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Osaka Journal of Mathematics

Open Access, Project Euclid

Seiji Hiraba. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 337--359.Abstract:
In general, for a Markov process which does not have an invariant
measure, it is possible to realize a stationary Markov process
with the same transition probability by extending the probability
space and by adding new paths which are born at random times.
The distribution (which may not be a probability measure)
is called a Kuznetsov measure . By using this measure
we can construct a stationary Markov particle system, which
is called an equilibrium process with immigration .
This particle system can be decomposed as a sum of the original
part and the immigration part (see [2]). In the present paper,
we consider an absorbing stable motion on a half space
$H$, i.e., a time-changed absorbing Brownian motion on $H$
by an increasing strictly stable process. We first give the
martingale characterization of the particle system. Secondly,
we discuss the finiteness of the number of particles near
the boundary of the immigration part. (cf. [2], [3], [4].) 2014/04/11 - 00:57

Toshihisa Kubo. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 359--375.Abstract:
Barchini, Kable, and Zierau constructed a number of conformally
invariant systems of differential operators associated to
parabolic subalgebras of Heisenberg type. When they constructed
such systems of operators, two constants, which play a role
for the construction, were defined as the constants of proportionality
between two expressions. In this paper we give concrete and
uniform expressions for these constants. To do so we introduce
a new constant inspired by a formula on the Dynkin index of
a finite dimensional representation of a complex simple Lie
algebra. 2014/04/11 - 00:57

Kouji Yano. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 375--405.Abstract:
For a minimal diffusion process on $(a,b)$, any possible extension
of it to a standard process on $[a,b]$ is characterized by
the characteristic measures of excursions away from the boundary
points $a$ and $b$. The generator of the extension is proved
to be characterized by Feller's boundary condition. 2014/04/11 - 00:57

Tomoo Matsumura, W. Frank Moore. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 405--425.Abstract:
In this paper, we introduce the notion of a connected sum
$K_{1} \#^{Z} K_{2}$ of simplicial complexes $K_{1}$ and $K_{2}$,
as well as define a strong connected sum. Geometrically,
the connected sum is motivated by Lerman's symplectic cut
applied to a toric orbifold, and algebraically, it is motivated
by the connected sum of rings introduced by Ananthnarayan--Avramov--Moore
[1]. We show that the Stanley--Reisner ring of a connected
sum $K_{1} \#^{Z} K_{2}$ is the connected sum of the Stanley--Reisner
rings of $K_{1}$ and $K_{2}$ along the Stanley--Reisner ring
of $K_{1} \cap K_{2}$. The strong connected sum $K_{1} \#^{Z}
K_{2}$ is defined in such a way that when $K_{1}$, $K_{2}$
are Gorenstein, and $Z$ is a suitable subset of $K_{1} \cap
K_{2}$, then the Stanley--Reisner ring of $K_{1} \#^{Z} K_{2}$
is Gorenstein, by work appearing in [1]. We also show that
cutting a simple polytope by a generic hyperplane produces
strong connected sums. These algebraic computations can be
interpreted in terms of the equivariant cohomology of moment
angle complexes and toric orbifolds. 2014/04/11 - 00:57

Humihiko Watanabe. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 425--439.Abstract:
The Wirtinger integral is the uniformization to the upper
half plane $H$ of the hypergeometric function defined on the
complex projective line $\mathbb{P}^{1}$. In [5] we established
the transformation formulas of the Wirtinger integral for
the linear fractional transformations $\tau\to\tau+2$ and
$\tau\to -1/\tau$ with the aide of the theory of theta functions.
As a corollary we obtain the transformation formulas of the
Wirtinger integral for the linear fractional transformations
$\tau\to\tau+2$ and $\tau\to \tau/(-2\tau+1)$ which are identified
with generators of the principal congruence subgroup $\varGamma(2)$
modulo center. These formulas correspond to the monodromy
matrices of the hypergeometric function for generators of
the fundamental group of $\mathbb{P}^{1}$ minus three points.
The purpose of this paper is to generalize this result, that
is, we establish the transformation formula of the Wirtinger
integral for a general element $\left(\begin{smallmatrix}
a & b \\ c & d \end{smallmatrix}\right)$
of $\varGamma(2)$, which corresponds to a general monodromy
matrix of the hypergeometric function. 2014/04/11 - 00:57

