1.
The Dirac Operator on Ultrahyperbolic Manifolds - Eelbode, David; Sommen, Frank
In this paper we consider a projective model for the time- and spacelike ultrahyperbolic unit balls in the orthogonal space $\mR^{m,m}$. By means of an associated principal fibre bundle, a Dirac operator on these mani\-folds is defined and its fundamental solution is constructed (in case $m \in 2\mN + 1$) with the aid of generalized Riesz distributions. Using the method of descent, we then construct fundamental solutions for the Dirac operator on time- or spacelike ultrahyperbolic unit balls in spaces of signature $(m,q)$ and $(p,m)$ respectively (with $p,q < m$).
2.
Numerical Methods for Chemically Reacting Fluid Flow Computation under Low-Mach Number Approximation - Arima, Toshiyuki
A mathematical model of environmental fluid is presented
to describe fluid flow motions with large density variations.
Moreover the associated numerical methods are discussed.
The model of environmental fluid is formulated as an unsteady low-Mach number flow
based on the compressible Navier-Stokes equations.
For low-Mach number flows, the acoustic effects are assumed to be weak relative to the advection effects.
Under this assumption, detailed acoustic effects can be removed from governing equations.
The low-Mach number formulation thus enables numerical flow analysis
with a projection methodology that uses high-order accurate upwind difference of the convection terms
with a time step restricted solely by an advection Courant-Friedrichs-Lewy (CFL) condition.
The algorithm presented...
3.
On $\frak{m}$-Full Powers of Parameter Ideals - MATSUOKA, Naoyuki
Let $Q$ be a parameter ideal in a Noetherian local
ring $A$ with the maximal ideal $\frak{m}$. Then $A$ is a
regular local ring and
$\frak{m}/Q$ is cyclic, if $\rm{depth}\ A > 0$ and $Q^n$ is
$\frak{m}$-full for some integer $n \geq 1$. Consequently, $A$
is a regular local ring and all the powers of
$Q$ are integrally closed in
$A$ once
$Q^n$ is integrally closed for some $n \geq 1$.
4.
Splittability of Stellar Singular Fiber with Three Branches - Ahara, Kazushi; Takamura, Shigeru
We are concerned with the splittability problem of degenerations with
stellar singular fibers.
In this paper we give an interesting splitting criterion
for such degenerations:
if a stellar singular fiber has exactly three branches,
and its central component (core) is the projective line,
then this degeneration admits a splitting deformation.
5.
Application of Local Linking to Asymptotically Linear Wave Equations with Resonance - Miyajima, Shizuo; Tanaka, Mieko
Existence of a time-periodic solution to a non-linear
wave equation with resonance is established by a variational method.
We consider the $2\pi$-periodic weak solution to a
wave equation $\Box u(x,t)=h(x,t,u(x,t))$ of
space dimension 1, where $h(x,t,\xi)$ is asymptotically linear in $\xi$
both as $\xi\to0$ or $\xi\to\infty$,
with the co-efficient as $\xi\to\infty$ belonging to $\sigma(\Box)$.
It is proved that there are some
cases, where the difference of $h(t,x,\xi)$ from
its linear approximation is not bounded, that guarantee the existence of
a non-trivial weak solutions.
The proof is based on local linking theory and $({\it WPS})^*$ condition
for the existence of a
non-trivial critical point of a functional.
7.
Antisymmetrically Deformed Quantum Homogeneous Spaces - Kamimura, Shingo
We construct dual objects for quantum complex projective spaces
as quantum homogeneous spaces of quantum unitary groups,
in which the deformation parameters are antisymmetric matrices.
We prove the splitting formula and the nondegeneracy of the
Hochschild dimensions for the quantum complex projective spaces.
8.
Surfaces in $S^{n}$ with Prescribed Gauss Map - Tanaka, Ayako
Let $G$ be a $C^{\infty }$-mapping from a connected Riemann surface $M$ into
the complex quadric $Q_{n-1}$ in the $n$-dimensional complex
projective space.
We give a condition for the existence of a surface in the
$n$-dimensional
Euclidean unit sphere $S^{n}$
such that the Gauss map is $G$.
Under this condition, if $M$ is a torus, there exists a
surface
in $S^{n}$ such that the Gauss map is $G$. We also show that for a connected
Riemann surface $M$
there exists an immersion $X:M\rightarrow RP^{n}$ such
that a neighborhood of each point of $X(M)$ is
covered by a surface in $S^{n}$ with prescribed Gauss map $G$ where
$RP^{n}$ is the $n$-dimensional real projective space.
9.
Principal Functions for High Powers of Operators - Ch?, Muneo; Huruya, Tadasi; Kim, An Hyun; Li, Chunji
For an operator $T$ with some trace class condition, let $g_{T^n}$ and $g_{{T^n}}^P$ be the principal functions related
to
the Cartesian decomposition $T^n=X_n+iY_n$ and the polar decomposition $T^n = U_n|T^n|$ for a positive integer
$n$, respectively. In this paper, we study properties of $g_{T^n}$ and $g_{T^n}^P$ and invariant subspaces of $T^n.$
10.
On DS-diagrams for 3-manifolds of Heegaard Genus 2 - Endoh, Mariko
The block number $Bl(M)$ introduced in our previous paper
is a new topological invariant of a closed orientable 3-manifold $M$
which estimates a combinatorial complexity of $M$ just like the Heegaard genus $HG(M)$.
