bluuebunny/crossref_metadata_2025 huggingface dataset:
On the comparison theorem for elementary irregular D-modules
Authors: Sabbah Claude
Published: July 2016

Let U be a smooth quasi-projective variety over C and let f be a regular function on U. Let DU be the sheaf of algebraic differential operators on U and let M be a regular holonomic DU-module: here, regular means that there exists some smooth compactification X of U and some extension of M as a DX-module which is regular holonomic on X (one also may avoid the use of a smooth compactification to define regularity, see [17]).
On the analytic structure of certain infinite dimensional Teicmüller spaces
Authors: Ohsawa Takeo
Published: July 2016

It is well known since long time that quasiconformally different finite Riemann surfaces give rise to biholomorphically nonequivalent Teichmüller spaces except for a few obvious cases (cf. [R], [E-K]). This is deduced as an application of Royden’s theorem asserting that the Teichmüller metric is equal to the Kobayashi metric. For the case of infinite Riemann surfaces, however, it is still unknown whether or not the corresponding result holds, although it has been shown by F. Gardiner [G] that Royden’s theorem is also valid for the infinite dimensional Teichmüller spaces. On the other hand, recent activity of several mathematicians shows that the infinite dimensional Teichmüller spaces are interesting objects of complex analytic geometry (cf. [Kru], [T], [N], [E-K-K]). Therefore, based on the generalized form of Royden’s theorem, one might well look for further insight into Teichmüller spaces by studying the above mentioned nonequivalence question.
On Dirichlet series whose coefficients are class numbers of binary quadratic forms
Authors: Datskovsky Boris A.
Published: July 2016

For an integer d > 0 (resp. d < 0) let hd denote the number of Sl2(Z)-equivalence classes of primitive (resp. primitive positive-definite) integral binary quadratic forms of discriminant d. For where t and u are the smallest positive integral solutions of the equation t2 − du2 = 4 if d is a non-square and εd = 1 if d is a square.
Classification of non-Gorenstein Q-Fano d-folds of Fano index greater than d − 2
Authors: Sano Takeshi
Published: July 2016

A d-dimensional normal projective variety X is called a Q-Fano d-fold if it has only terminal singularities and if the anti-canonical Weil divisor – Kx is ample. The singularity index I = I(X) of X is defined to be the smallest positive integer such that – IKX is Cartier. Then there is a positive integer r and a Cartier divisor H such that – IKX ~ rH. Taking the largest number of such r, we call r/I the Fano index of X.
Transformation Groups with (n-1)-Dimensional Orbits on Non-Compact Manifolds
Authors: Nagano Tadashi
Published: July 2016

When a Lie group G operates on a differentiable manifold M as a Lie transformation group, the orbit of a point p in M under G, or the G-orbit of p, is by definition the submanifold G(p) = {G(p); g∈G}. The purpose of this paper is to characterize the structure of a non-compact manifold M such that there exists a compact orbit of dimension (n — 1), n — dim M, under a connected Lie transformation group G, which is assumed to be compact or an isometry group of a Riemannian metric on M.
The characterizations of Laplacians in white noise analysis
Authors: He Sheng-Wu , Wang Jia-Gang , Yao Rong-Qin
Published: July 2016

The Laplacians form a class of the most important differential operators in white noise analysis. The goal of this paper is to give their characterizations. Our main tools are the Fock expansions of operators in terms of integral kernel operators and rotation-invariance. In Section 1, the fundamental setting of white noise analysis is introduced briefly. In Section 2, integral kernel operators and the Fock expansions of operators are given. The characterization theorems for number operator, Gross-Laplacian and Euler operator are given in Sections 3, 4 and 5 respectively.
A note on the mean value theorem for special homogeneous spaces
Authors: Morishita Masanori , Watanabe Takao
Published: July 2016

Let G be a connected linear algebraic group and X an algebraic variety, both defined over Q, the field of rational numbers. Suppose that G acts on X transitively and the action is defined over Q. Suppose that the set of rational points X(Q) is non-empty. Choosing x ∈ X(Q) allows us to identify G/Gx and X as varieties over Q, there Gx is the stabilizer of x.
Differential Galois theory of infinite dimension
Authors: Umemura Hiroshi
Published: July 2016

This paper is the second part of our work on differential Galois theory as we promised in [U3]. Differential Galois theory has a long history since Lie tried to apply the idea of Abel and Galois to differential equations in the 19th century (cf. [U3], Introduction). When we consider Galois theory of differential equation, we have to separate the finite dimensional theory from the infinite dimensional theory. As Kolchin theory shows, the first is constructed on a rigorous foundation. The latter, however, seems inachieved despite of several important contributions of Drach, Vessiot,…. We propose in this paper a differential Galois theory of infinite dimension in a rigorous and transparent framework. We explain the idea of the classical authors by one of the simplest examples and point out the problems.
On p-adic Dedekind sums
Authors: Kudo Aichi
Published: July 2016

For positive integers h, k and m, the higher-order Dedekind sums are defined
by
A local Hopf lemma for solutions of the one dimensional heat equation
Authors: Suzuki Noriaki
Published: July 2016

The boundary behavior of solutions of the heat equation (temperature functions) is investigated. It is proved that a temperature function is identically equal to zero if it vanishes of finite order at some lateral boundary point where it attains a local minimum.
Solutions of the second and fourth Painlevé equations, I
Authors: Umemura Hiroshi , Watanabe Humihiko
Published: July 2016

