bluuebunny/crossref_metadata_2025 huggingface dataset:
On completeness of holomorphic principal bundles
Authors: Takeuchi Shigeru
Published: July 2016

In this paper we shall investigate the structure of complex Lie groups from function theoretical points of view. A. Morimoto proved in [10] that every connected complex Lie group G has the smallest closed normal connected complex Lie subgroup Ge, such that the factor group G/Ge is Stein. On the other hand there hold the following two basic structure theorems (A1) and (A2) for a connected algebraic group G (cf. [12]). (A1): G has the smallest normal algebraic subgroup N such that the factor group G/N is an affine algebraic group. Moreover N is a connected central subgroup. (A2): G has the unique maximal connected affine algebraic subgroup L, where L is normal and the factor group G/L is an abelian variety.
On Periods of Meromorphic Eichler Integrals
Authors: Sato Hiroki
Published: July 2016

In this paper we treat cohomology groups H1(G, C2q-1, M) of meromorphic Eichler integrals for a finitely generated Fuchsian group G of the first kind. According to L. V. Ahlfors [2] and L. Bers [4], H1(G, C2q-1, M) is the space of periods of meromorphic Eichler integrals for G. In the previous paper [8], we had period relations and inequalities of holomorphic Eichler integrals for a certain Kleinian groups.
On Preserving the Kobayashi Pseudodistance
Authors: Campbell L. Andrew , Ogawa Roy H.
Published: July 2016

If X is a complex space, the Kobayashi pseudo-distance dx is an intrinsic pseudometric on X defined as follows. If p and q are points of X, a chain α from p to q consists of intermediate points p0, …, pr with p0 = p and pr = q together with maps fi of the unit disc D = {z ∈ Cl‖z| < 1} into X and points ai and bi in D such that fi(ai) = Pi−1 and fi(bi) = pi for i = 1, …, r.
Continuous Boundary Behaviour for Functions Defined in the Open Unit Disc
Authors: Brown Leon , Gauthier P. M. , Hengartner Walter
Published: July 2016

This paper deals with cluster sets. While cluster sets can be considered in a more abstract setting, we shall limit ourselves to the study of functions f defined in the open unit disc D of the complex plane and taking their values on the Riemann sphere C̅. For p a point of the unit circle C, we denote by C(f,p) the cluster set of f at p, i.e., the set of all values w ∈ C̅ for which there is a sequence {zn}, zn ∈ D, such that zn → p and f(zn) → w. The point p is called a point of determination for f if C(f, p) is a singleton. In Section 1 we characterize the set of points of determination of a function f defined in D.
On the Asymptotic Behaviour of a Diffusion Process with Singular Drift
Authors: Kaneta Hitoshi
Published: July 2016

We discuss some peculiar features of the diffusion process whose characterization is given below. Let D be a bounded domain in the d-dimensional Euclidean space Ed with a smooth boundary ∂D. The domain D contains open balls (i = 1, · · ·, n) which are mutually disjoint. Our process is a diffusion process on the state space D ∪ ∂D which is locally equivalent to the Brownian motion except on the spheres ∂ and the boundary ∂D. By a diffusion process we mean a continuous strong Markov process. As to the terminology about Markov processes we refer to [2].
Sur L’Unicité Du Cône Convexe Divisible Constitué Par De Noyaux De Convolution De Dirichlet
Authors: Itä Masayuki
Published: July 2016

Dans toute la suite Rn désignera l’espace euclidien à dimension n (≧ 1). Pour un point x = (x1, x2, · · ·, xn) de Rn, on notera |x| = .La coordonnée sphérique dans Rn s’écrira (r, σ). R+ désignera l’ensemble {t ∈ R1; t ≧ 0}.
Caractérisation Du Principe De Domination Pour Les Noyaux De Convolution Non-Bornés
Authors: Itô Masayuki
Published: July 2016

Dans toute la suite X désignera un groupe abélien localement compact, séparé et dénombrable à l’infini; ξ sera sa mesure de Haar. Rappelons qu’un noyau de convolution N sur X signifie une mesure de Radon positive dans X et que, pour une mesure de Radon réelle μ dans X, N*μ s’appelle le N-potentiel de μ dès que cette convolution est définie au sens des mesures. Dans cette note, pour simplifier la discussion, nous supposerons qu’il n’existe aucun sous-groupe compact de X excepté {0}.
Gaussian random fields with projective invariance
Authors: Noda Akio
Published: July 2016

We shall consider the class of Gaussian random fields Xα = {X(A); A ∈ Rn} such that E{X(A) − X(B)} = 0 and E{(X(A) − X(B))2} = |A − B|α (0 < α < 2), where |A − B| denotes the Euclidean distance between two points A and B.
On a hypoelliptic boundary value problem
Authors: Matsuzawa Tadato
Published: July 2016

This paper is devoted to the investigation of the hypoellipticity of the following first boundary value problem:
On a Theorem Concerning the Prolongation of a Differential System
Authors: Matsushima Yozô
Published: July 2016

E. Cartan has proved that the prolonged system of a Pfaffian system in involution is also in involution. But he has treated only the case of a Pfaffian system of some special type. On the other hand in his book [3] he has reduced the solution of any differential system to the solution of a Pfaffian system of the type mentioned above, and this reduction is precisely the method of the prolongation of a differential system. Therefore it seems to be disirable to establish the above mentioned theorem in the case of an arbitrary differential system.
On some Asymptotic Properties of Poisson Process
Authors: Hida Takeyuki
Published: July 2016

The Poisson process , as is well-known, is a temporally and spatially homogeneous Markoff process satisfying

(1)

