bluuebunny/crossref_metadata_2025 huggingface dataset:
Eichler Maps and Hyperbolic Fourier Expansion
Authors: Hiramatsu Toyokazu
Published: July 2016

In his lecture notes ([1, pp. 33-35], [2, pp. 145-152]), M. Eichler reduced ‘quadratic’ Hilbert modular forms of dimension —k {k is a positive integer) to holomorphic automorphic forms of dimension — 2k for the reproduced groups of indefinite ternary quadratic forms, by means of so-called Eichler maps.
On a Certain Function Analogous to log|η(z)|
Authors: Asai Tetsuya
Published: July 2016

The purpose of this paper is to give the limit formula of the Kronecker’s type for a non-holomorphic Eisenstein series with respect to a Hubert modular group in the case of an arbitrary algebraic number field. Actually, we shall generalize the following result which is well-known as the first Kronecker’s limit formula. From our view-point, this classical case is corresponding to the case of the rational number field Q.
Hypoelliptic Overdetermined Systems with Variable Coefficients
Authors: Hashimoto Yoshiaki
Published: July 2016

Let

(1) p(x,D)u = f

be a system of partial difierential equations. We shall say that p (x,D) is hypoelliptic if the distribution solution u is in C∞ wherever f∈C∞ (cf. section 2, Definition 5.)

Here we shall give a sufficient condition for the hypoellipticity of overdetermined systems with variable coefficients.
Some Groups Whose S3-Subgroups Have Maximal Class
Authors: Cline Ed
Published: July 2016

In this paper, we investigate several classes of groups, among which the most general is defined as follows:

Definition 1.1. A finite group G is a SR-group if it contains a subgroup P1 of order 3 satisfying:

(a)

A/S3-subgroup P2 of NGP1 is elementary of order 9;

(b)

NG(P2)/P2 acts semi-regularly by conjugation on the conjugates of P1 contained in P2.
Ga-Action of the Affine Plane
Authors: Miyanishi Masayoshi
Published: July 2016

Recently, R. Rentschler [4] proved that if k is a field of characteristic 0, any action of the additive group Ga on the affine plane is equivalent to an action of the form t(x, y) = (x, y + tf(x), where t∈Ga(k), (x, y)∈k2 and f∈k[X].
On Asymptotic Values of Slowly Growing Algebroid Functions
Authors: Suzuki Junji
Published: July 2016

Let f(z) be a k-valued algebroid function in |z| <. ∞ and

(1) F(z, f) ≡ A0(z)fk + A1(z)fk-1 + · · · Ak(z) = 0

be its defining equation such that the coefficients Ai(z) (i = 0, 1, · · ·, k) are entire functions without any common zero and the left hand side is irreducible.
Formal Moduli for p-Divisible Groups
Authors: Umemura Hiroshi
Published: July 2016

The formal moduli for one-parameter formal Lie groups was constructed by Lubin and Tate (1) by using Lazard’s methods. The aime of this paper is to prove the existence of the formal moduli for higher dimensional formal groups.
Sequential Gaussian Markov Integrals
Authors: Beekman John A.
Published: July 2016

In [6] R.H. Cameron defined and studied a sequential Wiener integral. This was motivated by the function space integral R.P. Feynman used in [12] to give a solution to the Schröedinger equation. In [5] the present author studied sequential Gaussian Markov integrals with a positive parameter. This paper gives sufficient conditions on the integrand for such integrals to exist, when the parameter is complex. These sequential integrals are related to ordianry Gaussian Markov integrals through a Fourier transform type formula extended from [5]. We shall show that such integrals are equal to conditional Wiener integrals of suitably modified functionals.
KSO-Groups for 4-Dimensional CW-Complexes
Authors: Sasao Seiya , Ando Yutaka
Published: July 2016

In this paper we shall determine KSO-groups for 4-dimensional CW-complexes by their cohomology rings. We denote by KSO(X) the group of orientable stable vector bundles over X. In 1959 A. Dold and H. Whitney [1] gave the classification of SO(n)-bundles over a 4-complex. It seems, however, to the authors that group structures of them are unknown. We shall give another definition of the difference bundles defined in [1], and we determine the group structure of KSO(X).
On Holomorphic Extension from the Boundary
Authors: Shiga Kiyoshi
Published: July 2016

