bluuebunny/crossref_metadata_2025 huggingface dataset:
Addendum to “On the Bergman kernel of hyperconvex domains”, Nagoya Math. J. 129 (1993), 43–52
Authors: Ohsawa Takeo
Published: July 2016

0. In [0-1] it was proved that for any bounded hyperconvex domain D in C2 the Bergman kernel function K(z, w) of D satisfies

In case n ═ 1, this is due to a behavior of sublevel sets of the Green function. The general case then follows by the extendability of L2 holomorphic functions.
Cauchy transforms on polynomial curves and related operators
Authors: Kang Hyeonbae , Seo Jin Keun
Published: July 2016

Let be a curve in R2 defined by y = A(x). The Cauchy transform on is defined by the kernel
Totally real orbits in affine quotients of reductive groups
Authors: Azad H. , Loeb J. J. , Qureshi M. N.
Published: July 2016

Let K be a compact connected Lie group and L a closed subgroup of K In [8] M. Lassalle proves that if K is semisimple and L is a symmetric subgroup of K then the holomorphy hull of any K-invariant domain in Kc/Lc contains K/L. In [1] there is a similar result if L contains a maximal torus of K. The main group theoretic ingredient there was the characterization of K/L as the unique totally real K-orbit in Kc/Lc. On the other hand, Patrizio and Wong construct in [9] special exhaustion functions on the complexification of symmetric spaces K/L of rank 1 and find that the minimum value of their exhaustions is always achieved on K/L. By a lemma of Harvey and Wells [6] one knows that the set where a strictly plurisubharmonic (briefly s.p.s.h) function achieves its minimum is totally real. There is a related result in [2, Lemma 1.3] which states that if φ is any differentiable function on a complex manifold M then the form ddcφ vanishes identically on any real submanifold N contained in the critical set of φ; in particular if φ is s.p.s.h then N must be totally real.
Global solution for the Yang-Mills gradient flow on 4-manifolds
Authors: Kozono Hideo , Maeda Yoshiaki , Naito Hisashi
Published: July 2016

In this paper, we will study a global weak solution for the Yang-Mills gradient flow on a closed (i.e., compact without boundary) 4-manifold. Let us explain some notion briefly to be able to state our results.
Local solvability and hypoellipticity for pseudodifferential operators of Egorov type with infinite degeneracy
Authors: Morimoto Yoshinori
Published: July 2016

Let P be a pseudodifferential operator of the form

where s, b ≥ 0 are even integers and is odd function with f′(t) > 0 (t ≠ 0). Here . We shall call P an operator of Egorov type because P with f(t) = tk, (k odd) is an important model of subelliptic operators studied by Egorov [1] and Hörmander [3], [4, Chapter 27]. Roughly speaking, any subelliptic operator can be reduced to this operator or Mizohata one after several steps of microlocalization arguments. In this paper we shall study the hypoellipticity of P and the local solvability of adjoint operator P* in the case where f(t) vanishes infinitely at the origin and moreover consider the case where ts and are replaced by functions with zero of infinite order.
Quantum Markov chains and classical random sequences
Authors: Lu Yun-Gang
Published: July 2016

Quantum Markov chain introduced by Accardi (cf. [1,2,3]) is one of natural generalization of classical Markov chain. It has many interesting applications in physics and the most important one is given by the paper of Fannes-Nachtergaele-Werner ([4]), where an application of quantum Markov chain’s technique enables us to understand the Valence bond states well.
On the convergence of the zeta function for certain prehomogeneous vector spaces
Authors: Yukie Akihiko
Published: July 2016

Let (G, V) be an irreducible prehomogeneous vector space defined over a number field k, P ∈ k[V] a relative invariant polynomial, and χ a rational character of G such that . For , let Gx be the stabilizer of x, and the connected component of 1 of Gx. We define L0 to be the set of such that does not have a non-trivial rational character. Then we define the zeta function for (G, Y) by the following integral

where Φ is a Schwartz-Bruhat function, s is a complex variable, and dg” is an invariant measure.
Units and Cyclotomic Units in Zp-Extensions
Authors: Kim Jae Moon
Published: July 2016

Let p be an odd prime and d be a positive integer prime to p such that d ≢ 2 mod 4. For technical reasons, we also assume that . For each integer n ≥ 1, we choose a primitive nth root ζn of 1 so that whenever n | m. Let be its cyclotomic Zp-extension, where is the nth layer of this extension. For n ≤ 1, we denote the Galois group Ga\(Kn/K0) by Gn, the unit group of the ring of integers of Kn by En, and the group of cyclotomic units of Kn by Cn. For the definition and basic properties of cyclotomic units such as the index theorem, we refer [6] and [7]. In this paper we examine the injectivity of the homomorphism between the first cohomology groups induced by the inclusion Cn → En.
A note on the variation of Riemann surfaces
Authors: Ohsawa Takeo
Published: July 2016

Let X be any Riemann surface. By Koebe’s uniformization theorem we know that the universal covering space of X is conformally equivalent to either Riemann sphere, complex plane, or the unit disc in the complex plane. If X is allowed to vary with parameters we may inquire the parameter dependence of the corresponding family of the universal covering spaces.
Generalized hypergroups and orthogonal polynomials
Authors: Obata Nobuaki , Wildberger Norman J.
Published: July 2016

