Recursos de colección
Project Euclid (Hosted at Cornell University Library) (192.977 recursos)
Journal of the Mathematical Society of Japan
Journal of the Mathematical Society of Japan
TAKEMURA, Kouichi
It is known that the Fuchsian differential equation which produces the sixth Painlevé equation corresponds to the Fuchsian differential equation with different parameters via Euler's integral transformation, and Heun's equation also corresponds to Heun's equation with different parameters, again via Euler's integral transformation. In this paper we study the correspondences in detail. After investigating correspondences with respect to monodromy, it is demonstrated that the existence of polynomial-type solutions corresponds to apparency of a singularity. For the elliptical representation of Heun's equation, correspondence with respect to monodromy implies isospectral symmetry. We apply the symmetry to finite-gap potentials and express the monodromy...
FUKUI, Toshizumi; HASEGAWA, Masaru; NAKAGAWA, Kouichi
We investigate the contact types of a regular surface in the Euclidean 3-space $\mathbb{R}^3$ with right circular cylinders. We present the conditions for existence of cylinders with $A_1$, $A_2$, $A_3$, $A_4$, $A_5$, $D_4$, and $D_5$ contacts with a given surface. We also investigate the kernel field of $A_{\ge 3}$-contact cylinders on the surface. This is defined by a cubic binary differential equation and we classify singularity types of its flow in the generic context.
DUMMIGAN, Neil
We show how many of the congruences between Ikeda lifts and non-Ikeda lifts, proved by Katsurada, can be reduced to congruences involving only forms of genus 1 and 2, using various liftings predicted by Arthur's multiplicity conjecture. Similarly, we show that conjectured congruences between Ikeda–Miyawaki lifts and non-lifts can often be reduced to congruences involving only forms of genus 1, 2 and 3.
POHL, Anke D.
It is well-known that reduced smooth orbifolds and proper effective foliation Lie groupoids form equivalent categories. However, for certain recent lines of research, equivalence of categories is not sufficient. We propose a notion of maps between reduced smooth orbifolds and a definition of a category in terms of marked proper effective étale Lie groupoids such that the arising category of orbifolds is isomorphic (not only equivalent) to this groupoid category.
SAMBALE, Benjamin
In this note we give applications of recent results coming mostly from the third paper of this series. It is shown that the number of irreducible characters in a $p$-block of a finite group with abelian defect group $D$ is bounded by $|D|$ (Brauer's $k(B)$-conjecture) provided $D$ has no large elementary abelian direct summands. Moreover, we verify Brauer's $k(B)$-conjecture for all blocks with minimal non-abelian defect groups. This extends previous results by various authors.
LÖH, Clara
Bounded-cohomological dimension of groups is a relative of classical cohomological dimension, defined in terms of bounded cohomology with trivial coefficients instead of ordinary group cohomology. We will discuss constructions that lead to groups with infinite bounded-cohomological dimension, and we will provide new examples of groups with bounded-cohomological dimension equal to 0. In particular, we will prove that every group functorially embeds into an acyclic group with trivial bounded cohomology.
CHOI, Suyoung; PARK, Boram; PARK, Seonjeong
Given a simple graph $G$, the graph associahedron $P_G$ is a convex polytope whose facets correspond to the connected induced subgraphs of $G$. Graph associahedra have been studied widely and are found in a broad range of subjects. Recently, S. Choi and H. Park computed the rational Betti numbers of the real toric variety corresponding to a graph associahedron under the canonical Delzant realization. In this paper, we focus on a pseudograph associahedron which was introduced by Carr, Devadoss and Forcey, and then discuss how to compute the Poincaré polynomial of the real toric variety corresponding to a pseudograph associahedron...
WADA, Masaki
We give a precise behavior of spectral functions for symmetric stable processes applying the asymptotic expansion of resolvent kernels.
IBUKIYAMA, Tomoyoshi; KITAYAMA, Hidetaka
In this paper, we give an explicit dimension formula for the spaces of Siegel paramodular cusp forms of degree two of squarefree level. As an application, we propose a conjecture on symplectic group version of Eichler–Jacquet–Langlands type correspondence. It is a generalization of the previous conjecture of the first named author for prime levels published in 1985, where inner twists corresponding to binary quaternion hermitian forms over definite quaternion algebras were treated. Our present study contains also the case of indefinite quaternion algebras. Additionally, we give numerical examples of $L$ functions which support the conjecture. These comparisons of dimensions and...
MATSUMOTO, Keiji; SASAKI, Takeshi; TERASOMA, Tomohide; YOSHIDA, Masaaki
We study an Appell hypergeometric system $E_2$ of rank four which is reducible, and show that its Schwarz map admits geometric interpretations: the map can be considered as the universal Abel–Jacobi map of a 1-parameter family of curves of genus 2.
