Mathematics and Physics Laboratory Group

Hiroyuki Sagawa Professor	Noriaki Kamiya Professor	Toshiro Watanabe Associate Professor	Kazuto Asai Associate Professor
Akira Fujitsu Associate Professor	Michio Honma Associate Professor	Katsutaro Shimizu Associate Professor	Shigeru Watanabe Associate Professor
Hiroshi Kihara Assistant Professor	Takao Maeda Assistant Professor	Masayuki Yamagami Assistant Professor	Alexey Severyukhin Visiting Researcher
Xian-Rong Zhou Visiting Researcher

The scope of activities of Mathematics and Physics Group 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 sstudies the physics of the many-body system of including atomic 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. T. Watanabe generalizes the unimodality problems of 1-dimensional infinitely divisible distributions to multi-dimensional cases in the use of analytical methods Prof. K. Shimizu advances the traditional quantum theory and creates the geometrical theory of quantum gravity Prof. K. Asai researches combinatorial identities for generalized Young tableaux, and also, several generating functions arising from algebraic combinatorics Prof. T. Watanabe generalizes the unimodality problems of 1-dimensional infinitely divisible distributions to multi-dimensional cases in the use of analytical methods 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. T. Maeda studies arithmetic of elliptic curves and modular forms and their applications Prof. S. Watanabe studies geometrical interpretations of generating functions for spherical functions on homogeneous spaces Prof. A. Fujitsu studies the numerical superstring and quantum gravity Prof. M. Yamagami studies the physics of atomic nuclei under the extreme condition based on the density functional theory Refereed Journal Papers [k-asai-01:2009] Kazuto Asai. Homogeneous partial differential equations for superpositions of indeterminate functions of several variables. Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, Russian Academy of Sciences, Steklov Mathematical Institute Izvestiya: Mathematics (English translation), London Mathematical Society, 73(1):31–48; 31–46 (English translation), 2009. Abstract: We determine essentially all partial differential equations satisfied by superpositions of tree type and of a further special type. These equations represent necessary and sufficient conditions for an analytic function to be locally expressible as an analytic superposition of the type indicated. The representability of a real analytic function by a superposition of this type is independent of whether that superposition involves real-analytic functions or C -functions, where the constant is determined by the structure of the superposition. We also prove that the function u defined by un = xua+yub+zuc+1 is generally non-representable in any real (resp. complex) domain as f(g(x; y); h(y; z)) with twice differentiable f and differentiable g, h (resp. analytic f, g, h). Keywords: superposition, essentially all PDEs, rooted trees, Hilbert’s 13th problem, minors. MSC: 12H05, 32A05, 32A10, 32A38, 35E15, 35E20, 35N05 [kamiya-01:2009] N. Kamiya and S. Hirabayashi. A generalization of Pythagorian numbers from the viewpoint of nonassociative algebras. Algebras, groups and geometries, 26:45–52, 2009. We discuss a generalization of Pythagorean numbers. In particular, the octonionic product can be showned to be useful when expressed in terms of the bilinear Hurwitz product. [kamiya-02:2009] Noriaki Kamiya and Susumu Okubo. Representation of ( ; ; ) triple systems. Linear and Multilinear algebras, Pages 617 - 643, 2009. This article is to study certain triple systems, in particular, (+,+,-),and structurable algebras. <[kamiya-03:2009]br> N. Kamiya, D. Mondoc, and S. Okubo. A structure theory of (-1,-1) Freudenthal-Kantor triple systems. Bull.Aust.Math., 81(1):32 - 15, 2009. This paper is to give a structure theory of triple systems. In particular,study simplicity and associated Jordan triple systems. [m-honma-01:2009] D. Steppenbeck, A. N. Deacon, S. J. Freeman, R. V. F. Janssens, S. Zhu, M. P. Carpenter, P. Chowdhury, M. Honma, T. Lauritsen, C. J. Lister, D. Seweryniak a nd J. F. Smith, S. L. Tabor, and B. J. Varley. High-spin structures in the neutron-rich isotopes 57􀀀60Mn. Phys. Rev. C, 81:014305/1–21, 2010. Excited states in the neutron-rich isotopes 57−60Mn have been studied with fusionevaporation reactions induced by 48Ca beams at 130 MeV on 13;14C targets. Level