Taizo Kanenobu. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 439--459.Abstract:
An $\SH(3)$-move is an unknotting operation on oriented knots
introduced by Hoste, Nakanishi and Taniyama. We consider
some relationships to other local moves such as a band surgery,
$\Gamma_{0}$-move, and $\Delta$-move, and give some criteria
for estimating the $\SH(3)$-unknotting number using the Jones,
HOMFLYPT, Q polynomials. We also show a table of $\SH(3)$-unknotting
numbers for knots with up to 9 crossings. 2014/04/11 - 00:57

Takanori Ayano. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 459--481.Abstract:
In this paper we consider a symplectic basis of the first
cohomology group and the sigma functions for algebraic curves
expressed by a canonical form using a finite sequence $(a_{1},
\ldots, a_{t})$ of positive integers whose greatest common
divisor is equal to one (Miura [13]). The idea is to express
a non-singular algebraic curve by affine equations of $t$
variables whose orders at infinity are $(a_{1}, \ldots, a_{t})$.
We construct a symplectic basis of the first cohomology group
and the sigma functions for telescopic curves, i.e., the curves
such that the number of defining equations is exactly $t-1$
in the Miura canonical form. The largest class of curves for
which such construction has been obtained thus far is $(n,
s)$-curves ([4] [15]), which are telescopic because they are
expressed in the Miura canonical form with $t=2$, $a_{1}=n$,
and $a_{2}=s$, and the number of defining equations is one. 2014/04/11 - 00:57

Daniel Daigle, Alejandro Melle-Hernándes. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 481--513.Abstract:
Given a unicuspidal rational curve $C \subset \mathbb{P}^{2}$
with singular point $P$, we study the unique pencil $\Lambda_{C}$
on $\mathbb{P}^{2}$ satisfying $C \in \Lambda_{C}$ and $\mathrm{Bs}(\Lambda_{C})=\{P\}$.
We show that the general member of $\Lambda_{C}$ is a rational
curve if and only if $\tilde{\nu}(C) \ge 0$, where $\tilde{\nu}(C)$
denotes the self-intersection number of $C$ after the minimal
resolution of singularities. We also show that if $\tilde{\nu}(C)
\ge0$, then $\Lambda_{C}$ has a dicritical of degree $1$.
Note that all currently known unicuspidal rational curves
$C \subset \mathbb{P}^{2}$ satisfy $\tilde{\nu}(C) \ge 0$. 2014/04/11 - 00:57

Tsuyoshi Itoh. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 513--537.Abstract:
Let $p$ be an odd prime, and $k_{\infty}$ the cyclotomic
$\mathbb{Z}_{p}$-extension of an abelian field $k$. For a
finite set $S$ of rational primes which does not include $p$,
we will consider the maximal $S$-ramified abelian pro-$p$
extension $M_{S} (k_{\infty})$ over $k_{\infty}$. We shall
give a formula of the $\mathbb{Z}_{p}$-rank of $\mathrm{Gal}(M_{S}
(k_{\infty})/k_{\infty})$. In the proof of this formula,
we also show that $M_{\{q\}} (k_{\infty})/L(k_{\infty})$ is
a finite extension for every real abelian field $k$ and every
rational prime $q$ distinct from $p$, where $L(k_{\infty})$
is the maximal unramified abelian pro-$p$ extension over $k_{\infty}$. 2014/04/11 - 00:57

