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: 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:
Prof. H. Sagawa

studies the physics of the manybody system of including
atomic nuclei, microclusters and quantum information
theory.

Prof. N. Kamiya

studies the theory of nonassociative algebras and a
structure theory of algebras from triple systems

Prof. K. Shimizu

advances the traditional quantum theory and creates
the geometrical theory of quantum gravity

Prof. T. Watanabe

generalizes the unimodality problems 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. 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

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

Refereed Journal Papers
[kasai01:2008]

Kazuto Asai. Homogeneous partial differential equations for superpositions
of indeterminate functions of several variables. Izvestiya Rossiiskoi
Akademii Nauk. Seriya Matematicheskaya, 73(1):31 – 48, 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 realanalytic functions or Cfunctions, where the constant ρ is
determined by the structure of the superposition. We also prove that the function u
defined by un = xua +yub +zuc +1 is generally nonrepresentable 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).

[kamiya01:2008]

N. Kamiya. On triple systems and Lie algebrasB 3 cases=.
RIMS,Kyoto Univ.2009, in press, Februay 2009.


In this paper, we study a special cases of construction of Lia algebras from generalized
FreudenthalKantor triple systems.

[kamiya02:2008]

N. Kamiya and S. Okubo. A representation of triple systems. Linear
and multilinear algebras, in press, March 2009.


This aricle is a generalization of triple systems and nonassociative algebras. That is,
structurable algebras, altenative algebras, etc.

<[kamiya03:2008]br>

N .Kamiya and D. Mondoc. Antistructurable algebras and Extended
Dynkin diagrams. JGLTA ((Sweden), in press, March 2009.


In This paper, we consider the correspondence of antistructurable algebras and
Dynkin diagram, that is, is given a characterization of Lie superalgebras.

[mhonma01:2008]

H. Iwasaki, S. Michimasa, M. Niikura, M. Tamaki, N. Aoi, H. Sakurai,
S. Shimoura, S. Takeuchi, S. Ota, M. Honma, T. K. Onishi, E. Takeshita,
H. J. Ong, H. Baba, Z. Elekes, T. Fukuchi, Y. Ichikawa, M. Ishihara, N. Iwasa,
S. Kanno, R. Kanungo, S. Kawai, T. Kubo, K. Kurita, T. Motobayashi,
A. Saito, Y. Satou, H. Suzuki, M. K. Suzuki, Y. Togano, and Y. Yanagisawa.
Persistence of the N=50 shell closure in the neutronrich isotope 80Ge.
Phys. Rev. C, 78:021304(R)/1–5, 2008.


The 2+
1 and 2+
2 states of the neutronrich isotope 80Ge were studied by intermediateenergy
heavyion scattering, providing for the first time the experimental value of
B(E2;2+
2 !0+
1 ) for 80Ge. The experimental data are well reproduced by largescale
shell model calculations, which suggest the important role of the proton particlehole
2p3/21f5/2 excitation in the configuration of the 2+
2 state.

[sagawa01:2008]

S. Yoshida and H. Sagawa. Effective Mass and Pairing correlations.
Phys. Rev. C, Vol. 77, pages 054308/15, 2008.


We study the effect of effective mass on pairing correlations in the ground states of
superfluid nuclei 124Sn and 136Sn. Various parameter sets of Skyrme interactions and
relativistic Lagrangians are adopted to study pairing correlations across a wide range
of effective mass. It is shown that surfacetype pairing interaction gives an almost
constant pairing gap as a function of the effective mass, while volumetype pairing
interaction shows rather strong dependence of the pairing gap upon the effective
mass. The local pair potentials of various effective interactions are also examined i n
relation to the effective mass.

[sagawa02:2008]

Y. Zhang, H. Sagawa, D. Yoshino, K. Hagino, and J. Meng. Shape
evolution of C isotopes in (β, γ) deformation plane. Progress of Theoretical
Physics, Vol. 120, pages 129142, 2008.