GRAFAKOS, Loukas; MIYACHI, Akihiko; VAN NGUYEN, Hanh; TOMITA, Naohito
We provide characterizations for boundedness of multilinear Fourier multiplier operators on Hardy or Lebesgue spaces with symbols locally in Sobolev spaces. Let $H^q(\mathbb R^n)$ denote the Hardy space when $0 \lt q \le 1$ and the Lebesgue space $L^q(\mathbb R^n)$ when $1 \lt q \le \infty$. We find optimal conditions on $m$-linear Fourier multiplier operators to be bounded from $H^{p_1}\times \cdots \times H^{p_m}$ to $L^p$ when $1/p=1/p_1+\cdots +1/p_m$ in terms of local $L^2$-Sobolev space estimates for the symbol of the operator. Our conditions provide multilinear analogues of the linear results of Calderón and Torchinsky [1] and of the bilinear results...
CAI, Li
In this paper we give a necessary and sufficient condition for a (real) moment-angle complex to be a topological manifold. The cup and cap products in a real moment-angle manifold are studied. Consequently, the cohomology ring (with coefficients integers) of a polyhedral product by pairs of disks and their bounding spheres is isomorphic to that of a differential graded algebra associated to $K$ and the dimensions of the disks.
ATSUJI, Atsushi
We discuss the value distribution of Borel measurable maps which are holomorphic along leaves of complex laminations. In the case of complex lamination by hyperbolic Riemann surfaces with an ergodic harmonic measure, we have a defect relation appearing in Nevanlinna theory. It gives a bound of the number of omitted hyperplanes in general position by those maps.
BENNETT, Jonathan; BEZ, Neal; JEAVONS, Chris; PATTAKOS, Nikolaos
We provide a comprehensive analysis of sharp bilinear estimates of Ozawa–Tsutsumi type for solutions $u$ of the free Schrödinger equation, which give sharp control on $|u|^2$ in classical Sobolev spaces. In particular, we generalise their estimates in such a way that provides a unification with some sharp bilinear estimates proved by Carneiro and Planchon–Vega, via entirely different methods, by seeing them all as special cases of a one-parameter family of sharp estimates. The extremal functions are solutions of the Maxwell–Boltzmann functional equation and hence Gaussian. For $u^2$ we argue that the natural analogous results involve certain dispersive Sobolev norms; in...
SAJI, Kentaro; UMEHARA, Masaaki; YAMADA, Kotaro
In a previous work, the authors introduced the notion of ‘coherent tangent bundle’, which is useful for giving a treatment of singularities of smooth maps without ambient spaces. Two different types of Gauss–Bonnet formulas on coherent tangent bundles on $2$-dimensional manifolds were proven, and several applications to surface theory were given.
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Let $M^n$ ($n\ge 2$) be an oriented compact $n$-manifold without boundary and $TM^n$ its tangent bundle. Let $\mathcal{E}$ be a vector bundle of rank $n$ over $M^n$, and $\phi:TM^n\to \mathcal{E}$ an oriented vector bundle homomorphism. In this paper, we show that one of these two Gauss–Bonnet formulas can be generalized...
AKIYAMA, Shigeki; CAALIM, Jonathan
We study a family of piecewise expanding maps on the plane, generated by composition of a rotation and an expansive similitude of expansion constant $\beta$. We give two constants $B_1$ and $B_2$ depending only on the fundamental domain that if $\beta$ > $B_1$ then the expanding map has a unique absolutely continuous invariant probability measure, and if $\beta$ > $B_2$ then it is equivalent to $2$-dimensional Lebesgue measure. Restricting to a rotation generated by $q$-th root of unity $\zeta$ with all parameters in $\mathbb{Q}(\zeta,\beta)$, the map gives rise to a sofic system when $\cos(2\pi/q) \in \mathbb{Q}(\beta)$ and $\beta$ is a...
KOBA, Hajime
This paper studies the stability of a stationary solution of the Navier–Stokes system in $3$-D exterior domains. The stationary solution is called a Leray's stationary solution if the Dirichlet integral is finite. We apply an energy inequality and maximal $L^p$-in-time regularity for Hilbert space-valued functions to derive the decay rate with respect to time of energy solutions to a perturbed Navier–Stokes system governing a Leray's stationary solution.
HARTMANN, Luiz; SPREAFICO, Mauro
We give an explicit formula for the $L^2$ analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the analytic torsion of the cone is the finite part of the limit obtained collapsing one of the boundaries, of the ratio of the analytic torsion of the frustum to a regularising factor. We show that the regularising factor comes from the set of the non square integrable eigenfunctions of the Laplace Beltrami operator on the cone.
TANIGUCHI, Naoki; PHUONG, Tran Thi; DUNG, Nguyen Thi; AN, Tran Nguyen
This paper studies the question of when the Rees algebras associated to arbitrary filtration of ideals are sequentially Cohen–Macaulay. Although this problem has been already investigated by [CGT], their situation is quite a bit of restricted, so we are eager to try the generalization of their results.
MATSUZAKI, Katsuhiko
For a regularly locally compact topological space $X$ of $\rm T_0$ separation axiom but not necessarily Hausdorff, we consider a map $\sigma$ from $X$ to the hyperspace $C(X)$ of all closed subsets of $X$ by taking the closure of each point of $X$. By providing the Thurston topology for $C(X)$, we see that $\sigma$ is a topological embedding, and by taking the closure of $\sigma(X)$ with respect to the Chabauty topology, we have the Hausdorff compactification $\widehat X$ of $X$. In this paper, we investigate properties of $\widehat X$ and $C(\widehat X)$ equipped with different topologies. In particular, we consider...