Recursos de colección
Project Euclid (Hosted at Cornell University Library) (191.996 recursos)
Osaka Journal of Mathematics
Osaka Journal of Mathematics
Lemmens, Bas; Roelands, Mark
We characterise the affine span of the midpoints sets, $\mathcal{M}(x,y)$, for Thompson's metric on symmetric cones in terms of a translation of the zero-component of the Peirce decomposition of an idempotent. As a consequence we derive an explicit formula for the dimension of the affine span of $\mathcal{M}(x,y)$ in case the associated Euclidean Jordan algebra is simple. In particular, we find for $A$ and $B$ in the cone positive definite Hermitian matrices that \[ \dim({\rm aff}\, \mathcal{M}(A,B))=q^2, \] where $q$ is the number of eigenvalues $\mu$ of $A^{-1}B$, counting multiplicities, such that \[ \mu\neq \max\{\lambda_+(A^{-1}B),\lambda_-(A^{-1}B)^{-1}\}, \] where $\lambda_+(A^{-1}B):=\max \{\lambda\colon \lambda\in\sigma(A^{-1}B)\}$...
Bauval, Anne; Hayat, Claude
If $p$ is a prime number, the cohomology ring with coefficients in $\mathbb{Z}/p\mathbb{Z}$ of an orientable or non-orientable Seifert manifold $M$ is obtained using a $\Delta$-simplicial decomposition of $M$. Several choices must be made before applying the Alexander-Whitney formula. The answers are given in terms of the classical cellular generators.
Ooto, Tomohiro
In this paper, we study Diophantine exponents $w_n$ and $w_n ^{*}$ for Laurent series over a finite field. Especially, we deal with the case $n=2$, that is, quadratic approximation. We first show that the range of the function $w_2-w_2 ^{*}$ is exactly the closed interval $[0,1]$. Next, we estimate an upper bound of the exponent $w_2$ of continued fractions with low complexity partial quotients.
Yamada, Takumi
In this paper, we consider a relation of non-degenerate closed $2$-forms and complex structures on compact real parallelizable nilmanifolds.
Sakurai, Yohei
We study Riemannian manifolds with boundary under a lower Ricci curvature bound, and a lower mean curvature bound for the boundary. We prove a volume comparison theorem of Bishop-Gromov type concerning the volumes of the metric neighborhoods of the boundaries. We conclude several rigidity theorems. As one of them, we obtain a volume growth rigidity theorem. We also show a splitting theorem of Cheeger-Gromoll type under the assumption of the existence of a single ray.
Berdinsky, Dmitry; Vyatkin, Yuri
We find analogues of the Willmore functional for each of the Thurston geometries with $4$--dimensional isometry group such that the CMC--spheres in these geometries are critical points of these functionals.
Nakamura, Hiroaki; Sakugawa, Kenji; Wojtkowiak, Zdzisław
The Coleman-Ihara formula expresses Soule's $p$-adic characters restricted to $p$-local Galois group as the Coates-Wiles homomorphism multiplied by $p$-adic $L$-values at positive integers. In this paper, we show an analogous formula that $\ell$-adic polylogarithmic characters for $\ell=p$ restrict to the Coates-Wiles homomorphism multiplied by Coleman's $p$-adic polylogarithms at any roots of unity of order prime to $p$.
Ishitani, Hiroshi; Ishitani, Kensuke
It is known that the Perron--Frobenius operators of piecewise expanding $\mathcal{C}^2$ transformations possess an asymptotic periodicity of densities. On the other hand, external noise or measurement errors are unavoidable in practical systems; therefore, all realistic mathematical models should be regarded as random iterations of transformations. This paper aims to discuss the effects of randomization on the asymptotic periodicity of densities.
Di Scala, Antonio J.; Vittone, Francisco
We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a $CR$-submanifold of a complex space form. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space. In case of a totally real submanifold we give two results about reduction of codimension. We describe explicitly the action of the normal holonomy in the case in which the totally real submanifold is contained in a totally real totally geodesic submanifold. In such a case we prove the compactness of the normal holonomy group.
Reschke, Paul
We classify two-dimensional complex tori admitting automorphisms with positive entropy in terms of the entropies they exhibit. For each possible positive value of entropy, we describe the set of two-dimensional complex tori admitting automorphisms with that entropy.
Tsuji, Shunsuke
We introduce a Lie algebra associated with a non-orientable
surface, which is an analogue for the Goldman Lie algebra
of an oriented surface. As an application, we deduce an explicit
formula of the Dehn twist along an annulus simple closed curve
on the surface as in Kawazumi--Kuno [4], [5] and Massuyeau--Turaev
[7].