Let D be a bounded domain of the complex n-space Cn(n≥2), or more generally a pair (M,D) a finite manifold (cf. Definition 2.1), and we assume the boundary ∂D is a smooth and connected submanifold. It is well known by Hartogs-Osgood’s theorem that every holomorphic function on a neighbourhood of ∂D can be continued holomorphically to D. Generalizing the above theorem we shall prove that if a differentiable function on ∂D satisfies certain conditions which are satisfied for the trace of a holomorphic function on a neighbourhood of ∂D, then it can be continued holomorphically to D (Theorem 2-5). The above conditions will be called the tangential Cauchy Riemann equations.
Bounded Energy-Finite Solutions of Δu = Pu on a Riemannian Manifold
Authors: Kwon Y.K. , Sario L. , Schiff J.
Published: July 2016

1. The classification of Riemann surfaces with respect to the equation Δu = Pu (P ≥ 0, P ≢ 0) was initiated by Ozawa [13] and further developed by L. Myrberg [8, 9], Royden [14], Nakai [10, 11], Sario-Nakai [15], Nakai-Sario [12], Glasner-Katz [3], and Kwon-Sario [7].
Some Identities on the Character Sum Containing x(x - 1)(x - λ)
Authors: Yamauchi Masatoshi
Published: July 2016

Let Fp be the prime field of characteristic p (p: an odd prime), and put = Fp - {0, 1}. Then for λ ∈ we define

,

where denotes the Legendre symbol, and consider the sum
P-Ample Bundles and Their Chern Classes
Authors: Gieseker David
Published: July 2016

In [9], Hartshorne extended the concept of ampleness from line bundles to vector bundles. At that time, he conjectured that the appropriate Chern classes of an ample vector bundle were positive, and it was hoped that there would be some criterion for ampleness of vector bundles similar to Nakai’s criterion for line bundles. In the same paper, Hartshorne also introduced the notion of p-ample when the ground field had characteristic p, proved that a p-ample bundle was ample and asked if the converse were true.
Characteristic Classes for PL Micro Bundles
Authors: Tsuchiya Akihiro
Published: July 2016

Let BSPL be the classifying space of the stable oriented PL micro bundles. The purpose of this paper is to determine H*(BSPL:Zp) as a Hopf algebra over Zp, where p is an odd prime number. In this chapter, p is always an odd prime number.
On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields
Authors: Shimura Goro
Published: July 2016

1. As Hecke showed, every L-function of an imaginary quadratic field K with a Grössen-character γ is the Mellin transform of a cusp form f(z) belonging to a certain congruence subgroup Γ of SL2(Z). We can normalize γ so that
On Derivations and Holomorphs of Nilpotent Lie Algebras
Authors: Leger G. , Luks E.
Published: July 2016

A linear Lie algebra is called toroidal if it is abelian and consists of semi-simple transformations. The maximum, t(L), of the dimensions of the toroidal subalgebras of the derivation algebra, Δ(L), is an invariant of L. This paper is mainly concerned with the relation between the magnitude of t(L) for nilpotent L and the structures of L and Δ(L).
Units of Real Quadratic Fields
Authors: Takaku Akira
Published: July 2016

1. Let D be a positive square-free integer. Throughout this note we shall use the following notations;

d = d(D): the discriminant of ,

t0, u0: the least positive solution of Pell’s equation t2 — du2 = 4,
Stable Manifolds of a Map and a Flow for a Compact Manifold
Authors: Kato Masaharu
Published: July 2016

The purpose of this paper is to generalize the notion of the stable manifolds in Smale [5] and [6], in which the stable manifolds of flows or diifeomorphisms for a singular point or a closed orbit are defined in certain conditions. This generalization is concerned with Fenichel [1], He considers the stable manifolds of flows and diifeomorphisms for a torus. Here, we consider the case of a compact manifold. But our argument does not exactly imply Fenichel’s result.
Comparison Theorems on Regular Points for Multidimensional Markov Processes of Transient Type
Authors: Kanda Mamoru
Published: July 2016

The study of regular points for the Dirichlet problem has a long history. The probabilistic approach to regular points is originated by Doob [2] and [3] for Brownian motion and the heat process. The extension to general Markov processes is discussed in Dynkin [4] and [5]. They also clarified the relation between the fine topology and regular points.

