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[87] Nobuoki Eshima, Claudio Giovanni Borroni, Minoru Tabata, Takeshi Kurosawa, An Entropy-Based Tool to Help the Interpretation of Common-Factor Spaces in Factor Analysis, Entropy 2021, 23(2), 140; DOI: 10.3390/e23020140

2019

[86] Minoru Tabata, Nobuoki Eshima, Approximation of Short-Run Equilibrium of the N-Region Core-Periphery Model in an Urban Setting. In: Smith F., Dutta H., Mordeson J. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham (2019) DOI: 10.1007/978-3-030-12232-4_17

2018

[85] Minoru Tabata, Nobuoki Eshima, Application of the Brouwer and the Kakutani fixed-point theorems to a discrete equation with a double singular structure, Fixed Point Theory and Applications, Springer, (2018), https://doi.org/10.1186/s13663-018-0649-9

[84] Nobuoki, Eshima, Minoru Tabata, Claudio Giovanni Borroni, An Entropy-Based Approach for Measuring Factor Contributions in Factor Analysis Models, Entropy, 2018, 20(9), 634; https://doi.org/10.3390/e20090634

[83] M. Tabata and N. Eshima, Existence of a short-run equilibrium of the Dixit-Stiglitz-Krugman model, Discrete Dynamics in Nature and Society, Volume 2018 (2018), Article ID 2193070, https://doi.org/10.1155/2018/2193070

2017

[82] Minoru Tabata, Nobuoki Eshima, Keiko Kanenoo, Ichiro Takagi, A stochastic agent-based approach to interregional migration in quantitative sociodynamics, Mathematical Research Summaries, 2017, 2, pp. 111

[81] M. Tabata and N. Eshima, Existence and uniqueness of solutions to the wage equation of Dixit-Stiglitz-Krugman model with no restriction on transport costs, Discrete Dynamics in Nature and Society, Volume 2017 (2017), Article ID 9341502, 7 pages, doi: 10.1155/2017/9341502

2016

[80] Nobuoki Eshima, Claudio Giovanni Borroni, and Minoru Tabata, Relative-importance assessment of explanatory variables in generalized linear models: an entropy-based approach, Statistica & Applicazioni, Vita e Pensiero - Pubblicazioni dell'Universita Cattolica del Sacro Cuore, Vol. XIV no. 2 (2016).

[79] M. Tabata and N. Eshima, Convergence of global solutions to the Cauchy problem for the replicator equation in spatial economics, Discrete Dynamics in Nature and Society, Volume 2016 (2016), Article ID 4021516, 8 pages, doi: 10.1155/2016/4021516

2015

[78] Nobuoki, Eshima, Minoru Tabata, Claudio Giovanni Borroni, Yutaka Kano, An entropy-based approach to path analysis of structural generalized linear models: a basic idea, Entropy 07/2015; 17(7):5117-5132. doi:10.3390/e17075117

[77] M. Tabata and N. Eshima, A population explosion in an evolutionary game in spatial economics: Blow up radial solutions to the initial value problem for the replicator equation whose growth rate is determined by the continuous Dixit-Stiglitz-Krugman model in an urban setting, Nonlinear Analysis Series B: Real World Applications, Elsevier Science, Vol 23 C, pp. 26-46, June, 2015

[76] M. Tabata, N. Eshima, and Y. Sakai, Existence and computation of solutions to the initial value problem for the replicator equation of evolutionary game defined by the Dixit-Stiglitz-Krugman model in an urban setting: Concentration of workers motivated by disparity in real wages, Applied Mathematics and Computation, Elsevier, Vol. 245C, (2015), pp. 419-451.

[75] M. Tabata, N. Eshima, Y. Kiyonari, and I. Takagi, The existence and uniqueness of short-run equilibrium of the Dixit-Stiglitz-Krugman model in an urban-rural setting, IMA Journal of Applied Mathematics, Oxford University Press, vol. 80, issue 2, pp. 474-493, 2015.