schemes have been deduced reaching spins of ∼ 16¯h and ∼ 27=2¯h in the odd-odd and odd-even isotopes, respectively. States with natural parity within an fp model space are compared to the predictions of large-scale shell-model calculations using the recently developed GXPF1A effective interaction. Quasirotational structures are evident in all of the isotopes and are discussed in terms of the deformationdriving potential of the g9=2 intruder orbital. It is apparent that an enlarged model space, incorporating at least the 1g9=2 intruder state, is necessary to reproduce the observed experimental systematics in a more satisfactory manner. [m-honma-02:2009] T. Suzuki, M. Honma, K. Higashiyama, T. Yoshida, T. Kajino, T. Otsuka, H. Umeda, and K. Nomoto. Neutrino-induced reactions on 56Fe and 56Ni, and production of 55Mn in population III stars. Phys. Rev. C, 79:061603(R)/1–4, 2009. Neutrino-induced reactions on 56Fe and 56Ni are investigated based on a new shellmodel Hamiltonian for pf shell. The calculated charged current reaction cross section on 56Fe induced by decay-at-rest (DAR) neutrinos is shown to be consistent with the observation. The Gamow-Teller strength in 56Ni is found to be more spread compared to previous calculations and result in a considerably large branching ratio for the proton knock-out channel. As a consequence of this, the production yields of heavy elements such as 55Mn in population III stars are shown to be enhanced for the new Hamiltonian [m-honma-03:2009] S. Zhu, R. V. F. Janssens, B. Fornal, S. J. Freeman, M. Honma, R. Broda, M. P. Carpenter, A. N. Deacon, E. Jackson, B. P. Kay, T. Lauritsen, C. J. Lister, P. F. Mantica, T. Otsuka, D. Seweryniak, J. F. Smith, D. Steppenbeck, and X. Wang. High-lying, non-yrast shell structure in 52Ti. Phys. Rev. C, 80:024318/1–11, 2009. Gamma rays from 52Ti have been studied with Gammasphere and the Fragment Mass Analyzer using reactions induced by a 48Ca beam on a 9Be target. The data have been used in combination with information from deep-inelastic reactions of 48Ca beams on a thick 238U target at an energy about 25% above the Coulomb barrier. The 52Ti level scheme was expanded considerably, and the lifetimes of some of the identified states were determined for the first time. The excitation of two protons and two neutrons outside the 48Ca core provide new tests of effective interactions in the full pf-shell model space. The positive-parity states in 52Ti were compared to theoretical predictions obtained with the GXPF1A, FPD6, and KB3G effective interactions. The comparisons favor, to a degree, the results computed with the GXPF1A interaction. [m-honma-04:2009] Takaharu Otsuka, Toshio Suzuki, Michio Honma, Yutaka Utsuno, Naofumi Tsunoda, Koshiroh Tsukiyama, and Morten Hjorth-Jensen. Novel Features of Nuclear Forces and Shell Evolution in Exotic Nuclei. Phys. Rev. Lett., 104:012501/1–4, 2010. Novel simple properties of the monopole component of effective nucleon-nucleon interactions are presented, leading to the so-called monopole-based universal interaction. Shell structures are shown to change as functions of N and Z, consistent with experiments. Some key cases of this shell evolution are discussed, clarifying the effects of central and tensor forces. The validity of the present tensor force is examined in terms of the low-momentum interaction Vlowk and the Qbox formalism. [m-honma-05:2009] M. Honma, T. Otsuka, T. Mizusaki, and M. Hjorth-Jensen. New effective interaction for f5pg9-shell nuclei. Phys. Rev. C, 80:064323/1–36, 2009. We present a new effective interaction for shell-model calculations in the model space consisting of the single-particle orbits 1p3=2, 0f5=2, 1p1=2, and 0g9=2. Starting with a realistic interaction based on the Bonn-C potential, 133 two-body matrix elements and four single-particle energies are modified empirically so as to fit 400 experimental energy data out of 69 nuclei with mass numbers A=63∼96. The systematics of binding energies, electromagnetic moments and transitions, and low-lying energy levels are described. The soft Z=28 closed core is observed, in contrast to the stable N=50 shell closure. The new interaction is applied to systematic studies of three different chains of nuclei, Ge isotopes around N=40, N=Z nuclei with A=64∼70, and N=49 odd-odd nuclei, focusing especially on the role of the g9=2 orbit. The irregular behavior of the 0+ 2 state in Ge isotopes is understood as a result of detailed