Center for Mathematical Sciences

Hiroyuki Sagawa Professor	Noriaki Kamiya Professor	Ken-ichi Funabashi Associate Professor	Katsutaro Shimizu Associate Professor
Kazuto Asai Assistant Professor	Michio Honma Assistant Professor	Hiroshi Kihara Assistant Professor	Shigeru Watanabe Assistant Professor
Toshiro Watanabe Assistant Professor	Zhou Xian Rong Visiting Researcher

The scope of activities of the Center for Mathematical Sciences spans all aspects of research and education in the fields of mathematical sciences. Our current researches in the field of mathematics are devoted to various subjects and problems arising in both pure and applied mathematics: non-associative algebras, neural networks, unimodality problems, algebraic combinatorics, spherical functions, and homotopy theory. In the fields of physics, theoretical research is performed in many-body theories, nuclear physics, quantum gravity and quantum mechanics of constrain system. There has been also a project to develop educational textbooks and software for mechanics, electromagnetism and quantum mechanics. The research areas assigned to each co-researcher are as follows: Prof. H. Sagawa studies the physics of the many-body system of including nuclei, microclusters and quantum information theory. Prof. N. Kamiya studies the theory of non-associative algebras and a structure theory of algebras from triple systems Prof. K. Funahashi researches the theory of the neural networks and function theory of several complex variables from a geometrical viewpoint Prof. K. Shimizu advances the traditional quantum theory and creates the geometrical theory of quantum gravity Prof. T. Watanabe generalizes the unimodalityproblems of 1-dimensional infinitely divisible distributions to multi-dimensional cases in the use of analytical methods Prof. K. Asai researches combinatorial identities for generalized Young tableaux, and also, several generating functions arising from algebraic combinatorics Prof. S. Watanabe studies geometrical interpretations of generating functions for spherical functions on homogeneous spaces Prof. M. Honma researches the microscopic structures and dynamics of the nuclei by the algebraic methods and geometrical models performing the quantitative analysis by the large-scale numeric calculations Prof. H. Kihara studies homotopy theory and its applications to various areas of mathematics

Refereed Journal Papers

[kamiya-01:2004]	N. Kamiya and S. Okubo. A construction of simple Lie superal-gebras of certain types from triple systems. Bull. Austral. Math. Soc., 69:113-123, 2004.
	We study a construction of Lie superalgebras from triple systems
[kamiya-02:2004]	N. Kamiya, A. Elduque, and S. Okubo. On reciprocity relation between triple systems and binary algebras from triple systems. RIMS.(KYOTO Univ), page to appear, 2005.
	We study a relation of triples and algebras
[m-honma-01:2004]	S. J. Freeman, R. V. F. Janssens, B. A. Brown, M.P. Carpenter, S. M. Fischer, N. J. Hammond, M. Honma, and et al. Low-lying levels in 59Cr: Inadequacy of the fp model space and onset of deformation. Phys. Rev. C, 69:064301/1-7, 2004.
[m-honma-02:2004]	K. L. Yurkewicz, D. Bazin, B. A. Brown, C. M. Campbell, J. A. Church, D.-C. Dinca, A. Gade, M. Honma, and et al. Intermediate-energy Coulomb excitation of 52Fe. Phys. Rev. C, 70:034301/1-5, 2004.
[m-honma-03:2004]	K. L. Yurkewicz, D. Bazin, B. A. Brown, C. M. Campbell, J. A. Church, D.-C. Dinca, A. Gade, M. Honma, and et al. Nuclear structure in the vicinity of N = Z = 28 56Ni. Phys. Rev. C, 70:054319/1-7, 2004.
[m-honma-04:2004]	Y. Utsuno, T. Otsuka, T. Glasmacher, T. Mizusaki, and M. Honma. Onset of intruder ground state in exotic Na isotopes and evolution of the N =20 shell gap. Phys. Rev. C, 70:044307/1-8, 2004.
[m-honma-05:2004]	N. Shimizu, T. Otsuka, T. Mizusaki, and M. Honma. Anomalous properties of quadrupole collective states in 136Te and beyond. Phys. Rev. C, 70:054313/1-8, 2004.
	The onset of intruder ground states in Na isotopes is investigated by comparing experimental data and shell-model calculations.
[m-honma-06:2004]	S. N. Liddick, P. F. Mantica, R. Broda, B. A. Brown, M. P. Carpenter, A. D. Davies, B. Fornal, M. Honma, and et al. Development of shell closures at N= 32,34. I. decay of neutron-rich Sc isotopes. Phys. Rev. C, 70:064303/1-9, 2004.
[m-honma-07:2004]	B. Fornal, S. Zhu, R. V. F. Janssens, M. Honma, R. Broda, P. F.Mantica, B. A. Brown, M. P. Carpenter, and et al. Development of shell closures at N = 32,34. II. Lowest yrast excitations in eveneven Ti isotopes from deep-inelastic heavy-ion collisions. Phys. Rev. C, 70:064304/1-6, 2004.
[m-honma-08:2004]	K. L. Yurkewicz, D. Bazin, B. A. Brown, C. M. Campbell, J. A. Church, D.-C. Dinca, A. Gade, M. Honma, and et al. E2 excitation strength in Ni: Coupling of the Ni 2 collective core vibration 1 to the f7/2 odd neutron hole. Phys. Rev. C, 70:064321/1-4, 2004.
[sagawa-01:2004]	S. Yoshida and H. Sagawa. Neutron skin and EOS in asymmmetric nuclear matter. Phys. Rev.C, 69:024318/1-10, 2004.
	The neutron skin thickness of stable and unstable nuclei is studied in Skyrme Hartree-Fock (SHF) and relativistic mean field (RMF) models to investigate the relation between the pressure and the equation of state (EOS) in neutron matter. Wefounda clear linear correlation between the neutron skin thickness in heavy nuclei, 132Sn and 208Pb and the pressure of neutron matter in both SHF and RMFmodels, while the correlation i s weak in the unstable nuclei 32Mg and 44Ar. Relations between the ne utron skin thickness and other nuclear matter properties such as the symmetry energy coefficients and the nuclear incompressibility are discussed.
[sagawa-02:2004]	Koichi Hagino, Nguyen Van Giai, and H. Sagawa. Continuum QRPA response for deformed neutron-rich nuclei. Nucl.Phys. A, 731:264-272, 2004.
	We discussed properties of the quadrupole collective excitations of the deformed neutron-rich nucleus 38Mg within the framework of quasi-particle random phase approximation (QRPA). We first selve the coupledchannels equations to obtain the single particle levels, and contruct the ground state by treatibg the pairing correlations in the BCS approximation. We then solve the QRPA equation using the response function formalism, by including the continuum spectra.
[sagawa-03:2004]	I. Hamamoto and H. Sagawa. Weakly bound p neutrons and 3=2 spin-response function in the many-body pair correlation of neutron drip line nuclei. Phys. Rev. C, 70:034317/1-8, 2004.
[sagawa-04:2004]	H. Sagawa, X. R. Zhou, X. Z. Zhang, and Toshio Suzuki. Deformations and electromagnetic moments in carbon and neon isotopes. Phys. Rev. C, 70:054316/1-14, 2004.
[sagawa-05:2004]	K. Hagino and H. Sagawa. Perturbative Hartree-Fock-Bogoliubov model for many-body pairing correlations. Phys. Rev. C 71, 71:044302/1-5, 2005.
[shimizu-01:2004]	Shimizu K. Discretized BRST Transformations and Quantum Mechanical Potential of a Free Particle on S. Modern physics letters A, 20(9):699-706, 2005.
	We study a quantummechanical potential of a free particle on D-dimentional sphere. This system has the second class constraints. We change the second classconstraints intothe first class ones with new canonical variables. ABRST transformation is induced by the first class constraints and is disctrtized. A disctretized BRST invariant path integral is considered and the quantum mechanical potential is evaluated as R/12.