[74] M. Tabata and N. Eshima, The existence and uniqueness of global solutions to the initial value problem for the system of nonlinear integro-partial differential equations in spatial economics: The dynamic continuous Dixit-Stiglitz-Krugman model in an urban-rural setting, Abstract and Applied Analysis, 2015, the special issue "Advances on Integrodifferential Equations and Transforms" Vol. 2015, Article ID 760136, 12 pages, 2015. doi:10.1155/2015/760136

2014

[73] M. Tabata, N. Eshima, and Y. Sakai, Existence, uniqueness, and computation of short-run and long-run equilibria of the Dixit–Stiglitz–Krugman model in an urban setting, Applied Mathematics and Computation, Elsevier, Vol. 234, 15 May 2014, pp. 339-355

[72] M. Tabata, N. Eshima, and I. Takagi, A Mathematical-Modeling Approach to Urbanization Caused by Migration, in ''Urbanization: Global Trends, Role of Climate Change and Effects on Biodiversity'', Nova Science Publishers, Inc. Pub. Date: 2014 - 1st Quarter, Pages: 6x9 - (NBC-R) ISBN: 978-1-63117-063-8

[71] M. Tabata, N. Eshima, Keiko Kanenoo, and I. Takagi, A Stochastic Agent-Based Approach to Interregional Migration in Quantitative Sociodynamics, "Mathematical Modelling in Social Sciences and Engineering", Nova Science Publishers, Inc. 2014 Pub. Date: 2014 - 2nd Quarter, Pages: 7x10 - (NBC-C) ISBN: 978-1-63117-335-6

2013

[70] M. Tabata, N. Eshima, Yuusuke Sakai, and I. Takagi, An extension of Krugman's core-periphery model to the case of a continuous domain: Existence and uniqueness of solutions of a system of nonlinear integral equations in spatial economics, Nonlinear Analysis Series B: Real World Applications, 14 (2013) pp. 2116-2132, Elsevier Science,

2011

[69] N. Eshima, M. Tabata, Tetsuji Ohyama, Path Analysis for Recursive Generalized Linear Model Systems, Proceedings Conference: 2011 World Statistics Congress, At Dublin, Volume: CPS053 Path Analysis for Recursive Generalized Linear Model Systems

[68] M. Tabata, N. Eshima, and I. Takagi, A mathematical modeling approach to the formation of urban and rural areas: Convergence of global solutions of the mixed problem for the master equation in sociodynamics. Nonlinear Analysis Series B: Real World Applications, Elsevier Science, Amsterdam, Vol. 12, Issue 6, December 2011, pp. 3261-3293.

[67] N. Eshima and M. Tabata, Three predictive power measures for generalized linear models: Entropy coefficient of determination, entropy correlation coefficient and regression correlation coefficient, Computational Statistics & Data Analysis, Vol. 55, 2011, pp. 3049-3058, Elsevier Science, Amsterdam.

[66] N. Eshima, Osamu Tokumaru, Shohei Hara, Kira Bacal, Seigo Korematsu, M. Tabata, Shigeru Karukaya, Yoshinori Yasui, Nobuhiko Okabe, Toyojiro Matsuishi, Sex- and age-related differences in morbidity rates of 2009 pandemic influenza A H1N1 virus of swine origin in Japan. PLoS ONE 6(4): e19409. doi:10.1371/journal.pone.0019409

[65] M. Tabata and N. Eshima, A stochastic agent-based approach to the Fokker-Planck equation in human population dynamics, In: Partial Differential Equations: Theory, Analysis and Applications, Editor: Christopher L. Jang, 2010 Nova Science Publishers, Inc.Series: Mathematics Research Developments, Pub. Date: 2011 1st quarter, ISBN: 978-1-61122-858-8

2010

[64] M. Tabata, N. Eshima, I. Takagi, A mathematical-model approach to human population explosions caused by migration, Nonlinear Analysis Series B: Real World Applications, Elsevier Science, Amsterdam, Vol. 11, Issue 5, October 2010, pp. 4027-4042.

[63] N. Eshima, M. Tabata, Entropy coefficient of determination for generalized linear models, Computational Statistics & Data Analysis, Elsevier Science, Amsterdam, Volume 54, Issue 5, 1 May 2010, pp. 1381-1389.