(2)

where k is a non-negative integer and λ is a positive constant. In this note we consider the random variable Lm(ω) which denotes the length of t-interval such that X(t, w) = m (m = 0, 1, 2,…) and some of other properties concerning them.
A Property of some Open Riemann Surfaces and Its Application
Authors: Kuroda Tadashi
Published: July 2016

As L. Sario [8] and the others have shown, an important method to investigate the properties of an open Rlemann surface F is the use of an exhaustion of F consisting of compact domains on F. But, for the same purpose, the investigation of properties of a non-compact region on F is also important.
Note on the Cohomology Groups of Associative Algebras
Authors: Nagao Hirosi
Published: July 2016

The cohomology theory of associative algebras has been developed by G. liochschild [1], [2], [3], and the 1-, 2-, and 3-dimensional cohomology groups have been interpreted with reference to classical notions of structure in his papers. Recently M. Ikeda has obtained, by a detailed analysis of Hochschild’s modules, an interesting structural characterization of the class of algebras whose 2-dimensional cohomology groups are all zero [5].
Über die Beziehung der Klassenzahlen der Unterkörper des bizyklischen bizuadratischen Zahlkörpers
Authors: Kubota Tomio
Published: July 2016

Mit Hilfe der Dedekindschen ζ-Funktion erhält man bekanntlich Klassenzahlrelationen gewisser algebraischen Zahlkörper. Ais ein Spezialfall gilt der

Satz l.1) Es sei K ein bizyklischer biquadratischer Zahlkörper und seien k0, k1und k2die drei quadratischen Teilkörper von K. Ferner seien h, h0, h1und h2die Klassenzahlen von K, k0, k1bzw. k3. Dann besteht die Relation

Hier ist Q der Index der Grupps der Einheiten , welche von der Einheiten von ki (i = 0, 1, 2) erzeugt wird, in der vollen Gruppe der Einheiten E von K: d.h. .
Regularity of solutions for quasi-linear parabolic equations
Authors: Ikeda Yoshiaki
Published: July 2016

Let Ω be a bounded domain in n-dimensional Euclidian space En (n ≧ 2), and consider the space-time cylinder Q = Ω × (0, T] for some fixed T > 0. In this paper we deal with the Cauchy and Dirichlet problem for a second order quasi-linear equation

(1.1) ut — div A(x, t, u, ux) + B(x, t, u, ux) = 0 for (x, t) ∈ Q,

(1.2) u(x, 0) = (ϕ)(x) in Ω and u(x, t) = tψ(x, t) for (x, t) ∈ Γ = ∂Ω × (0, T] ,

where ∂Ω is a boundary of Ω which satisfies the following condition (A) : Condition (A). There exist constants ρ0 and »0 both in (0,1) such that, for any sphere K(ρ) with center on ∂Ω and radius ρ ≦ ρ0, the inequality meas [K(ρ) ∩ Ω] ≦ (1 — λ0) × meas E(ρ) holds, where meas E means the measure of a measurable set E.
Boundary value problems of biharmonic functions
Authors: Tanaka Hidematu
Published: July 2016

Let Ω be a bounded domain of n-dimensional Euclidean space Rn (n ≥ 2). On Ω we consider the biharmonic equation
A complex Airy integral
Authors: Kubota Tomio
Published: July 2016

The Airy integral is a formula concerning the Fourier transform of a function like sin x3 or cos x3, and is written, for instance in [2], as

for x ≧ 0.
Hasse principles and the u-invariant over formally real fields
Authors: Ware Roger
Published: July 2016

In this paper we investigate the connection between the u-invariant, u(F), of a formally real field F as defined by Elman and Lam [2] and certain Hasse Principles studied by Elman, Lam and Prestel in [3].
Sur le semi-groupe de l’operateur inverse de Δ
Authors: Ito Yoshifusa
Published: July 2016

Soient N le noyau newtonien sur l’espace euclidien Rn à dimension n ≧ 3 et E l’espace de Banach formé par des fonctions finies et continues définies dans Rn s’annulant à l’infini et normé usuellement. Définissons l’opérateur de convolution K par Kf = –N*f. Dans cette note nous traitrons l’opérateur K dans E.
On the generalized Teichmüller spaces and differential equations
Authors: Kuribayashi Akikazu
Published: July 2016

It is well known that for the family F of Riemann surfaces {R(z)} defined by the equations y2 = x(x — l)(x — z), zεC — {0,1}, we have one independent abelian differential ω = y−1dx on each R(z) and if we consider z as a parameter on C — {0,1}, the integrals are solutions of the Gauss’s differential equation
Another approach to a non-elliptic boundary problem
Authors: Kato Yoshio
Published: July 2016

Let Ω be a bounded domain in ndimensional Euclidian space Rn(n ≧ 2)with C∞boundary Γ of dimension n— 1 and let there be given two real-valued C∞–functions α, β on Γ such that α≧ 0, β ≧ 0and α + β = lthroughout Γ.Then we consider the non-elliptic boundary value problem with λ ≧ 0 (which is always assumed, and in particular when λ =0, we further assume β ≢ 0,throughout this paper) :

(1)
Ample vector bundles on a rational surface (higher rank)
Authors: Hosoh Toshio
Published: July 2016

In the previous paper [1], we showed that the set of simple vector bundles of rank 2 on a rational surface with fixed Chern classes is bounded and we gave a sufficient condition for an H-stable vector bundle of rank 2 on a rational surface to be ample. In this paper, we shall extend the results of [1] to the case of higher rank.
On quantum theory in terms of white noise
Authors: Hida T. , Streit L.
Published: July 2016

It has often been pointed out that a much more manageable structure is obtained from quantum theory if the time parameter t is chosen imaginary instead of real. Under a replacement of t by i·t the Schrödinger equation turns into a generalized heat equation, time ordered correlation functions transform into the moments of a probability measure, etc. More recently this observation has become extremely important for the construction of quantum dynamical models, where criteria were developed by E. Nelson, by K. Osterwalder and R. Schrader and others [8] which would permit the reverse transition to real time after one has constructed an imaginary time (“Euclidean”) model.
The decay of the local energy for wave equations with discontinuous coefficients
Authors: Tamura Hideo
Published: July 2016

