Center for Mathematical Sciences

Hiroyuki Sagawa Professor	Noriaki Kamiya Professor	Ken-ichi Funahashi 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, homotopy theory, and arithmetic 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 unimodality problems 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. 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 Prof. S. Watanabe studies geometrical interpretations of generating functions for spherical functions on homogeneous spaces Prof. T. Watanabe generalizes the unimodality problems of 1-dimensional infinitely divisible distributions to multi-dimensional cases in the use of analytical methods

Refereed Journal Papers

[kamiya-01:2005]	N. Kamiya. Examples of Peirce decomposition of generalized Jordan triple systems of second order, -balanced cases. Contemporary Mathematics., 391:157-165, 2005.
	We consider examples of decomposition of GJTS of second order. By virtue of a tripotent element for triple systems,we can give several types.
[kamiya-02:2005]	A. Eluduque, N. Kamiya, and S. Okubo. (-1,-1)-Balanced Freudenthal-Kantor triple systems and noncommutative algebras. J.Alg., 294:19-40, 2005.
	This paper is to show that the triple product is determined by the binary product in the algebra, and is classified.
[m-honma-01:2005]	D.-C. Dinca, R. V. F. Janssens, A. Gade, D. Bazin, R. Broda, B. A. Brown, C. M. Campbell, M. P. Carpenter, P. Chowdhury, J. M. Cook, A. N. Deacon, B. Fornal, S. J. Freeman, T. Glasmacher, M. Honma, F. G. Kondev, J.-L. Lecouey, S. N. Liddick, P. F. Mantica, W. F. Mueller, H. Olliver, T. Otsuka, J. R. Terry, B. A. Tomlin, and K. Yoneda. Reduced transition probabilities to the first 2+ state in 52,54,56Ti and development of shell closures at N =32,34. Phys. Rev. C, 71:041302(R)/1-4, 2005.
	The even 52-56Ti isotopes have been studied with intermediate-energy Coulomb excitation and absolute B(E2;0+ �� 2 ) transition rates have been obtained. These data confirm the presence of a subshell closure at neutron number N=32 in neutron-rich nuclei above the doubly magic nucleus 48Ca and provide no direct evidence for the predicted N=34 closure. Large-scale shell model calculations with the most recent effective interactions are unable to reproduce the magnitude of the measured strengths in the semimagic Ti nuclei and their strong variation with neutron number.
[m-honma-02:2005]	L. A. Riley, M. A. Abdelqader, D. Bazin, M. J. Bojazi, B. A. Brown, C. M. Campbell, J. A. Church, P. D. Cottle, D. C. Dinca, J. Enders, A. Gade, T. Glasmacher, M. Honma, S. Horibe, Z. Hu, K. W. Kemper, W. F. Mueller, H. Olliver, T. Otsuka, B. C. Perry, B. T. Roeder, B. M. Sherrill, T. P. Spencer, and J. R. Terry. Thicktarget inverse-kinematics proton scattering from 46Ar and the N =28 shell below 48Ca. Phys. Rev. C, 72:024311/1-7, 2005.
	Low-lying excited states of 46Ar have been studied via inverse-kinematics proton scattering with a thick target. Coupled-channels calculations have been used to extract the deformation length of the 2 state. This result, combined with existing Coulomb excitation data, yields a ratio of the neutron-to-proton transition matrix elements of M n/M p = 1.19(25)N/Z, showing a departure from the proton dominance observed in the N=28 isotones above 48Ca. The status of the N=28 shell below 48Ca is discussed.
[m-honma-03:2005]	A. Burger, T.R. Saito, H. Grawe, H. Hubel, P. Reiter, J. Gerl, M. G'orska, H.J. Wollersheim, A. Al-Khatib, A. Banu, T. Beck, F. Becker, P. Bednarczyk, G. Benzoni, A. Bracco, S. Brambilla, P. Bringel, F. Camera, E. Cl'ement, P. Doornenbal, H. Geissel, A. Gorgen, J. Gr,ebosz, G. Hammond, M. Hellstrom, andM. Kavatsyuk M. Honma, O. Kavatsyuk, M. Kmiecik, I. Kojouharov, W. Korten, N. Kurz, R. Lozeva, A. Maj, S. Mandal, B. Million, S. Muralithar, A. Neusser, F. Nowacki, T. Otsuka, Zs. Podoly'ak, N. Saito, A.K. Singh, H. Weick, C. Wheldon, O. Wieland, M. Winkler, and RISING Collaboration. Relativistic Coulomb excitation of neutron-rich 54,56,58Cr: On the pathway of magicity from N=40 to N=32. Physics Letters B, 622:29-34, 2005.
	The first excited 2+ states in 54,56,58Cr were populated by Coulomb excitation at relativistic energies and fl rays were measured using the RISING setup at GSI. For 56Cr and 58Cr the B(E2;2 �� 0+) values relative to the previously known B(E2) value for 54Cr are determined as 8.7(3.0) and 14.8(4.2) W.u., respectively. The results are consistent with a subshell closure at neutron number N=32 which was already indicated by the higher energy of the 2 state in 56Cr. Recent large-scale shell model calculations using effective interactions reproduce the trend in the excitation energies, but fail to account for the minimum in the B(E2) values at N=32.
[m-honma-04:2005]	B. Fornal, S. Zhu, R. V. F. Janssens, M. Honma, R. Broda, B. A. Brown, M. P. Carpenter, S. J. Freeman, N. Hammond, F. G. Kondev, W. Kr'olas, T. Lauritsen, S. N. Liddick, C. J. Lister, S. Lunardi, P. F. Mantica, N. Marginean, T. Mizusaki, E. F. Moore, T. Otsuka, T. Pawlat, D. Seweryniak, B. E. Tomlin, C. A. Ur, I. Wiedenhover, and J. Wrzesi'nski. Yrast structure of neutron-rich 53Ti. Phys. Rev. C, 72:044315/1-6, 2005.
	�� rays from neutron-rich Ti nuclei in the vicinity of N=32 have been studied at Gammasphere using deep-inelastic reactions induced by 48Ca beams on thick 208Pb and 238U targets. The 53Ti yrast cascade was identified for the first time, and the location in energy of states with spin up to I = 21/2 was determined. The excitations of 53Ti provide new tests of effective interactions for full-pf-shell calculations. Comparisons between theory and experiment for the highest spin states in 53Ti favor the recently proposed GXPF1A interaction, which accounts for the appearance of a neutron subshell closure at N=32 in Ti isotopes as well as for the lack of a similar subshell closure at N=34, as predicted by earlier calculations with another interaction.