2009

[62] N. Eshima, Osuke Iwata, Sachiko Iwata, M. Tabata, Yasunori Higuchi, Toyojiro Matsuishi, and Shigeru Karukaya, Age and gender specific prevalence of HTLV-1: a hidden paradox, Journal of Clinical Virology, Elsevier Science, Amsterdam, Volume 45, Issue 2, June 2009, pp. 135-138.

[61] M. Tabata & N. Eshima, The Kramers-Moyal expansion of the master equation that describes human migration in a bounded domain, Nonlinear Analysis Series B: Real World Applications, Elsevier Science, Amsterdam, (2009), Vol. 10, pp. 639－664

[60] M. Tabata, T. Moriyama, S. Motoyama, and N. Eshima, A mathematical-model approach to chlamydial infection in Japan. In: Progress in Nonlinear Analysis Research, ISBN: 978-1-60456-359-7 Editor: Erik T. Hoffmann, pp. 25-33, Chapter 2, 2009 Nova Science Publishers, Inc

2008

[59] N. Eshima1, M. Tabata, Yasunori Higuchi, & Shigeru Karukaya, Is the innate bio-protection power against human virus the same between males and females? A conclusion based on blood donor data of HTLV-I infection. Nature Precedings, hdl:10101/npre.2008.1987.1

2007

[58] N. Eshima, T. Kohda, and M. Tabata, Statistical solution to the capacity problem in direct-sequence code-division multi-access communication system, IMA Journal of Mathematical Control and Information, Oxford University Press, (2007), Vol.24, pp. 289-298.

[57] N Eshima, M. Tabata, T Okada: Why is the distribution of HTLV-I carriers geographically biased?: an answer through a mathematical epidemic model, Mathematical Medicine and Biology: A Journal of the IMA, Oxford University Press, Vol. 24, pp. (2007), 149-167.

[56] N. Eshima & M. Tabata, Entropy correlation coefficient for measuring predictive power of generalized linear models, Statistics & Probability Letters, Elsevier Science, Amsterdam, Vol. 77, Issue 6, 15 March 2007, pp. 588-593

2006

[55] M. Tabata, A geometrical similarity between diffusion of biological particles and migration of human population in mathematical sociology, Suuriken Kokyuroku (Kyoto, 2005). No. 1474, (2006), 127-143.

[54] M. Tabata, N. Eshima, I Takagi, A geometrical similarity between migration of human population and diffusion of biological particles, Nonlinear Analysis Series B: Real World Applications, Elsevier Science, Amsterdam, (2006/9), Vol.7, Issue 4, pp. 872-894.

2004

[53] M. Tabata, N. Eshima, The Fokker-Planck equation and the master equation in the theory of migration. IMA Journal of Applied Mathematics, Oxford University Press, (2004/10), Vol. 69, pp. 585-603.

SJR

[52] M. Tabata, N. Eshima, The behavior of stochastic agent-based models when the number of agents and the time variable tend to infinity, Applied Mathematics and Computation, Elsevier Science, Amsterdam, (2004/4), Vol. 152, No.1 pp. 47-70.

[51] N. Eshima, M. Tabata, An Entropy Measure for the Predictive Power of Generalized Linear Models, The Japanese Journal of Behaviormetrics 30(2), 239, 2004-01-30

2003

[50] N. Eshima, M. Tabata, T. Okada, and S. Karukaya, Population dynamics of HTLV-I infection: A discrete-time mathematical epidemic model approach, Mathematical Medicine and Biology: A Journal of the IMA, Oxford University Press. (2003/5), Vol.20 Issue 1, pp. 29-45.

[49] M. Tabata and N. Eshima, A self-referential agent-based model that consists of a large number of agents moving stochastically in a discrete bounded domain, Applied Mathematics and Computation, Elsevier Science, Amsterdam, (2003/8), Vol. 143, No. 2-3, pp. 443-483.