balance between the N=40 single-particle energy gap and the collective effects. The development of the band structure in N=Z nuclei is interpreted in terms of successive excitations of nucleons into the g9=2 orbit. The triaxial/ -soft structure in 64Ge and the prolate/oblate shape coexistence in 68Se are predicted, showing a good correspondence with the experimental data. The isomeric states in 66As and 70Br are obtained with the structure of an aligned proton-neutron pair in the g9=2 orbit. Low-lying energy levels in N=49 odd-odd nuclei can be classified as proton-neutron pair multiplets, implying that the obtained single-particle structure in this neutron-rich region appears to be appropriate. These results demonstrate that, in spite of the modest model space, the new interaction turns out to describe rather well properties related to the g9=2 orbit in various cases, including moderately deformed nuclei. [m-honma-06:2009] M. Sugawara, Y. Toh, M. Oshima, M. Koizumi, A. Kimura, A. Osa, Y. Hatsukawa, H. Kusakari, J. Goto, M. Honma, M. Hasegawa, and K. Kaneko. Medium-spin states in 70Ge and the role of the g9=2 orbital. Phys. Rev. C, 81:024309/1–10, 2010. Medium-spin states of 70Ge have been studied via the 60Ni(12C,2p )70Ge reaction at 45 MeV. The ground-state band and the second 0+ band have been extended to the 12+ and 8+ states, respectively. Two negative-parity bands, one of which has a coupled structure and the other has a decoupled structure, have been observed additionally. Although the latter decoupled structure was known up to the (21−) state from a previous experiment, the part of the level scheme up to the 15− state has been largely modified by the present experiment. Backbendings observed in the positive- and negative-parity yrast bands have been compared with those of the neighboring even Ge isotopes. The experimental level structure has been compared with the shell-model calculations in the model space (2p3=2, 1f5=2, 2p1=2, 1g9=2) employing two kinds of effective interactions, one of which is an extended P+QQ interaction with monopole interactions and the other is developed from a renormalized G matrix. Microscopic structures of the observed bands have been discussed with the help of the shell-model calculations. [sagawa-01:2009] C.L. Bai, H.Q. Zhang, X.Z. Zhang, F.R.Xu, H. Sagawa, and G. Col`o. Quenching of Gamow-Teller strength due to Tensor Correlations in 90Zr and 208Pb. Phys. Rev. C, 79:041301(R)/pp.1–5, 2009. We performed self-consistent HF+RPA calculations for charge exchange 1+ states in 90Zr and 208Pb by using Skyrme interactions with tensor terms. We have employed a parameter set in which the tensor terms are added to the SGII interaction. It is pointed out that Gamow-Teller(GT) states can couple strongly with the spinquadrupole (SQ) 1+ states in the high energy region above Ex=30 MeV due to the tensor interactions. As the result of this coupling, more than 10% of the GT strength is shifted to the energy region above 30 MeV, and the main GT peak is moved 2 MeV downward. At the same time, the main SQ 1+ peak is moved upward by more than 10 MeV due to the tensor correlations. Schematic separable interactions are proposed to elucidate the quenching mechanism induced by the tensor interaction on the GT state [sagawa-02:2009] K. Hagino, H. Sagawa, T. Nakamura, and T. Shimoura. Two-particle Correlations in Continuum dipole excitations in Borromean nuclei. Phys. Rev. C, 80:031301(R)pp.1–4, 2009. We discuss the energy and angular distributions of two emitted neutrons from the dipole excitation of typical weakly-bound Borromean nuclei, 11Li and 6He.We use a three-body model with a density dependent contact interaction between the valence neutrons. Our calculation indicates that the 2D energy distributions for the emitted neutrons are considerably different between the two nuclei, although both the nuclei show similar strong dineutron correlations in the ground state to each other.This different behaviour of the energy distributions is primarily attributed to the presence of s-wave virtual state in the residual neutron-core system 10Li, which is absent in 5He. It is also pointed out that the angular distribution for 11Li in the low energy region shows a clear manifestation of the strong dineutron correlation, whereas the angular distribution for 6He exhibits a strong anticorrelation effect. [sagawa-03:2009] Li-Gang Cao, G. Col`o, P.F. Bortignon, H. Sagawa and L. Sciacchitano. Effect