[m-honma-05:2005]	T. Adachi, Y. Fujita, P. von Brentano, A. F. Lisetskiy, G. P. A. Berg, C. Fransen, D. De Frenne, H. Fujita, K. Fujita, K. Hatanaka, M. Honma, E. Jacobs, J. Kamiya, K. Kawase, T. Mizusaki, K. Nakanishi, A. Negret, T. Otsuka, N. Pietralla, L. Popescu, Y. Sakemi, Y. Shimbara, Y. Shimizu, Y. Tameshige, A. Tamii, M. Uchida, T. Wakasa, M. Yosoi, and K. O. Zell. High-resolution study of GamowTeller transitions from the Tz = 1 nucleus 46Ti to the Tz = 0 nucleus 46V. Phys. Rev. C, 73:024311/1-10, 2006.
	The Gamow-Teller (GT) transition strengths in fp-shell nuclei are important parameters in presupernova models. A high-energy-resolution (3He,t) experiment was performed on the Tz=1 nucleus 46Ti at 0ffi and at an intermediate incident energy of 140 MeV/nucleon for the study of precise GT transition strengths to the final Tz=0 nucleus 46V. With an energy resolution of 33 keV, individual GT transitions were observed and GT strengths were derived for them up to the excitation energy of 4.5 MeV. The GT strengths were compared with shell-model calculations using various effective interactions. In this low-lying region, most GT states have isospin T =0. A few GT states with isospin T =1 were identified from the existence of the corresponding (analog) M1 states in 46Ti. By comparing the GT strength with the corresponding (analogous) M1 transition strength studied in 46Ti(e,e') or (fl, fl0) measurements, a large constructive interference of orbital and spin terms was suggested for one of these M1 transitions.
[sagawa-01:2005]	K. Hagino and H. Sagawa. Perturbative Hartree-FockBogoliubov model for many-body pairing correlations. Phys. Rev. C, 71:044302/1-8, 2005.
[sagawa-02:2005]	H. Sagawa, X. R. Zhou, and X. Z. Zhang. Evolution of deformations in medium-mass nuclei. Phys. Rev. C, 72:054311/1-14, 2005.
	Evolution of quadrupole deformations in sd and pf shell nuclei with mass A=18�`56 is studied by using deformed Skyrme Hartree-Fock (HF) model with pairing correlations. We point out that the quadrupole deformations of the nuclei with the isospin T=0 and T=1 show in a systematic study of the ratios between the proton and neutron deformations in nuclei with T=|Tz|=1. Calculated quadrupole and hexadecapole deformations are compared with shell model results and available experimental data. A relation between the skin thickness and the intrinsic Q2 moments is also discussed.
[sagawa-03:2005]	A. Odahara, Y. Gono, T. Fukuchi, Y. Wakabayashi, H. Sagawa, W. Satula, and W.Nazarewicz. Pairing Correlations in the High-Spin Isomers. Phys. Rev. C, 72:061303/1-4, 2005.
	Nuclear high-spin isomers (HSI) are known to be excellent laboratories of a transition from superfluid to normal motion. As those states are formed by the blocking of single-particle levels near the Fermi surface (i.e., by consecutive increase of the degree of quasi-particle excitation or seniority), their structure reflects the gradual decrease of pairing correlations with energy and angular momentum. There exists an extensive literature on the subject of pairing phase transition. In particular, in the context of HSI, pairing gap exhibits successive reductions with the seniority quantum number. While the dynamics of the superfluid-to-normal transition is an interesting subject in itself, the subject of this work is to study pairing correlations in specific HSI.
[sagawa-04:2005]	K. Hagino and H. Sagawa. Pairing correlations in nuclei on the neutron-drip line. Phys. Rev. C, 72:044321/1-8, 2005.
	Paring correlations in weakly bound nuclei on the edge of neutron drip line is studied by using a three-body model. A density-dependent contact interaction is employed to calculate the ground state of halo nuclei 6He and 11Li, as well as a skin nucleus 24O. Dipole excitations in these nuclei are also studied within the same model. We point out that the di-neutron type correlation plays a dominant role in the halo nuclei 6He and 11Li having the coupled spin of the two neutrons S=0, while the correlation similar to the BCS type is important in 24O. Contributions of the spin S=1 and S=0 configurations are separately discussed in the low energy dipole excitations.
[sagawa-05:2005]	Satoshi Yoshida and Hiroyuki Sagawa. Isovector nuclear matter properties and neutron skin thickness. Phys. Rev. C, 73:044320/1-12, 2006.
	Correlations among several nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and the isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. A linear correlation between the neutron skin thickness and the pressure of the neutron matter is given in terms of the ratio between the neutron and nuclea r matter densities. We also discovered that the correlations between the isovector properties and the incompressibility K show a singularity at the critical incompressi bility Kc=306 MeV. We show that the neutron skin thickness gives crucial information about not only for the neutron EOS but also about the isovector nuclear matter properties a nd about the parameterization of Skyrme interaction.
[sigeru-w-01:2005]	S. Watanabe. Symmetric pairs, Gelfand pairs and pairs such that generating functions of zonal spherical functions define unitary operators-the case of the compact type. Journal of Functional Analysis, 2005.
	We show that a new notion which is equivalent neither to that of Riemannian symmetric pair nor to that of Gelfand pair can be defined by generating functions.
[t-watanb-01:2005]	T. Shimura and T. Watanabe. Infinite divisibility and generalized subexponentiality. Bernoulli, 11(3):445-469, 2005.
	We define O-subexponentiality for one-sided distributions. We characterize O-subexponentiality of one-sided infinitely divisible distributions. Moreover we prove that the class of one-sided infinitely divisible distributions is not closed under convolution roots.
[t-watanb-02:2005]	K. Sato and T. Watanabe. Last exit times for transient semistable processes. Ann. Inst. Poincare, 41:929-951, 2005.
	We characterize the oder of moments of last exit times of transient semistable processes. We classify all semistable processes into weakly transient or strongly transient. The results are applied to limit theorems involving capacities.