A rigorous proof of the irreducibility of the second and fourth Painlevé equations is given by applying Umemura’s theory on algebraic differential equations ([26], [27], [28]) to the two equations. The proof consists of two parts: to determine a necessary condition for the parameters of the existence of principal ideals invariant under the Hamiltonian vector field; to determine the principal invariant ideals for a parameter where the principal invariant ideals exist. Our method is released from complicated calculation, and applicable to the proof of the irreducibility of the third, fifth and sixth equation (e.g. [32]).
The norm estimate of the difference between the Kac operator and the Schrödinger semigroup: A unified approach to the nonrelativistic and relativistic cases
Authors: Ichinose Takashi , Takanobu Satoshi
Published: July 2016

An Lp operator norm estimate of the difference between the Kac operator and the Schrödinger semigroup is proved and used to give a variant of the Trotter product formula for Schrödinger operators in the Lp operator norm. The method of the proof is probabilistic based on the Feynman-Kac formula. The problem is discussed in the relativistic as well as nonrelativistic case.
On the Local Theory of Continuous Infinite Pseudo Groups I
Authors: Kuranishi Masatake
Published: July 2016

The local theory of continuous (infinite) pseudo-groups of transformations was originated by S. Lie, and developed by himself, F. Engel, E. Vessiot, E. Cartan, etc. In the beginning, the definition was not clear and we can find several different definitions in the papers of pioneers. In 1902, E. Cartan introduced a definition using his theory of exterior differential systems and made an extensive study in his series of papers [1], [2], and [31 The writer will adopt his definition in this series of papers. A continuous pseudo-group of transformations is, roughly speaking, a collection of real (or complex) analytic homeo-morphisms of domains in a real (or complex) euclidean space, which is closed under the operations of composition and inverse, and which forms the general solutions of a system of partial differential equations.
Uniqueness problem with truncated multiplicities in value distribution theory
Authors: Fujimoto Hirotaka
Published: July 2016

In 1929, H. Cartan declared that there are at most two meromorphic functions on ℂ which share four values without multiplicities, which is incorrect but affirmative if they share four values counted with multiplicities truncated by two. In this paper, we generalize such a restricted H. Cartan’s declaration to the case of maps into PN (ℂ). We show that there are at most two nondegenerate meromorphic maps of ℂn into PN(ℂ) which share 3N + 1 hyperplanes in general position counted with multiplicities truncated by two. We also give some degeneracy theorems of meromorphic maps into PN (ℂ) and discuss some other related subjects.
Density measure of rational points on Abelian varieties
Authors: Waldschmidt Michel
Published: July 2016

Letbe a simple Abelian variety of dimensiongover ℚ, and let ℓ be the rank of the Mordell-Weil group(ℚ). Assume ℓ ≥ 1. A conjecture of Mazur asserts that the closure of(ℚ) into(ℝ) for the real topology contains the neutral component(ℝ)0of the origin. This is known only under the extra hypothesisℓ ≥ g2- g +1. We investigate here a quantitative refinement of this question: for each given positiveh, the set of points in(ℚ) of Néron-Tate height≤ his finite, and we study how these points are distributed into the connected component(ℝ)0. More generally we consider an Abelian varietyAover a number fieldKembedded in ℝ, and a subgroupΓof(K) of sufficiently large rank. The effective result of density we obtain relies on an estimate of Diophantine approximation, namely a lower bound for linear combinations of determinants involving Abelian logarithms.
-problem on weakly 1-complete Kähler manifolds
Authors: Kazama Hideaki , Takayama Shigeharu
Published: July 2016

We consider a problem whether Kodaira’s -Lemma holds on weakly 1-complete Kähler manifolds or not. This problem was proposed by S. Nakano. We prove that the Lemma holds for some class of complex quasi-tori ℂn/Γ, and it does not hold for the other class of them. Every complex quasi-tori is weakly 1-complete and complete Kähler. Then we get a negative answer for the above problem.
Sous-algèbres birégulières d’une algèbre de Kac-Moody-Borcherds
Authors: Bardy Nicole
Published: July 2016

Let be a Kac-Moody-Borcherds algebra on a field associated to a symetrizable matrix and with Cartan subalgebra . Let be an ad -invariant subalgebra such that the restriction to of the standard bilinear form is nondegenerate. We show that the root system Ψ of is a subsystem according to [Ba] of . Moreover, if a subsystem Ω satisfies some conditions (i.e. Ω is “réduit et presque-clos”) of Ψ, we construct inside of a Kac-Moody-Borcherds algebra with root system Ω.

Let k be a subfield of . We prove similar results in the case of an action of a finite group of k-semi-automorphisms. In particular, we obtain a generalization to the Kac-Moody case of a result by Borel and Tits.