We study in this paper a generalization of the notion of a discrete hypergroup with particular emphasis on the relation with systems of orthogonal polynomials. The concept of a locally compact hypergroup was introduced by Dunkl [8], Jewett [12] and Spector [25]. It generalizes convolution algebras of measures associated to groups as well as linearization formulae of classical families of orthogonal polynomials, and many results of harmonic analysis on locally compact abelian groups can be carried over to the case of commutative hypergroups; see Heyer [11], Litvinov [17], Ross [22], and references cited therein. Orthogonal polynomials have been studied in terms of hypergroups by Lasser [15] and Voit [31], see also the works of Connett and Schwartz [6] and Schwartz [23] where a similar spirit is observed.
A Remark on the Commutativity of Algebraic Rings
Authors: Nakayama Tadasi
Published: July 2016

Let F be a commutative ring with unit element 1. A ring R is called an algebraic ring over F by Drazin, in his recent paper [2], when R is an algebra over F and every element x of R satisfies an equation of lower monic form
An Investigation on the Logical Structure of Mathematics (VII): Set-Theoretical Contradictions
Authors: Kuroda Sigekatu
Published: July 2016

For an investigation on the foundations of mathematics to get an adequate mutual understanding, it is necessary to describe the generalities of the investigation with the parallel description of its particularities. Although one should obtain an exact and precise knowledge only through the latter, it is almost impossible, without the former, to get the underlying ideas and the fundamental principles, upon which the investigation is based.
Even canonical surfaces with small K2, III
Authors: Konno Kazuhiro
Published: July 2016

This is a continuation of [5]. In the present part, we study irregular even surfaces of general type with K < 4χ, where K and χ denote respectively a canonical divisor and the holomorphic Euler-Poincaré characteristic. As the first main theorem, we show the following:

THEOREM 1. For any irregular even surface of general type with K < 4χ, the image of the Albanese map is a curve.
Covariant derivatives on Kähler C-spaces
Authors: Tojo Koji
Published: July 2016

Let (M, g) be a Kähler C-space. R and ∇ denote the curvature tensor and the Levi-Civita connection of (M, g), respectively.

In [6], Takagi have proved that there exists an integer n such that
Classification of surfaces in three-sphere in Lie sphere geometry
Authors: Yamazaki Takayoshi , Yoshikawa Atsuko Yamada
Published: July 2016

We studied plane curves in Lie sphere geometry in [YY]. Especially we constructed Lie frames of curves in S2 and classified them by the Lie equivalence. In this paper we are concerned with surfaces in S3. We construct Lie frames and classify them. We moreover obtain the necessary and sufficient condition that two surfaces are Lie equivalent.
Volume-preserving geodesic symmetries on four-dimensional Hermitian Einstein spaces
Authors: Cho J. T. , Sekigawa K. , Vanhecke L.
Published: July 2016

We prove that a four-dimensional Hermitian Einstein space is weakly *-Einsteinian and use this result to show that all geodesic symmetries are volume-preserving (up to sign) if and only if it is local symmetric.
On a product related to the cubic Gauss sum, II
Authors: Ito Hiroshi
Published: July 2016

We continue the investigation of the product whose argument has been shown, in [2], to be related to the cubic Gauss sum.
Stability of Hölder estimates for on pseudoconvex domains of finite type in ℂ2
Authors: Cho S. , Ahn H. , Kim S.
Published: July 2016

Let Ω be a smoothly bounded pseudoconvex domain in ℂ2 and let bΩ be of finite type m. Then we prove the stability of Hölder estimates for under some perturbations of bΩ. As an application, we prove the Mergelyan property with respect to () norms for 0 ≤ α < 1/m.
A quasianalytic singular spectrum with respect to the Denjoy-Carleman class
Authors: Chung Soon-Yeong , Kim Dohan
Published: July 2016

Making use of the FBI (Fourier-Bros-Iagolnitzer) transforms we simplify the quasianalytic singular spectrum for the Fourier hyperfunctions, which was defined for distributions by Hörmander as follows; for any Fourier hyperfunction u, (x0, ξ0) does not belong to the quasianalytic singular spectrum W FM(u) if and only if there exist positive constants C, γ and N, and a neighborhood of x0 and a conic neighborhood Г of ξ0 such that

for all x ∈ U, |ξ| ∈ Γ and |ξ| ≥ N, where M(t) is the associated function of the defining sequence Mp. This result simplifies Hörmander’s definition and unify the singular spectra for the C∞ class, the analytic class and the Denjoy-Carleman class, both quasianalytic and nonquasianalytic.
On transient Markov processes of Ornstein-Uhlenbeck type
Authors: Yamamuro Kouji
Published: July 2016

For Hunt processes on Rd, strong and weak transience is defined by finiteness and infiniteness, respectively, of the expected last exit times from closed balls. Under some condition, which is satisfied by Lévy processes and Ornstein-Uhlenbeck type processes, this definition is expressed in terms of the transition probabilities. A criterion is given for strong and weak transience of Ornstein-Uhlenbeck type processes on Rd, using their Lévy measures and coefficient matrices of linear drift terms. An example is discussed.
Green’s functions of free products of operators, with applications to graph spectra and to random walks
Authors: Gutkin Eugene
Published: July 2016

We systematically develop an algebraic technique of free products of operators and their Green’s functions. We apply this framework to obtain, in a simple and uniform fashion, several results on the spectra of graph Laplaceans and random walks.
Mourre theory for time-periodic systems
Authors: Yokoyama Koichiro
Published: July 2016

Studies for A.C. Stark Hamiltonian are closely related to that for the self-adjoint operator on torus. In this paper we use Mourre’s commutator method, which makes great progress for the study of time-independent Hamiltonian. By use of it we show the asymptotic behavior of the unitary propagator as σ → ± ∞.
A Function Algebra on Riemann Surfaces
Authors: Nakai Mitsuru
Published: July 2016

In this note, we treat the problem to determine the conformal structure of the closed surface by the structure of the differentiable function algebra as the normed algebra with a certain norm.

