Professor 
Professor 
Associate Professor 
Associate Professor 
Assistant Professor 
Assistant Professor 
Assistant Professor 
Assistant Professor 
Assistant Professor 
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: nonassociative algebras, neural networks, unimodality problems, algebraic combinatorics, spherical functions, homotopy theory, and arithmetic theory. In the fields of physics, theoretical research is performed in manybody 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 coresearcher are as follows:

[kamiya01:2005] 
N. Kamiya. Examples of Peirce decomposition of generalized Jordan triple systems of second order, balanced cases. Contemporary Mathematics., 391:157165, 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. 

[kamiya02:2005] 
A. Eluduque, N. Kamiya, and S. Okubo. (1,1)Balanced FreudenthalKantor triple systems and noncommutative algebras. J.Alg., 294:1940, 2005. 
This paper is to show that the triple product is determined by the binary product in the algebra, and is classified. 

[mhonma01:2005] 
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 ^{52,54,56}Ti and development of shell closures at N =32,34. Phys. Rev. C, 71:041302(R)/14, 2005. 
The even ^{5256}Ti isotopes have been studied with intermediateenergy 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 neutronrich nuclei above the doubly magic nucleus ^{48}Ca and provide no direct evidence for the predicted N=34 closure. Largescale 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. 

[mhonma02:2005] 
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 inversekinematics proton scattering from ^{46}Ar and the N =28 shell below ^{48}Ca. Phys. Rev. C, 72:024311/17, 2005. 
Lowlying excited states of ^{46}Ar have been studied via inversekinematics proton scattering with a thick target. Coupledchannels 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 neutrontoproton 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 ^{48}Ca. The status of the N=28 shell below ^{48}Ca is discussed. 

[mhonma03:2005] 
A. Burger, T.R. Saito, H. Grawe, H. Hubel, P. Reiter, J. Gerl, M. G'orska, H.J. Wollersheim, A. AlKhatib, 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 neutronrich ^{54,56,58}Cr: On the pathway of magicity from N=40 to N=32. Physics Letters B, 622:2934, 2005. 
The first excited 2^{+} states in ^{54,56,58}Cr were populated by Coulomb excitation at relativistic energies and fl rays were measured using the RISING setup at GSI. For ^{56}Cr and ^{58}Cr the B(E2;2 0^{+}) values relative to the previously known B(E2) value for ^{54}Cr 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 ^{56}Cr. Recent largescale 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. 

[mhonma04:2005] 
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 neutronrich ^{53}Ti. Phys. Rev. C, 72:044315/16, 2005. 
rays from neutronrich Ti nuclei in the vicinity of N=32 have been studied at Gammasphere using deepinelastic reactions induced by ^{48}Ca beams on thick ^{208}Pb and ^{238}U targets. The ^{53}Ti 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 ^{53}Ti provide new tests of effective interactions for fullpfshell calculations. Comparisons between theory and experiment for the highest spin states in ^{53}Ti 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. 

[mhonma05:2005] 
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. Highresolution study of GamowTeller transitions from the Tz = 1 nucleus ^{46}Ti to the Tz = 0 nucleus ^{46}V. Phys. Rev. C, 73:024311/110, 2006. 
The GamowTeller (GT) transition strengths in fpshell nuclei are important parameters in presupernova models. A highenergyresolution (3He,t) experiment was performed on the Tz=1 nucleus ^{46}Ti 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 ^{46}V. 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 shellmodel calculations using various effective interactions. In this lowlying 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 ^{46}Ti. By comparing the GT strength with the corresponding (analogous) M1 transition strength studied in ^{46}Ti(e,e') or (fl, fl0) measurements, a large constructive interference of orbital and spin terms was suggested for one of these M1 transitions. 

[sagawa01:2005] 
K. Hagino and H. Sagawa. Perturbative HartreeFockBogoliubov model for manybody pairing correlations. Phys. Rev. C, 71:044302/18, 2005. 
[sagawa02:2005] 
H. Sagawa, X. R. Zhou, and X. Z. Zhang. Evolution of deformations in mediummass nuclei. Phys. Rev. C, 72:054311/114, 2005. 
Evolution of quadrupole deformations in sd and pf shell nuclei with mass A=18`56 is studied by using deformed Skyrme HartreeFock (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. 

[sagawa03:2005] 
A. Odahara, Y. Gono, T. Fukuchi, Y. Wakabayashi, H. Sagawa, W. Satula, and W.Nazarewicz. Pairing Correlations in the HighSpin Isomers. Phys. Rev. C, 72:061303/14, 2005. 
Nuclear highspin 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 singleparticle levels near the Fermi surface (i.e., by consecutive increase of the degree of quasiparticle 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 superfluidtonormal transition is an interesting subject in itself, the subject of this work is to study pairing correlations in specific HSI. 

[sagawa04:2005] 
K. Hagino and H. Sagawa. Pairing correlations in nuclei on the neutrondrip line. Phys. Rev. C, 72:044321/18, 2005. 
Paring correlations in weakly bound nuclei on the edge of neutron drip line is studied by using a threebody model. A densitydependent contact interaction is employed to calculate the ground state of halo nuclei ^{6}He and ^{11}Li, as well as a skin nucleus ^{24}O. Dipole excitations in these nuclei are also studied within the same model. We point out that the dineutron type correlation plays a dominant role in the halo nuclei ^{6}He and 11Li having the coupled spin of the two neutrons S=0, while the correlation similar to the BCS type is important in ^{24}O. Contributions of the spin S=1 and S=0 configurations are separately discussed in the low energy dipole excitations. 