Sergio Albeverio, Shuji Kawasaki. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 1--39.Abstract:
Wavelet coefficients of a process have arguments shift and
scale. It can thus be viewed as a time series along shift
for each scale. We have considered in the previous study general
wavelet coefficient domain estimators and revealed a localization
property with respect to shift. In this paper, we formulate
the localization property with respect to scale, which is
more difficult than that of shift. Two factors that govern
the decay rate of cross-scale covariance are indicated. The
factors are both functions of vanishing moments and scale-lags.
The localization property is then successfully applied to
formulate limiting variance in the central limit theorem associated
with Hurst index estimation problem of fractional Brownian
motion. Especially, we can find the optimal upper bound $J$
of scales $1, \ldots, J$ used in the estimation to be $J =
5$ by an evaluation of the diagonal component of the limiting
variance, in virtue of the scale localization property. 2014/04/09 - 15:52

H.R. Salimi Moghaddam. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 39--47.Abstract:
In this paper we consider invariant Matsumoto metrics which
are induced by invariant Riemannian metrics and invariant
vector fields on homogeneous spaces, and then we give the
flag curvature formula of them. Also we study the special
cases of naturally reductive spaces and bi-invariant metrics.
We end the article by giving some examples of geodesically
complete Matsumoto spaces. 2014/04/09 - 15:52

Huijie Qiao. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 47--67.Abstract:
In this paper we show that stochastic differential equations
with jumps and non-Lipschitz coefficients have $(\xi,W,N_{p})$-pathwise
unique strong solutions by the Euler--Maruyama approximation.
Moreover, the Euler--Maruyama discretisation has an optimal
strong convergence rate. 2014/04/09 - 15:52

Mayumi Nakayama. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 67--89.Abstract:
We shall introduce a notion of $S^{1}$-fibred nilBott tower .
It is an iterated $S^{1}$-bundle whose top space is called
an $S^{1}$-fibred nilBott manifold and the $S^{1}$-bundle
of each stage realizes a Seifert construction . The
$S^{1}$-fibred nilBott tower is a generalization of real
Bott tower from the viewpoint of fibration. In this note
we shall prove that any $S^{1}$-fibred nilBott manifold is
diffeomorphic to an infranilmanifold. According to
the group extension of each stage, there are two classes of
$S^{1}$-fibred nilBott manifolds which is defined as finite
type or infinite type . We discuss their properties. 2014/04/09 - 15:52

Anthony Bahri, Matthias Franz, Nigel Ray. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 89--121.Abstract:
For any weight vector $\chi$ of positive
integers, the weighted projective space $\mathbb{P}(\chi)$
is a projective toric variety, and has orbifold singularities
in every case other than standard projective space. Our principal
aim is to study the algebraic topology of $\mathbb{P}(\chi)$,
paying particular attention to its localisation at individual
primes $p$. We identify certain $p$-primary weight vectors
$\pi$ for which $\mathbb{P}(\pi)$ is homeomorphic to an iterated
Thom space, and discuss how any weighted projective space
may be reassembled from its $p$-primary parts. The resulting
Thom isomorphisms provide an alternative to Kawasaki's calculation
of the cohomology ring of $\mathbb{P}(\chi)$, and allow us
to recover Al Amrani's extension to complex $K$-theory. Our
methods generalise to arbitrary complex oriented cohomology
algebras and their dual homology coalgebras, as we demonstrate
for complex cobordism theory, the universal example. In particular,
we describe a fundamental class that belongs to the complex
bordism coalgebra of $\mathbb{P}(\chi)$, and may be interpreted
as a resolution of singularities. 2014/04/09 - 15:52

Yongnam Lee, Yongjoo Shin. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 121--141.Abstract:
In this paper we study involutions on minimal surfaces of
general type with $p_{g} = q = 0$ and $K^{2} = 7$. We focus
on the classification of the birational models of the quotient
surfaces and their branch divisors induced by an involution. 2014/04/09 - 15:52

