Center for Mathematical Sciences

Hiroyuki SagawaNoriaki KamiyaKatsutaro Shimizu
Hiroyuki Sagawa
Noriaki Kamiya
Katsutaro Shimizu
Associate Professor
Kenichi FunahashiToshiro WatanabeHiroshi Kihara
Kenichi Funahashi
Associate Professor
Toshiro Watanabe
Assistant Professor
Hiroshi Kihara
Assistant Professor
Shigeru WatanabeMichio HonmaKazuto Asai
Shigeru Watanabe
Assistant Professor
Michio Honma
Assistant Professor
Kazuto Asai
Assistant Professor
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 performedinmany-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. There search are as assigned to each co-researcher are as follows:
Prof. H. Sagawastudies the physics of the many-bodysystem including nuclei and microclusters, and also quantum information theory.
Prof. N. Kamiyastudies the theory of non-associative algebras and a structure theory of algebras from triple systems
Prof. K. Funahashiresearches the theory of the neural networks and function theory of several complex variables from a geometrical viewpoint
Prof. K. Shimizuadvances the traditional quantum theory and creates the geometrical theory of quantum gravity
Prof. T. Watanabegeneralizes the unimodalityproblems of 1-dimensional infinitely divisible distributions to multi-dimensional cases in the use of analytical methods
Prof. K. Asairesearches combinatorial identities for generalized Young tableaux, and also, several generating functions arising from algebraic combinatorics
Prof. S. Watanabestudies geometrical interpretations of generating functions for spherical functions on homogeneous spaces
Prof. M. Honmaresearches 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. Kiharastudies homotopy theory and its applications to various areas of mathematics

Refereed Journal Papers

[kamiya-01:2003]N.Kamiya. On radicals of triple systems. Groups,Rings,Lie and Hopf Algebras, Kluw.Acad.Pub., Math.and its appl. vol.555, 555:75-84, 2003.

[kamiya-02:2003]A.Elduque, N.Kamiya, and S.Okubo. simple (-1,-1)balanced Freudenthal- antor triplesystems. Glasgow Math. J., 45:353-372, 2003.

[kamiya-03:2003]I.Kantor and N.Kamiya. A peirce decomposition for G.J.T.S. Comm in Algebras, 31:5875-5913, 2003.

[m-honma-01:2003]A. F. Lisetskiy, N. Pietralla, M.Honma,A. Schmidt, I. Schneier, A. Gade, P. von Brentano, T. Otsuka, T. Mizusaki, and B. A. Brown. Experimental evidence for 56Ni-core breaking from the low-spin structure of the N = Z nucleus 5829Cu29Phys. Rev. C, (68):034316/1-10, 2003.

Low-spin states in the odd-odd N =Z nucleus 58Cu were investigated with the 58Ni(p;nγ)58Cu fusion evaporation reaction at the FN-TANDEM accelerator in Cologne. The new data are compared to full pf-shell-model calculations with the GXPF1 residual interaction. The role of the 56Ni core excitations for the low-spin structure in 58Cu is discussed.
[m-honma-02:2003]S. N. Liddick, P. F. Mantica, R. V. F. Janssens, R. Broda, B. A. Brown, M. P. Carpenter, B. Fornal, M. Honma, T. Mizusaki, A. C. Morton, W. F. Mueller, T. Otsuka, J. Pavan, A. Stolz, S. L. Tabor, B. E. Tomlin, and M. Wiedeking. Lowest Excitations in 56Ti and the Predicted N = 34 Shell Closure. Phys. Rev. Lett., (92):072502/1-4, 2004.

Recent experimental characterization of the subshell closure at N = 32 in the Ca, Ti, and Cr isotones has stimulated shell-model calculations that indicated the possibility that the N = 34 isotones of these same elements could exhibit characteristics of a shell closure, namely, a high energy for the first excited 2+ level. To that end, wehave studied the decay of 56Sc produced in fragmentation reactions and identified new γ rays in the daughter N = 34 isotones 56Ti. The first 2 level is found at an energy of 1127 keV, well below the expected position that would indicate the presence of an N = 34 shell closure in 56Ti.
[m-honma-03:2003]M. Honma, T. Otsuka, B. A. Brown, and T. Mizusaki. New effective interaction for pf-shell nuclei and its implications for the stability of the N=Z=28 closed core. Phys. Rev. C, (69):034335/1-34, 2004.