Unreferred Papers

[k-asai-01:2004]

Kazuto Asai. Homogeneous partial differential equations for superpositions of indeterminate functions of several variables. submitted to J. Math. Anal. Appl., Elsevier, under review, submitted 2004.

Grants

[sagawa-06:2004]

H. Sagawa. Ministry of Education Scientific Research Fund of Bacis Research C, 2000-2004.

Ph.D. and Other Theses

[sagawa-07:2004]	Tadamichi Takeda. Graduation Thesis: Quantum Game Theory, University of Aizu, 2004.
[sagawa-08:2004]	Yuya Sato. Graduation Thesis: Quantum Teleportation and Quantum Dense Coding, University of Aizu, 2004.
[sagawa-09:2004]	Takeshi Umeki. Graduation Thesis: Parallel Computer Simulation of Shor's Algorithm, University of Aizu, 2004.
[sagawa-10:2004]	Hidenori Makabe. Graduation Thesis: Quantum Teleportation Network with Continuous Variables, University of Aizu, 2004.
[sigeru-w-01:2004]	Chisano Imai. Graduation Thesis: Accuracy of Longest One-way Ticket by Integer Programming, University of Aizu, 2004. Thesis Advisor: Watanabe, S
[sigeru-w-02:2004]	Shouma Kaneko. Graduation Thesis: New Constraint Qualifications for First-order Optimality, University of Aizu, 2004. Thesis Advisor: Watanabe, S
[sigeru-w-03:2004]	Jun iti Suzuki. Graduation Thesis: Traveling Salesman Problem with a time limit, University of Aizu, 2004. Thesis Advisor: Watanabe, S
[sigeru-w-04:2004]	Hidekazu Narushima. Graduation Thesis: Analysis and Classification of Authors by Statistics, University of Aizu, 2004. Thesis Advisor: Watanabe, S

Others

[kihara-01:2004]	Hiroshi Kihara. Around Oka's Priciple, September 2004.
	Algebraic and Geometric Models of Spaces and Their Applications (at Shinsyuu University)
[kihara-02:2004]	Hiroshi Kihara. A Rationalization - Completion Approach to Phantom Maps II, November 2004.
	Symposium on Homotopy Theory

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