Refereed Proceeding Papers

[m-honma-06:2005]	M. Honma, T. Otsuka, B. A. Brown, and T. Mizusaki. Shellmodel description of neutron-rich pf-shell nuclei with a new effective interaction GXPF1. In W. Nazarewicz C. J. Gross and Editor K. P. Rykaczewski, editors, The 4th International Conference on Exotic Nuclei and Atomic Masses, pages 499-502. Springer, 2005.
	The shell-model effective interaction GXPF1 is tested for the description of unstable pf-shell nuclei. The GXPF1 successfully describes the N = 32 shell gap in Ca, Ti and Cr isotopes, while the deviation of predicted Ex(2 ) in 56Ti from the recent experimental data requires the modification of the Hamiltonian especially in the T = 1 matrix elements related to the p1/2 and f5/2 orbits. The modified interaction gives improved description simultaneously for all these isotope chains.
[m-honma-07:2005]	M. Honma, T. Otsuka, T. Mizusaki, Y. Utsuno, and N. Shimizu. Frontiers of Shell-Model Description for Atomic Nuclei. In T. Kawano R. C. Haight, M. B. Chadwick and Editor P. Talou, editors, Proceedings of the International Conference on Nuclear Data for Science and Technology, pages 1277-1282. AIP, 2005.
	An overview, recent developments and future perspectives of the Monte-Carlo shell-model (MCSM) calculations are described. The advantage of the MCSM over the conventional diagonalization method, its applicability to huge systems in large model spaces and with many valence nucleons, is clarified through various practical examples. An attempt to describe many nuclei in a wide mass range with a unified framework is presented. In order to obtain reliable effective interactions for such purposes, we can modify microscopic interactions empirically by using the information from experimental data.
[m-honma-08:2005]	M. Honma, T. Otsuka, T. Mizusaki, M. Hjorth-Jensen, and B. A. Brown. Effective interaction for nuclei of A=50-100 and GamowTeller properties. In T. Otsuka T. Suzuki and Editor M. Ichimura, editors, International Symposium on Correlation Dynamics in Nuclei, pages 7-12. IOP, 2005.
	A new effective interaction is proposed for shell-model calculations in the model space consisting of single-particle orbits p3/2, f5/2, p1/2, and g9/2. Starting from a realistic interaction derived from the nucleon-nucleon potential, Hamiltonian parameters are modified by a least-squares fit to experimental energy data. The resultant interaction JUL32 is tested from various viewpoints. The property of Gamow-Teller transition strength is studied in the full pf -shell model space focusing on nuclei around 56Ni, where the shell-model results show significant dependence on the choice of the effective interaction.

