


 Centers 
 Center for Mathematical Sciences 

   
 Hiroyuki Sagawa Professor  Noriaki Kamiya Professor  Katsutaro Shimizu Associate Professor 
   
 Kenichi Funahashi Associate Professor  Toshiro Watanabe Assistant Professor  Hiroshi Kihara Assistant Professor 
   
 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: nonassociative algebras, neural networks, unimodality problems, algebraic combinatorics, spherical functions, and homotopy theory. In the fields of physics, theoretical research is performedinmanybody 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 coresearcher are as follows: 
 Prof. H. Sagawa  studies the physics of the manybodysystem including nuclei and microclusters, and also quantum information theory. 
 Prof. N. Kamiya  studies the theory of nonassociative 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 1dimensional infinitely divisible distributions to multidimensional 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 largescale numeric calculations 
 Prof. H. Kihara  studies homotopy theory and its applications to various areas of mathematics 


 [kamiya01:2003]  N.Kamiya. On radicals of triple systems. Groups,Rings,Lie and Hopf Algebras, Kluw.Acad.Pub., Math.and its appl. vol.555, 555:7584, 2003.

 [kamiya02:2003]  A.Elduque, N.Kamiya, and S.Okubo. simple (1,1)balanced Freudenthal antor triplesystems. Glasgow Math. J., 45:353372, 2003.

 [kamiya03:2003]  I.Kantor and N.Kamiya. A peirce decomposition for G.J.T.S. Comm in Algebras, 31:58755913, 2003.

 [mhonma01:2003]  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 ^{56}Nicore breaking from the lowspin structure of the N = Z nucleus ^{58}_{29}Cu_{29}Phys. Rev. C, (68):034316/110, 2003.
Lowspin states in the oddodd N =Z nucleus ^{58}Cu were investigated with the ^{58}Ni(p;nγ)^{58}Cu fusion evaporation reaction at the FNTANDEM accelerator in Cologne. The new data are compared to full pfshellmodel calculations with the GXPF1 residual interaction. The role of the ^{56}Ni core excitations for the lowspin structure in ^{58}Cu is discussed. 
 [mhonma02:2003]  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 ^{56}Ti and the Predicted N = 34 Shell Closure. Phys. Rev. Lett., (92):072502/14, 2004.
Recent experimental characterization of the subshell closure at N = 32 in the Ca, Ti, and Cr isotones has stimulated shellmodel 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 ^{56}Sc produced in fragmentation reactions and identified new γ rays in the daughter N = 34 isotones ^{56}Ti. 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 ^{56}Ti. 
 [mhonma03:2003]  M. Honma, T. Otsuka, B. A. Brown, and T. Mizusaki. New effective interaction for pfshell nuclei and its implications for the stability of the N=Z=28 closed core. Phys. Rev. C, (69):034335/134, 2004.
The effective interaction GXPF1 for shellmodel calculations in the full pf shell is tested in detail from various viewpoints such as binding energies, electromagnetic moments and transitions, and excitation spectra. The semimagic structure is successfully described for N or Z=28 nuclei, ^{53}Mn, ^{54}Fe, ^{55}Co and ^{ 56,57,58,59}Ni, suggesting the existence of significant coreexcitations in lowlying nonyrast states as well as in highspin yrast states. The results of N = Z oddodd nuclei, ^{54}Co and ^{58}Cu, also confirm the reliability of GXPF1 interaction in the isospin dependent properties. Studies of shape coexistence suggest an advantage of Monte Carlo Shell Model over conventional calculations in cases where fullspace calculations still remain too large to be practical. 
 [sagawa01:2003]  Toshio Suzuki, Koichi Hagino, andH. Sagawa. Electric magnetic moments and electric dipole transitions in Carbon Isotopes. Phys. Rev. C, 68:014317/110, 2003.
We studied firstly the ground state properties of Cisotopes using a deformed HartreeFock(HF)+BCSmodel with Skyrme interactions. Shallow deformation minima are found in several neutronrich Cisotopes. It is shown also that the deformation minima appear in both the oblate and the prolate sides in ^{17}C and ^{19}Chaving almost the same binding energies. Secondly, we carried out shell model calculations to study electromagnetic moments and electric dipole transitions of the Cisotopes. We point out the clear configuration dependence of the quadrupole and magnetic moments in the odd Cisotopes which will be useful to find out the deformations and the spinparities of the ground states of these nuclei. We studied electric dipole states of Cisotopes focusing on the interplay between low energy Pigmy strength and giant dipole resonances. 
 [sagawa02:2003]  Toshio Suzuki and H. Sagawa. GamowTeller and SpinDipole Strength in ^{208}_{83}Bi_{125} and Neutrino Induced Reactions. Nucl. Phys. A, 718:446448, 2003.
GamowTeller and spindipole 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 ^{208}Pb are evaluated using the calculated strength distributions. Charged current reaction cross section for ^{208}Pb (υ_{e},e^{})^{208}Bi induced by neutrinos from pion decay at rest (DAR) is calculated. 
 [sagawa03:2003]  H. Sagawa, Toshio Suzuki, and Koichi Hagino. New structure problems in drip line nuclei. Nucl. Phys. A722 pp. 183c189c (2003), 722:183189, 1984.
We study the ground state properties ofC isotopes using a deformed HartreeFock (HF) + BCS model with Skyrme interactions. Isotope dependence of the deformation properties is investigated in relation to JahnTeller 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 spinparities of the ground states of these nuclei. 
 [sagawa04:2003]  S. Yoshida and H. Sagawa. Neutron skin and EOS in asymmmetric nuclear matter. Phys. Rev. C, 69:024318/110, 2004. Neutron skin thickness of stable and unstable nuclei are studied by using Skyrme HartreeFock(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 ^{132}Sn and ^{208}Pb and the pressure of neutron matter in both SHF and RMF, while the correlation is weak in unstable nuclei ^{32}Mg and ^{44}Ar. Relations between the neutron skin and other nuclear matter properties such as the symmetry energy coeAEcients and the nuclear compression moduli are discussed.