Seiji Nishioka. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 141--161.Abstract:
Poincaré proved existence of meromorphic function solution
of a certain kind of system of multiplication formulae and
claimed that the class of those functions is new. In this
paper we exemplify Poincaré's meromorphic functions
being truly new in a rigorous sense. We prove that those functions
cannot be expressed rationally (nor algebraically) by solutions
of linear difference equations, the exponential function $\mathrm{e}^{x}$,
the trigonometric functions $\cos x$ and $\sin x$, the Weierstrass
function $\wp(x)$ and any other functions satisfying first
order algebraic difference equations, where the transforming
operator of the difference equations is one sending $y(x)$
to $y(2x)$, not to $y(x+1)$. 2014/04/09 - 15:52

Giuseppe Della Sala. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 161--171.Abstract:
On the basis of a result of Barrett [2], we show that members
of certain classes of abstract Levi flat manifolds with boundary,
whose Levi foliation contains a compact leaf with contracting,
flat holonomy, admit no $\mathit{CR}$ embedding as a hypersurface
of a complex manifold. In particular, it follows that the
foliation constructed in [6] is not embeddable. 2014/04/09 - 15:52

John Murray. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 171--179.Abstract:
M. Kiyota, T. Okuyama and T. Wada recently proved that each
$2$-block of a symmetric group $\Sigma_{n}$ contains a unique
irreducible Brauer character of height $0$. We present a more
conceptual proof of this result. 2014/04/09 - 15:52

Antonio Iannizzotto, Nikolaos S. Papageorgiou. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 179--203.Abstract:
We consider a parametric nonlinear elliptic equation driven
by the Dirichlet $p$-Laplacian. We study the existence, nonexistence
and multiplicity of positive solutions as the parameter $\lambda$
varies in $\mathbb{R}^{+}_{0}$ and the potential exhibits
a $p$-superlinear growth, without satisfying the usual in
such cases Ambrosetti--Rabinowitz condition. We prove a bifurcation-type
result when the reaction has ($p-1$)-sublinear terms near
zero (problem with concave and convex nonlinearities). We
show that a similar bifurcation-type result is also true,
if near zero the right hand side is ($p-1$)-linear. 2014/04/09 - 15:52

Atsushi Kanazawa, P.M.H. Wilson. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 203--215.Abstract:
Let $X$ be a Calabi--Yau threefold and $\mu$ the symmetric
trilinear form on the second cohomology group $H^{2}(X,\mathbb{Z})$
defined by the cup product. We investigate the interplay between
the Chern classes $c_{2}(X)$, $c_{3}(X)$ and the trilinear
form $\mu$, and demonstrate some numerical relations between
them. When the cubic form $\mu(x,x,x)$ has a linear factor
over $\mathbb{R}$, some properties of the linear form and
the residual quadratic form are also obtained. 2014/04/09 - 15:52

Mitsuhiko Imada. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 215--225.Abstract:
We are interested in periodic points on the boundaries of
rotation domains of rational functions. R. Pérez-Marco
showed that there are no periodic points on the boundaries
of Siegel disks having Jordan neighborhoods with certain properties
[12]. In this paper, we consider periodic points on the boundaries
of rotation domains under more weakly conditions. 2014/04/09 - 15:52

Honghai Liu. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 225--245.Abstract:
In this paper we obtain the $L^{p}$-boundedness
for the maximal functions and the singular integrals associated
to surfaces $(y,\phi(\lvert y\rvert))$ with rough kernels,
$1 < p < \infty$. The analogue estimate is also established
for the corresponding maximal singular integrals. 2014/04/09 - 15:52

Liang Zhao. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 245--257.Abstract:
In this paper, we study the gradient estimates for positive
solutions to the following nonlinear parabolic equation
\frac{\partial u}{\partial t} = \triangle_{f}u+cu^{-\alpha}
on complete noncompact manifolds with Bakry--Émery
Ricci curvature bounded below, where $\alpha$, $c$ are two
real constants and $\alpha > 0$. 2014/04/09 - 15:52