We study the shape evolution of C isotopes in the full (β, γ) deformation plane by
using a constrained Skyrme HartreeFock + BCS method in the coordinate space. It
is shown that the deformation of the energy minimum varys drastically in the (β,γ)
plane as a function of mass number which can be viewed as a clear manifestation of
the spontaneous symmetry breaking effect in finite manybody system

[sagawa03:2008]

N. Yoshida, H. Sagawa, A. Odahara, and Toru Suzuki. Electric
quadrupole transitions between highspin isomer bands in 147Gd. Prog. Theor.
Phys., Vol. 121, pages 8595, 2009.


The electronic quadrupole matrix elements are calculated between the highspin isomers
with different deformations. The experimental bands in 147Gd are analyzed.

[sagawa04:2008]

J. Margueron, H. Sagawa, and K. Hagino. Effective Pairing Interactions
with Isospin Density Dendence. Phys. Rev. C, Vol. 77, pages 054309/1
10, 2008.


We perform HartreeFockBogoliubov (HFB) calculations for semimagic Calcium,
Nickel, Tin and Lead isotopes and N=20, 28, 50 and 82 isotones using densitydependent
pairing interactions recently derived from a microscopic nucleonnucleon
interaction. These interactions have an isovector component so that the pairing gaps
in symmetric and neutron matter are reproduced. Our calculations well account for
the experimental data for the neutron number dependence of binding energy, two
neutrons separation energy, and oddeven mass staggering of these isotopes. This
result suggests that by introducing the isovector term in the pairing interaction, one
can construct a global effective pairing interaction which is applicable to nuclei in a
wide range of the nuclear chart.

[sagawa05:2008]

J. Peng, H. Sagawa, S. Q. Zhang, J. M. Yao, Y. Zhang, , and J. Meng.
Search for Multiple Chiral doublets in Rhodium Isotopes. Phys. Rev. C, Vol.
77, pages 024309/16, 2008.


Multiple Chiral doublets in Rhodium Isotopes are discussed. Relativistic and Skyrme
HartreeFock models are used to study the chirality.

[sagawa06:2008]

H. Sagawa, X. R. Zhou, Toshio Suzuki, and N. Yoshida. Possible
Shape Coexistence and Magnetic Dipole Transitions in 17C and 21Ne. Phys.
Rev. C78, Vol. 78, pages 041304(R)/14, 2008.


Magnetic dipole(M1) transitions of N=11 nuclei, 17C and 21Ne are investigated by
using shell model and deformed Skyrme HartreeFock+blocked BCS wave functions.
Shell model calculations predict well observed energy spectra and magnetic dipole
transitions in 21Ne, while the results are rather poor to predict these observables in
17C. In the deformed HF calculations, the ground states of two nuclei are shown to
have large prolate deformations close to β2=0.4.

[sagawa07:2008]

A. Odahara, Y. Gono, T. Fukuchi, Y. Wakabayashi, and H. Sagawa.
Possible Shape Isomerism at HighSpin States of N=83 Isotones. Journal of
the Physical Society of Japan, Vol. 77, pages 114201/14, 2008.


Decays of highspin isomers with I=49/2 in 143Nd and 147Gd are studied in terms
of shape isomerism. Observed large hindrance factors of the electric dipole transition
deexciting HSI in 143Nd and the electric quadrupole transition deexciting HSI in
147Gd are analyzed by using deformed independent particle model.

[sagawa08:2008]

P. Moller, R. Bengtsson, B. G. Carlsson, P. Olivius, T. Ichikawa,
H. Sagawa, and A. Iwamoto. Axial and reflection asymmetry of the nuclear
ground state. Atomic Data and Nuclear Data Tables, Vol 94, pages 758780,
2008.