The effective interaction GXPF1 for shell-model calculations in the full pf shell is tested in detail from various viewpoints such as binding energies, electro-magnetic moments and transitions, and excitation spectra. The semimagic structure is successfully described for N or Z=28 nuclei, 53Mn, 54Fe, 55Co and 56,57,58,59Ni, suggesting the existence of significant core-excitations in low-lying non-yrast states as well as in high-spin yrast states. The results of N = Z odd-odd nuclei, 54Co and 58Cu, also confirm the reliability of GXPF1 interaction in the isospin dependent properties. Studies of shape co-existence suggest an advantage of Monte Carlo Shell Model over conventional calculations in cases where full-space calculations still remain too large to be practical.
[sagawa-01:2003]Toshio Suzuki, Koichi Hagino, andH. Sagawa. Electric magnetic moments and electric dipole transitions in Carbon Isotopes. Phys. Rev. C, 68:014317/1-10, 2003.

We studied firstly the ground state properties of C-isotopes using a deformed Hartree-Fock(HF)+BCSmodel with Skyrme interactions. Shallow deformation minima are found in several neutron-rich C-isotopes. It is shown also that the deformation minima appear in both the oblate and the prolate sides in 17C and 19Chaving almost the same binding energies. Secondly, we carried out shell model calculations to study electromagnetic moments and electric dipole transitions of the C-isotopes. We point out the clear configuration dependence of the quadrupole and magnetic moments in the odd C-isotopes which will be useful to find out the deformations and the spin-parities of the ground states of these nuclei. We studied electric dipole states of C-isotopes focusing on the interplay between low energy Pigmy strength and giant dipole resonances.
[sagawa-02:2003]Toshio Suzuki and H. Sagawa. Gamow-Teller and Spin-Dipole Strength in 20883Bi125 and Neutrino Induced Reactions. Nucl. Phys. A, 718:446-448, 2003.

Gamow-Teller and spin-dipole strength is evaluated within HF+TDA(RPA) model. Calculated strength is shown to describe the observed distributions rather well below the main resonances [2,3]. Cross sections of neutrino induced reactions on 208Pb are evaluated using the calculated strength distributions. Charged current reaction cross section for 208Pb (υe,e-)208Bi induced by neutrinos from pion decay at rest (DAR) is calculated.
[sagawa-03:2003]H. Sagawa, Toshio Suzuki, and Koichi Hagino. New structure problems in drip line nuclei. Nucl. Phys. A722 pp. 183c-189c (2003), 722:183-189, 1984.

We study the ground state properties ofC isotopes using a deformed Hartree-Fock (HF) + BCS model with Skyrme interactions. Isotope dependence of the deformation properties is investigated in relation to Jahn-Teller effect. We carry out also shell model calculations to study electromagneticmoments and electric dipole transitions of C isotopes. We point out the clear configuration dependence of the quadrupole and magnetic moments in the odd C isotopes, which will be useful to find out the deformation and spin-parities of the ground states of these nuclei.
[sagawa-04:2003]S. Yoshida and H. Sagawa. Neutron skin and EOS in asymmmetric nuclear matter. Phys. Rev. C, 69:024318/1-10, 2004. Neutron skin thickness of stable and unstable nuclei are studied by using Skyrme Hartree-Fock(SHF)models and relativistic mean field(RMF)models in relation with the pressure of EOS in neutron matter. We found a clear linear correlation between the neutron skin sizes in 132Sn and 208Pb and the pressure of neutron matter in both SHF and RMF, while the correlation is weak in unstable nuclei 32Mg and 44Ar. Relations between the neutron skin and other nuclear matter properties such as the symmetry energy coeAEcients and the nuclear compression moduli are discussed.