The exponential decay of the local energy for wave equations in exterior domains of the odd dimensional space has been proved in [1] ~ [6] etc. under the Dirichlet boundary condition and in [5], [7] under the Neumann condition and the other conditions. In this paper, we shall consider this problem for the following equation:
Über den Index geschlossener Geodätischer auf Flächen
Authors: Klingenberg Wilhelm
Published: July 2016

Wir betrachten geschlossene Geodatische c = (c(t), 0 ≤ t ≤ 1) auf Flächen. Der Einfachheit halber nehmen wir an, daß die Fläche kompakt ist, obwohl diese Annahme nur für einen Teil unserer Untersuchungen, insbesondere die Existenzsätze, notwendig ist. Die Geodätische c besitzt einen Index; es ist dies die maximale Anzahl von Parametern, mit der man Variationen von c bilden kann, die sämtlich aus kürzeren Kurven bestehen. Dabei sei hier vorausgesetzt, daß die geschlossene Geodätische c nicht-entartet ist.
Eine Darstellung der Intuitionistischen Logik in der Klassischen
Authors: Maehara Shôji
Published: July 2016

Für jeden, der sich an die klassische Logik gewöhnt ist, mag undenkbar sein, dass der „Satz vom ausgeschlossenen Dritten” in der intuitionistischen Logik im allgemeinen nicht anerkannt ist. Aber es ist ganz natürlich, wenn man diejenige Tatsache beobachtet, dass eine äusserlich gleiche Aussage in der klassischen Logik und in der intuitionistischen doch ungleiche inhaltliche Sinne haben kann.
Cycles and Endomorphisms of Abelian Varieties
Authors: Morikawa Hisasi
Published: July 2016

In the present paper we shall remark that to each class of algebraically equivalent cycles on a Jacobian variety we can attach a symmetric element of the ring of endomorphisms of the variety and shall prove some formulae concerning attached symmetric elements.
A Lemma on a Free Group
Authors: Morimoto Akihiko
Published: July 2016

The purpose of this note is to prove the following proposition, which is made use of in the preceding paper by Mr. M. Kuranishi in this number. First we shall explain the notations. Let be a word with respect to two letters, and let G be a free group generated by two free generators x and y.
Construction of fundamental solutions of hypoelliptic equations by the use of a probabilistic method
Authors: Matsuzawa T.
Published: July 2016

A. Friedman, [5] has constructed the fundamental solutions for a class of degenerate parabolic equations of the second order by making use of a probabilistic method and obtained the estimates for the fundamental solutions, especially near the degenerating manifolds (obstacles) of given operators, where a probabilistic method plays an important role.
On bimeromorphic automorphisms of hyperbolic complex spaces
Authors: Kodama Akio
Published: July 2016

Let X be a hyperbolic complex space in the sense of S. Kobayashi [2]. We write Aut(X)(resp. Bim (X)) for the group of all biholomorphic (resp. bimeromorphic) automorphisms of X.
The coerciveness for integro-differential quadratic forms and Korn’s inequality
Authors: Kato Yoshio
Published: July 2016

Let Q be a bounded open set of Rn (n ≧ 2) with a C∞ boundary Γ and assume that be functions in such that where s1, …, sN are integers ≧ and are n-tuples of non-negative integers with
Principal polarizations of abelian surfaces over finite fields
Authors: Turner Stuart
Published: July 2016

In § 1 of this note we construct abelian varieties of dimension two defined over Fpn, n odd, which admit infinitely many distinct principal polarizations. These polarizations determine an infinite family of geometrically non-isomorphic complete singular curves defined and irreducible over Fpn which have isomorphic Jacobian varieties. In § 2 we calculate the zeta function of these curves.
Completeness of two theories on ordered abelian groups and embedding relations
Authors: Komori Yuichi
Published: July 2016

The first order language ℒ that we consider has two nullary function symbols 0, 1, a unary function symbol –, a binary function symbol +, a unary relation symbol 0 <, and the binary relation symbol = (equality). Let ℒ′ be the language obtained from ℒ, by adding, for each integer n > 0, the unary relation symbol n| (read “n divides”).
Moduli spaces of the stable vector bundles over abelian surfaces
Authors: Umemura Hiroshi
Published: July 2016

Let X be a projective non-singular variety and H an ample line bundle on X. The moduli space of H-stable vector bundles exists by Maruyama [4]. If X is a curve defined over C, the structure of the moduli space (or its compactification) M(X, d, r) of stable vector bundles of degree d and rank r on X is studied in detail. It is known that the variety M(X, d, r) is irreducible. Let L be a line bundle of degree d and let M(X, L, r) denote the closed subvariety of M(X, d, r) consisting of all the stable bundles E with det E = L.
Formal meromorphic functions and cohomology on an algebraic variety
Authors: Speiser Robert
Published: July 2016

Let X be a projective Gorenstein variety, Y ⊂ X a proper closed subscheme such that X is smooth at all points of Y, so that the formal completion of X along Y is regular.
Realization of Chern classes by subvarieties with certain singularities
Authors: Morimoto Hiroshi
Published: July 2016

In this paper we are concerned with subvarieties which realize Chern classes of holomorphic vector bundles. The existence of these subvarieties is known in some cases (for instance, see A. Grotheridieck [2] for projective algebraic varieties and M. Cornalba and P. Griffiths [1] for Stein manifolds). In the present paper we realize Chern classes by subvarieties with singularities of a certain type. Our main theorem is as follows (see Def. 1.1.3 for the definition of quasilinear subvarieties).
Perturbed billiard systems II. Bernoulli properties
Authors: Kubo Izumi , Murata Hiroshi
Published: July 2016