A similar investigation is found in Myers [1]. He concerns himself with determining the Riemannian structure of the compact manifold using a certain normed algebra of differentiable functions.
Homogeneous Sphere Bundles and the Isotropic Riemann Manifolds
Authors: Nagano Tadashi
Published: July 2016

Let M be a connected metric space and H an isometry group of M which leaves fixed a point p in M. M is said H isotropic at p when, for any two points q and r of M at the same distance from p, there exists an isometry in H which carries q to r. When H coincides with the maximum isometry group leaving p fixed, M is said merely isotropic at p.
Imbedding Infinitely Distributive Lattices Completely Isomorphically
Into Boolean Algebras
Authors: Funayama Nenosuke
Published: July 2016

It is well known that any distributive lattice can be imbedded in a Boolean algebra ([1], [2], [4] and others). This imbedding is in general only finitely isomorphic in the sense that the imbedding preserves finite sums (supremums) and finite products (infimums) (but not necessarily infinite ones). Indeed, in order to be able to be imbedded into a Boolean algebra completely isomorphically (i.e. preserving every supremum and infimum) a distributive lattice L must satisfy the infinite distributive law, as the infinite distributivity holds in Boolean algebras. The main purpose of this paper is to prove that the converse is also true, that is, any infinitely distributive lattice can be imbedded completely isomorphically in a Boolean algebra (Theorem 6). Since we show, on the other hand, that any relatively complemented distribu tive lattice is infinitely distributive (Theorem 2), Theorem 6 implies that every relatively complemented distributive lattice can be imbedded completely isomorphically in a Boolean algebra (Theorem 4).
A Note On Umbilics of a Closed Surface
Authors: Kurita Minoru
Published: July 2016

In this paper we investigate indices of umbilics of a closed surface in the euclidean space. Most part of the discussion is concerned with a symmetric tensor field of degree 2, or rather a direction field, on a Riemannian manifold of dimension 2.
Limit theorems for hitting times of 1-dimensional generalized diffusions
Authors: Tomisaki Matsuyo , Yamazato Makoto
Published: July 2016

Limit theorems are obtained for suitably normalized hitting times of single points for 1-dimensional generalized diffusion processes as the hitting points tend to boundaries under an assumption which is slightly stronger than that the existence of limits γ + 1 of the ratio of the mean and the variance of the hitting time. Laplace transforms of limit distributions are modifications of Bessel functions. Results are classified by the one parameter {γ}, each of which is the degree of corresponding Bessel function. In case the limit distribution is degenerate to one point, by changing the normalization, we obtain convergence to the normal distribution. Regarding the starting point as a time parameter, we obtain convergence in finite dimensional distributions to self-similar processes with independent increments under slightly stronger assumption.
The theory of KM2O-Langevin equations and its applications to data analysis (III): Deterministic analysis
Authors: Okabe Yasunori , Yamane Toshiyuki
Published: July 2016

A technique is given for detecting deterministic dynamics in time series. Some stochastic difference equations, called KM2O-Langevin equations, are extracted directly from given data. We can find deterministic dynamics in time series by evaluating the magnitude of innovation part of the KM2O-Langevin equations. We can further find chaotic dynamics in time series by predicting it from the viewpoint of the theory of KM2O-Langevin equations.

We apply our method to the data of measles and chicken pox, which are also treated by G. Sugihara and R.M. May in [1]. The result of numerical experiments indicates that there seem to exist some deterministic dynamics in both time series. It also suggests, however, that the data of measles seems to be chaotic while that of chicken pox not, which corresponds to the result of G. Sugihara and R.M. May.
Distribution of length spectrum of circles on a complex hyperbolic space
Authors: Adachi Toshiaki
Published: July 2016

It is well-known that all geodesics on a Riemannian symmetric space of rank one are congruent each other under the action of isometry group. Being concerned with circles, we also know that two closed circles in a real space form are congruent if and only if they have the same length. In this paper we study how prime periods of circles on a complex hyperbolic space are distributed on a real line and show that even if two circles have the same length and the same geodesic curvature they are not necessarily congruent each other.
Twisted Maaß–Koecher series and spinor zeta functions
Authors: Breulmann Stefan , Kohnen Winfried
Published: July 2016

It is shown that a Siegel-Hecke eigenform of integral weight k and genus 2 is uniquely determined by its Fourier coefficients indexed by nT where T runs over all half-integral positive definite primitive matrices of size 2 and n over all squarefree positive integers. The proof uses analytic arguments involving Koecher-Maaß series and spinor zeta functions.
Complete system of finite order for the embeddings of pseudo-hermitian manifolds into ℂN+1
Authors: Kim Sung-Yeon
Published: July 2016

Let (M, ν, θ) be a real analytic (2n+1)-dimensional pseudo-hermitian manifold with nondegenerate Levi form and F be a pseudo-hermitian embedding into ℂn+1. We show under certain generic conditions that F satisfies a complete system of finite order. We use a method of prolongation of the tangential Cauchy-Riemann equations and pseudo-hermitian embedding equation. Thus if F ∈ Ck(M) for sufficiently large k, F is real analytic. As a corollary, if M is a real hypersurface in ℂn+1, then F extends holomorphically to a neighborhood of M provided that F is sufficiently smooth.
On geometric variation theory
Authors: Shikata Yoshihiro
Published: July 2016