[t-watanb-01:2003]K. Sato and T.Watanabe. Moments of last exit times for Levy processes. Ann. Inst. Poincare Probab. Statist., 40(3):207-225, 2004.

We study the moment ofthe last exit time from a ball for a transient Levyprocess. A dichotomy for moments is given. A criterion in terms of the logarithm of the characteristic function is given. One dimensional case is completely solved when the expectation is finite.

Refereed Proceeding Papers

[sagawa-05:2003]H. Sagawa. Breaking of Isospin Symmetry in Nuclei and Cabibbo-Kobayashi-Maskawa Unitarity. In H. Abele and D. Mund, editors, Proc. of Int. Workshop on Quark-Mixing and CMK-Unitarity, pages 161-168, Heidelberg, Sep. 2003. Mattes Verlag.

We studied the effect of isospin impurity on the super-allowed Fermi β decay using microscopic HF and RPA (or TDA) model taking into account CSB and CIB interactions. It is found that the super- allowed transitions between odd-odd J=0nuclei and even-even J=0nuclei are quenched because of the cancellation of the isospin impurity effects of mother and daughter nuclei. An implication of the calculated Fermi transition rate on the unitarity of Cabbibo-Kobayashi-Maskawa mixing matrix is also discussed.


[sagawa-06:2003]H. Sagawa and N. Yoshida. Quantum Information Theory. Springer-Verlag Tokyo, Tokyo, 2003.


[sagawa-07:2003]H. Sagawa. Japanese Ministry of Education, Science, Sports and Culture Grant-In-Aid for Scientific Research under the program number C(2) 12640284, 2000-2003.

Academic Activities

[sagawa-08:2003]H. Sagawa, June 2003.

International Advisary Committe member of Int. Conf. on Giant Resonances
[sagawa-09:2003]H. Sagawa, Oct. 2003.

An organizer of International Workshop on Nuclear Strucuture under the extreme conditions
[shimizu-01:2003]K Shimizu, Mar. 2004.

Member of The Physical Society of Japan

Ph.D and Other Theses

[sagawa-10:2003]Toru Nakajima. Graduation Thesis: Research on Incoherent Eavesdropping with Laser Pulses, University of Aizu, 2003.

Thesis Advisor: H. Sagawa

[sigeru-w-01:2003]Hiraku Kajiwara. Graduation Thesis: Series solutions of Legendre differential equations, University of Aizu, 2003.

Thesis Advisor: Watanabe, S

[sigeru-w-02:2003]Ai Yokokawa. Graduation Thesis: Second-order differential equations and Hermite differential equations, University of Aizu, 2003.

Thesis Advisor: Watanabe, S

[sigeru-w-03:2003]Seijiro Imabayashi. Master Thesis: Runs test and its application, University of Aizu, 2003.

Thesis Advisor: Watanabe, S

[sigeru-w-04:2003]Masayasu Ichida. Master Thesis: Orthonormal systems in Hilbert spaces and orthogonal polynomials, University of Aizu, 2003.

Thesis Advisor: Watanabe, S

[sigeru-w-05:2003]Manabu Ichimura. Master Thesis: Karush-Kuhn-Tucker conditions and a suAEcient condition for Abadie's constraint qualification, University of Aizu, 2003.

Thesis Advisor: Watanabe, S


[kihara-01:2003]Hiroshi Kihara. Homotopical Algebra of Double Complexes, October 2002.

Symposium on Homotopy Theory

[kihara-02:2003]Hiroshi Kihara. Simplicial Homotopy Theory(Introduction), September 2002.

Algebraic Models of Spaces and Their Perspectives(at Okayama University)

[kihara-03:2003]Hiroshi Kihara. Homotopical Algebra(Introduction), September 2002.

Algebraic Models of Spaces and Their Perspectives(at Okayama University)

[kihara-04:2003]Hiroshi Kihara. Holomorphic Homotopy and Homotopical Algebra, July 2003.

International Conference on Algebraic Topology

[kihara-05:2003]Hiroshi Kihara. From Holomorphic Homotopy to Homotopy of Double Complexes, September 2003.

Algebraic Models and Geometric Models of Spaces(at Okayama University)