One of the authors has shown the ergodicity of the perturbed billiard system which can describe the motion of a particle in a potential field of a special type [5], [6]. Since then, some development has been made, and we are now able to show the Bernoulli property of the system in this article. We hope, the result gives a new progress in statistical mechanics. Our method of the proof is inspired by the idea of D. S. Ornstein and B. Weiss [9], which has been used by G. Gallavotti and D. S. Ornstein [3] for a Sinai billiard system.
Rings of convergent power series and Weierstrass Preparation Theorem
Authors: Sugatani Takasi
Published: July 2016

Let B be a B-ring with a nonarchimedean valuation | |, i.e., B is an integral domain satisfying the following conditions: (i) B is bounded (| a | ≤ 1 for every a ∊ B), (ii) the boundary forms a multiplicative group.
Two algebraic deformations of a K3 surface
Authors: Comenetz Daniel
Published: July 2016

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.
The coincidence of fields of moduli for non-hyperelliptic curves and for their jacobian varieties
Authors: Sekiguchi Tsutomu
Published: July 2016

The notion of fields of moduli introduced first by Matsusaka [8] has been developed by Shimura [12] exclusively in the area of polarized abelian varieties. Later Koizumi [7] gave an axiomatic treatment for the notion.
Brownian motion parametrized with metric space of constant curvature
Authors: Takenaka Shigeo , Kubo Izumi , Urakawa Hajime
Published: July 2016

P. Lévy introduced a generalized notion of Brownian motion in his monograph “Processus stochastiques et mouvement brownien” by taking the time parameter space to be a general metric space. Let (M, d) be a metric space and let O be a fixed point of M called the origin. Following his definition, a Brownian motion parametrized with the metric space (M, d) is a Gaussian system ℬ = {B(m); m ∈ M} such that the difference B(m) − B(m′) is a random variable with mean zero and variance d(m, m′), and that B(O) = 0.
Some lie algebras of vector fields and their derivations Case of partially classical type
Authors: Kanie Yukihiro
Published: July 2016

Let be a smooth foliated manifold, and the Lie algebra of all leaf-tangent vector fields on M.
Sur l’inégalité fondamentale de H. Cartan pour les systèmes de fonctions entières
Authors: Toda Nobushige
Published: July 2016

Soit f = (f0, f1, …, fn) (n ≧ 1) un système transcendant dans le plan |z| < ∞; c’est-à-dire, les fonctions f0, f1, … , fn sont entières sans zéros communs à toutes et
Homotopy classification of connected sums of sphere bundles over spheres, I
Authors: Ishimoto Hiroyasu
Published: July 2016

In the classification problems of manifolds, the connected sums of sphere bundles over spheres appear frequently. In fact, the manifolds with certain tangential and homotopy properties come to such connected sums (cf. Tamura [15], [16], Ishimoto [6], [8], [9]). Motivated by those, in this paper and the subsequent paper, we classify connected sums of sphere bundles over spheres up to homotopy equivalence by extending the results of I. M. James and J. H. C. Whitehead [10], [11], which correspond to the case that the connected sums of the above happen to be single sums. We also use Wall [17] in the case when the fibres and the base spaces of bundles are same dimensional.
Super-Łukasiewicz propositional logics
Authors: Komori Yuichi
Published: July 2016

In [8] (1920), Łukasiewicz introduced a 3-valued propositional calculus with one designated truth-value and later in [9], Łukasiewicz and Tarski generalized it to an m-valued propositional calculus (where m is a natural number or ) with one designated truth-value.
On the cohomology of congruence subgroups of symplectic groups
Authors: Lai K. F.
Published: July 2016

This paper is concerned with the cohomology at “infinity” (in the sense of Harder [4], [5]) of a congruence subgroup of the symplectic group G = Sp(2l, R). G is the subgroup of GL(2l, R) consisting of matrices g satisfying tgJg = J where
On the douady space of a compact complex space in the category
Authors: Fujiki Akira
Published: July 2016

Let X be a complex space. Let Dx be the Douady space of compact complex subspaces of X [6] and px: Zx→ Dx the corresponding universal family of subspaces of X.
On some dimension formula for automorphic forms of weight one I
Authors: Hiramatsu Toyokazu
Published: July 2016

Let Γ be a fuchsian group of the first kind not containing the element . We shall denote by d0 the number of linearly independent automorphic forms of weight 1 for Γ. It would be interesting to have a certain formula for d0. But, Hejhal said in his Lecture Notes 548, it is impossible to calculate d0 using only the basic algebraic properties of Γ. On the other hand, Serre has given such a formula of d0 recently in a paper delivered at the Durham symposium ([7]). His formula is closely connected with 2-dimensional Galois representations.
Integral representations with trivial first cohomology groups
Authors: Endo Shizuo , Miyata Takehiko
Published: July 2016

Let Π be a finite group and denote by MΠ the class of finitely generated Z-free ZΠ-modules. In [2] we defined a certain equivalence relation on MΠ and constructed the abelian semigroup T(Π), which was studied in [3] (see [1] and [5], too).
On the distribution (mod 1) of polynomials of a prime variable
Authors: Liu Ming-Chit , Tsang Kai-Man
Published: July 2016

Throughout, ε is any small positive number, θ any real number, n, nj, k, N some positive integers and p, pj any primes. By ‖θ‖ we mean the distance from θ to the nearest integer. Write C(ε), C(ε, k) for positive constants which may depend on the quantities indicated inside the parentheses.
Independence of the increments of Gaussian random fields
Authors: Inoue Kazuyuki , Noda Akio
Published: July 2016