Axial and reflection asymmetry of the nuclear ground state was discussed.We tabulate
energies and deformations of secondary minima in calculated nuclear potentialenergy
surfaces, which corespond to nuclear shape isomers, for nuclei from A = 31 to N =
160.An additional result of our potentialenergy calcuations is tha t we find that
more than one hundred nuclei are axially deformed in their ground state. We also
tablulate the groundstate properties of those nuclei and investigate the effect of axial
asymmetry on nuclear groundstate masses.

[sagawa09:2008]

D. Yoshino and H. Sagawa. Monte Carlo Simulation of Spiral Galaxy
Formation. Fractals, Vol. 16, pages 119127, 2008.


We study Monte Carlo Simulation of Spiral Galaxy Formation.Fractal dimenstion
of spiral galaxies is analuzed by using the parcolation model and other microscopic
models.

[sagawa10:2008]

K. Hagino, N. Takahashi, and H. Sagawa. Strong dineutron correlation
in 8He and in 18C. Phys. Rev. C, Vol. 77, pages 054317/19, 2008.


We study the spatial structure of four valence neutrons in the ground state of 8He and
18C nuclei using a core+4n model. For this purpose, we employ a densitydependent
contact interaction among the valence neutrons, and solve the fivebody Hamiltonian
in the HartreeFockBogoliubov (HFB) approximation. We show that two neutrons
with the coupled spin of S=0 exhibit a strong dineutron correlation around the surface
of these nuclei, whereas the correlation between the two dineutrons is much weaker.

Grants
[sagawa11:2008]

H. Sagawa. Kakenhi, Kiban Kenkyu C, 2008.

Academic Activities
[sigeruw01:2008]

S Watanabe, 2008.
Reviewer of Mathematical Reviews published by the American Mathematical Society

[tmaeda01:2008]

Takao Maeda, Oct. 2008.
Chief Coordinator, ACM International Collegiate Programming Contest Asia Regional
Contest, 2008, Aizu

Ph.D,Master and Bachelor Theses
[sagawa12:2008]

Kazuki Shige. Graduation Thesis: Observation of FourPhoton GHZ
Entanglement, School of Computer Science and Engineering, 2008.
Thesis Adviser: H. Sagawa

[sagawa13:2008]

Yoshitaka Kato. Graduation Thesis: Experimental Demonstration of
ThreePhoton Entanglement with GHZ States, School of Computer Science and
Engineering, 2008.
Thesis Adviser: H. Sagawa

[sagawa14:2008]

Tatsuya Koga. Graduation Thesis: Devices for Experiment of Quantum
Nonlocality,School of Computer Science and Engineering, 2008.
Thesis Adviser: H. Sagawa

[sigeruw02:2008]

Chihiro Itagaki. Graduation Thesis: New Functions Defined by a
Generating Function Associated with Laguerre Polynomials, University of Aizu,
2008.
Thesis Adviser: S. Watanabe

[sigeruw03:2008]

Yuji Habe. Graduation Thesis: New Functions Derived by Taylor
Expansions of Trigonometric Functions, University of Aizu, 2008.
Thesis Adviser: S. Watanabe

[sigeruw04:2008]

Yurie Sato. Graduation Thesis: New Functions Defined by Laguerre
Polynomials, University of Aizu, 2008.
Thesis Adviser: S. Watanabe

[sigeruw052008]

Azusa Yashima. Master Thesis: Bessel functions and related new
functions, University of Aizu, 2008.
Thesis Adviser: S. Watanabe

[sigeruw06:2008]

Hirotaka Hiramoto. Graduation Thesis: A New Function Obtained
by Utilizing Frobenius Method, University of Aizu, 2008.
Thesis Adviser: S. Watanabe

[sigeruw07:2008]

Akira Murakoshi. Graduation Thesis: A New System of Functions
Obtained by Frobenius Method, University of Aizu, 2008.
Thesis Adviser: S. Watanabe

2010 THE UNIVERSITY OF AIZU ALL RIGHTS RESERVED
