List of Dissertation Abstract（Information Media and Environment Sciences
NameHiroki YAGISupervisor
SeiyaNEGAMI

Environmental Mathematical Analysis Course）

Title

Abstract
The theme of this study is Bringing the movie to reality by interaction. This paper describes the system

Please fill in here the English title[Interactive Film] and [Sound Surround] that was developed based on the this theme and feeling the occurs
to the viewer by the systems.
I define two reductions a 4-contradiction and a twin-contraction for even triangulation on a surface.
It is well known that these reductions preserve some properties of graphs.

Yoshihiro

Atsuhiro

Generating even triangulations on

The complete lists of minimal even triangulations for the sphere, the projective plane and the torus withASAYAMA

NAKAMOTO

the Klein bottle

respect to these reductions have already determined.
In my master's thesis, I make the complete list of minimal even triangulations of the Klein bottle and provesome applications by cheking the list.
Let {0,…,n-1} be a set of n colors. A coloring of a triangulation G is called an n-triad coloring if any

Yumiko OHNO

Seiya

Triad colorings of trianuglationsNEGAMI

on closed surfaces

adjacent vertices of G get different colors and three consecutive colors appear on any face of G. In thispaper, we shall show that a triangulation G has an n-triad coloring for n > 4 if and only if G has a 3-coloringby notions of algebraic topology. Moreover, we shall show that the coloring expanded an n-triad coloring
becomes a 3-coloring or an n-triad coloring by changing labels of colors suitably.
An embedding is drawing a graph on a closed surface with no crossing edge. When does a triangulation ona closed surface have re-embeddings? In previous researches, the re-embedding structures have been

Shota OGANO

Seiya

Automatic generation of re-classified by manpower partially. We shall create a computer program to classify the re-embedding

NEGAMI

embedding structures ofstructures automatically, and then classify the re-embedding structures of a triangulation on the Klein bottle

triangulations on closed surfaces

by using it. Furthermore, we shall classify concrete structures composing the re-embeddings of atriangulation on the torus and the projective plane considering a notion called “re-embedding pairs”.

Generationg thorem for minor
Yuichiro

Atsuhiro

relations of quadrangulations

KawasakiNakamoto

with minimum degree at least 3
on the sphere

Let Q3 be the set of quadrangulations on the sphere with minimum degree 3.Nakamoto proved that anygraph G∈Q3 can be reduced to the cube , only through G∈Q3 by a sequence of three reductions.In mytalk, we prove that every graph G∈Q3 can be reduced to the cube by 13 reductions, only through Q3,preserving the minor relation of graphs, that is, in each step when we obtain a new graph H from G by oneof the reductions, H is always a minor of G.

TatukiAtsushi

The Weierstrass points on aKOBAYASHINOMAdouble cover of algebraic curves

Mitsuya SATO

AtsushiNOMA

Gröbner basis of the ideal of theembedding of an elliptic curve in a
projective space

We calculate the bases of the linear system of divisors nP where P is a Weierstrass point of double cover of anon-singular curve of genus 3 over the complex number field. And we give two method in the process of thecalcuration .
It is well-known that the ideal which defines the image of an elliptic curve embedded in a projective spaceby the complete linear system of line bundle is generated by quadratic homogeneous polynomials. In thisstudy, we calculated this ideal and proved that quadratic gröbner basis can be required by determining
term order of them in general odd dimension cases.
I suggested a new method that is applied to "the Dispartion characteristics of fractional Brownian motion

Yuto

Naoko

SANOMA

ARIMITSU

Analysis Characteristics of Fractal
Time Series and Time Series
Modeling(fBm)" to estimate a fractal dimension of time series. I found that this new method is highly precision as aconventional " Higuchi method" and needs less time to estimate it than conventional method. A behavior offBm is depending on a fractal dimension. I found a quantitative relation between a fractal dimension of fBm
and parameters of ARIMA model. ARIMA model is one of the model of a prediction of time series . I
applied this relation to forecast changes in the future, and I gained appropriate result.
Recently, in problems of colorings of graphs, many kinds of special colorings have been studied. Thedistinguishing coloring is one of such special colorings. A coloring c of a graph G is called a distinguishing

Taku TOJO

SeiyaDistinguishing colorings of locally coloring if there is no color-preserving automorphism of G other than identity map. In this paper, weNEGAMI

planar graphs with six colors

consider distinguishing colorings of some non-planar graphs. As results of that, we construct 6distinguishing colorings of locally planar graphs which use color 6 only for one vertex and determine theminimum number of colors required for distinguishing colorings of 4-regular quadrangulations on the torus.
CFD(Computational Fluid Dynamics) analysis of growth and large deformation of a soap bubble formed by

Kenta

MinoruTOMARUSHIRAZAKICFD analysis of growth and large
deformation of a soap bubble byblowing air

thin liquid film by blowing air has been performed. This paper mainly discusses the effect of inlet velocity
and surface tension on the thin liquid film behavior. The numerical results have demonstrated mainly twothings. One is that a soap bubble is oscillating while expanding although inlet velocity is constant and its
oscillation depends on magnitude of inlet velocity and surface tension. The other is that variation in inlet
velocity can cause larger deformation of bubble.

We considered the distribution of the branch points and feasible monodromy groups of the nonsingular
AsatoNakamura

Atushi Noma

Feasible Monodromy Groups ofprojective plane curve of degree 4 over the field of complex numbers. We paid attention to the combinations

The Projective Plane Curve ofof numbers and the degree of branch points and examained those 19 cases. We proved feasible monodromy

Degree 4groups of that curve correspond with one of five groups, the symmetric group, the alternating group, and thedihedral group of degree 4, among other things.
Let L be the splitting field of F(y) = y2n-2f(z)yn+g(z) over the field of rational functions with one variable z

KouheiAtsushiThe Galois group of F(y)=y^(2n)-over the complex number field ℂ, ℂ(z). We proved the Galois group of the field extension L/ℂ(z) isHARAGUCHI

NOMA

2f(z)y^n+g(z).

isomorphism to the group which has a similar operation to the semidirect product group of ℤ/nℤ×ℤ/nℤ andℤ/2ℤ.

RyoAtsuhiro

MATSUKAWA NAKAMOTO

N-flips in triangulations with twoodd degree vertices

We prove that any two triangulations G and G′ on the sphere with exactly two odd degree vertices can betransformed into each other by two local transformations, called an N-flip and a P2-flip, if |V (G)| = |V (G′)|.
Moreover, we consider about triangulations on the projective pane with exactly two odd degree vertices.
It is a basic research on the minimum absolute value method regression analysis. In this research, wepropose new indices to evaluate the fitness of linear regression model. By using this new index, it became

Takanobu

Junji

Coefficient of determination of the possible to compare with the least squares model for the fit of the regression analysis. In addition, by using

MURAOKA

NUKATA

minimum absolute value method

the minimum absolute value regression analysis in combination with this new index, it is possible to expect
higher outlier detection power than when applying the conventional least squares method determination
coefficient.
It is pointed out that there are a lot of high school students who can’t find interest ormotivation in mathematics learning. In order to solve this problem, some studies have been

YoshiroSeiya

WATABENEGAMI

Investigation into values ofreviewed from the standpoint of teacher education. I investigate the values of mathematics inmathematics in sciencescience college students from the following three points of view, “how to approach to thecollege students

problem”, “the structure of consciousness to mathematics” “learning motivation and learningview”. The results of the investigation revealed that there are a lot of students withinsufficient qualities as a mathematical teacher.