Let be an almost-k-split form of a Kac-Moody algebra. We construct a Kac-Moody k-algebra with root system similar to the system of (save on some multiples of certain roots).
On some 3-dimensional CR submanifolds inS6
Authors: Hashimoto Hideya , Mashimo Katsuya
Published: July 2016

We give two types of 3-dimensional CR-submanifolds of the 6-dimensional sphere. First we study whether there exists a 3-dimensinal CR-submanifold which is obtained as an orbit of a 3-dimensional simple Lie subgroup ofG2. There exists a unique (up toG2) 3-dimensional CR-submanifold which is obtained as an orbit of reducible representations ofSU(2) onR7. As orbits of the subgroup which corresponds to the irreducible representation ofSU(2) onR7, we obtained 2-parameter family of 3-dimensional CR-submanifolds. Next we give a generalization of the example which was obtained by K. Sekigawa.
Hooke’s law in statistical manifolds and divergences
Authors: Henmi Masayuki , Kobayashi Ryoichi
Published: July 2016

The concept of the canonical divergence is defined for dually flat statistical manifolds in terms of the Legendre transform between dual affine coordinates. In this article, we introduce a new two point function defined for any triple (g,∇, ∇*) of a Riemannian metric g and two affine connections ∇ and ∇*. We show that this interprets the canonical divergence without refering to the existence of special coordinates (dual affine coordinates) but in terms of only classical mechanics concerning ∇- and ∇*-geodesics. We also discuss the properties of the two point function and show that this shares some important properties with the canonical divergence defined on dually flat statistical manifolds.
An analogue of Pitman’s 2M – Xtheorem for exponential Wiener functionals: Part I: A time-inversion approach
Authors: Matsumoto Hiroyuki , Yor Marc
Published: July 2016

Letbe a one-dimensional Brownian motion with constant driftµ∈ R starting from 0. In this paper we show that

gives rise to a diffusion process and we explain how this result may be considered as an extension of the celebrated Pitman’s2M - Xtheorem. We also derive the infinitesimal generator and some properties of the diffusion processand, in particular, its relation to the generalized Bessel processes.
Iteration of Analytic Multifunctions
Authors: Klimek Maciej
Published: July 2016

It is shown that iteration of analytic set-valued functions can be used to generate composite Julia sets in CN. Then it is shown that the composite Julia sets generated by a finite family of regular polynomial mappings of degree at least 2 in CN, depend analytically on the generating polynomials, in the sense of the theory of analytic set-valued functions. It is also proved that every pluriregular set can be approximated by composite Julia sets. Finally, iteration of infinitely many polynomial mappings is used to give examples of pluriregular sets which are not composite Julia sets and on which Markov’s inequality fails.
An Analogue of Pitman’s 2M — X Theorem for Exponential Wiener Functionals Part II: The Role of the Generalized Inverse Gaussian Laws
Authors: Matsumoto Hiroyuki , Yor Marc
Published: July 2016

In Part I of this work, we have shown that the stochastic process Z(µ) defined by (8.1) below is a diffusion process, which may be considered as an extension of Pitman’s 2M — X theorem. In this Part II, we deduce from an identity in law partly due to Dufresne that Z(µ) is intertwined with Brownian motion with drift µ and that the intertwining kernel may be expressed in terms of Generalized Inverse Gaussian laws.
L2(ℝn) boundedness for the commutators of convolution operators
Authors: Hu Guoen
Published: July 2016

The commutators of convolution operators are considered. By localization and Fourier transform estimates, a sufficient condition such that these commutators are bounded on L2(ℝn) is given. As applications, some new results about the L2(ℝn) boundedness for the commutators of homogeneous singular integral operators are established.
deLeeuw’s theorem on Littlewood-Paley functions
Authors: Chen Chang-Pao , Fan Dashan , Sato Shuichi
Published: July 2016

We establish certain deLeeuw type theorems for Littlewood-Paley functions. By these theorems, we know that the boundedness of a Littlewood-Paley function on ℝn is equivalent to the boundedness of its corresponding Littlewood-Paley function on the torus Tn.
Some results and examples about the behavior of harmonic functions and Green’s functions with respect to second order elliptic operators
Authors: Ancona Alano
Published: July 2016

Let M be a manifold and let L be a sufficiently smooth second order elliptic operator in M such that (M, L) is a transient pair. It is first shown that if L is symmetric with respect to some density in M, there exists a positive L-harmonic function in M which dominates L-Green’s function at infinity. Other classes of elliptic operators are investigated and examples are constructed showing that this property may fail if the symmetry assumption is removed. Another part of the paper deals with the existence of critical points for certain L-harmonic functions with periodicity properties. A class of small perturbations of second order elliptic operators is also described.
Multi-flag systems and ordinary differential equations
Authors: Kumpera A. , Rubin J. L.
Published: July 2016

We discuss the Monge problem for under-determined systems of ordinary differential equations with an arbitrary degree of freedom and give a sufficient condition, in terms of truncated multi-flag systems, for the Monge property to hold. This condition extends in a natural way the Cartan criterion valid for systems with one degree of freedom.
A determinant formula for a class of rational solutions of Painlevé V equation
Authors: Masuda Tetsu , Ohta Yasuhiro , Kajiwara Kenji
Published: July 2016

We give an explicit determinant formula for a class of rational solutions of the Painlevé V equation in terms of the universal characters.
On Gorenstein surfaces dominated by P2
Authors: Gurjar R. V. , Pradeep C. R. , Zhang D.-Q.
Published: July 2016

In this paper we prove that a normal Gorenstein surface dominated by P2 is isomorphic to a quotient P2/G, where G is a finite group of automorphisms of P2 (except possibly for one surface ). We can completely classify all such quotients. Some natural conjectures when the surface is not Gorenstein are also stated.
Glauber dynamics for fermion point processes
Authors: Shirai Tomoyuki , Yoo Hyun Jae
Published: July 2016

We construct a Glauber dynamics on {0, 1}ℛ, ℛ a discrete space, with infinite range flip rates, for which a fermion point process is reversible. We also discuss the ergodicity of the corresponding Markov process and the log-Sobolev inequality.
Special tight closure
Authors: Huneke Craig , Vraciu Adela
Published: July 2016