We construct here a framework for a geometric variation of 1 dimensional geometric figures regarding them as sets of ordered points. In this framework, we can make full use of cut and paste technique to find a way to go down to the geometric smallest figure, including the topological change of the parameter space. Therefore we can discuss practical problems like switching of current flows and the minimal networks not only multiple closed geodesics.
Locally trivial fibrations with singular 1-dimensional Stein fiber over q-complete spaces
Authors: Colţoiu Mihnea , Vâjâitu Viorel
Published: July 2016

In connection with Serre’s problem, we consider a locally trivial analytic fibration π : E → B of complex spaces with typical fiber X. We show that if X is a Stein curve and B is q-complete, then E is q-complete.
Malgrange’s vanishing theorem in 1-concave CR manifolds
Authors: Laurent-Thiébaut Christine , Leiterer Jürgen
Published: July 2016

We prove a vanishing theorem for the -cohomology in top degree on 1-concave CR generic manifolds.
On the Dirichlet problem of prescribed mean curvature equations without H-convexity condition
Authors: Hayasida Kazuya , Nakatani Masao
Published: July 2016

The Dirichlet problem of prescribed mean curvature equations is well posed, if the boundery is H-convex. In this article we eliminate the H-convexity condition from a portion Γ of the boundary and prove the existence theorem, where the boundary condition is satisfied on Γ in the weak sense.
Käahler identity on Levi flat manifolds and application to the embedding
Authors: Ohsawa Takeo , Sibony Nessim
Published: July 2016

It is shown that any compact Levi flat manifold admitting a positive line bundle is embeddable into ℙn by a CR mapping with an arbitrarily high, though finite, order of regularity.
A Remark on Relative Homology and Cohomology Groups of a Group
Authors: Nakayama Tadasi
Published: July 2016

Let G be a group and H a subgroup of G. With a left G-module M, relative cohomology groups Hn(G, H, M) of G on M, relative to H, have been defined by Adamson [1] and may be expressed as (Z, M) in the notation of relative homological algebra of Hochschild [2], where Z denotes the G-module of rational integers (acted by G trivially). Regarding M as a right G-module, (M, Z) are similarly relative homology groups Hn(G, H, M). In case H is of finite index in G, Hochschild [2] defines further negative-dimensional relative homology and cohomology groups.
Relative Distance and Quasi-Conformal Mappings
Authors: Storvick D. A.
Published: July 2016

1. Introduction. M. A. Lavrentiev made use of a relative distance function to establish some important results concerning the correspondence between the frontiers under a conformal mapping of a simply connected domain onto the unit circle. The purpose of this note is to show that some of these results are valid for the boundary correspondences induced by the more general class of quasi-conformal mappings.
On an Application of Intermediate Logics
Authors: Umezawa Toshio
Published: July 2016

In [1] I investigated some logics intermediate between intuitionistic and classical predicate logics. The purpose of this paper is to show the possibility of applying some intermediate logics to mathematics namely, to show that some mathematical theorems which are provable in the classical logic but not provable in the intuitionistic logic are provable in some intermediate logics. Let LZ be the logical system obtained from LJ′ a variant of Gentzen’s LJ [2], by adding as axioms all those sequents which can be obtained from a sequent scheme Z by substitution for propositional, predicate, or individual variables.
On A Property of the Boundary Correspondence under Quasiconformal Mappings
Authors: Ikoma Kazuo
Published: July 2016

Let w = f(z) be a quasiconformal mapping, in the sense of Pfluger [5]-Ahlfors [1], with maximal dilatation K, which will be simply referred to a K-QC mapping. As is well known, any K-QC mapping w = f(z) of Im z > 0 onto Im w > 0 can be extended to a homeomorphism from Im z ≧ 0 onto Im w ≧ 0 and hence it transforms any set of logarithmic capacity zero on Im z = 0 into a set with the same property on Im w = 0.
A Property of Some Poincaré Theta-Series
Authors: Akaza Tohru
Published: July 2016

Consider circles cν(ν = ±1, ±2, …) with centers ξν on the real axis of the z-plane such that they are disjoint from each other and cluster to infinity z = ∞ from the both sides of the real axis. Here, without loss of generality, we may assume that for every positive integer ν.
Quotients of L-functions
Authors: Heim Bernhard E.
Published: July 2016

In this paper a certain type of Dirichlet series, attached to a pair of Jacobi forms and Siegel modular forms is studied. It is shown that this series can be analyzed by a new variant of the Rankin-Selberg method. We prove that for eigenforms the Dirichlet series have an Euler product and we calculate all the local L-factors. Globally this Euler product is essentially the quotient of the standard L-functions of the involved Jacobi- and Siegel modular form.
Passage-Time Moments for Positively Recurrent Markov Chains
Authors: Shiga Tokuzo , Shimizu Akinobu , Soshi Takahiro
Published: July 2016

Fractional moments of the passage-times are considered for positively recurrent Markov chains with countable state spaces. A criterion of the finiteness of the fractional moments is obtained in terms of the convergence rate of the transition probability to the stationary distribution. As an application it is proved that the passage time of a direct product process of Markov chains has the same order of the fractional moments as that of the single Markov chain.
Kernel systems on finite groups
Authors: Lescot Paul
Published: July 2016

We introduce a notion of kernel systems on finite groups: roughly speaking, a kernel system on the finite group G consists in the data of a pseudo-Frobenius kernel in each maximal solvable subgroup of G, subject to certain natural conditions. In particular, each finite CA-group can be equipped with a canonical kernel system. We succeed in determining all finite groups with kernel system that also possess a Hall p′-subgroup for some prime factor p of their order; this generalizes a previous result of ours (Communications in Algebra 18(3), 1990, pp. 833-838). Remarkable is the fact that we make no a priori abelianness hypothesis on the Sylow subgroups.
Global existence and convergence of solutions of the Calabi flow on Einstein 4-manifolds
Authors: Chang Shu-Cheng
Published: July 2016