Let be a mean zero Gaussian random field (n ⋜ 2). We call X Euclidean if the probability law of the increments X(A) − X(B) is invariant under the Euclidean motions. For such an X, the variance of X(A) − X(B) can be expressed in the form r(|A − B|) with a function r(t) on [0, ∞) and the Euclidean distance |A − B|.
On non-elliptic boundary problems
Authors: Kato Yoshio
Published: July 2016

The purpose of this paper is to study the boundary value problems for the second order elliptic differential equation
Homogeneous Siegel domains
Authors: Dorfmeister Josef
Published: July 2016

In 1935 E. Cartan classified all symmetric bounded domains [6]. At that time he proved that a bounded symmetric domain is homogeneous with respect to its group of holomorphic automorphisms. Thus the more general problem of investigating homogeneous bounded domains arose. It was known to E. Cartan that all homogeneous bounded domains of dimension ≤3 are symmetric [6]. For domains of higher dimension little was known. The first example of a 4-dimensional, homogeneous, non-symmetric bounded domain was provided by I. Piatetsky-Shapiro [41]. In several papers he investigated homogeneous bounded domains [20], [21], [41], [42], [43]. One of the main results is that all such domains have an unbounded realization of a certain type, as a so-called Siegel domain. But many questions still remained open. Amongst them the question for the structure and explicit form of the infinitesimal automorphisms of a homogeneous Siegel domain.
Dirichlet integral and Picard principle
Authors: Nakai Mitsuru , Tada Toshimasa
Published: July 2016

A density P on the punctured unit disk Ω:0 < |z| <1 is a 2-form P(z)dxdy whose coefficient P(z) is a real valued nonnegative locally Hölder continuous function on the closed punctured unit disk Ω:0< |z| <≦1. Here we consider Ω as an end of the punctured sphere 0 < |z| ≦ + + so that the point z = 0 is viewed as the ideal boundary δΣ of Σ and the unit circle |z| = 1 as the relative boundary δΣ of Σ. We denote by D = D(Σ) the family of densities on Σ.
Modular representations of abelian groups with regular rings of invariants
Authors: Nakajima Haruhisa
Published: July 2016

Let k be a field of characteristic p and G a finite subgroup of GL(V) where V is a finite dimensional vector space over k. Then G acts naturally on the symmetric algebra k[V] of V. We denote by k[V]G the subring of k[V] consisting of all invariant polynomials under this action of G. The following theorem is well known.

Theorem 1.1 (Chevalley-Serre, cf. [1, 2, 3]). Assume that p = 0 or (|G|, p) = 1. Then k[V]G is a polynomial ring if and only if G is generated by pseudo-reflections in GL(V).
Existence and bifurcation of solutions for Fredholm operators with nonlinear perturbations
Authors: Niikura Yasuo
Published: July 2016

In this paper we shall discuss nonlinear eigenvalue problems for the equations of the form

where L is a linear operator on a real Banach space X with non-zero kernel, K(-) is a linear or nonlinear operator on X and M(·, ·) is an operator from X X R into X. Equations of the form (1) arise in various fields of physics and engineering.
Maximal algebraic subgroups of the Cremona group of three variables—Imprimitive algebraic subgroups of exceptional type
Authors: Umemura Hiroshi
Published: July 2016

Enriques and Fano [4], [5] classified all the maximal connected algebraic subgroups of Cr3. Our aim is to give modern and rigorous proofs to their results. In [10], we studied the primitive subgroups. In this paper, we deal with exceptional imprimitive groups. The imprimitivity is an analytic notion. The natural translation of the imprimitivity in algebraic geometry is the de Jonquières type operation (definition (2.1)). Every de Jonquières type operation is imprimitive. However, the difference of these notions is subtle.
Families of abelian surfaces with real multiplication over Hilbert modular surfaces
Authors: van der Geer G. , Ueno K.
Published: July 2016

Around the beginning of this century G. Humbert ([9]) made a detailed study of the properties of compact complex surfaces which can be parametrized by singular abelian functions. A surface parametrized by singular abelian functions is the image under a holomorphic map of a singular abelian surface (i.e. an abelian surface whose endomorphism ring is larger than the ring of rational integers). Humbert showed that the periods of a singular abelian surface satisfy a quadratic relation with integral coefficients and he constructed an invariant D of such a relation with respect to the action of the integral symplectic group on the periods.
A property of new coordinates defining augmented Schottky spaces
Authors: Sato Hiroki
Published: July 2016

In the previous paper [3], we introduced new coordinates to the Schottky space, and defined the augmented Schottky spaces . Here, in § 1, we will define fiber spaces over the augmented Schottky spaces. In §2, we will consider a property of the new coordinates, namely, we will state a relation between limits of sequences of elements of the new coordinates and limits of sequences of length of loops on Riemann surfaces.
On maximal orders of division quaternion algebras over the rational number field with certain optimal embeddings
Authors: Ibukiyama Tomoyoshi
Published: July 2016

In this paper, we shall give explicitZ-basis of certain maximal orders of definite quaternion algebras over the rational number fieldQ(See Theorems below). We shall also give some remarks on symmetric maximal orders in Ponomarev [9] and Hashimoto [6] (Proposition 4.3). More precise contents are as follows. LetDbe a division quaternion algebra overQ.
Onp-adic ArtinL-functions
Authors: Greenberg Ralph
Published: July 2016

In this paper we will discussp-adic ArtinL-functions. The existence of these functions is a simple consequence of a theorem of Deligne and Ribet [4]. One can formulate a “p-adic Artin conjecture” for these functions. Our primary purpose here is to relate this conjecture to the “main conjecture” discussed by Coates in [3]. We will describe the precise formulations of these conjectures that we will use later. Our main result will be that in fact the main conjecture implies thep-adic Artin conjecture.
On the base field change of P-rings and P-2 rings
Authors: Tanimoto Hiroshi
Published: July 2016