We study the notion of special tight closure of an ideal and show that it can be used as a tool for tight closure computations.
Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy
Authors: Kawashita Mishio , Nakazawa Hideo , Soga Hideo
Published: July 2016

We consider the behavior of the total energy for the wave equation with the dissipative term. When the dissipative term works well uniformly in every direction, several authors obtain uniform decay estimates of the total energy. On the other hand, if the dissipative term is small enough uniformly in every direction, it is known that there exists a solution whose total energy does not decay. We examine the case that the dissipative term vanishes only in a neighborhood of a half-line. We introduce a uniform decay property, which is a natural generalization of the uniform decay estimates, and show that this property does not hold in our case. We prove this by constructing asymptotic solutions supported in the place where the dissipative term vanishes.
Toeplitz operators on harmonic Bergman spaces
Authors: Choe Boo Rim , Lee Young Joo , Na Kyunguk
Published: July 2016

We study Toeplitz operators on the harmonic Bergman spaces on bounded smooth domains. Two classes of symbols are considered; one is the class of positive symbols and the other is the class of uniformly continuous symbols. For positive symbols, boundedness, compactness, and membership in the Schatten classes are characterized. For uniformly continuous symbols, the essential spectra are described.
Amalgams Determined By Locally Projective Actions
Authors: Ivanov A. A. , Shpectorov S. V.
Published: July 2016

A locally projective amalgam is formed by the stabilizer G(x) of a vertex x and the global stabilizer G{x, y} of an edge (containing x) in a group G, acting faithfully and locally finitely on a connected graph Γ of valency 2n - 1 so that (i) the action is 2-arc-transitive; (ii) the subconstituent G(x)Γ(x) is the linear group SLn(2) = Ln(2) in its natural doubly transitive action and (iii) [t, G{x, y}] < O2(G(x) n G{x, y}) for some t G G{x, y} \ G(x). D. Z. Djokovic and G. L. Miller [DM80], used the classical Tutte’s theorem [Tu47], to show that there are seven locally projective amalgams for n = 2. Here we use the most difficult and interesting case of Trofimov’s theorem [Tr01] to extend the classification to the case n > 3. We show that besides two infinite series of locally projective amalgams (embedded into the groups AGLn(2) and O2n+(2)) there are exactly twelve exceptional ones. Some of the exceptional amalgams are embedded into sporadic simple groups M22, M23, Co2, J4 and BM. For each of the exceptional amalgam n = 3, 4 or 5.
On i-Adic Iterated integrals, I analog of zagier conjecture
Authors: Wojtkowiak ZdzisLaw
Published: July 2016

We are studying some aspects of the action of Galois groups on the torsor of paths connecting two (possibly tangential) points on a projec-tive line minus a finite number of points. We obtain objects which formally behave like classical iterated integrals and polylogarithms. We formulate an analog of Zagier conjecture for these l-adic analogs of iterated integrals and polylogarithms.
Averaging Formula for Nielsen Numbers
Authors: Kim Seung Won , lee Jong Bum , Lee Kyung Bai
Published: July 2016

We prove that the averaging formula for Nielsen numbers holds for continuous maps on infra-nilmanifolds: Let M be an infra-nilmanifold and ƒ: M → M be a continuous map. Suppose MK is a regular covering of M which is a compact nilmanifold with π1(MK = K. Assume that f*(K) ⊂ K. Then ƒ has a lifting . We prove a question raised by McCord, which is for any with an essential fixed point class, fix =1. As a consequence, we obtain the following averaging formula for Nielsen numbers
Entire Solutions of
Authors: li Bao Qin
Published: July 2016

The paper is concerned with description of entire solutions of the partial differential equations where m ≥ 2, n ≥ 2 are integers and g is a polynomial or an entire function in C2. Descriptions are given and complemented by various examples.
Addendum to the Paper “A note on Weighted bergman Spaces and the cesaro operator”
Authors: Chang Der-Chen , Stević Stevo
Published: July 2016

Let H(Dn) be the space of holomorphic functions on the unit polydisk Dn, and let , where p, q> 0, α = (α1,…,αn) with αj > -1, j =1,..., n, be the class of all measurable functions f defined on Dn such that

where Mp(f,r) denote the p-integral means of the function f. Denote the weighted Bergman space on . We provide a characterization for a function f being in . Using the characterization we prove the following result: Let p> 1, then the Cesàro operator is bounded on the space .
The Ohsawa-Takegoshi Extension Theorem on Some Unbounded Sets
Authors: Dinew Żywomir
Published: July 2016

We use a method of Berndtsson to obtain a simplification of Ohsawa’s result concerning extension of L2-holomorphic functions. We also study versions of the Ohsawa-Takegoshi theorem for some unbounded pseudoconvex domains, with an application to the theory of Bergman spaces. Using these methods we improve some constants, that arise in related inequalities.
Hartogs Type Theorems for CR L2 Functions on Coverings of Strongly Pseudoconvex Manifolds
Authors: Brudnyi Alexander
Published: July 2016

We prove an analog of the classical Hartogs extension theorem for CR L2 functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a question formulated in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds.
Hecke’s Integral Formula for Relative Quadratic Extensions of Algebraic Number Fields
Authors: Yamamoto Shuji
Published: July 2016

