List of Dissertation Abstract（Information Media and Environment Sciences Environmental Mathematical Analysis Course）
NameSupervisor

TitleAbstract
The detection of seismo-electromagnetic abnormal phenomena before earthquakes is one of earthquake

Ririe UNOTSU

Naoko
ARIMITSU

Multifractal Analysis of ULF

prediction techniques. In this paper, we show the multifractal characteristics of detrended fluctuations ofGeomagnetic Variations before

ULF(Ultra-Low-Frequency) noise data before the Guam(1993) earthquake by using Multifractal Probability

Earthquakes

Density Function Analysis. In addition, the seismo-electromagnetic signature of the earthquake wassuccessfully detected.
An edge-coloring of a graph is an assignment of a color to each edge of the graph with adjacent edges

Toshiki ABE

Atsuhiro
NAKAMOTO

The signature of edge-colorings

distinct colors. As an open problem, list-edge-coloring conjecture is known and partially solved by using theand list-edge-colorings of regularsignature of edge-colorings. Moreover, the signature of planar graphs has already obtained in another thesis.

graphs on the projective plane

In this paper, we obtain the signature of edge-colorings on the projective plane and have an application tothe list-coloring conjecture.

Resolution of singularity points
Takahiro ISHII

Atsushiusing to two-dimension nomal

NOMA

Toric vareities and Newton
diagram

From the process of blow-up of the curve C_ (a, b): (x ^ a + y ^ b = 0) (a and b are natural numbers) having
a singular point on the affine plane, it is determined by the curve C_ (a, b) We showed that a dual Newton
diagram of a Newton diagram can be made into a nonsingular fan by Euclid's algorithm.
It is well-known that every 3-connected planar graph is uniquely embeddable on the sphere, but it is not

Kengo ENAMI

SeiyaNEGAMI

Re-embedding Structures of 3connected 3-regular planar graphs
into the torus

uniquely embeddable on any surface other than the sphere. In this paper, we classify structures ofembeddings of 3-connected 3-regular planar graphs on the torus. This enables us to determine whether a 3connected 3-regular graph embedded on the torus is planar or not. Moreover, we can establish a polynomial
delay algorithm for enumerating all the inequivalent embeddings of a given 3-connected 3-regular planargraph on the torus.

This paper considers the influence of high school students' preschool propensity and career selection onKeitaJunji

KONDOUNUKATAThe influence of high school

career formation process and aims to obtain knowledge about the influence of mathematics on career

students' preference for schoolingformation. In addition to the findings obtained from related studies such as those earning basic

and course selection on careermathematical power gains higher income over the lifetime, it is clear that mathematics has influenced theformation processcareer formation process such as not only the income but also the desired work, among other students who
are good at mathematics and poor mathematics, there is a difference in the process of forming a career.

The Classification of Singular
Ayako

AtsushiFibres of the Double Covering ofSASAKINOMACurves Which Have Six Branch
Points on Projective LineSaaya TOKITA

Atsuhiro
NAKAMOTO

The number of diagonal flip intriangulations on the projectiveplane

The family of curves which I studied is defined by y^2-g(x,t)=0(g(x,t) is an expression of degree 5 of x). I
introduced (i)the curve defined by g(x,t)=0 is nonsingular, (ii)the curve has a double point and (iii) twodouble points.
I proved that any two triangulations on the projective plane with n vertices can be transformed into eachother by at most 19𝑛𝑛−106 diagonal flips, up to isotopy. This problem was considered by Nakamoto andMori in 2005, but they had given a wrong proof to the problem. So I decided to correct it and succeeded ingiving a correct proof.
CFD analysis of the motion of a Japanese traditional rain chain gutter in multiphase flow has been

TakuyaMinoruNAGATSUKASHIRAZAKI

Numerical Analysis of the Motionof the Multiple Connected Objects
in Multiphase Flow.

performed. This paper mainly discusses the relationship between the motion of the chain gutter and mass,water discharge, connecting method (constraint condition), or the number of the connections. It is found thatproperties of the motion depend on water discharge, and there is water discharge in which the chain gutter ishardly moved. The influence of inertia is large when the water discharge is small, and the influence of thefluid force becomes large when the water discharge is large.
Caccetta-Haggkvist conjecture says that every digraph with n vertices and minimum out-degree r contains aJunki HIGA