 [twatanb01:2003]  K. Sato and T.Watanabe. Moments of last exit times for Levy processes. Ann. Inst. Poincare Probab. Statist., 40(3):207225, 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 

 [sagawa05:2003]  H. Sagawa. Breaking of Isospin Symmetry in Nuclei and CabibboKobayashiMaskawa Unitarity. In H. Abele and D. Mund, editors, Proc. of Int. Workshop on QuarkMixing and CMKUnitarity, pages 161168, Heidelberg, Sep. 2003. Mattes Verlag.
We studied the effect of isospin impurity on the superallowed 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 oddodd J=0nuclei and eveneven 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 CabbiboKobayashiMaskawa mixing matrix is also discussed. 


 [sagawa06:2003]  H. Sagawa and N. Yoshida. Quantum Information Theory. SpringerVerlag Tokyo, Tokyo, 2003. 


 [sagawa07:2003]  H. Sagawa. Japanese Ministry of Education, Science, Sports and Culture GrantInAid for Scientific Research under the program number C(2) 12640284, 20002003. 


 [sagawa08:2003]  H. Sagawa, June 2003.
International Advisary Committe member of Int. Conf. on Giant Resonances 
 [sagawa09:2003]  H. Sagawa, Oct. 2003.
An organizer of International Workshop on Nuclear Strucuture under the extreme conditions 
 [shimizu01:2003]  K Shimizu, Mar. 2004.
Member of The Physical Society of Japan 


 [sagawa10:2003]  Toru Nakajima. Graduation Thesis: Research on Incoherent Eavesdropping with Laser Pulses, University of Aizu, 2003.
Thesis Advisor: H. Sagawa

 [sigeruw01:2003]  Hiraku Kajiwara. Graduation Thesis: Series solutions of Legendre differential equations, University of Aizu, 2003.
Thesis Advisor: Watanabe, S

 [sigeruw02:2003]  Ai Yokokawa. Graduation Thesis: Secondorder differential equations and Hermite differential equations, University of Aizu, 2003.
Thesis Advisor: Watanabe, S

 [sigeruw03:2003]  Seijiro Imabayashi. Master Thesis: Runs test and its application, University of Aizu, 2003.
Thesis Advisor: Watanabe, S

 [sigeruw04:2003]  Masayasu Ichida. Master Thesis: Orthonormal systems in Hilbert spaces and orthogonal polynomials, University of Aizu, 2003.
Thesis Advisor: Watanabe, S

 [sigeruw05:2003]  Manabu Ichimura. Master Thesis: KarushKuhnTucker conditions and a suAEcient condition for Abadie's constraint qualification, University of Aizu, 2003.
Thesis Advisor: Watanabe, S 


 [kihara01:2003]  Hiroshi Kihara. Homotopical Algebra of Double Complexes, October 2002.
Symposium on Homotopy Theory

 [kihara02:2003]  Hiroshi Kihara. Simplicial Homotopy Theory(Introduction), September 2002.
Algebraic Models of Spaces and Their Perspectives(at Okayama University)

 [kihara03:2003]  Hiroshi Kihara. Homotopical Algebra(Introduction), September 2002.
Algebraic Models of Spaces and Their Perspectives(at Okayama University)

 [kihara04:2003]  Hiroshi Kihara. Holomorphic Homotopy and Homotopical Algebra, July 2003.
International Conference on Algebraic Topology

 [kihara05:2003]  Hiroshi Kihara. From Holomorphic Homotopy to Homotopy of Double Complexes, September 2003.
Algebraic Models and Geometric Models of Spaces(at Okayama University) 