In this paper, firstly, we show the Bondi-mass type estimate of solutions of Calabi flow on closed 4-manifolds. Secondly, in our applications, we obtain the long time existence on closed 4-manifolds. In particular, we are able to show the asymptotic convergence of a subsequence of solutions of the Calabi flow on closed Einstein 4-manifolds.
Lifting of supersingular points on X0 (pr) and lower bound of ramification index
Authors: Momose Fumiyuki , Shimura Mahoro
Published: July 2016

Let K be a finite extension of (= the maximal unramified extension of Qp) of degree eK, its integer ring, p a rational prime and r a positive integer. If there exists a one parameter formal group defined over whose reduction is of height 2 with a cyclic subgroup V of order pr defined over , then .

We apply this result to a criterion for non-existence of Q-rational point of . (This criterion is Momose’s theorem in [14] except for the cases p = 5 and p = 13, but our new proof does not require defining equations of modular curves except for the case p = 2.)
Lower bounds for fundamental units of real quadratic fields
Authors: Tomita Koshi , Yamamuro Kouji
Published: July 2016

Let d be a square-free positive integer and l(d) be the period length of the simple continued fraction expansion of ωd, where ωd is integral basis of ℤ[]. Let εd = (td + ud)/2 (> 1) be the fundamental unit of the real quadratic field ℚ(). In this paper new lower bounds for εd, td, and ud are described in terms of l(d). The lower bounds of εd are sharper than the known bounds and those of td and ud have been yet unknown. In order to show the strength of the method of the proof, some interesting examples of d are given for which εd and Yokoi’s d-invariants are determined explicitly in relation to continued fractions of the form .
The asymptotics of string matching probabilities for Gaussian random sequences
Authors: Ihara Shunsuke , Kubo Masashi
Published: July 2016

Wyner and Ziv (1989) studied the asymptotic properties of recurrence times of stationary ergodic processes, and applied the results to obtain optimal data compression schemes in information transmission. Since then many data compression algorithms based upon string matching of a sequence from an information source with a database have been proposed and studied. In this paper we consider Gaussian stationary processes representing an information source and a database, and study problems of string matching with distortion. We prove theorems concerning the asymptotic behavior of the probability of string matching with distortion and the waiting time for the string matching.
Deformation invariance of plurigenera
Authors: Tsuji Hajime
Published: July 2016

We prove the invariance of plurigenera under smooth projective deformations in full generality.
On the moduli of stable sheaves on a reducible projective scheme and examples on a reducible quadric surface
Authors: Inaba Michi-Aki
Published: July 2016

We study the moduli space of stable sheaves on a reducible projective scheme by use of a suitable stratification of the moduli space. Each stratum is the moduli space of “triples”, which is the main object investigated in this paper. As an application, we can see that the relative moduli space of rank two stable sheaves on quadric surfaces gives a nontrivial example of the relative moduli space which is not flat over the base space.
Boundary behavior of the Bergman metric
Authors: Chen Bo-Yong
Published: July 2016

Let Ω be a bounded pseudoconvex domain in Cn. We give sufficient conditions for the Bergman metric to go to infinity uniformly at some boundary point, which is stated by the existence of a Hölder continuous plurisubharmonic peak function at this point or the verification of property (P) (in the sense of Coman) which is characterized by the pluricomplex Green function.
Singular invariant hyperfunctions on the square matrix space and the alternating matrix space
Authors: Muro Masakazu
Published: July 2016

Fundamental calculations on singular invariant hyperfunctions on the n ×n square matrix space and on the 2n × 2n alternating matrix space are considered in this paper. By expanding the complex powers of the determinant function or the Pfaffian function into the Laurent series with respect to the complex parameter, we can construct singular invariant hyperfunctions as their Laurent expansion coefficients. The author presents here the exact orders of the poles of the complex powers and determines the exact supports of the Laurent expansion coefficients. By applying these results, we prove that every quasi-relatively invariant hyperfunction can be expressed as a linear combination of the Laurent expansion coefficients of the complex powers and that every singular quasi-relatively invariant hyperfunction is in fact relatively invariant on the generic points of its support. In the last section, we give the formula of the Fourier transforms of singular invariant tempered distributions.
On a generalized divisor problem II
Authors: Lau Yuk-Kam
Published: July 2016

We investigate the Ω±-result of Δa(x) and its number of sign-changes in an interval [1, T], denoted by Xa(T), for -1 ≤ a < -1/2. We can prove that T ≪aXa(T) which is the best possible in order of magnitude.
Local zeta functions and Newton polyhedra
Authors: Zuniga-Galindo W. A.
Published: July 2016

To a polynomial f over a non-archimedean local field K and a character χ of the group of units of the valuation ring of K one associates Igusa’s local zeta function Z (s, f, χ). In this paper, we study the local zeta function Z(s, f, χ) associated to a non-degenerate polynomial f, by using an approach based on the p-adic stationary phase formula and Néron p-desingularization. We give a small set of candidates for the poles of Z (s, f, χ) in terms of the Newton polyhedron Γ(f) of f. We also show that for almost all χ, the local zeta function Z(s, f, χ) is a polynomial in q−s whose degree is bounded by a constant independent of χ. Our second result is a description of the largest pole of Z(s, f, χtriv) in terms of Γ(f) when the distance between Γ(f) and the origin is at most one.
Topological types of Pfaffian manifolds
Authors: Fujita Masato , Shiota Masahiro
Published: July 2016

Let Ω = (ω1,…,ωn-k) be differential 1-forms with polynomial coefficients in Rn. A Pfaffian manifold of Ω is by definition a maximal integral k-manifold of Ω. It is shown that the number of homeomorphism classes of all Pfaffian manifolds of Rolle Type of Ω is finite and, moreover, bounded by a computable function in variables n, k and the degree of ω1,…, ωn-k. Finiteness is proved also in any o-minimal structure.

