Recursos de colección
TSUTSUMI, Yukihiro
It is known that any genus one hyperbolic knot in the 3-dimensional sphere admits at most
seven mutually disjoint and mutually non-parallel genus one Seifert surfaces. In this
note, it is shown that for any integers $g>1$ and $n>0$, there is a hyperbolic knot
of genus $g$ in the 3-dimensional sphere which bounds $n$ mutually disjoint and mutually
non-parallel genus $g$ Seifert surfaces.
KOBAYASHI, Masanori
A duality of weight systems which corresponds to Batyrev's toric mirror symmetry is
given. It is shown that Arnold's strange duality for exceptional unimodal singularities
reduces to this duality.
GAMBIOLI, Andrea
We discuss the interaction between the geometry of a quaternion-K\"{a}hler manifold $M$
and that of the Grassmannian $\mathbb{G}_3(\mathfrak{g})$ of oriented $3$-dimensional
subspaces of a compact Lie algebra $\mathfrak{g}$. This interplay is described mainly
through the moment mapping induced by the action of a group $G$ of quaternionic isometries
on $M$. We give an alternative expression for the imaginary quaternionic endomorphisms
$I,J,K$ in terms of the structure of the Grassmannian's tangent space. This relies on a
correspondence between the solutions of respective twistor-type equations on $M$ and
$\mathbb{G}_3(\mathfrak{g})$.
TAHARA, Hidetoshi
The paper deals with the following nonlinear partial differential equation $(t
\partial/\partial t)^m u = F (t,x, \{(t \partial/\partial t)^j (\partial/\partial
x)^{\alpha} u\}_{j+\alpha \leq m, j
HIROTA, Yuji
We introduce notions of Morita equivalence for both twisted symplectic groupoids and
integrable twisted Poisson manifolds without terms of groupoids. We show that two
integrable twisted Poisson manifolds are Morita equivalent if and only if their associated
groupoids are Morita equivalent as twisted symplectic groupoids.
KOJIMA, Michitaka
One of Silverman's results gives a relationship between the number of integral points and
the rank of elliptic curves over $\mathbb{Q}$. This paper generalizes this result for all
imaginary quadratic fields.
ROSSMAN, Wayne; SULTANA, Nahid
We prove a theorem about elliptic operators with symmetric potential functions, defined
on a function space over a closed loop. The result is similar to a known result for a
function space on an interval with Dirichlet boundary conditions. These theorems provide
accurate numerical methods for finding the spectra of those operators over either type of
function space. As an application, we numerically compute the Morse index of constant mean
curvature tori of revolution in the unit $3$-sphere $\mathbb{S}^3$, confirming that every
such torus has Morse index at least five, and showing that other known lower bounds for
this Morse index are close to optimal.
NAKANO, Tetsuo
We show that the moduli space $\mathcal{M}_{g,1}^N$ of pointed algebraic curves of genus
$g$ with a given numerical semigroup $N$ is an irreducible rational variety if
$N$ is generated by less than five elements for low genus ($ g \leq 6$) except one case.
As a corollary to this result, we get a computational proof of the rationality of the
moduli space $\mathcal{M}_{g,1}$ of pointed algebraic curves of genus $g$ for $1 \leq g
\leq 3$. If $g \leq 5$, we also have that $\mathcal{M}_{g,1}^N$ is an irreducible rational
variety for any semigroup $N$ except two cases. It is known that such a moduli space
$\mathcal{M}_{g,1}^N$ is...
KAWAZOE, Takeshi
We obtain some uncertainty inequalities for the Jacobi transform $\hat
f_{\alpha,\beta}(\lambda)$, where we suppose $\alpha, \beta\in\mathbb{R}$ and
$\rho=\alpha+\beta+1\geq 0$. As in the Euclidean case, analogues of the local and global
uncertainty principles hold for $\hat f_{\alpha,\beta}$. In this paper, we shall obtain a
new type of an uncertainty inequality and its equality condition: When $\beta\leq 0$ or
$\beta\leq\alpha$, the $L^2$-norm of $\hat f_{\alpha,\beta}(\lambda)\lambda$ is estimated
below by the $L^2$-norm of $\rho f(x)(\cosh x)^{-1}$. Otherwise, a similar inequality
holds. Especially, when $\beta>\alpha+1$, the discrete part of $f$ appears in the
Parseval formula and it influences the inequality. We also apply these uncertainty
principles to the spherical Fourier transform on $SU(1,1)$....