of the Tensor Force on Multipole Response in Finite Nuclei. Phys. Rev. C, 80:064304/pp. 1–8, 2009. We present a thorough analysis of the effect of the tensor interaction on the multipole response of magic nuclei, using the fully self-consistent Random Phase Approximation (RPA) model with Skyrme interactions. The role of the tensor correlations is dissentangled on the static mean-field and the residual particle-hole (p-h) interaction, separately , for quadrupole (2+), hexadecupole (3−) and also magnetic dipole resposes (1+). It is pointed out that the tensor force has a larger effect on the magnetic dipole states than the natural parity ones 2+ and 3−, especially in the mean field level. Perspectives for a better assessment of the tensor force parameters are eventually discussed. [sagawa-04:2009] J. Margueron, S. Goriely, M. Grasso, S. Goriely, G. Col´o, and H. Sagawa. Extended Skyrme Interaction: ground states of nuclei and of nuclear matter. J. Phys. G, 36:125103/pp.1–14, 2009. We study the effect of time-odd components of the Skyrme energy density functionals on the ground state of finite nuclei and in nuclear matter. The spin-dependent terms are shown to change the total binding energy of odd nuclei by only few tenths of keV, while time-odd components of standard Skyrme interactions give an effect that is larger by one order of magnitude. The HFB-17 mass formula based on SKyrme interaction is adusted including the new spin-density dependent terms. [sagawa-05:2009] C.L. Bai, H. Sagawa, H.Q. Zhang, X.Z. Zhang, G. Col`o, and F.R. Xu. Effect of Tensor Correlations on Gamow-Teller States in 90Zr and 208Pb. Phys. Lett. B, 675:28–31, 2009. The tensor terms of the Skyrme effective interaction are included in the selfconsistent Hartree-Fock plus Random Phase Approximation (HF+RPA) model. The Gamow-Teller (GT) strength function of 90Zr and 208Pb are calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA. A microscopic origin of the quenching of GT sum ruleis discussed in relation with the coupling to giant spin-quadrupole excitations by the tensor interactions. [sagawa-06:2009] H.-J. Schulze, Myaing Thi Win, K. Hagino, and H. Sagawa. Hyperons as a probe of nuclear deformation. Prog. Theor. Phys., 123:pp.569–580, 2010. We study the change of nuclear deformation induced by the presence of one or two lambda hyperons in light and medium-heavy nuclei, comparing Skyrme-Hartree- Fock and relativistic mean field model predictions. The physical origin of the deformation changes is discussed in terms of the lambda and nucleon mean field potentials. We identify 30Si and 30S as candidates with possible large deformation differences between the core nucleus and the hypernucleus. [sagawa-07:2009] Peter M¨oller, Ragnar Bengtsson, Hiroyuki Sagawa, and Takatoshi Ichikawa. Global Calculations of Nuclear Shape Coexistence. Phys. Rev. Lett., 103:212501/pp.1–4, 2009. Nuclear shape isomers are well-known in the Kr and Pb regions. To establish how prevalent shape isomers are across the nuclear chart we use a well-benchmarked macroscopic-microscopic model to calculate potential-energy surfaces as functions of spheroidal (Q2), hexadecapole (Q4), and axial-asymmetry (γ) shape coordinates for 7206 nuclei from A = 31 to A = 290. We analyze these and identify the deformation and energies of all minima deeper than 0.2 MeV. The results allow us to identify nuclei in which shape isomers may be experimentally observed. We find that the vast majority of nuclear shape isomers occur in the A = 80 region, A = 100 region, and in a more extended region centered around 208Pb. We compare our model to experimental data for a sequence of Kr data and find encouraging agreement, which motivated our global calculation. Our main result is given in a contour diagram versus N and Z, which for each nucleus shows the number of minima obtained. The results reveal one fairly unexplored region of shape isomerism, which is experimentally accessible, namely the region north-east of 208 Pb82, that is Z > 82andN > 126. [sagawa-08:2009] W.H. Long, J. Meng, T. Nakatsukasa, H. Nakada, and H. Sagawa. Z=64 shell shell closure and single-particle states. Phys. Lett. B (2009), 680:pp. 428–431, 2009. Evolutions of Single-particle energies and Z = 64 sub-shell along the isotonic chain of N = 82 are investigated in the density dependent relativistic Hartree-Fock (DDRHF) theory in comparison with other commonly used mean field models such as Skyrme HF, Gogny HF