[sagawa05:2005] 
Satoshi Yoshida and Hiroyuki Sagawa. Isovector nuclear matter properties and neutron skin thickness. Phys. Rev. C, 73:044320/112, 2006. 
Correlations among several nuclear matter properties are investigated in the Skyrme HartreeFock (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. 

[sigeruw01:2005] 
S. Watanabe. Symmetric pairs, Gelfand pairs and pairs such that generating functions of zonal spherical functions define unitary operatorsthe 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. 

[twatanb01:2005] 
T. Shimura and T. Watanabe. Infinite divisibility and generalized subexponentiality. Bernoulli, 11(3):445469, 2005. 
We define Osubexponentiality for onesided distributions. We characterize Osubexponentiality of onesided infinitely divisible distributions. Moreover we prove that the class of onesided infinitely divisible distributions is not closed under convolution roots. 

[twatanb02:2005] 
K. Sato and T. Watanabe. Last exit times for transient semistable processes. Ann. Inst. Poincare, 41:929951, 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. 
[mhonma06:2005] 
M. Honma, T. Otsuka, B. A. Brown, and T. Mizusaki. Shellmodel description of neutronrich pfshell 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 499502. Springer, 2005. 
The shellmodel effective interaction GXPF1 is tested for the description of unstable pfshell nuclei. The GXPF1 successfully describes the N = 32 shell gap in Ca, Ti and Cr isotopes, while the deviation of predicted Ex(2 ) in ^{56}Ti 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. 

[mhonma07:2005] 
M. Honma, T. Otsuka, T. Mizusaki, Y. Utsuno, and N. Shimizu. Frontiers of ShellModel 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 12771282. AIP, 2005. 
An overview, recent developments and future perspectives of the MonteCarlo shellmodel (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. 

[mhonma08:2005] 
M. Honma, T. Otsuka, T. Mizusaki, M. HjorthJensen, and B. A. Brown. Effective interaction for nuclei of A=50100 and GamowTeller properties. In T. Otsuka T. Suzuki and Editor M. Ichimura, editors, International Symposium on Correlation Dynamics in Nuclei, pages 712. IOP, 2005. 
A new effective interaction is proposed for shellmodel calculations in the model space consisting of singleparticle orbits p3/2, f5/2, p1/2, and g9/2. Starting from a realistic interaction derived from the nucleonnucleon potential, Hamiltonian parameters are modified by a leastsquares fit to experimental energy data. The resultant interaction JUL32 is tested from various viewpoints. The property of GamowTeller transition strength is studied in the full pf shell model space focusing on nuclei around ^{56}Ni, where the shellmodel results show significant dependence on the choice of the effective interaction. 
[kasai01:2005] 
Kazuto Asai. Homogeneous partial differential equations for superpositions of indeterminate functions of several variables. submitted to Kodai Math. Journal, under review, submitted 2005. 
[sagawa06:2005] 
H. Sagawa. Ministry of Education Scientific Research Fund C(2), 20042006. 
[sagawa07:2005] 
Mami Watanabe. Graduation Thesis: Quantum Cryptography Using BB84 and B92 protocols, University of Aizu, 2005. Thesis Advisor: H. Sagawa 
[sagawa08:2005] 
Masahiko Sekine. Graduation Thesis: Potential vulnerability of modern cryptography in quantum algorithum, University of Aizu, 2005. Thesis Advisor:H. Sagawa 
[sagawa09:2005] 
Katsuyuki Takano. Graduation Thesis: Present status and potentiality of quantum computing, University of Aizu, 2005. Thesis Advisor:H. Sagawa 
[sagawa10:2005] 
Takashi Tsumura. Graduation Thesis: Computer simulation of Shor's algorithm, University of Aizu, 2005. Thesis Advisor:H. Sagawa 
[sigeruw02:2005] 
Kenji Otake. Graduation Thesis: Class Composition Problem by Linear Programming, University of Aizu, 2005. Thesis Advisor: Watanabe, S 
[sigeruw03:2005] 
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 
[sigeruw04:2005] 
Tadashi Kato. Graduation Thesis: A New System of Functions Related to Trigonometric Functions, University of Aizu, 2005. Thesis Advisor: Watanabe, S 
[sigeruw05:2005] 
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 
[sigeruw06:2005] 
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 
[sigeruw07:2005] 
Satomi Tanaka. Graduation Thesis: A New System of Functions Associated with Logarithms, University of Aizu, 2005. Thesis Advisor: Watanabe, S 
[kihara01:2005] 
Hiroshi Kihara. Homotopical Algebra of Double Complexes, October 2002. Symposium on Homotopy Theory 
[kihara02:2005] 
Hiroshi Kihara. Simplicial Homotopy Theory(Introduction), September 2002. Algebraic Models of Spaces and Their Perspectives(at Okayama University) 
[kihara03:2005] 
Hiroshi Kihara. Homotopical Algebra(Introduction), September 2002. Algebraic Models of Spaces and Their Perspectives(at Okayama University) 
[kihara04:2005] 
Hiroshi Kihara. Holomorphic Homotopy and Homotopical Algebra, July 2003. International Conference on Algebraic Topology 
[kihara05:2005] 
Hiroshi Kihara. From Holomorphic Homotopy to Homotopy of Double Complexes, September 2003. Algebraic Models and Geometric Models of Spaces(at Okayama University) 
[kihara06:2005] 
Hiroshi Kihara. Around the principle of Oka, September 2004. Algebraic Models of Spaces and Their Perspectives(at Shinshuu University) 
[kihara07:2005] 
Hiroshi Kihara. A rationalizationcompletion approach to phantom maps II, November 2004. Symposium on Homotopy Theory 
[kihara081:2005] 
Hiroshi Kihara. Compactly generated groups and infinite dimensional Lie groups, September 2005. Algebraic Models of Spaces and Their Perspectives(at Kouchi University) 