2002

[48] N. Eshima and M. Tabata, A mathematical epidemic model approach to an investigation of smallpox type infections. EPIDEMIOLOGY Volume：13 Issue：4 Page：S97

[47] M. Tabata and N. Eshima, The Cauchy problem for the nonlinear integro-partial differential equation in quantitative sociodynamics, Applied Mathematics and Computation, Elsevier Science, Amsterdam, (2002/11), Vol. 132, No. 2-3, pp. 537-552.

[46] M. Tabata and N. Eshima, Blowing up solutions to the Cauchy problem for the master equation, Applied Mathematics and Computation, Elsevier Science, Amsterdam, (2002/3), Vol.127, No. 2-3, pp. 181-193.

[45] M. Tabata, A. Ide, N. Eshima, I. Takagi, and Y. Takei, A functional-analytic and numerical-analytic approach to nonlinear economic models described by the master equation, in "Empirical Science of Financial Fluctuations" (Ed. H. Takayasu), Chapter III, Section 1, pp. 304-311, Springer-Verlag, (2002/4).

[44] M. Tabata, N. Eshima, and I. Takagi, An infinite continuous model which derives from a finite discrete model describing the time evolution of the density of firms, Applied Mathematics and Computation, Elsevier Science, Amsterdam, (2002/1), Vol.125, No. 1, pp. 105-132.

2001

[43] N. Eshima, M. Tabata, S. Karukaya, Estimation of Infection Probability of Human T-Cell Leukemia Virus Type I in the Japanese People:Bulletin of the Computational Statistics of Japan 13(2), 137, 2001-05-30, http://doi.org/10.20551/jscswabun.13.2_137_3

[42] N. Eshima, M. Tabata, H. Kikuchi, S. Karukaya, and T. Taguchi, Analysis of the infection system of human T-cell leukemia virus type 1 based on a mathematical epidemic model, Statistics in Medicine, John-Wiley & Sons, Ltd., New York, (2001/12), Vol. 20, Issue 24, pp. 3891-3900.

[41] N. Eshima, M. Tabata, and Geng Zhi, Path analysis with logistic regression models: Effect analysis of fully recursive causal systems of categorical variables, Journal of the Japan Statistical Society, Vol. 31. No. 1, pp. 1-14, (2001/9).

[40] M. Tabata, A. Ide, N. Eshima, I. Takagi, and Y. Takei, Self-organization exhibited by a stochastic agent-based model of firms seeking higher desirability in business expressed by the market potential, in "Proceedings of the Fourth International Conference on Computational Intelligence and Multimedia Applications ICCIMA 2001", pp. 4-8, IEEE Computer Society Press, (2001/10), pp. 4-8.

[39] M. Tabata, N. Eshima, The Cauchy problem for the nonlinear integro-partial differential equation that describes the time evolution of sociodynamic quantities, Qualitative theory of functional equations and its application to mathematical science, (Kyoto 2000), Surikaisekikenkyusyo Kokyuroku, No. 1216, (2001), 13-22

[38] A. Ide, I. Oseto, and M. Tabata, The analysis of problems between engineering and law in using filtering softwears. Memoirs of the Graduate School of Science and Technology, Kobe University, (2001/4), Vol. 19-A. pp 167-188.

[37] M. Tabata, N. Eshima, and I. Takagi, The master equation approach to self-organization in labor mobility, in Evolutionary Controversies in Economics : A New Transdisciplinary Approach (Ed. Y. Aruka), Part V, Section 3, pp. 201-212, Springer-Verlag, (2001/6).

[36] N. Eshima, M. Tabata, and M. Tsujitani, Property of the RC(M) association model and a summary measure of association in the contingency table, Journal of the Japan Statistical Society, (2001/6), Vol. 31, No. 1, pp. 15-26.

[35] M. Tabata, N. Eshima, and I. Takagi, The master equation approach to self-organization in labor mobility, in Evolutionary Controversies in Economics : A New Transdisciplinary Approach (Ed. Y. Aruka), Part V, Section 3, pp. 201-212, Springer-Verlag, (2001/6).