In our previous paper, we have shown an inequality $HG(M) \leq Bl(M)$ for any $M \ne S^2 \times S^1$.
In this paper, we will show that $Bl(M)=HG(M)$ for any $M$ with $HG(M)=2$
and moreover that $Bl(M) \leq 4$ for any $M$ with $HG(M)=3$.
11.
A Generalization of the Hankel Transform and the Lorentz Multipliers - Sato, Enji
Let $\phi$ be a bounded function on $[0,\infty)$ continuous except on a null set, and $\phi_{\epsilon}(\xi)=\phi(\epsilon\xi)\ (\epsilon>0).$ Also let $\tilde{T}_{\epsilon}$ be the operator on Jacobi series such that $(\tilde{T}_{\epsilon}f)^{\wedge}(n)=\phi_{\epsilon}(n)\hat{f}(n)\ (n\in{\bf Z})$, where $\hat{f}(n)$ is the coefficient of Jacobi expanstion of $f$, and ${\cal H}_{\alpha}(Tf)(\xi)$ be defined by $\phi(\xi){\cal H}_{\alpha}f(\xi)\ (\xi\in(0,\infty))$, where ${\cal H}_{\alpha}f$ is the modified Hankel transform of $f$ with order $\alpha$. Then the author [7] proved that if the operator norm of $\tilde{T}_{\epsilon}$ is uniformly bounded for all $\epsilon>0$, $T$ is a bounded operator on the modified Hankel transforms in the Lorentz spaces, and we have the maximal...
13.
Compact Quotients of Large Domains in a Complex Projective 3-space - Kato, Masahide
In a complex projective 3-space, we consider a domain with a projective line.
If there is a compact non-singular quotient of the domain
and the quotient manifold admits a non-constant meromorphic function, then
the domain is dense in the projective 3-space and its complement is properly
contained in a finite union of complex hypersurfaces and
a set with Hausdorff dimension not more than two.
Further, if the complement admits a certain fiber space structure, then
it is either a disjoint union of two projective lines, a projective line, or
an empty set.
14.
Two-bridge links with strong triviality - Torisu, Ichiro
In this article, we study strong triviality of two-bridge links. We prove that every (non-trivial) two-bridge link can not be strongly $n$-trivial for $n\geq 1$.
16.
A Cohomology ($p$+1) Form Canonically Associated with Certain Codimension-$q$ Foliations on a Riemannian Manifold - Baditoiu, Gabriel; Escobales, Richard H.; Ianus, Stere
Let $(M^{n},g)$ be a closed, connected,
oriented, $C^{\infty}$, Riemannian, $n$-manifold with a transversely oriented foliation
$\mathbb{F}$. We show that if $\lbrace X,Y \rbrace$ are basic vector fields, the leaf
component of $[X,Y]$, $\Cal{V}[X,Y]$, has vanishing leaf divergence whenever
${\kappa}\wedge \chi_{\mathbb{F}}$ is a closed (possibly zero) de Rham cohomology $(p+1)$-form. Here
${\kappa}$ is the mean curvature one-form of the foliation $\mathbb{F}$ and
$\chi_{\mathbb{F}}$ is its characteristic form. In the codimension-$2$ case,
${\kappa}\wedge \chi_{\mathbb{F}}$ is closed if and only if ${\kappa}$
is horizontally closed. In certain restricted cases, we give necessary and sufficient conditions for
${\kappa}\wedge{\chi_{\mathbb{F}}}$ to be harmonic. As an application,
we give a characterization of when certain closed $3$-manifolds
are locally...
18.
Mehler Kernel Approach to Tempered Distributions - DHUNGANA, Bishnu P.
Using the Mehler kernel $E(x,\xi,t)$,
we show that the solution of the Hermite heat equation
$({\partial}_{t} - \triangle
+ |x|^{2})U(x,t) = 0$ in ${\BR}^{n}\times (0,T)$ satisfying
$\sup_{x\in{\BR}^{n}}|U(x,t)|\leq C(1+ t^{-N})
$ for some constants $C$ and $N$ can be expressed as
$U(x,t) = \langle u(\xi), E(x,\xi,t)\rangle$ for unique $u$ in
${\mathcal S}^{'}({\BR}^{n})$. This is a parallel result
with the one in (Theorem 1.2, T. Matsuzawa, {\it A calculus approach to
hyperfunctions} III, Nagoya Math. J. {\bf 118} (1990), 133--153).
Moreover we represent
the tempered distributions
as initial values of solution of the Hermite
heat equation and apply it to
generalize a theorem by Strichartz [Theorem 3.2,
Trans. Amer. Math. Soc. {\bf 338} (1993), 971--979]
in the space...
19.
A Remark on the Mordell-Weil Rank of Elliptic Curves over the Maximal Abelian Extension of the Rational Number Field - KOBAYASHI, Emi
In this paper, we study the Mordell-Weil ranks of elliptic curves defined over
the maximal abelian extension of the rational number field, assuming several conjectures
on the Hasse-Weil $L$-functions.
We prove that an elliptic curve defined over an abelian field with odd degree
has infinite rank over the maximal abelian extension of the rational number field.
This result gives affirmative evidence for \lq the largeness' (in the sense of Pop) of the maximal abelian extension of
the rational number field.
1.