Let K/F be a quadratic extension of number fields. After developing a theory of the Eisenstein series over F, we prove a formula which expresses a partial zeta function of K as a certain integral of the Eisenstein series. As an application, we obtain a limit formula of Kronecker’s type which relates the 0-th Laurent coefficients at s = 1 of zeta functions of K and F.
A Packing Problem for Holomorphic Curves
Authors: Tsukamoto Masaki
Published: July 2016

We propose a new approach to the value distribution theory of entire holomorphic curves. We definepacking densityof Brody curves, and show that it has various non-trivial properties. The packing density of Brody curves can be considered as an infinite dimensional version of characteristic number, and it has an application to Gromov’s mean dimension theory.
Canonical Bases of Borcherds-Cartan Type
Authors: Li Yiqiang , Lin Zongzhu
Published: July 2016

We study the canonical basis for the negative part U- of the quantum generalized Kac-Moody algebra associated to a symmetric Borcherds-Cartan matrix. The algebras U- associated to two different matrices satisfying certain conditions may coincide (6.3). We show that the canonical bases coincide provided that the algebras U- coincide (Theorem 6.3.5). We also answer partially a question by Lusztig in [L3] (Theorem 7.1.1).
On Okuyama’s Theorems about Alvis-Curtis Duality
Authors: Cabanes Marc
Published: July 2016

We report on theorems by T. Okuyama about complexes generalizing the Coxeter complex and the action of parabolic subgroups on them, both for finite BN-pairs and finite dimensional Hecke algebras. Several simplifications, using mainly the surjections of [CaRi], allow a more compact treatment than the one in [O].
The Common Limit of a Quadruple Sequence and the Hypergeometric Function Fd of Three Variables
Authors: Kato Takayuki , Matsumoto Keiji
Published: July 2016

We study a quadruple sequence and express its common limit by Lauricella’s hypergeometric function FD(¼,¼,¼.¼, 1; z1, z2, z3)of three variables. We give a functional equation of FD, which is the key to get our expression of the common limit.
Motivic zeta functions for curve singularities
Authors: Moyano-Fernández J. J. , Zúňiga-Galindo W. A.
Published: July 2016

LetXbe a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristicpbig enough. Given a local ringOp,x at a rational singular pointPofX, we attached a universal zeta function which is a rational function and admits a functional equation ifOp,x is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré series attached to singular points of algebraic curves. In particular, for the local ring attached to a complex analytic function in two variables, our universal zeta function specializes to the generalized Poincaré series introduced by Campillo, Delgado, and Gusein-Zade.
Localized Morrey-Campanato spaces on metric measure spaces and applications to Schrüdinger operators
Authors: Yang Dachun , Yang Dongyong , Zhou Yuan
Published: July 2016

Letbe a space of homogeneous type in the sense of Coifman and Weiss, and letbe a collection of balls in. The authors introduce the localized atomic Hardy spacethe localized Morrey-Campanato spaceand the localized Morrey-Campanato-BLO (bounded lower oscillation) spacewithα∊ ℝ andp∊ (0, ∞) , and they establish their basic properties, includingand several equivalent characterizations forIn particular, the authors prove that when α > 0 andp∊ [1, ∞), thenand whenp∈(0,1], then the dual space ofisLetρbe an admissible function modeled on the known auxiliary function determined by the Schrödinger operator. Denote the spacesand, respectively, byandwhenis determined byρ. The authors then obtain the boundedness fromof the radial and the Poisson semigroup maximal functions and the Littlewood-Paleyg-function, which are defined via kernels modeled on the semigroup generated by the Schrödinger operator. These results apply in a wide range of settings, for instance, the Schrödinger operator or the degenerate Schrödinger operator on ℝd, or the sub-Laplace Schrödinger operator on Heisenberg groups or connected and simply connected nilpotent Lie groups.
On the boundary of the moduli spaces of log Hodge structures: Triviality of the torsor
Authors: Hayama Tatsuki
Published: July 2016

This paper examines the moduli spaces of log Hodge structures introduced by Kato and Usui. This moduli space is a partial compactification of a discrete quotient of a period domain. This paper treats the following two cases: (A) where the period domain is Hermitian symmetric, and (B) where the Hodge structures are of the mirror quintic type. Especially it addresses a property of the torsor.
On a Type of Subgroups of a Compact Lie Group
Authors: Matsushima Yozô
Published: July 2016

Let G be a connected compact Lie group and H a connected closed subgroup. Then H is an orientable submanifold of G and we may consider H as a cycle in G. In his interesting paper on the topology of group manifolds H. Samelson has proved that, if H is not homologous to 0, then the homology ring of the coset space G/H is isomorphic to the homology ring of a product space of odd dimensional spheres and the homology ring of G is isomorphic to that of the product of the spaces H and G/H. On the other hand, in a recent investigation of fibre bundles’ T. Kudo has shown that, if the homology ring of the coset space G/H is isomorphic to that of an odd dimensional sphere, then H is not homologous to 0.
On the Canonical Form of Turbulence
Authors: Itô Seizô
Published: July 2016

In K, Itô’s paper [1] on the theory of turbulence, the problem to determine the canonical form of the moment tensor of temporally homogeneous and isotropic turbulence, has not been solved. In the present paper, the author will solve the problem by making use of the result of his preceding paper [2]. We shall treat the turbulence in R3 but the similar argument is possible in Rn.
Note on Blocks of Symmetric Groups
Authors: Nakayama Tadasi , Osima Masaru
Published: July 2016