Zajj Daugherty, Arun Ram, Rahbar Virk. Source: Osaka Journal of Mathematics, Volume 51, Number 1, 257--285.Abstract:
The degenerate affine and affine BMW algebras arise naturally
in the context of Schur--Weyl duality for orthogonal and symplectic
Lie algebras and quantum groups, respectively. Cyclotomic
BMW algebras, affine Hecke algebras, cyclotomic Hecke algebras,
and their degenerate versions are quotients. In this paper
the theory is unified by treating the orthogonal and symplectic
cases simultaneously; we make an exact parallel between the
degenerate affine and affine cases via a new algebra which
takes the role of the affine braid group for the degenerate
setting. A main result of this paper is an identification of
the centers of the affine and degenerate affine BMW algebras
in terms of rings of symmetric functions which satisfy a ``cancellation
property'' or ``wheel condition'' (in the degenerate case,
a reformulation of a result of Nazarov). Miraculously, these
same rings also arise in Schubert calculus, as the cohomology
and K-theory of isotropic Grassmannians and symplectic loop
Grassmannians. We also establish new intertwiner-like identities
which, when projected to the center, produce the recursions
for central elements given previously by Nazarov for degenerate
affine BMW algebras, and by Beliakova--Blanchet for affine
BMW algebras. 2014/04/09 - 15:52

Tillmann Jentsch. Source: Osaka Journal of Mathematics, Volume 51, Number 2, 285--337.Abstract:
A submanifold of a Riemannian symmetric space is called parallel
if its second fundamental form is parallel. We classify parallel
submanifolds of the Grassmannian $\mathrm{G}^{+}_{2}(\mathbb{R}^{n+2})$
which parameterizes the oriented 2-planes of the Euclidean
space $\mathbb{R}^{n+2}$. Our main result states that every
complete parallel submanifold of $\mathrm{G}^{+}_{2}(\mathbb{R}^{n+2})$,
which is not a curve, is contained in some totally geodesic
submanifold as a symmetric submanifold. The analogous result
holds if the ambient space is the Riemannian product of two
Euclidean spheres of equal curvature or the non-compact dual
of one of the previously considered spaces. We also give a
characterization of parallel submanifolds with curvature isotropic
tangent spaces of maximal possible dimension in any symmetric
space of compact or non-compact type. 2014/04/09 - 15:52

Jong-Shenq Guo, Ying-Chin LinSource: Osaka J. Math., Volume 50, Number 3, 607--629.Abstract:
We study entire solutions for a discrete diffusive equation
with bistable convolution type nonlinearity. We construct
three different types of entire solutions. Each of these entire
solutions behaves as two traveling wavefronts connecting two
of those three equilibria as time approaches minus infinity.
Moreover, the first and second ones are solutions which behave
as two traveling wavefronts approaching each other from both
sides of $x$-axis. The behavior of the second one is like
the first one except it connects two different wavefronts.
The third one is a solution which behaves as two different
traveling wavefronts and one chases another from the same
side of $x$-axis. 2013/10/02 - 11:20

Keomkyo SeoSource: Osaka J. Math., Volume 50, Number 3, 631--641.Abstract:
We give a classification of the translation hypersurfaces
with constant mean curvature or constant Gauss--Kronecker
curvature in Euclidean space or Lorentz--Minkowski space.
We also characterize the minimal translation hypersurfaces
in the upper half-space model of hyperbolic space. 2013/10/02 - 11:20

Matteo Penegini, Francesco PolizziSource: Osaka J. Math., Volume 50, Number 3, 643--686.Abstract:
We construct a connected, irreducible component of the moduli
space of minimal surfaces of general type with $p_{g} = q
= 2$ and $K^{2} = 5$, which contains both examples given by
Chen--Hacon and the first author. This component is generically
smooth of dimension $4$, and all its points parametrize surfaces
whose Albanese map is a generically finite triple cover. 2013/10/02 - 11:20