and density dependent relativistic Hartree model (DDRMF).It is pointed out that DDRHF reproduces well characteristic features of experi mental Z dependence of both spin orbital and pseudo-spin orbital splittings around the subshell clo sure Z = 64. Exchange terms of the isoscalar and ! couplings play dominant r oles in the enhancements of the spin-orbit splitting of 2d states, which is the key ingredient to give the Z = 64 sub-shell closure properly. On the other hand, the and tensor contributions for the spin-orbit splitting cancel each other and the net effect becomes rather small. The enhancement of the sub-shell gaps towards Z = 64 is studied by the DDRHF, for which the local terms of the sc alar and vector meson couplings are found to be important. [sagawa-09:2009] C.A. Bertulani, Hongfeng L¨u, and H. Sagawa. Odd-even mass difference and isospin dependent pairing interaction. Phys. Rev. C, 80:027303/pp.1–4, 2009. The neutron and proton odd-even mass differences are studied with Hartree- Fock+BCS (HFBCS) calculations with Skyrme interactions and an isospin dependent contact pairing interaction, which is recently derived from a microscopic nucleon-nucleon interaction. To this end, we perform HFBCS calculations for even and odd semi-magic Tin and Lead isotopes together with even and odd Z isotones with N= 50 and 82. The filling approximation is applied to the last unoccupied particle in odd nuclei. Comparisons with the experimental data show a clear manifestation of the isospin dependent pairing correlations in both proton and neutron pairing gaps. [sagawa-10:2009] J. Margueron and H. Sagawa. Extended Skyrme interaction: spin fluctuations in dense matter. J. Phys. G, 36:125102/pp.1–11, 2009. Most of the Skyrme interactions are known to predict spin or isospin instabilities beyond the saturation density of nuclear matter which contradict predictions based on realistic interactions. A modification of the standard Skyrme interaction is proposed so that the ferromagnetic instability is removed. The new terms are density dependent and modify only the spin p-h interaction in the case of spinsaturated system. Consequences for the nuclear response function and neutrino mean free path are shown. The overall effect of the RPA correlations makes dense matter more transparent for neutrino propagation by a factor of 2 to 10 depending of the density. [sigeru-w-01:2009] S. Watanabe. Symmetry in Generating Functions. Symmetry, 2(1):346–365, March 2010. Generating functions play important roles in theory of orthogonal polynomials. In particular, it is important to consider generating functions that have symmetry. This paper is a survey on generating functions that define unitary operators. First, classical generating functions that define unitary operators are discussed. Next, group theoretical approach to generating functions that have unitarity are discussed. [t-watanb-01:2009] T. Watanabe and K. Yamamuro. Ratio of The Tail of An Infinitely Divisible Distribution on The Line to That of Its Levy Measure. Electronic Journal of Probability, 15:44–74, 2010. A necessary and sufficient condition for the tail of an infinitely divisible distribution on the real line to be estimated by the tail of its Levy measure is found. The lower limit and the upper limit of the ratio of the right tail of an infinitely divisible distribution to the right tail ofits Levy measure are estimated from above and below by reviving Teugels’s classical method. The exponential class and the dominated varying class are studied in detail. [yamagami-01:2009] Y. R. Shimizu M. Yamagami and T. Nakatsukasa. Optimal pair density functional for the description of nuclei with large neutron excess. Phys. Rev. C, 80:064301 /1–10, 2009. Toward a universal description of pairing properties in nuclei far from stability, we extend the energy density functional by enriching the isovector density dependence in the particle-particle channel (pair density functional, pair-DF). We emphasize the necessity of both the linear and quadratic isovector density terms. The parameters are optimized by the Hartree-Fock-Bogoliubov calculation for 156 nuclei of mass number A=118 to 196 and asymmetry parameter (N-Z)/A¡0.25. We clarify that the pair-DF should include the isovector density dependence in order to take into account in a consistent manner the effect of the isoscalar and isovector effective masses in the particle-hole channel. The different Skyrme forces can give