KIMIZUKA, Maro; SASAKI, Ryuji
In this article, we define $M$-matrices of the ternary Golay code and build fundamental
properties of the ternary Golay code on $M$-matrices. Moreover, using four $M$-matrices of
the ternary Golay code, we give order three elements, in the Mathieu group $M_{12}$, which
generate $M_{11}$ and $M_{12}$.
KURIBAYASHI, Izumi
NIITSUMA, Yasuhiro
We give explicit formulas of the number of rational points and those of the congruence
zeta functions for the hyperelliptic curves over a finite field defined by affine
equations $y^2=x^6+a$, $y^2=x^{12}+a$ and $y^2=x(x^6+a)$.
KOUFOGIORGOS, Themis; TSICHLIAS, Charalambos
This paper analytically describes the local geometry of a generalized $(\kappa,\mu
)$-manifold $M(\eta,\xi,\phi,g)$ with $\kappa<1$ which satisfies the condition ``the
function $\mu$ is constant along the integral curves of the characteristic vector field
$\xi$''. This class of manifolds is especially rich, since it is possible to construct in
$R^3$ two families of such manifolds, for any smooth function $\kappa$ ($\kappa<1$) of
one variable. Every family is determined by two arbitrary functions of one variable.
ENOLSKII, Victor; MATSUTANI, Shigeki; ÔNISHI, Yoshihiro
This article shows explicit relations between fractional expressions of Schottky-Klein
type for hyperelliptic $\sigma$-functions and a product of differences of the algebraic
coordinates on each stratum of a natural stratification in a hyperelliptic Jacobian.
SUZUKI, Taro; TAKAKURA, Tatsuru
We consider the symplectic quotient for a direct product of several integral coadjoint
orbits of $SU(3)$ and investigate its symplectic volume. According to a fundamental
theorem for symplectic quotients, it is equivalent to studying the dimension of the
trivial part in a tensor product of several irreducible representations for $SU(3)$, and
its asymptotic behavior. We assume that either all of coadjoint orbits are flag manifolds
of $SU(3)$, or all are complex projective planes. As main results, we obtain an explicit
formula for the symplectic volume in each case.
WONGSAWASDI, Jaipong; YAMAGUCHI, Masaru
We shall consider IBVP to a nonlinear equation of suspended string with uniform density
to which a nonlinear time-independent outer force works. We shall show the existence of
time-global weak solutions of IBVP. To prove our result we shall use the function spaces
defined by [Ya1], and apply the method due to Sattinger [Sat] based on the potential-well
and the Galerkin method.
YAZAWA, Hikaru
For any given integers $d_0, d_1 \ge 1$, let $\mathcal{F}$ be the family of polynomial
maps $f$ such that $f$ has a fixed point at the origin, and moreover has just two distinct
critical points 1 and $c_f\neq 1$ of multiplicies $d_0$ and $d_1$, respectively. For the
central hyperbolic component $\mathcal{H}$ of $\mathcal{F}$, a monodromy map on
$\mathcal{H}$ is obtained by Branner-Hubbard deformations. We show that for any given
$\lambda$ with $0 < |\lambda| < 1$ and for any given integer $n \ge 1$, the
monodromy map transitively acts on the family of all polynomial maps $f\in \mathcal{H}$
with $f^{\prime}(0) = \lambda$ and $f^{\circ n}(c_f) = 1$.
GOYAL, Ritu
The aim of this paper is to extend the domain of polygamma function from the set of
complex numbers to the set of bicomplex numbers. We also discuss integral representation,
recurrence relation, multiplication formula and reflection formula for this function.
TANIGUCHI, Taiji
The Turaev-Viro invariants are topological invariants of closed 3-manifolds. In this
paper, we give a formula of the Turaev-Viro invariants of all orientable closed Seifert
fibered manifolds. Our formula is based on a new construction of special spines of all
orientable closed Seifert fibered manifolds and the``gluing lemma'' of topological quantum
field theory. By using our formula, we get sufficient conditions of coincidence of the
Turaev-Viro invariants of orientable closed Seifert fibered manifolds.
SANDER, Torsten
In this work a precise condition for the singularity of a circuit distance power
$C_n^{(d)}$ is derived. Namely, either $n$ and $d$ are not relatively prime or the order
of 2 in $d+1$ is strictly smaller than in $n$. It is also shown that the simple
eigenvalues of circuit distance powers are contained in $\{-2,0,2d\}$, generalizing a
well-known result for circuits. Further, the nullity of $C_n^{(d)}$ is calculated.