One finds the following example in [3, (34, B)]:

Let k be a field of characteristic p and be n-variables over k. Then if p > 0 and [k : kp] = ∞, is an n-dimensional regular local ring but not a Nagata ring. In particular it is not an excellent ring.
Galois action on some ideal section points of the abelian variety associated with a modular form and its application
Authors: Momose Fumiyuki
Published: July 2016

For an integer N let X1(N) be the modular curve defined over Q which corresponds to the modular group Γ1(N) To each primitive cusp form f ═ Σ amqm, a1═1, (Γ normalized new form in the sense of [1]) on Γ1(N) of weight 2, there corresponds a factor Jf of the jacobian variety of X1(N) (cf. Shimura [19]).
Chow instability of certain projective varieties
Authors: Ishii Shihoko
Published: July 2016

A pair (X, D) of a projective variety X and a very ample divisor D on X is called stable (resp. semi-stable, resp. unstable) if the Chow point corresponding to the embedding is SL(N + 1)-stable (resp. semi-stable, resp. unstable). The criterion for stability is one of the most important steps in proving the existence of moduli spaces.
The extended plus-one hypothesis—A relative consistency result
Authors: Slaman Theodore A.
Published: July 2016

This paper includes a proof, relative to the consistency of ZFC, of the consistency of ZFC, the continuum has singular cardinality and the extended plus-one hypothesis.
Descent of P-property by proper surjective morphisms
Authors: Ogoma Tetsushi
Published: July 2016

It is well known that the quasi-exellent property (i.e. G-ring and J-II) ascends by finite type morphisms. On the other hand Greco showed in [2, Proposition 4.1 and Proposition 2.3] that G-property (i.e. formal fibers are geometrically regular) does not descend by finite type morphisms, although J-II property (i.e. any finite type algebra has regular locus open) does.
Symmetric homogeneous convex domains
Authors: Tsuji Tadashi
Published: July 2016

Let D be a convex domain in the n-dimensional real number space Rn, not containing any affine line and A(D) the group of all affine transformations of Rn leaving D invariant. If the group A(D) acts transitively on D, then the domain D is said to be homogeneous. From a homogeneous convex domain D in Rn, a homogeneous convex cone V = V(D) in Rn+1 = Rn × R is constructed as follows (cf. Vinberg [11]):

which is called the cone fitted on the convex domain D.
A Mordell-Weil group of rank 8, and a subgroup of finite index
Authors: Schwartz Charles F.
Published: July 2016

It is well known [c.f. Kas] that every elliptic surface, with geometric genus 0, is given by a Weierstrass equation of the form

(relative to a suitable parameter, u, for the base) where the a’s and b’s are constants. For sufficiently general choices of a’s and b’s, the Mordell-Weil group (i.e., the group of solutions (x, y), with x and y rational functions of u) has rank 8.
A norm residue map for central extensions of an algebraic number field
Authors: Furuta Yoshiomi
Published: July 2016

Let K be a finite Galois extension of an algebraic number field k with G = Gal (K/k), and M be a Galois extension of k containing K. We denote by resp. the genus field resp. the central class field of K with respect to M/k. By definition, the field is the composite of K and the maximal abelian extension over k contained in M. The field is the maximal Galois extension of k contained in M satisfying the condition that the Galois group over K is contained in the center of that over k. Then it is well known that Gal is isomorphic to a factor group of the Schur multiplicator H-3(G, Z), and is isomorphic to H-3(G, Z) when M is sufficiently large. In this case we call M abundant for K/k (See Heider [3, § 4] and Miyake [6, Theorem 5]).
On central extensions of a Galois extension of algebraic number fields
Authors: Miyake Katsuya
Published: July 2016

Let k be an algebraic number field of finite degree, and K a finite Galois extension of k. A central extension L of K/k is an algebraic number field which contains K and is normal over k, and whose Galois group over K is contained in the center of the Galois group Gal(L/k). We denote the maximal abelian extensions of k and K in the algebraic closure of k by kab and Kab respectively, and the maximal central extension of K/k by MCK/k. Then we have Kab⊃MCK/k⊃kab·K.
Integrable derivations in rings of unequal characteristic
Authors: Restuccia Gaetana , Matsumura Hideyuki
Published: July 2016

In this paper we will investigate integrability of derivations in rings of unequal characteristic. Generally speaking this case is more difficult than the case of characteristic p which was studied in [4], New interesting phenomena arise, cf. e.g. Theorem 1 and Example 3. Although we obtain useful sufficient conditions for integrability only in very restricted cases, we also give several examples to illuminate the situation.
The invariant polynomial algebras for the groups IU(n) and ISO(n)
Authors: Kaneta Hitoshi
Published: July 2016

By the coadjoint representation of a connected Lie group G with the Lie algebra g we mean the representation CoAd(g) = tAd(g-1) in the dual space g*. Imitating Chevalley’s argument for complex semi-simple Lie algebras, we shall show that the CoAd (G)-invariant polynomial algebra on g* is finitely generated by algebraically independent polynomials when G is the inhomogeneous linear group IU(n) or ISO(n). In view of a well-known theorem [8, p. 183] our results imply that the centers of the enveloping algebras for the (or the complexified) Lie algebras of these groups are also finitely generated. Recently much more inhomogeneous groups have been studied in a similar context [2]. Our results, however, are further reaching as far as the groups IU(n) and ISO(n) are concerned [cf. 3, 4, 6, 7, 9].
Weak solutions of a quasi-linear degenerate elliptic system with discontinuous coefficients
Authors: Ikeda Yoshiaki
Published: July 2016