Regular points are by definition reflected in the behaviour of sample paths of Markov processes. Further the inclusion relation of collections of regular points for open sets determines the strength and the weakness of fine topologies between two processes. Hence it is meaningful to compare the collections of regular points for compact or open sets between two Markov processes apart from the Dirichlet problem.
Singularities of Projective Embedding (Points of order n on an Elliptic Curve)
Authors: Kato Akikuni
Published: July 2016

In the Plücker formula for a curve embedded in a higher dimensional projective space, one encounters the notion of stationary point (cf, [B], [W]). W. F. Pohl gave new view point about it in terms of vector bundles and he defined “the singularities of embedding” (cf. [P]). At first, we shall give dual formulation of Pohl’s one by means of the sheaf of principal parts of order n, and next we shall prove the following: If an elliptic curve is embedded in (n — l)-dimensional projective space as a curve of degree n, singularities of projective embedding of order n — 1 are exactly the points of order n with suitable choice of a neutral element on the curve which is an abelian variety of dimension one. The proof is given by making use of the relation between and Schwarzenberger’s secant bundle which we shall also give.
Manifolds Without Green’s Formula
Authors: Glasner Moses
Published: July 2016

Recently attention has been focused on manifolds that carry covariant tensors that are merely bounded measurable. In terms of these tensors global differential equations are defined and their weak solutions are called harmonic functions. Nakai initiated the classification of these manifolds with respect to the global properties of the harmonic functions that they carry.
Non-Essential Cluster Values and Normal Functions
Authors: Belna C. L.
Published: July 2016

We consider continuous functions f which map the open unit disk D into the Riemann sphere W. For a point ζ on the unit circle C, we say that χ is a chord at ζ if χ is a chord of C having one endpoint at ζ and that Δ is a Stolz angle at ζ if Δ is a Stolz angle with vertex ζ. Suppose S denotes either a chord at ζ, a Stolz angle at ζ, or D.
Ultimate Boundedness of the Systems Governed by Stochastic Differential Equations
Authors: Miyahara Yoshio
Published: July 2016

The stability of the systems given by ordinary differential equations or functional-differential equations has been studied by many mathematicians. The most powerful tool in this field seems to be the Liapunov’s second method (see, for example [6]).
Direction de Julia de Systèmes et Somme de Fonctions Normales
Authors: Toda Nobushige
Published: July 2016

Dans ce mémoire, on étend quelques résultats obtenus dans [10] au système et comme application, on considère sur la somme de fonctions normales.
La Dimension Cohomologique des Surfaces Algebriques
Authors: Umemura Hiroshi
Published: July 2016

En Géométrie Algébrique on a un critère pour qu’une surface moins une courbe soit affiine (Hartshorne (5)). Dans (5), on demande s’il existe un analogue analytique. Le but de cet article est de donner une condition numérique necessaire pour les surfaces complexes compactes (Théorème 1) et une condition suffisante pour les surfaces réglées (Théorème 2).
Surfaces with Mean Curvature Vector Parallel in the Normal Bundle
Authors: Chen Bang-Yen , Ludden Gerald D.
Published: July 2016

Let M be a connected surface immersed in a Euclidean m-space Em. Let h be the second fundamental form of this immersion it is a certain symmetric bilinear mapping for X ∈ M, where Tx is the tangent space and the normal space of M at x. Let H be the mean curvature vector of M in Em. If there exists a real λ such that for all tangent vectors X, Y in Tx, then ilf is said to be pseudo-umbilical at x.
Φ-Bounded Harmonic Functions and the Classification of Harmonic Spaces
Authors: Ow Wellington H.
Published: July 2016

By a harmonic space we mean a pair (X, H) where X is a locally compact, non-compact, connected, locally connected Hausdorff space ; and H is a sheaf of harmonic functions defined as follows: Suppose to each open set Ω ⊂ X there corresponds a linear space H(Ω) of finitely-continuous real-valued functions defined on Ω. Then H = {H(Ω)}Ω must satisfy the three axioms of Brelot (1) and in addition Axiom 4 of Loeb (4): 1 is H-superharmonic in X.
Le Nombre de Combinaisons Linéaires Exceptionnelles au sens de Nevanlinna et ses Applications
Authors: Toda Nobushige
Published: July 2016

Soient f = (f0, …, fn) un système transcendant dans le plan |z| < ∞ et X = {F} un ensemble de combinaisons des fonctions f0,…,fn, linéaires, homogènes à coefficients constants et linéairement indépendantes n + 1 à n + 1. Alors, combien de combinaisons exceptionnelles au sens de Nevanlinna y-a-t-il dans X? On sait que 1) il y en a une infinité dénombrable au plus en général ([5]) et 2) si l’ordre inférieur de f est égal à zéro, il y en a n au plus ([4]).
Invariant Measures of Ultimately Bounded Stochastic Processes
Authors: Miyahara Yoshio
Published: July 2016

The author discussed in [4] the ultimate boundedness of a system which is governed by a stochastic differential equation
Qualitative Theory of Codimension-One Foliations
Authors: Yamato Kazuo
Published: July 2016

The object of the present paper is to give a method of studying the topological properties of integral manifolds defined by a completely integrable one-form.