Ishikawa, Isao
Bertolini--Darmon and Mok proved a formula of the second derivative
of the two-variable $p$-adic $L$-function of a modular elliptic
curve over a totally real field along the Hida family in terms
of the image of a global point by some $p$-adic logarithm
map. The theory of $p$-adic indefinite integrals and $p$-adic
multiplicative integrals on $p$-adic upper half planes plays
an important role in their work. In this paper, we generalize
these integrals for $p$-adic measures which are not necessarily
$\mathbb{Z}$-valued, and prove a formula of the second derivative
of the two-variable $p$-adic $L$-function of an abelian variety
of $\mathrm{GL}(2)$-type associated to a Hilbert modular form of weight
2.
Mizusawa, Yasushi
Based on the method of Boston and Leedham-Green et al. for
computing the Galois groups of tamely ramified $p$-extensions
of number fields, this paper gives a large family of triples
of odd prime numbers such that the maximal totally real $2$-extension
of the rationals unramified outside the three prime numbers
has the Galois group of order $512$ and derived length $3$.
This family is characterized arithmetically, and the explicit
presentation of the Galois group by generators and relations
is also determined completely.
Sung, Chanyoung
Using $G$-monopole invariants, we produce infinitely many
exotic non-free actions of $\mathbb{Z}_{k}\oplus H$ on some
connected sums of finite number of $S^{2}\times S^{2}$, $\mathbb{C}P_{2}$,
$\overline{\mathbb{C}P}_{2}$, and $K3$ surfaces, where $k\geq
2$, and $H$ is any nontrivial finite group acting freely on
$S^{3}$.
Yang, Shihai; Zhao, Tiehong
In this note we establish a new discreteness criterion for
a non-elementary group $G$ in $\mathit{SL}(2, \mathbb{C})$. Namely,
$G$ is discrete if all the two-generator subgroups are discrete,
where one generator is a non-trivial element $f$ in $G$, and
the other is in the conjugacy class of $f$.
Nagasato, Fumikazu; Tran, Anh T.
We show that all twist knots and certain double twist knots
are minimal elements for a partial ordering on the set of
prime knots. The keys to these results are presentations of
their character varieties using Chebyshev polynomials and
a criterion for irreducibility of a polynomial of two variables.
These give us an elementary method to discuss the number of
irreducible components of the character varieties, which concludes
the result essentially.
Grindstaff, Gillian Roxanne; Nelson, Sam
We define enhancements of the quandle counting invariant for
knots and links with a finite labeling quandle $Q$ embedded
in the quandle of units of a Lie algebra $\mathfrak{a}$ using
Lie ideals. We provide examples demonstrating that the enhancement
is stronger than the associated unenhanced counting invariant
and image enhancement invariant.
Morimoto, Masaharu
Let $G$ be a finite group. The Smith equivalence for real
$G$-modules of finite dimension gives a subset of real representation
ring, called the primary Smith set. Since the primary Smith
set is not additively closed in general, it is an interesting
problem to find a subset which is additively closed in the
real representation ring and occupies a large portion of the
primary Smith set. In this paper we introduce an additively
closed subset of the primary Smith set by means of smooth
one-fixed-point $G$-actions on spheres, and we give evidences
that the subset occupies a large portion of the primary Smith
set if $G$ is an Oliver group.
Park, Jeongho
It is shown that when a real quadratic integer $\xi$ of fixed
norm $\mu$ is considered, the fundamental unit $\varepsilon_{d}$
of the field $\mathbb{Q}(\xi) = \mathbb{Q}(\sqrt{d})$ satisfies
$\log \varepsilon_{d} \gg (\log d)^{2}$ almost always. An
easy construction of a more general set containing all the
radicands $d$ of such fields is given via quadratic sequences,
and the efficiency of this substitution is estimated explicitly.
When $\mu = -1$, the construction gives all $d$'s for which
the negative Pell's equation $X^{2} - d Y^{2} = -1$ (or more
generally $X^{2} - D Y^{2} = -4$) is soluble. When $\mu$ is
a prime, it gives all of the real quadratic fields in...
Hao, Yanlong; Liu, Xiugui; Sun, Qianwen
In this paper, we describe the homotopy type of the homotopy
fixed point sets of $S^{3}$-actions on rational spheres and
complex projective spaces, and provide some properties of
$S^{1}$-actions on a general rational complex.