We give also an example of a semi-algebraic C1 differential form on a semi-algebraic C2 3-manifold whose Pfaffian manifolds have homeomorphism classes of the cardinality of continuum. Hence the cardinality of all manifolds is the continuum (not countable).
Existence and uniqueness of positive eigenfunctions for certain eigenvalue systems
Authors: Xue Ru-Ying , Yang Yi-Min
Published: July 2016

The existence and uniqueness of eigenvalues and positive eigenfunctions for some quasilinear elliptic systems are considered. Some necessary and sufficient conditions which guarantee the existence and uniqueness of eigenvalues and positive eigenfunctions are given.
On the existence and boundedness of square function operators on Campanato spaces
Authors: Sun Yongzhong
Published: July 2016

Let g(f) be a Littlewood-Paley square function of f, which belongs to Campanato spaces . We prove that if g(f)(x0) exists (i.e. g(f)(x0) < ∞) for a single point x0 ∈ Rn, then g(f)(x) exists almost everywhere in Rn and . Thus we give an improvement of some earlier results such as in [8], where it is always needed to assume g(f)(x) exists in a set of positive measure in order to get the a.e. existence and boundedness of g(f)(x).
Linear relations between Fourier coefficients of special Siegel modular forms
Authors: Kohnen Winfried
Published: July 2016

In this paper we give certain linear relations between the Fourier coefficients of Siegel modular forms that are obtained from Ikeda lifts.
A construction of quintic rings
Authors: Kable Anthony C. , Yukie Akihiko
Published: July 2016

We construct a discriminant-preserving map from the set of orbits in the space of quadruples of quinary alternating forms over the integers to the set of isomorphism classes of quintic rings. This map may be regarded as an analogue of the famous map from the set of equivalence classes of integral binary cubic forms to the set of isomorphism classes of cubic rings and may be expected to have similar applications. We show that the ring of integers of every quintic number field lies in the image of the map. These results have been used to establish an upper bound on the number of quintic number fields with bounded discriminant.
On planar Cremona maps of prime order
Authors: de Fernex Tommaso
Published: July 2016

This paper contains a new proof of the classification of prime order elements of Bir(ℙ2) up to conjugation. The first results on this topic can be traced back to classic works by Bertini and Kantor, among others. The innovation introduced by this paper consists of explicit geometric constructions of these Cremona transformations and the parameterization of their conjugacy classes. The methods employed here are inspired to [4], and rely on the reduction of the problem to classifying prime order automorphisms of rational surfaces. This classification is completed by combining equivariant Mori theory to the analysis of the action on anticanonical rings, which leads to characterize the cases that occur by explicit equations (see [28] for a different approach). Analogous constructions in higher dimensions are also discussed.
Geometric determination of the Poles of Highest and second Highest order of Hodge And motivic Zeta functions
Authors: Rodrigues B.
Published: July 2016

To any f ∈ ℂ[x1, … ,xn] \ ℂ with f(0) = 0 one can associate the motivic zeta function. Another interesting singularity invariant of f-1{0} is the zeta function on the level of Hodge polynomials, which is actually just a specialization of the motivic one. In this paper we generalize for the Hodge zeta function the result of Veys which provided for n = 2 a complete geometric determination of the poles. More precisely we give in arbitrary dimension a complete geometric determination of the poles of order n − 1 and n. We also show how to obtain the same results for the motivic zeta function.
Some Function Spaces Relative to Morrey-Campanato Spaces on Metric Spaces
Authors: Yang Dachun
Published: July 2016

In this paper, the author introduces the Morrey-Campanato spacesLsp(X)and the spacesCps(X)on spaces of homogeneous type including metric spaces and some fractals, and establishes some embedding theorems between these spaces under some restrictions and the Besov spaces and the Triebel-Lizorkin spaces. In particular, the author proves thatLsp(X)=Bs∞,∞(X)if 0 <s< ∞ and µ(X)< ∞. The author also introduces some new function spacesAsp(X)andBsp(X)and proves that these new spaces when 0 <s< 1 and 1 <p< ∞ are just the Triebel-Lizorkin spaceFsp,∞(X)ifXis a metric space, and the spacesA1p(X)andB1p(X) when 1 <p< ∞ are just the Hajłasz-Sobolev spacesW1p(X). Finally, as an application, the author gives a new characterization of the Hajłasz-Sobolev spaces by making use of the sharp maximal function.
Fiber Cones of Ideals with Almost Minimal Multiplicity
Authors: Jayanthan A. V. , Verma J. K.
Published: July 2016

Fiber cones of 0-dimensional ideals with almost minimal multiplicity in Cohen-Macaulay local rings are studied. Ratliff-Rush closure of filtration of ideals with respect to another ideal is introduced. This is used to find a bound on the reduction number with respect to an ideal. Rossi’s bound on reduction number in terms of Hilbert coefficients is obtained as a consequence. Sufficient conditions are provided for the fiber cone of 0-dimensional ideals to have almost maximal depth. Hilbert series of such fiber cones are also computed.
Gorenstein Resolutions of 3-Dimensional Terminal Singularities
Authors: Hayakawa Takayuki
Published: July 2016

