusion and the asymptotic behavior of the occupation time on the half line.

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Allotted class

  • 2024   Fundamental Mathematics A1   Department

  • 2024   Fundamental Mathematics A2   Department

  • 2024   Calculus I   Department

  • 2024   Calculus II   Department

  • 2024   General Education Seminar Ⅰ(Natural Sciences)   Department

  • 2024   General Education Seminar Ⅱ(Natural Sciences)   Department

  • 2024   Linear Algebra I   Department

  • 2024   Linear Algebra II   Department

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