Our method is differential-topological. Through the singular points of the variation equation of the given one-form, we investigate the qualitative properties of the integral manifolds.
Note on the Harmonic Measure of the Accessible Boundary of a Covering Riemann Surface
Authors: Ohtsuka Makoto
Published: July 2016

The following relation was set up in [5] for an open covering Riemann surface ℜ with positive boundary over an abstract Riemann surface

(1)

when the universal covering surface of the projection is not of hyperbolic type when is of hyperbolic type this relation is reduced to

(2)
On the Product of L(1, χ)
Authors: Tatuzawa Tikao
Published: July 2016

Let k(≧3) be a positive integer and φ(k) be the Euler function. We denote by % one of the φ(k) characters formed with modulus k, and by % the principal character. Let Lis, %) be the L-series corresponding to % Throughout the paper we use c and c(ε) to denote respectively an absolute positive constant and a positive constant depending on parameter ε( >0) alone, not necessarily the same at their various occurrences. We use the symbol y = O(Z) for positive X when there exists a c satisfying Y ≦ in the full domain of existence of X and Y.
Meromorphic Functions with Large Sets of Julia Points
Authors: Colwell Peter
Published: July 2016

Let D = {z : |z| < 1} and C = {z : |z| = 1}. If W denotes the Riemann sphere equipped the chordal metric X, let f: D → W be meromorphic. A chord T lying in D except for an endpoint γ ∈ C is called a Julia segment for f if for each Stolz angle Δ in D at γ which contains T, f assumes infinitely often in Δ all values of W with at most two exceptions. We call γ ∈ C a Julia point for f if every chord in D ending at γ is a Julia segment for f, and we denote by J(f) the set of Julia points of f.
On Meromorphic Mappings into Taut Complex Analytic Spaces
Authors: Urata Toshio
Published: July 2016

In this paper, we study a certain difference between meromorphic mappings and holomorphic mappings into taut complex analytic spaces. We prove in §2 that, for any complex analytic space X, there exists a unique proper modification of X with center Sg (X) which is minimal with respect to the property that M(X) is normal and, for any T-meromorphic mapping f: X → Y (see Definition 1.3) into a complex analytic space Y, there exists a unique holomorphic mapping such that except some nowhere dense complex analytic set, where Sg(X) denotes the set of all singular points of X.
Order Comparisons on Canonical Isomorphisms
Authors: Nakai Mitsuru
Published: July 2016

Consider a nonnegative Hölder continuous 2-form P(z)dxdy (z = x + iy) on a connected Riemann surface R. We denote by P(R) the linear space of solutions u of the equation Δu = Pu on R and by PX(R) the subspace of P(R) consisting of those u with a certain boundedness property X. We also use the standard notations H(R) and HX(R) for P(R) and PX(R) with P ≡ 0.
Sur le Principe de Domination Pour les Noyaux de Convolution
Authors: Itô Masayuki
Published: July 2016

Dans toute la suite X désigne un groupe abélien localement compact et dénombrable à l’infini; ξ est sa mesure de Haar. Nous rappelons qu’un noyau de convolution N sur X signifie une mesure de Radon positive dans X. Il est connu que le principe de domination pour N joue un grand rôle dans la théorie du potentiel. Nous remarquons ici qu’il existe deux sortes des principes de domination pour N; l’un est défini par G. Choquet et J. Deny (cf. [3]), qui est très utile pour discuter le principe du balayage, et l’autre est introduit de celui dans le cardre plus large (cf. [8]). Nous montrerons d’abord que ceux sont équivalents. Par conséquent, on pourra discuter, en même temps, sur les mesures balayées relativement au noyau N et sur la résolvante associée au noyau N.
On some degenerate parabolic equations
Authors: Matsuzawa Tadato
Published: July 2016

Let Ω, I be open intervals in Rx = (— ∞ < x < ∞), Rt = (— ∞ < t < ∞) respectively. For a function a(x, t) ∈ C∞(Ω × I), consider the partial differential operator

(1.1) .
Two theorems on the class number of positive definite quadratic forms
Authors: Kitaoka Yoshiyuki
Published: July 2016

In this note we study the estimate from above and below and the asymptotic behaviour of the class number of positive definite integral quadratic forms.
Hironaka’s additive group schemes
Authors: Mizutani Hiroyuki
Published: July 2016

In [1] and [2], Hironaka referred to the importance of an additive group scheme BPn,P, which is associated with a point p in Pn, in connection with the resolution of singularities in characteristic p > 0. Also he showed that if the dimension of BPn,p is not greater than p, then it is a vector group.
On the behaviour of functions with finite weighted dirichlet integral near the boundary
Authors: Murai Takafumi
Published: July 2016

L. Carleson ([6]) proved the following theorem:

Let u be a finite continuous function in the unit open ball B with center zero in the complex plane.
On the theorem of Kishi for a continuous function-kernel
Authors: Higuchi Isao , Itô Masayuki
Published: July 2016

In the potential theory with respect to a non-symmetric function-kernel, the following theorem is obtained by M. Kishi ([3]).