Trinh Khanh Duy, Satoshi TakanobuSource: Osaka J. Math., Volume 50, Number 3, 687--713.Abstract:
The indicator function of the set of $k$-th power free integers
is naturally extended to a random variable $X^{(k)}({}\cdot{})$
on $(\hat{\mathbb{Z}},\lambda)$, where $\hat{\mathbb{Z}}$
is the ring of finite integral adeles and $\lambda$ is the
Haar probability measure. In the previous paper, the first
author noted the strong law of large numbers for $\{X^{(k)}({}\cdot{}+n)\}_{n=1}^{\infty}$,
and showed the asymptotics: $E^{\lambda}[(Y_{N}^{(k)})^{2}]
\asymp 1$ as $N \to \infty$, where $Y_{N}^{(k)}(x) := N^{-1/2k}
\sum_{n=1}^{N} (X^{(k)}(x+n) - 1/\zeta(k))$. In
the present paper, we prove the convergence of $E^{\lambda}[(Y_{N}^{(k)})^{2}]$.
For this, we present a general proposition of analytic number
theory, and give a proof to this. 2013/10/02 - 11:20

Xiaoli ChaoSource: Osaka J. Math., Volume 50, Number 3, 715--723.Abstract:
In this paper, by modifying Cheng--Yau's technique to complete
spacelike hypersurfaces in the de Sitter ($n+1$)-space $S_{1}^{n+1}(1)$,
we prove a rigidity under the hypothesis of the mean curvature
and the normalized scalar curvature being linearly related.
As a corollary, we have the Theorem 1.1 of [3]. 2013/10/02 - 11:20

Fatima Zohra MezeghraniSource: Osaka J. Math., Volume 50, Number 3, 725--747.Abstract:
In this paper we study and obtain some necessary and sufficient
conditions on the data for the existence, uniqueness of the
strict solution and maximal regularity for some second-order
differential equations with mixed boundary conditions whose
forcing term belongs to Hölder continuous spaces. A
few illustrative examples related to the interpolation theory
are discussed. 2013/10/02 - 11:20

Yamile Godoy, Marcos SalvaiSource: Osaka J. Math., Volume 50, Number 3, 749--763.Abstract:
Let $M$ be the three dimensional complete simply connected
manifold of constant sectional curvature $0,1$ or $-1$. Let
$\mathcal{L}$ be the manifold of all (unparametrized) complete
oriented geodesics of $M$, endowed with its canonical pseudo-Riemannian
metric of signature $(2,2)$ and Kähler structure $J$.
A smooth curve in $\mathcal{L}$ determines a ruled surface
in $M$. We characterize the ruled surfaces of $M$ associated
with the magnetic geodesics of $\mathcal{L}$, that is, those
curves $\sigma$ in $\mathcal{L}$ satisfying $\nabla_{\dot{\sigma}}\dot{\sigma}=J\dot{\sigma}$.
More precisely: a time-like (space-like) magnetic geodesic
determines the ruled surface in $M$ given by the binormal
vector field along a helix with positive (negative) torsion.
Null magnetic geodesics describe cones, cylinders or, in the
hyperbolic case, also cones with vertices at infinity. This
provides a relationship between the geometries of $\mathcal{L}$
and $M$. 2013/10/02 - 11:20

Ali Beldi, Nedra Belhaj Rhouma, Ali BenAmorSource: Osaka J. Math., Volume 50, Number 3, 765--793.Abstract:
We establish pointwise estimates for the ground states of
some classes of positivity preserving operators. The considered
operators are negatively perturbed (by measures) strongly
local Dirichlet operators. These estimates will be written
in terms of the Green's kernel of the considered operators,
whose existence will be proved. In many circumstances our
estimates are even sharp so that they recover known results
about the subject. The results will deserve to obtain large
time heat kernel estimates for the related operators. 2013/10/02 - 11:20

Hiroaki IshidaSource: Osaka J. Math., Volume 50, Number 3, 795--806.Abstract:
We show that any $(\mathbb{C}^{*})^{n}$-invariant stably complex
structure on a topological toric manifold of dimension $2n$
is integrable. We also show that such a manifold is weakly
$(\mathbb{C}^{*})^{n}$-equivariantly isomorphic to a toric
manifold. 2013/10/02 - 11:20