2000

[34] M. Tabata, N. Eshima, Blow-up solutions to initial-value problems for nonlinear integro-partial differential equations that appear in quantitative sociology, Nonlinear evolution equations and their applications, (Kyoto 1999), Surikaisekikenkyusyo Kokyuroku, No. 1135, (2000), 41-51

[33] M. Tabata and N. Eshima, Decay of solutions to the mixed problem for the linearized Boltzmann equation with a potential term in a polyhedral bounded domain. Rendiconti del Seminario Matematico dell Universita di Padova, (2000/9), Vol. 103, No.1, pp. 133-155.

[32] M. Tabata and N. Eshima, The point spectrum of the linearized Boltzmann operator with an external potential in an unbounded domain. Taiwanese J. Math., (2000/6), Vol. 4, No. 2, pp. 297-306.

[31] M. Tabata and N. Eshima, The behavior of solutions to the Cauchy problem for the master equation. Applied Mathematics and Computation, Elsevier Science, Amsterdam, (2000/5), Vol. 112, No. 1, pp. 79-98.

[30] M. Tabata, N. Eshima, and I. Takagi, The behavior of solutions of the nonlinear integro-partial differential equation in mathematical economics and its economic meanings, Papers of the Fourth Annual Conference of the Japan Association for Evolutionary Economics, JAFEE 2000 (2000/5), pp.41-43.

1999

[29] N. Eshima and M. Tabata, Effect analysis in loglinear model approach to path analysis of categorical variables, Behaviormetrika, Springer, (1999/9), Vol. 26, No.2, pp. 221-233. https://doi.org/10.2333/bhmk.26.221

[28] M. Tabata, N. Eshima, and I. Takagi, The nonlinear integro-partial differential equation describing the logistic growth of human population with migration, Applied Mathematics and Computation, Elsevier Science, Amsterdam, (1999/2), Vol. 98, No. 2-3, pp. 169-183.

1998

[27] M. Tabata, N. Eshima, I. Takagi, and T. Hiroyama, The Cauchy problem for the system of equations describing migration motivated by regional economic disparity. Applied Mathematics and Computation, Elsevier Science, Amsterdam, (1998/8), Vol. 94, No. 1, pp. 45-64.

[26] M. Tabata and N. Eshima, A model for the geographic spread of an epidemic which infects human beings. Memoirs of the Graduate School of Science and Technology, Kobe University, (1998/3), Vol. 16-A. pp 167-188.

1997

[25] M. Tabata, The linearized Boltzmann equation with an external force, Nonlinear evolution equations and their applications, (Kyoto 1996), Surikaisekikenkyusyo Kokyuroku, No. 1009, (1997), 1-21

[24] N. Eshima and M. Tabata, The RC(M) association model and canonical correlation analysis. Journal of the Japan Statistical Society, (1997/6), Vol. 27, No. 1, pp. 109-120.

[23] M. Tabata, N. Eshima, I. Takagi, and T. Hiroyama, The system of equations describing economic growth with labor mobility. Memoirs of the Graduate School of Science and Technology, Kobe University, (1997/3), Vol. 15-A. pp 167-188.

[22] M. Tabata and N. Eshima, The spectrum of the transport operator with a potential term under the spatial periodicity condition. Rendiconti del Seminario Matematico dell'Universita di Padova, (1997/3), Vol. 97, No.1, pp. 211-233.

[21] M. Tabata and N. Eshima, The spectrum of the linear transport operator with a force in a torus. Acta Math. Hungarica, (1997/1), Vol 74, No. 1-2, pp. 63-81.

1996

[20] M. Tabata N. Eshima, T. Hiroyama, I. Takagi, and A. Yagi, A numerical analysis of the system of equations describing urbanization process. Memoirs of the Graduate School of Science and Technology, Kobe University, (1996/3), Vol. 14-A, pp. 141-152.

[19] M. Tabata and N. Eshima, The point spectrum of the linearized Boltzmann operator with the external-force term in a bounded domain. Journal of Partial Differential Equations, (1996/2), Vol. 9, No. 2, pp. 103-110.

[18] N. Eshima, C. Asano, and M. Tabata, A developmental path model and causal analysis of latent dichotomous variables. British Journal of Mathematical and Statistical Psychology. (1996), Vol. 49, pp. 43-56.