A conjecture concerning characterization of blocks of representations of symmetric groups by means of Young diagrams, given formerly by one of the writers, was affirmed recently by R. Brauer and G. de B. Robinson jointly. Namely, it was proved in Brauer’s paper, relying on his general, and profound, theory of blocks in finite groups, that the number of p-blocks in a symmetric group of degree n, is exactly equal to the number of p-cores, or p-kernels in the terminology of NI, with n- Ip (l= 0, 1, 2,…) nodes, and that certain statements designated as (A), (B) and (C) would secure that two irreducible representations with a same p-core belong to a same block (whence the conjecture itself when combined with the estimate of the number of blocks). Then these statements (A), (B), (C) were proved actually in Robinson’s paper.
Coarse dynamics and fixed-point theorem
Authors: Fukaya Tomohiro
Published: July 2016

We study semigroup actions on a coarse space and the induced actions on the Higson corona from a dynamical point of view. Our main theorem states that if an action of an abelian semigroup on a proper coarse space satisfies certain conditions, the induced action has a fixed point in the Higson corona. As a corollary, we deduce a coarse version of Brouwer’s fixed-point theorem.
Cohen-Macaulay binomial edge ideals
Authors: Ene Viviana , Herzog Jürgen , Hibi Takayuki
Published: July 2016

We study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen-Macaulay.
Quantitative extensions of pluricanonical forms and closed positive currents
Authors: Berndtsson Bo , Păun Mihai
Published: July 2016

We establish here several “invariance of plurigenera type” theorems for twisted pluricanonical forms and metrics of adjoint ℝ-bundles.
q-Titchmarsh-Weyl theory: series expansion
Authors: Annaby M. H. , Mansour Z. S. , Soliman I. A.
Published: July 2016

We establish aq-Titchmarsh-Weyl theory for singularq-Sturm-Liouville problems. We defineq-limit-point andq-limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jacksonq-Bessel functions is given. This example leads to the completeness of a wide class ofq-cylindrical functions.
Vanishing theorems on complete manifolds with weighted Poincaré inequality and applications
Authors: Fu Hai-Ping , Yang Deng-Yun
Published: July 2016

Two vanishing theorems for harmonic map andL2harmonic 1-form on complete noncompact manifolds are proved under certain geometric assumptions, which generalize results of [13], [15], [18], [19], and [20]. As applications, we improve some main results in [2], [4], [6], [9], [12], [20], [22], [24], and [25].
A Noether-Lefschetz theorem for varieties of r-planes in complete intersections
Authors: Jiang Zhi
Published: July 2016

We prove a Noether-Lefschetz type theorem for varieties ofr-planes in complete intersections. We then use it to study the Abel-Jacobi map of planes on a smooth cubic fivefold.
Finite symplectic actions on the K3 lattice
Authors: Hashimoto Kenji
Published: July 2016

In this paper, we study finite symplectic actions onK3 surfacesX, that is, actions of finite groupsGonXwhich act onH2,0(X) trivially. We show that the action on theK3 latticeH2(X, ℤ) induced by a symplectic action ofGonXdepends only onGup to isomorphism, except for five groups.
On the Kottwitz-Shelstad normalization of transfer factors for automorphic induction for GLn
Authors: Hiraga Kaoru , Ichino Atsushi
Published: July 2016

Automorphic induction for GLnis a case of endoscopic transfer, and its character identity was established by Henniart and Herb, up to a constant of proportionality. We determine this constant in terms of the Kottwitz-Shelstad normalization of transfer factors, which involves certainε-factors.
On zeta functions associated to symmetric matrices, II: Functional equations and special values
Authors: Ibukiyama Tomoyoshi , Saito Hiroshi
Published: July 2016

New simple functional equations of zeta functions of the prehomogeneous vector spaces consisting of symmetric matrices are obtained, using explicit forms of zeta functions in the previous paper, Part I, and real analytic Eisenstein series of half-integral weight. When the matrix size is 2, our functional equations are identical with the ones by Shintani, but we give here an alternative proof. The special values of the zeta functions at nonpositive integers and the residues are also explicitly obtained. These special values, written by products of Bernoulli numbers, are used to give the contribution of “central” unipotent elements in the dimension formula of Siegel cusp forms of any degree. These results lead us to a conjecture on explicit values of dimensions of Siegel cusp forms of any torsion-free principal congruence subgroups of the symplectic groups of general degree.
Centrioles in symmetric spaces
Authors: Quast Peter
Published: July 2016

We describe all centrioles in irreducible simply connected pointed symmetric spaces of compact type in terms of the root system of the ambient space, and we study some geometric properties of centrioles.
Deformations of elliptic fiber bundles in positive characteristic
Authors: Partsch Holger
Published: July 2016

We study the deformation theory of elliptic fiber bundles over curves in positive characteristics. As applications, we give examples of nonliftable elliptic surfaces in characteristics 2 and 3, which answer a question of Katsura and Ueno. Also, we construct a class of elliptic fibrations, whose liftability is equivalent to a conjecture of Oort concerning the liftability of automorphisms of curves. Finally, we classify deformations of bielliptic surfaces.
On Crossed Products of a Sfield
Authors: Ikeda Masatoshi
Published: July 2016

In the previous paper [3] the author has shown a possibility to construct a series of sfields by taking sfields of quotients of split crossed products of a sfield. In this paper the same problem is treated, and, by considering general crossed products, a generalization of the previous result is given: Let K be a sfield and G be the join of a well-ordered ascending chain of groups Gα of outer automorphisms of K such that a) G1 is the identity automorphism group, b) Gα is a group extension of Gα-1 by a torsion-free abelian group for each non-limit ordinal α, and c) for each limit ordinal α. Then an arbitrary crossed product of K with G is an integral domain with a sfield of quotients Q and the commutor ring of K in Q coincides with the centre of K.
A Proof of Brauer’s Theorem on Generalized Decomposition Numbers
Authors: Nagao Hirosi
Published: July 2016

In [3] R. Brauer gave a proof of his theorem on generalized decomposition numbers which was first announced in [1], and a simplification of it has been made by K. Iizuka [5]. In this note we shall show that the theorem may be proved from another point of view by using some results obtained by J. A. Green in [4].