Farah Abbes, Mohamed HbaibSource: Osaka J. Math., Volume 50, Number 3, 807--816.Abstract:
The aim of this paper is to give families of Pisot and Salem
elements $\beta$ in $\mathbb{F}_{q}((x^{-1}))$ with the curious
property that the $\beta$-expansion of any rational series
in the unit disk $D(0,1)$ is purely periodic. In contrast,
the only known family of reals with the last property are
quadratic Pisot numbers $\beta>1$ that satisfy $\beta^{2}
= n\beta+1$ for some integer $n \geq 1$. 2013/10/02 - 11:20

Manfred G. Madritsch, Attila PethőSource: Osaka J. Math., Volume 50, Number 3, 817--825.Abstract:
Akiyama et al. [2] proved an asymptotic formula for the distribution
of CNS polynomials with fixed constant term. The objective
of the present paper is to improve that result by providing
an error term too. 2013/10/02 - 11:20

Hélène Esnault, Vasudevan SrinivasSource: Osaka J. Math., Volume 50, Number 3, 827--846.Abstract:
We show that, as in de Rham cohomology over the complex numbers,
the value of the entropy of an automorphism of the surface
over a finite field $\mathbb{F}_{q}$ is taken on the span
of the Néron--Severi group inside of $\ell$-adic cohomology. 2013/10/02 - 11:20

A. LaradjiSource: Osaka J. Math., Volume 50, Number 3, 591--605.Abstract:
Let $N \triangleleft G$ where $G$ is a finite group and let
$B$ be a $p$-block of $G$, where $p$ is a prime. A Brauer
character $\psi \in \mathop{\mathrm{IBr}}_{p}(B)$ is said to
be of relative height zero with respect to $N$ provided that
the height of $\psi$ is equal to that of an irreducible constituent
of $\psi_{N}$. Now assume $G$ is $p$-solvable. In this paper,
we count the number of relative height zero irreducible Brauer
characters of $B$ with respect to $N$ that lie over any given
$\varphi \in \mathop{\mathrm{IBr}}_{p}(N)$. As a consequence,
we show that if $D$ is a defect group of $B$ and $\hat{B}$
is the unique $p$-block of $NN_{G}(D)$ with defect group $D$
such that $\hat{B}^{G} = B$, then $B$ and $\hat{B}$ have equal
numbers of relative height zero irreducible Brauer characters
with respect to $N$. 2013/09/29 - 15:29

Yoshikata KidaSource: Osaka J. Math., Volume 50, Number 2, 309--337.Abstract:
For all but finitely many compact orientable surfaces, we
show that any superinjective map from the complex of separating
curves into itself is induced by an element of the extended
mapping class group. We apply this result to proving that
any finite index subgroup of the Johnson kernel is co-Hopfian.
Analogous properties are shown for the Torelli complex and
the Torelli group. 2013/06/25 - 10:58

Hatem HamrouniSource: Osaka J. Math., Volume 50, Number 2, 339--346.Abstract:
A finitely generated torsion free nilpotent group is called
an $\mathrsfs{F}$-group. To each $\mathrsfs{F}$-group $\Gamma$
there is associated a connected, simply connected nilpotent
Lie group $G_{\Gamma}$. Let TUF be the class of all $\mathrsfs{F}$-group
$\Gamma$ such that $G_{\Gamma}$ is totally unimodular. A group
in TUF is called TUF-group. In this paper, we are interested
in finding non-zero Euler characteristic on the class TUF
and therefore, on TUFF, the class of groups $K$ having a subgroup
$\Gamma$ of finite index in TUF. An immediate consequence
we obtain that any two isomorphic finite index subgroups of
a TUFF-group have the same index. As applications, we give
two results, the first is a generalization of Belegradek's
result, in which we prove that every TUFF-group is co-hopfian.
The second is a known result due to G.C. Smith, asserting
that every TUFF-group is not compressible. 2013/06/25 - 10:58