We shall discuss regularities and related topics on weak solutions of the system of the following quasi-linear elliptic differential equations (a combination of almost single equations)

in a bounded domain Ω in Rn (n ≧ 2), where A1j … (A1j …, Anj) are given vector functions of (x, u, ▽uj), Bj are scalar functions of the same variables, and ▽uj = (∂uj/∂x1, …, ∂uj/∂xj denote the gradients of the uj = uj(x) (j = 1, …, m).
On Northcott-Rees theorem on principal systems
Authors: Yoshino Yuji
Published: July 2016

Let R be a local ring with maximal ideal m and let us make the following definition according to the paper [NR] of Northcott and Rees, which is essentially due to F. S. Macaulay.
Abundant central extensions of non-trivial genera
Authors: Miyake K. , Ormerod N.
Published: July 2016

Let k be either a local or a global field, and K be a finite Galois extension of k with g = Gal (K/k). Let L be a Galois extension of K which is also Galois over k. Such an extension is called central if Gal(L/iT) lies inside the centre of Gal(L/K). Clearly L is abelian over K. Next set L* = L∩K · kab where kab is the maximal abelian extension of k in its algebraic closure. This is the genus field of L over K/k.
A limit theorem for two-dimensional conditioned random walk
Authors: Shimura Michio
Published: July 2016

Let {(Sn, Tn), n = 0, 1, 2, …} be a two-dimensional random walk with stationary independent increments starting at the origin 0. Throughout the paper we always assume the following condition:
The variational theory of higher-order linear differential equations
Authors: Teranishi Yasuo
Published: July 2016

In his paper [2], [3], D. A. Hejhal investigated the variational theory of linear polynomic functions. In this paper we are concerned with the variational theory of higher-order differential equations. To be more precise, consider a compact Riemann surface having genus g > 1. As is well known, we can choose a projective coordinate covering U = (Ua, za). Fix this coordinate covering of X. We shall be concerned with linear ordinary differential operators of order n defined in each projective coordinate open set Ua
A characterization of internal functions on multiply connected regions
Authors: Rubel Lee A.
Published: July 2016

The notion of internal function enters naturally in the study of factorization of function in Lumer’s Hardy spaces—see [RUB], where this aspect is developed in some detail.
Boundedness of singular integral operators of Calderon type, III
Authors: Murai Takafumi
Published: July 2016

In this paper we investigate the boundedness of Cauchy kernels. The Cauchy kernel associated with a locally integrable real-valued function θ(x) is defined by
Kählerian submanifolds in a complex projective space with second fundamental form of polynomial type
Authors: Takagi Ryoichi
Published: July 2016

Let PN be an iV-dimensional complex projective space with Fubini-Study metric of constant holomorphic sectional curvature, and M be a Kählerian submanifold in PN. Let H be the second fundamental tensor + of M, and be the covariant derivative of type (1, 0) on M.
Tensor products of positive definite quadratic forms, VII
Authors: Kitaoka Yoshiyuki
Published: July 2016

In this paper we generalize results of the third paper of this series. As a corollary we can show the following: Let Li (1 ≤ i ≤ n) be a positive definite quadratic form which is equivalent to one of Cartan matrices of Lie algebras of type An (n ≥ 2), Dn (n ≥ 4), E6, E7, E8 and assume that is positive definite quadratic forms and satisfies that rk Mt ≥ 2 and implies rk K or rk L = 1. Then we have n = m and Lt is equivalent to a constant multiple of Ms(i) for some permutation s. Therefore we get the uniqueness of decompositions with respect to tensor products in this case.
p-Torsion points on elliptic curves defined over quadratic fields
Authors: Momose Fumiyuki
Published: July 2016

Let p be a prime number and k an algebraic number field of finite degree d. Manin [14] showed that there exists an integer n = n(k,p) (≧0) which satisfies the condition
A zeta function connected with the eigenvalues of the Laplace-Beltrami operator on the fundamental domain of the modular group
Authors: Fujii Akio
Published: July 2016

Let ; … run over the eigenvalues of the discrete spectrum of the Laplace-Beltrami operator on L2(H/yΓ), where H is the upper half of the complex plane and we take Γ = PSL(2, Z). It is well known that Let a be a positive number. Here we are concerned with the zeta function defined by
On solutions of variational inequalities constrained on a subset of positive capacity
Authors: Hayasida Kazuya , Nagase Haruo
Published: July 2016

1. Let Ω be a bounded domain of Rn with boundary ∂Ω and let E be a compact subset of Ω. We assume that both ∂Ω and E have positive capacity. The norm and the inner product in L2(Ω) are simply denoted by ‖ ‖ and (,) respectively.
On a dual relation for addition formulas of additive groups II
Authors: Watanabe Toshihiro
Published: July 2016

This paper is a continuation of our previous memoir [28], hereafter referred to as I, and constitutes the second chapter of this series. As stated in I, our aim in this series is to examine properties of a polynomial sequence with several variables satisfying an addition formula by means of the down-ladder, and to give a generalization of so called classical polynomials.
On the rank of CM-Type
Authors: Yanai Hiromichi
Published: July 2016

In the present note, we prove that every simple CM-type is non-degenerate (i.e. the rank is maximal) if the dimension of corresponding abelian varieties is a prime. This follows directly from the argument of Tankeev [5], in which he has treated the 5-dimensional case.