After stating some results by Green and Osima in the first and second sections we first prove a theorem on characters (Theorem 1) and by using the theorem we prove Brauer’s theorem in the fourth section.
Some Note on Exceptional Values of Meromorphic Functions
Authors: Matsumoto Kikuji
Published: July 2016

LetEbe a totally-disconnected compact set in thez-plane and letΩbe its complement with respect to the extendedz-plane. ThenΩis a domain and we can consider a single-valued meromorphic functionw = f(z)onΩwhich has a transcendental singularity at each point ofE. Suppose thatEis a null-set of the classWin the sense of Kametani [4] (the classNBin the sense of Ahlfors and Beurling [1]). Then the cluster set off(z)at each transcendental singularity is the wholew-plane, and hencef(z)has an essential singularity at each point ofE. We shall say that a valuewis exceptional forf(z)at an essential singularity ζ ∈Eif there exists a neighborhood of ζ where the functionf(z)does not take this valuew.
Analytic Functions on Some Riemann Surfaces
Authors: Toda Nobushige , Matsumoto Kikuji
Published: July 2016

Some years ago, Kuramochi gave in his paper [5] a very interesting theorem, which can be stated as follows.

THEOREM OF KURAMOCHI. Let R be a hyperbolic Riemann surface of the class Of OHR(OHD,resp.). Then, for any compact subset K of R such that R—K is connected, R—K as an open Riemann surface belongs to the class 0AB(OAD resp.).
Class Number and Ramification in Number Fields
Authors: Brumer Armand , Rosen Michael
Published: July 2016

In the ring Ok of algebraic integers of a number field K the group Ik of ideals of Ok modulo the subgroup Pk of principal ideals is a finite abelian group of order hk, the class number of K. The determination of this number is an outstanding problem of algebraic number theory.
Chern Classes of Projective Modules
Authors: Ozeki Hideki
Published: July 2016

In topology, one can define in several ways the Chern class of a vector bundle over a certain topological space (Chern [2], Hirzebruch [7], Milnor [9], Steenrod [15]). In algebraic geometry, Grothendieck has defined the Chern class of a vector bundle over a non-singular variety. Furthermore, in the case of differentiable vector bundles, one knows that the set of differentiable cross-sections to a bundle forms a finitely generated projective module over the ring of differentiable functions on the base manifold. This gives a one to one correspondence between the set of vector bundles and the set of f.g.-projective modules (Milnor [10]). Applying Grauert’s theorems (Grauert [5]), one can prove that the same statement holds for holomorphic vector bundles over a Stein manifold.
Radial Limits of Quasiconformal Functions
Authors: Storvick D. A.
Published: July 2016

Beurling and Ahlfors [1] answered a fundamental question concerning the boundary correspondence induced by a quasiconformal mapping when they proved that the correspondence need not be given by an absolutely continuous function. They proved this by characterizing the boundary correspondences of quasiconformal mappings of the upper half-plane lm(z)>0 onto the upper half-plane lm(w)>0 under which the boundary points at infinity correspond. They proved that a necessary and sufficient condition that the strictly monotone increasing function μ(x) carrying the real axis onto itself be the boundary correspondence induced by such a quasiconformal mapping is that μ(X) should satisfy a ρ-condition
On Some Boundary Problems in the Theory of Conformal Mappings of Jordan Domains
Authors: Matsumoto Kikuji
Published: July 2016

It is a well-known result in the theory of conformal mappings of Jordan domains that if a domain D in the z-plane bounded by a closed Jordan curve C is mapped conformally on the disc |w;|<1 by a function w = f(z), analytic and univalent in D, then f(z) will be continuous on the closure of D and will map C on |w| =1 in a one to one manner (Carathéodory [2]), and that if C is rectifiable, then f(z) will map sets E of points of linear measure zero on C onto sets of linear measure zero on the circumference |w| = 1 and sets E of positive linear measure onto sets of positive linear measure on |w| =1 (F. and M. Riesz [12] and Lusin and Privaloff [8]).
On the Metrical Theorems of Cluster Sets of Meromorphic Functions
Authors: Tanaka Chuji
Published: July 2016

Recently the important contributions to the cluster sets theory of the meromorphic functions in the unit-disc have been done by many authors. For its recent development, we refer to K. Noshiro [10]. Roughly speaking, these studies can be divided into two classes ; the first one is topological, and the second one is metrical. As far as the author knows, there exist very few results on the metrical theorems on cluster sets of functions meromophic in an arbitrary connected domain, except for the case that its boundary is of logarithmic capacity zero. (K. Noshiro [10] pp. 5-31).
Applications of Extremal Length to Classification of Riemann Surfaces
Authors: Fuji’i’e Tatsuo
Published: July 2016

Let D be a subregion of a Riemann surface F, whose relative boundary consists of at most countable number of analytic curves which do not cluster in F. For a regular exhaustion {Fn} of F, we put Dn = D∩ (F— Fn), and define the extremal radius R(P, ∂Dn) of the relative boundary ∂Dn of Dn, measured at a point P(∈F0) of F with respect to the connected component of F - Dn which contains P. Let K(|z|≦r) be a disk centered at P and contained in a parametric disk of P.
Crossed Products and Maximal Orders
Authors: Williamson Susan
Published: July 2016

Let I’ be a maximal order over a complete discrete rank one valuation ring R in a central simple algebra over the quotient field of R. The purpose of this paper is to determine necessary and sufficient conditions for I’ to be equivalent to a crossed product over a tamely ramified extension of R.