the small difference in the pairing gaps toward the neutron drip line if the optimal pair-DF, consistent with the particle-hole channel, is employed. [yamagami-02:2009] M. Yamagami H. Nakada, K. Mizuyama and M. Matsuo. RPA calculations with Gaussian expansion method. Nucl. Phys. A, 828:283–305, 2009. The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the massindependent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the WoodsSaxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1-, 2+ and 3 － collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in 60Ca are investigated in some detail. [yamagami-03:2009] T. Nakatsukasa M. Yamagami, Y. R. Shimizu. Density functional for description of novel pairing properties in nuclei far from -stability. RIKEN Accel. Prog. Rep., 42:47, 2009. Aiming for a universal description of pairing correlations in nuclei far from - stability, we extend the energy density functional (DF) by enriching the density dependence of the isoscalar and isovector couplings in the particle-particle channel (pair-DF). We emphasize the necessity of the quadratic isovector density term in addition to the linear terms for description of pairing properties in nuclei with large neutron excess. [yamagami-04:2009] M. Yamagami S. Mizutori H. Ogasawara, K. Yoshida and K. Matsuyanagi. Rotational Frequency Dependence of Octupole Vibrations on Superdeformed States in 40Ca. Prog. Theor. Phys., 121:357–374, 2009. By means of the random phase approximation (RPA) calculation based on cranked deformed Woods-Saxon potential, we investigate how rotational motion affects the properties of octupole vibrations built on superdeformed states in 40Ca. A major structure change of the superdeformed yrast states toward a reflection-asymmetric shape is suggested to take place in the region of angular momentum a little higher than the observed maximum value 16¯h, owing to a cooperative effect of octupole vibrational correlation and the rotation-aligned particle-hole excitations from the f7=2 to the g9=2 shell. Unrefereed Papers [kihara-01:2009] Hiroshi Kihara. Spaces of homomorphisms of Lie groups and Lie algebras. In Katsuhiko Kuribayashi Takeshi Torii, editor, Proceedings of Algebraic and Geometric Models of Spaces and Their Perspectives 2009, pages pp. 96–104, 2009. Books Chapters in Book [sagawa-11:2009] H. Sagawa and N Yohida. Quantum Information Theory (second edition). Springer-Japan, 2009. Grants [sagawa-12:2009] H. Sagawa. Recent progress on quantum many-body systems, pages pp. 122 – 130. Science Cooperation( in Japan), 1 2010. [sagawa-13:2009] H. Sagawa. A study of asymmetric nuclear matter and nuclei with the paring correlations and energy density functionals., 2009. JSPS research grant Academic Activities [sigeru-w-02:2009] S. Watanabe, 2009-2010. Reviewer : Mathematical Reviews published by the American Mathematical Society [t-maeda-01:2009] Takao Maeda, March 2010. At the Information Processing Society of Japan 50th Anniversary 72nd National Convention of IPSJ, presented “Introduction of PC Koshien Activities” and participated in panel discussion on “To foster IT talents through programming contests.” Ph.D,Master and Graduation Theses [m-honma-07:2009] Shogo Yoshida. Graduation Thesis: Computer Simulations for Chemical Oscillations, University of Aizu, 2010. Thesis Advisor: M. Honma [sagawa-14:2009] Yuuta Ninomiya. Graduation Thesis: Experimental Violation of Bell Inequality using Hybrid Entangles pairs., School of Computer Science and Engineering, 2009. Thesis Advisor: H. Sagawa [sigeru-w-03:2009] Tomomi Uchiyama. Graduation Thesis: History of Calculus as a Teaching Approach, University of Aizu, 2009. Thesis Adviser: S. Watanabe [sigeru-w-04:2009] Junichi Yamauchi. Graduation Thesis: Development of teaching materials that use history of mathematics, University of Aizu, 2009. Thesis Adviser: S. Watanabe [sigeru-w-05:2009] Kayoko Shinjo. Graduation Thesis: New Functions Defined by Generating Functions Associated with Hermite Polynomials, University of Aizu, 2009. Thesis Adviser: S. Watanabe [sigeru-w-06:2009] Masahiro Suwa. Graduation Thesis: A History of Mathematics: Implications for Mathematics Education in Junior High School, University of Aizu, 2009. Thesis Adviser: S. Watanabe [sigeru-w-07:2009] Misaki Nemoto. Graduation Thesis: New Functions Associated with Hermite Polynomials, University of Aizu, 2009. Thesis Adviser: S. Watanabe 2011 THE UNIVERSITY OF AIZU ALL RIGHTS RESERVED