Unrefereed Papers

[k-asai-01:2005]

Kazuto Asai. Homogeneous partial differential equations for superpositions of indeterminate functions of several variables. submitted to Kodai Math. Journal, under review, submitted 2005.

Grants

[sagawa-06:2005]

H. Sagawa. Ministry of Education Scientific Research Fund C(2), 2004-2006.

Ph.D and Other Theses

[sagawa-07:2005]	Mami Watanabe. Graduation Thesis: Quantum Cryptography Using BB84 and B92 protocols, University of Aizu, 2005. Thesis Advisor: H. Sagawa
[sagawa-08:2005]	Masahiko Sekine. Graduation Thesis: Potential vulnerability of modern cryptography in quantum algorithum, University of Aizu, 2005. Thesis Advisor:H. Sagawa
[sagawa-09:2005]	Katsuyuki Takano. Graduation Thesis: Present status and potentiality of quantum computing, University of Aizu, 2005. Thesis Advisor:H. Sagawa
[sagawa-10:2005]	Takashi Tsumura. Graduation Thesis: Computer simulation of Shor's algorithm, University of Aizu, 2005. Thesis Advisor:H. Sagawa
[sigeru-w-02:2005]	Kenji Otake. Graduation Thesis: Class Composition Problem by Linear Programming, University of Aizu, 2005. Thesis Advisor: Watanabe, S
[sigeru-w-03:2005]	Hiroyuki Akatsu. Graduation Thesis: A New System of Functions Defined by a Generating Function Associated with Legendre Polynomials, University of Aizu, 2005. Thesis Advisor: Watanabe, S
[sigeru-w-04:2005]	Tadashi Kato. Graduation Thesis: A New System of Functions Related to Trigonometric Functions, University of Aizu, 2005. Thesis Advisor: Watanabe, S
[sigeru-w-05:2005]	Daisuke Kamoshita. Graduation Thesis: A New System of Functions Defined by a Generating Function Associated with Exponential Functions, University of Aizu, 2005. Thesis Advisor: Watanabe, S
[sigeru-w-06:2005]	Naoko Kobayashi. Graduation Thesis: New System of Functions Defined by a Generating Function Related to Exponential Functions, University of Aizu, 2005. Thesis Advisor: Watanabe, S
[sigeru-w-07:2005]	Satomi Tanaka. Graduation Thesis: A New System of Functions Associated with Logarithms, University of Aizu, 2005. Thesis Advisor: Watanabe, S

Others

[kihara-01:2005]	Hiroshi Kihara. Homotopical Algebra of Double Complexes, October 2002. Symposium on Homotopy Theory
[kihara-02:2005]	Hiroshi Kihara. Simplicial Homotopy Theory(Introduction), September 2002. Algebraic Models of Spaces and Their Perspectives(at Okayama University)
[kihara-03:2005]	Hiroshi Kihara. Homotopical Algebra(Introduction), September 2002. Algebraic Models of Spaces and Their Perspectives(at Okayama University)
[kihara-04:2005]	Hiroshi Kihara. Holomorphic Homotopy and Homotopical Algebra, July 2003. International Conference on Algebraic Topology
[kihara-05:2005]	Hiroshi Kihara. From Holomorphic Homotopy to Homotopy of Double Complexes, September 2003. Algebraic Models and Geometric Models of Spaces(at Okayama University)
[kihara-06:2005]	Hiroshi Kihara. Around the principle of Oka, September 2004. Algebraic Models of Spaces and Their Perspectives(at Shinshuu University)
[kihara-07:2005]	Hiroshi Kihara. A rationalization-completion approach to phantom maps II, November 2004. Symposium on Homotopy Theory
[kihara-081:2005]	Hiroshi Kihara. Compactly generated groups and infinite dimensional Lie groups, September 2005. Algebraic Models of Spaces and Their Perspectives(at Kouchi University)

2007 THE UNIVERSITY OF AIZU ALL RIGHTS RESERVED