Atsuhiro
NAKAMOTO

cycle of length at most ⌈n/r⌉. To solve the special case of conjecture, Seymour proposed the second

neighborhood conjecture. It says that every antisymmetric digraph has a vertex whose second neighborhood
is not smaller than the first one. This conjecture is still open, but it was partly solved by assuming certain
conditions. Especially, the second neighborhood conjecture was solved for digraphs with r-out-regular andconnectivity r-1. In this paper, we improve the former result for connectivity by adding a certain condition.

In algebraic geometry and number theory, p-divisible groups are important research objects. In this paper,

Nobuhiro

ShushiHIGUCHIHARASHITAOn the codimension-one
specializations of minimal pdivisible groups

we study specializations of minimal p-divisible groups, which play an important role in the theory of pdivisible groups. A minimal p-divisible group is associated with a line graph called Newton polygon. We
classify codimension-one specializations (the most generic specializations) of a minimal p-divisible group,
when its Newton polygon consists of two segments, and in a special case we determine the Newton
polygons of these specializations.
A dominating set of a graph G =( V, E) is a subset D of V such that every vertex not in D is adjacent to someSuguruAtsuhiro

HIRANUMA

NAKAMOTO

vertex in D. The domatic number d(G) of G is the maximum positive integer k such that V can beOn domatically full graphpartitioned into k pairwise disjoint dominating sets. By the definition, the domatic number is less than andequal to the minimum degree plus one, and a graph is domatically full if G attain the equality. In my masterthesis, I characterize the Cartesian product between path and tree that is domatically full.
A graph is said to be distinguishing k-colorable if it has a proper k-coloring such that no automorphism

Masayuki

Seiya

FUJITA

NEGAMI

Distinguishing 3-colorings of 3-other than the identity map preserves the colors. Such a coloring is called a distinguishing k-coloring. It hasconnected 3-regular maps on thebeen already known that almost all 3-regular maps on the surface have distinguishing 4-colorings with color

sphere4 used at most once. In this paper, we shall show any truncated 3-regular connected graphs, any truncatedpolyhedrons and any fullerene graphs have a distinguishing coloring without color 4.

Classification of normal
YusukeAtsushisingularity of dimension 2 by theMASUDA

NOMA

maximal ideal cycle andthe fundamental cycle

In affine space of dimension 3, I've researched about correspondence of coefficients of the maximal ideal
cycle and the fundamental cycle obtained from resolution of the singularity at origin on curved surface
defined by some equation. In particular, I supposed that if the equation was specific form, the singularity
would be classified a fixed type, so I calculated the coefficients of the cycles and classified the singularities
concretely through changing the orders of the monomials in the equation and so on.
Three dimensional CFD (Computational Fluid Dynamics) analysis of self-propelled fish swimming near

Three Dimensional Numericalwater surface and jumping has been performed. The present studies showed mainly two things. One is thatYuki

MinoruAnalysis of Efficient Swimming

behavior of swimming near water surface is classified into three patterns, (1) slightly slower, (2) slower, (3)MATSUSHITASHIRAZAKIand Jumping of Fish near Water

finally slightly faster, than swimming in the water and the behavior can be expected with the Froude

Surfacenumber defined as the ratio of the flow inertia to gravity. The other is that power consumption required forswimming with jumping is totally less than for swimming without jumping.

It is known that any polygon on the plane can be triangulated by straight line segment and any twoYuri

AtsuhiroMANAGO

NAKAMOTO

Flipping Edges in
Quadrangulations of evenpolygons

triangulations of a polygon can be transformed each other by flipping edges. In this thesis, we consider thesame problem for quadrangulations. A k-spiral polygon is an even polygon on the plane such that thenumber of intervals of consecutive concave vertices is at most k. We proved that any 1-spiral polygon canbe quadrangulated by straight line segments and any two quadrangulations of a 1-spiral polygon can betransformed each other by flipping edges.