Let X be a 3-dimensional terminal singularity of index ≥ 2. We shall construct projective birational morphisms ƒ: Y → X such that Y has only Gorenstein terminal singularities and that ƒ factors the minimal resolution of a general member of | −KX |. We also study prime divisors of ƒ, especially the discrepancies of these prime divisors.
Normal Families of meromorphic mappings of several complex variables into PN(C)
Authors: Mai Pham Ngoc , Thai Do Duc , Trang Pham Nguyen Thu
Published: July 2016

The first aim in this article is to give some sufficient conditions for a family of meromorphic mappings of a domain D in Cn into PN(C) omitting hypersurfaces to be meromorphically normal. Our result is a generalization of the results of Fujimoto and Tu. The second aim is to investigate extending holomorphic mappings into the compact complex space from the viewpoint of the theory of meromorphically normal families of meromorphic mappings.
Combinatorial descriptions of toric extremal Contractions
Authors: Sato Hiroshi
Published: July 2016

In this paper, we give explicit combinatorial descriptions for toric extremal contractions under the relative setting, where varieties are not complete. It is well-known that the complete case is settled by using Reid’s wall theory which can not be applied to the non-complete case. Therefore, we can achieve them by using the notion of extremal primitive relations. As applications, we can generalize some of Mustaţă’s results related to Fujita’s conjecture on toric varieties for the relative case.
Base change of Invariant subrings
Authors: Hashimoto Mitsuyasu
Published: July 2016

Let R be a Dedekind domain, G an affine flat R-group scheme, and B a flat R-algebra on which G acts. Let A → BG be an R-algebra map. Assume that A is Noetherian. We show that if the induced map K ⊗ A → (K ⊗B)K⊗G is an isomorphism for any algebraically closed field K which is an R-algebra, then S ⊗ A → (S ⊗ B)S⊗G is an isomorphism for any R-algebra S.
Annihilator, Completeness and Convergence of Wavelet System
Authors: Ho Kwok-Pun
Published: July 2016

We show that if is a frame and {ψＱ}Ｑ∈Q ∈ ∩ Mα(ℝn) is its dual frame (for the definition of Mα(ℝn), see Definition 2.1), where Q is the collection of dyadic cubes, then for any f ∈ S′(ℝn), there exists a sequence of polynomials, PL,L′,L″, such that

(0.1)

in the topology of S′(ℝn), where δ(i) = max(2i, 1). We prove this result by explicitly constructing the polynomials PL,L′,L″. Furthermore, using the above result, we assert that the linear span of the one-dimensional wavelet system is dense in a function space if and only if the dual space of this function space has an trivial intersection with the set of polynomials. This is proved by using the annihilator of the one-dimensional wavelet system.
Gluing an Infinite Number of Instantons
Authors: Tsukamoto Masaki
Published: July 2016

This paper is one step toward infinite energy gauge theory and the geometry of infinite dimensional moduli spaces. We generalize a gluing construction in the usual Yang-Mills gauge theory to an “infinite energy” situation. We show that we can glue an infinite number of instantons, and that the resulting ASD connections have infinite energy in general. Moreover they have an infinite dimensional parameter space. Our construction is a generalization of Donaldson’s “alternating method”.
The Geometric Theory of the Fundamental Germ
Authors: Gendron T. M.
Published: July 2016

The fundamental germ is a generalization of π1, first defined for laminations which arise through group actions [4]. In this paper, the fundamental germ is extended to any lamination having a dense leaf admitting a smooth structure. In addition, an amplification of the fundamental germ called the mother germ is constructed, which is, unlike the fundamental germ, a topological invariant. The fundamental germs of the antenna lamination and the PSL(2,ℤ) lamination are calculated, laminations for which the definition in [4] was not available. The mother germ is used to give a new proof of a Nielsen theorem for the algebraic universal cover of a closed surface of hyperbolic type.
On Cocharacters Associated to Nilpotent Elements of Reductive Groups
Authors: Fowler Russell , Röhrle Gerhard
Published: July 2016

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we consider particular classes of connected reductive subgroups H of G and show that the cocharacters of H that are associated to a given nilpotent element e in the Lie algebra of H are precisely the cocharacters of G associated to e that take values in H. In particular, we show that this is the case provided H is a connected reductive subgroup of G of maximal rank; this answers a question posed by J. C. Jantzen.
Automorphisms of Coxeter Groups and Lusztig’s Conjectures for Hecke Algebras with Unequal Parameters
Authors: Bonnafé Cédric
Published: July 2016

Let (W,S) be a Coxeter system, let G be a finite solvable group of automorphisms of (W, S) and let ϕ be a weight function which is invariant under G. Let ϕG denote the weight function on WG obtained by restriction from ϕ. The aim of this paper is to compare the a-function, the set of Duflo involutions and the Kazhdan-Lusztig cells associated with (W, ϕ) and to (WG,ϕG), provided that Lusztig’s Conjectures hold.
On Some Properties of Locally Compact Groups with no Small Subgroup
Authors: Gotô Morikuni , Yamabe Hidehiko
Published: July 2016

Let G be a locally compact group. Under a neighbourhood U we mean a symmetric (i.e. U = U−1) neighbourhood of the identity e, with the compact closure Ū. If there exists a neighbourhood U containing no subgroup other than the identity group, we say that G has no small subgroup.
Note on Subdirect Sums of Rings
Authors: Nagata Masayoshi
Published: July 2016