It is a classical result that every central simple algebra over a field k is equivalent to a crossed product over a Galois extension of k. Furthermore, it has been proved by Auslander and Goldman in [2] that every central separable algebra over a local ring is equivalent to a crossed product over an unramified extension.
On Some Infinite Dimensional Representations of Semi-Simple Lie Algebras
Authors: Kimura Hiroshi
Published: July 2016

Let g be a semi-simple Lie algebra over an algebraically closed field K of characteristic 0. For finite dimensional representations of g, the following important results are known;

1) H1(g, V) = 0 for any finite dimensional g space V. This is equivalent to the complete reducibility of all the finite dimensional representations,

2) Determination of all irreducible representations in connection with their highest weights.

3) Weyl’s formula for the character of irreducible representations [9].

4) Kostant’s formula for the multiplicity of weights of irreducible representations [6],

5) The law of the decomposition of the tensor product of two irreducible representations [1].
On a Theory Objects Based on a Single Axiom Scheme
Authors: Ono Katuzi
Published: July 2016

There are some fundamental mathematical theories, such as the Fraenkel set-theory and the Bernays-Gödel set-theory, in which, I believe, all the actually important formal theories of mathematics can be embedded. Formal theories come into existence by being shown their consistency. As far as this is admitted, not all the axioms of set theory are necessary for a fundamental mathematical theory. The fundierung axiom is proved consistent by v. Neumann, the axiom of extensionality is proved consistent by Gandy, and even the axiom of choice is proved consistent by Göldel. Although it is not evident that a set-theory does not cease from being a fundamental theory of mathematics after abandoning these axioms all at once, the theory must be enough for being a fundamental theory of mathematics without some of them.
On Metric Properties of Sets of Angular Limits of Meromorphic Functions
Authors: Mcmillan J. E.
Published: July 2016

Let f be a nonconstant function meromorphic in the unit disc , with circumference C, and let Ez be a subset of C with positive (linear) measure. Suppose that at each ζ ∈ Ezf has an angular limit aζ and let It is known that Ew contains a closed set with positive harmonic measure (see Priwalow [6, p. 210] or Tsuji [7, p. 339]).
Characterization of Finite Dedekind Groups
Authors: Baer Reinhold
Published: July 2016

If U=U(0), U(i) is a maximal subgroup of U(i + 1) and U(n) = V, then we term the U(i) a densest chain connecting U and V; and n is the length of this chain. The subgroup U of V will furthermore be termed an n-uniserial subgroup of V if there exists one and only one densest chain connecting U and V and if its length is n. The principal aim of this note is to give characterizations of dedekind groups [ = groups all of whose subgroups are normal] in terms of the normality of uniserial subgroups. We quote one of our results:
An Action of the Symplectic Modular Group
Authors: Solomon Louis
Published: July 2016

1. Let V be a free Z-module of rank 2n. Let G=Sp(2n, Z) be the symplectic modular group and let Φ be the non-singular alternating bilinear form on V left invariant by G. Let p ∊ Z be a prime and let X be the set of all endomorphisms ξ of V such that
Nil Semi-Groups of Rings with a Polynomial Identity
Authors: Amitsur S. A.
Published: July 2016

The basic properties of associative rings R satisfying a polynomial identity p[x1…, xn] = 0 were obtained under the assumptions that the ring was an algebra [e.g., [4] Ch. X], or with rather strong restrictions on the ring of operators ([1]). But it is desirable to have these properties for arbitrary rings, and the present paper is the first of an attempt in this direction. The problem is almost trivial for prime or semi-prime rings but quite difficult in arbitrary rings. The known proofs for algebras have to be modified and in some cases new proofs have to be obtained as the existing proofs fail to exploit the known structure. In the present paper we extend the results of [1] on the nil subalgebras of a ring with an identity for arbitrary multiplicative nil semi-groups of the ring and for arbitrary rings.
On Extensions of Triads
Authors: Nomura Yasutoshi
Published: July 2016

As an extension of a result due to W. D. Barcus and J. P. Meyer [4], T. Ganea [8] has recently proved a theorem concerning the fibre of the extension E∪CF→B of a fibre map p: E→B to the cone CF erected over the fibre F. In this paper we shall establish a generalized Ganea theorem which asserts that the homotopy type of the fibre of a canonical extension ξ′ of a triad (cf. [13]) is determined by those of f and g (see Theorem 3.4).
On the Degrees of Irreducible Representations of a Finite Group
Authors: Itô Noboru
Published: July 2016

In 1896 G. Frobenius proved: the degree of any (absolutely) irreducible representation of a finite group divides its order. This theorem was improved by I. Schur in 1904 as follows: the degree of any irreducible representation of a finite group divides the index of its centre.