Recently, S. G. Tankeev and K. A. Ribet have established similar results for more general types of abelian varieties (see [3], [4], [6]).
On the number of diffeomorphism classes in a certain class of Riemannian manifolds
Authors: Yamaguchi Takao
Published: July 2016

The study of finiteness for Riemannian manifolds, which has been done originally by J. Cheeger [5] and A. Weinstein [13], is to investigate what bounds on the sizes of geometrical quantities imply finiteness of topological types, —e.g. homotopy types, homeomorphism or diffeomorphism classes-— of manifolds admitting metrics which satisfy the bounds. For a Riemannian manifold M we denote by RM and KM respectively the curvature tensor and the sectional curvature, by Vol (M) the volume, and by diam(M) the diameter.
Countable -admissible Ordinals
Authors: Shinoda Juichi
Published: July 2016

In [3], Platek constructs a hierarchy of jumps indexed by elements a of a set of ordinal notations. He asserts that a real X ⊆ ω is recursive in the superjump S if and only if it is recursive in some . Unfortunately, his assertion is not correct as is shown in [1]. In [1], it also has been shown that an ordinal > ω is -admissible if it is |a|S-recursively inaccessible, where |a|s- is the ordinal denoted by a.
Projective structures of elliptic differential operators
Authors: Ueno Kazushige
Published: July 2016

In the study of differential equations from the standpoint of the automorphism pseudogroups, the differential invariants of the pseudogroups play an important role.

A general study of pseudogroups and their differential invariants originated with Sophus Lie. He applied his study to the classification of ordinary and partial differential equations. So as to study differential equations from his point of view, it is very important to write the given differential equation by the differential invariants of the automorphism pseudogroup. That is to say, the geometric structure of a differential equation is contained in the expression of the equation by its differential invariants.
Ideals with sliding depth
Authors: Herzog J. , Vasconcelos W.V. , Villarreal R.
Published: July 2016

We study here a class of ideals of a Cohen-Macaulay ring {R, m} somewhat intermediate between complete intersections and general Cohen-Macaulay ideals. Its definition, while a bit technical, rapidly leads to the development of its elementary properties. Let I = (x1 … xn) = (x) be an ideal of R and denote by H*(x) the homology of the ordinary Koszul complex K*(x) built on the sequence x. It often occurs that the depth of the module Hi i > 0, increases with i (as usual, we set depth (0) = ∞).
p-Adic properties of Siegel modular forms of degree 2
Authors: Nagaoka Shōyū
Published: July 2016

H. P. F. Swinnerton-Dyer determined the structure of the algebra of modular forms mod p for all prime numbers p in elliptic modular case (cf. [10]). Using his result, J.-P. Serre investigated the properties of p-adic modular forms and succeeded to construct the p-adic zeta functions for any totally real number fields (cf. [8]).
Construction of a solution of a certain evolution equation II
Authors: Shimizu Akinobu
Published: July 2016

Let D be a bounded domain in Rd with smooth boundary ∂D. We denote by Bt, t ≥ 0, a one-dimensional Brownian motion. We shall consider the initial-boundary value problem
On eigenvalues in the continuum of 2-body or many-body Schrödinger operators
Authors: Mochizuki Kiyoshi , Uchiyama Jun
Published: July 2016

Let us consider the following two problems.

(A) Does either

or

hold for the not identically vanishing solution of the equation

for x ∈ Ω ⊂ Rn (n ≥ 3), where λ is a constant satisfying λ > E0 and V(x) is a 2-body or many-body potential?
On the existence of condenser potentials
Authors: Berg Christian
Published: July 2016

The existence of condenser potentials was established in the framework of Dirichlet spaces by Beurling and Deny, cf. Deny [5] or Landkof [10], simply by choosing the potential of minimal energy within a certain convex set. This same idea works for non-symmetric Dirichlet spaces, cf. Bliedtner [3].
A note on some ordered ring
Authors: Yasumoto Masahiro
Published: July 2016

An ordered ring with the least positive element 1 is a “Z-ring” if for each natural number n,
Tensor Products of Positive definite Quadratic forms III
Authors: Kitaoka Yoshiyuki
Published: July 2016

In the previous papers [2], [3] we treated the following two questions. Let L,M,N be positive definite quadratic lattices over Z:

(i) If L, M are indecomposable, then is L⊗M indecomposable?

(ii) Does L ⊗ M ⋍ L ⊗ N imply M ⋍ N?
On the maximal abelianℓ-extension of a finite algebraic number field with given ramification
Authors: Miki Hiroo
Published: July 2016

Letkbe a finite algebraic number field and letℓbe a fixed odd prime number. In this paper, we shall prove the equivalence of certain rather strong conditions on the following four things (1) ~ (4), respectively :

(1) the class number of the cyclotomicZℓ-extension ofk,

(2) the Galois group of the maximal abelianℓ-extension ofkwith given ramification,

(3) the number of independent cyclic extensions ofkof degreeℓ, which can be extended to finite cyclic extensions ofkof anyℓ-power degree, and

(4) a certain subgroupBk(m, S) (cf. § 2) ofk×/k×)ℓmfor any natural numberm(see the main theorem in §3).
A Note on Infinitesimal Holonomy Groups
Authors: Nijenhuis Albert
Published: July 2016

In a recent paper [1], H. Ozeki has extended the author’s results [2] on local and infinitesimal holonomy groups for connections in linear fiber bundles (whose fiber is a vector space) to general fiber bundles whose structure group is a Lie group. Ozeki’s Lemma 7 (corresponding to the author’s Lemma 5.2) appears to be rather crucial in the development, while the proof is somewhat involved.—This note intends to present a more direct proof of the lemma, stating a case in which the local holonomy group H*(x)and the infinitesimal holonomy group H’(x)coincide:
Sur Un Théorème de M. Matsushima
Authors: Yano Kentaro
Published: July 2016

Dans une Note parue dans ce Journal, M. Matsushima [1] a démontré le

Théorème. Dans un espace compact de Kähler-Einstein dont la courbure est positive, un vecteur analytique contrevariant u peut s’écrire d’une et d’une seule manière sous la forme u = v + Fw où v et w sont tous les deux les vecteurs de Killing et F le tenseur définissant la structure complexe de l’espace.