In my previous paper “On the theory of semi-local rings,” we saw that if a semi-local ring R with maximal ideals p1…,ph is a subdirect sum of local rings Rm,2) then R is the direct sum of R[p1] (proposition 15, (slr)1)) and that a complete semi-local ring is a direct sum of complete local rings (Remark to proposition 5, (slr)).
A Group of Automorphisms of the Homotopy Groups
Authors: Uehara Hiroshi
Published: July 2016

It is well known that the fundamental group π1(X) of an arcwise connected topological space X operates on the n-th homotopy group πn(X) of X as a group of automorphisms. In this paper I intend to construct geometrically a group 𝒰(X) of automorphisms of πn(X), for every integer n ≥ 1, which includes a normal subgroup isomorphic to π1(X) so that the factor group of 𝒰(X) by π1(X) is completely determined by some invariant Σ(X) of the space X. The complete analysis of the operation of the group on πn(X) is given in §3, §4, and §5,
On Maximally Central Algebras
Authors: Azumaya Gorô
Published: July 2016

Let A be a primary algebra with unit element over a field K and Z its center. Let Ā be the simple residue class algebra of A modulo its radical. Then it is known, and can readily be seen, that there holds the inequality where t is the rank of A over its center. We call A maximally central if in particular i.e. if the rank [Z: K] takes its maximum value. Further, an algebra which is a direct sum of those primary algebras will be called maximally central too. The notion was introduced in Azumaya-Nakayama [5], as a by-product of the study of absolutely uni-serial algebras.
Doubling zeta integrals and local factors for metaplectic groups
Authors: Gan Wee Teck
Published: July 2016

We develop the theory of the doubling zeta integral of Piatetski-Shapiro and Rallis for metaplectic groups Mp2n, and we use it to give precise definitions of the local γ-factors,L-factors, and ε-factors for irreducible representations of Mp2n× GL1, following the footsteps of Lapid and Rallis.
Extensions of representations of p-adic groups
Authors: Adler Jeffrey D. , Prasad Dipendra
Published: July 2016

We calculate extensions between certain irreducible admissible representations of p-adic groups.
A Note on a Conjecture of Brauer
Authors: Fong Paul
Published: July 2016

In [1] R. Brauer asked the following question: Letbe a finite group,pa rational prime number, andBa p-block ofwith defectdand defect group. Is it true thatis abelian if and only if every irreducible character inBhas height 0 ? The present results on this problem are quite incomplete. Ifd-0, 1, 2 the conjecture was proved by Brauer and Feit, [4] Theorem 2. They also showed that ifis cyclic, then no characters of positive height appear inB. Ifis normal in, the conjecture was proved by W. Reynolds and M. Suzuki, [12]. In this paper we shall show that for a solvable group, the conjecture is true for the largest prime divisorpof the order of. Actually, one half of this has already been proved in [7]. There it was shown that ifis a p-solvable group, wherepis any prime, and ifis abelian, then the condition on the irreducible characters inBis satisfied.
A Remark on Decompositions of the Permutation Representation of a Permutation Group
Authors: Tsuzuku Tosiro
Published: July 2016

Let be a permutation group on n-letters 1, 2,… ,n . Let be the subgroup of fixing suitable one letter, say 1. For any element G of , a non-singular matrix G* = (gij) of degree n is defined by the equation
On Cartan Pseudo Groups
Authors: Rodrigues A. M.
Published: July 2016

Let M be a domain in an Euclidean space and let Γ be a pseudo group of transformations of M. We say that Γ is a Cartan pseudo group [1, 2] if the following conditions are satisfied:

1)There exists a domain M′ and a projection ρ: M-→M′, such that the orbits of Γ are the fibers of the projection ρ.
Skew Tensor Products and Groups of Class Two
Authors: Conrad Paul
Published: July 2016

Let Δ and N be abelian groups and let f be a mapping of Δ × Δ into N that is bilinear, skew symmetric and satisfies f(α, α) = 0 for all α ∈ Δ. Such a mapping f is called a (*)-mapping. By the Schreier extension theory Δ, N and f determine a nilpotent group G(Δ, N, f) of class two that consists of the set Δ × N with composition

(α, a) + (β, b) = (α + β, f(α, β) + a + b).
On the Dirichlet Problem in the Axiomatic Theory of Harmonic Functions
Authors: Boboc N. , Constantinescu C. , Cornea A.
Published: July 2016

In the frame of the recent axiomatic theories of harmonic functions [2], [3], [1], it has been shown that the continuous bounded functions on the boundaries of relatively compact open sets are resolutive [5], [1]. The aim of the present paper is to substitute in these results the continuous functions by Borel-measurable functions and to leave out the restriction that the open sets are relatively compact. H. Bauer has replaced the axiom 3 of Brelot’s axiomatic by two weaker axioms: the axiom of separation (Trennungsaxiom) and the axiom K1. Since the axiom of separation is not fulfilled in some important cases (e.g. the compact Riemann surfaces) we shall weaken this axiom too, substituting it by one of its consequences: the minimum principle for hyperharmonic functions.
Analytic Functions on Some Riemann Surfaces, II
Authors: Matsumoto Kikuji
Published: July 2016

In their paper [12], Toda and the author have concerned themselves in the following

Theorem of Kuramochi. Let R be a hyperbolic Riemann surface of the class OHB(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 OAB(OAD, resp.) (Kuramochi [4]).

They have raised there the question as to whether there exists a hyperbolic Riemann surface, which has no Martin or Royden boundary point with positive harmonic measure and has yet the same property as stated in Theorem of Kuramochi, and given a positive answer to the Martin part of this question.