[17] M. Tabata and N. Eshima, The point spectrum of the linearized Boltzmann operator with the external-potential term in an exterior domain. J. Korean Math. Soc., (1996), Vol. 33, No. 1, pp. 89-99.

1995

[16] M. Tabata, The point spectrum of the linearized Boltzmann operator with an external-force potential in an exterior domain. Transport Theory and Statistical Physics, Marcel Dekker, New York, (1995/11), Vol. 24, No. 9, pp. 1271-1294.

[15] M. Tabata, T. Hiroyama, I. Takagi, and A. Yagi, An economic analysis of urbanization process: the system of nonlinear ordinary differential equations. Journal of Research Institute of General Education of Kyushu Tokai Univ., (1995/4), Vol. 7, pp. 1-20.

[14] M. Tabata and N. Eshima, The point spectrum of the linearized Boltzmann operator with the potential term in an unbounded domain. Memoirs of the Graduate School of Science and Technology, Kobe University, (1995/3), Vol. 13-A. pp. 169-185.

[13] M. Tabata and N. Eshima, The point spectrum of the linearized Boltzmann operator with the potential term in a semi-infinite domain and the corresponding eigenspaces. Rendiconti del Seminario Matematico Universit? e Politecnico Torino, (1995/11), Vol. 53, No. 2, pp. 99-108.

[12] M. Tabata, The purely imaginary point spectrum of the linearized Boltzmann operator with a singular external potential. Kobe Journal of Mathematics, (1995/12), Vol. 12, No. 2, pp. 147-153.

[11] M. Tabata, Decay of solutions to the mixed problem for the linearized Boltzmann equation with an external potential in a bounded domain. Mathematical analysis of phenomena in fluid and plasma dynamics, Surikaisekikenkyusyo Kokyuroku, (Kyoto 1994), No. 914, (1995), 80-84

1994

[10] M. Tabata, Decay of solutions to the Cauchy problem for the linearized Boltzmann equation with an unbounded external-force potential. Transport Theory and Statistical Physics, Marcel Dekker, New York, (1994/6), Vol. 23, No. 6, pp. 741-780.

[9] N. Eshima and M. Tabata, Separating Equations in latent scalogram analysis. Journal of Research Institute of General Education of Kyushu Tokai University, (1994/10), Vol. 6, pp. 15-21.

[8] M. Tabata, The point spectrum of the linearized Boltzmann operator with an external-force potential in an unbounded domain. Mathematical analysis of phenomena in fluid and plasma dynamics, Surikaisekikenkyusyo Kokyuroku, (Kyoto 1993), No. 862, (1994), 118-128

1993

[7] M. Tabata, Decay of solutions to the Cauchy problem for the linearized Boltzmann equation with some external-force potential, Japan Journal of Industrial and Applied Mathematics, (1993/6), Vol. 10, No. 2, pp. 237-253.

[6] M. Tabata, Decay of solutions to the mixed problem with the periodicity boundary condition for the linearized Boltzmann equation with conservative external force. Communications in Partial Differential Equations, Marcel Dekker, New York, (1993/11), Vol. 18, No. 11, pp. 1823-1846.

[5] M. Tabata, Doctoral Thesis, Decay of solutions to the Cauchy problem for the linearized Boltzmann equation with some external-force potential, https://doi.org/10.11501/3072881, http://iss.ndl.go.jp/books/R100000039-I001485715-00

1992

[4] M. Tabata, The point spectrum of the linearized Boltzmann operator with the potential term. Kobe Journal of Mathematics, (1992/12), Vol. 9, No. 2, pp. 183-194.

[3] M. Tabata, Local solutions to the Cauchy problem for the system of equations describing the motion of a mixture of compressible viscous and heat-conductive fluids. Kobe Journal of Mathematics, (1992/12), Vol. 9, No. 2, pp. 195-205.

1987

[2] M. Tabata, On the mixed problem for the discretized Boltzmann equation. Japan Journal of Applied Mathematics, (1987/2), Vol. 4, No 1, pp. 173-184.

1976

[1] M. Tabata, ある演算の有限性について数学セミナー（日本評論社）雑誌コード：05423, 1976.11.01, pp. 97-98