Let X be a locally compact Hausdorff space and G be a lower semi-continuous function-kernel on X. Assume that G(x, x)>0 for any x in X and that G and the adjoint kernel Ğ of G satisfy “the continuity principle”.
The three-arc and three-separated-arc properties of meromorphic functions
Authors: Bagemihl Frederick
Published: July 2016

Let Γ be the unit circle and D be the open unit disk in the complex plane, and denote the Riemann sphere by Ω. Suppose that f(z) is a meromorphic function in D, and that ζ ∈ Γ.
On the existence of various bounded harmonic functions with given periods, II
Authors: Hara Masaru
Published: July 2016

Given a harmonic function u on a Riemann surface R, we define a period function

for every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.
Canonical isomorphisms of energy finite solutions of Δu = Pu on open Riemann surfaces
Authors: Nakai Mitsuru
Published: July 2016

We call a second order differential P(z)dxdy on a Riemann surface R a density if it is not identically zero and P(z) is a nonnegative Hölder continuous function of the local parameter z = x + iy in each parametric disk. To each density P on R we associate the linear space P(R) of C2 solutions of the equation Δu(z) = P(z)u(z) invariantly defined on R. We also consider subspaces PX(R) of P(R) consisting of solutions with certain boundedness properties X.
A note on a result of A. J. Lohwater and George Piranian
Authors: Csordas G. L.
Published: July 2016

Let I denote the set of all inner functions in H∞, where H∞ is the Banach algebra of all bounded analytic functions on the open unit disk D. Let I* denote the set of all functions f(z) in H∞ for which the cluster set C(f,α) at any point α on the circumference C = {α| |α| = 1} is either the closed unit disk |w| ≤ 1 or else a single point of modulus one. Clearly, I is a subset of I*. In [3] the author has proved that I is properly contained in I*. Recently, Lohwater and Piranian [7] have shown that there is an outer function in I*. The purpose of this note is to point out some applications of this result. In particular we shall show in Theorem 2.3 that there exist outer functions whose boundary behavior is similar to that of inner functions.
On Equivariant Vector Bundles on an Almost Homogeneous Variety
Authors: Kaneyama Tamafumi
Published: July 2016

Let k be an algebraically closed field of arbitrary characteristic. Let T be an n-dimensional algebraic torus, i.e. T = Gm × · · · × Gm n-times), where Gm = Spec (k[t, t-1]) is the multiplicative group.
Deformation Methods and the Strong Unbounded Representation Type of p-Groups
Authors: Donald J. D. , Flanigan F. J.
Published: July 2016

A basic problem in the representation theory of a finite group G is the determination of all indecomposable G-modules. Thus, for G = C(n) = a cyclic group of order n over an arbitrary field, the indecomposable representations, finite in number, are known from the theory of a single linear transformation. In 1954 Higman [9] showed that, in sharp contrast to the classical case of characteristic zero, an arbitrary finite group G has indecomposables of arbitrarily high dimension over any field of prime characteristic p iff the p-Sylow subgroup of G is non-cyclic (cf. unbounded representation type [3, p. 431]). Examples published by Heller and Reiner [8] in 1961 indicated that this phenomenon is even more extensive; reinterpreting a result of Dieudonné [4] as classifying the indecomposable modules for a square zero algebra on two generators, they showed that G = C(p) × C(p) (and therefore many other groups) has infinitely many non-isomorphic indecomposables in every even dimension over an infinite field of characteristic p (cf. strong unbounded representation type).
Démonstration Simple de la Representation Intégrale Du Noyau Complètement Sous-Harmonique et Invariant Par Rotations
Authors: Itä Masayuki
Published: July 2016

Dans toute la suite Rn désigne l’espace euclidien à dimension n (≧1). On désigne par Δ l’opérateur de Laplace sur Rn. Dans la théorie du potentiel, un noyau de convolution sur Rn signifie une mesure de Radon positive dans Rn. Rappelons qu’un noyau de convolution de Dirichlet N sur Rn est un noyau de convolution sur Rn tel que 1/N̂ soit égal à une fonction définie-négative dans Rn à valeurs réelles, où N̂ désigne la transformée de Fourier de N (cf. [1]). Pour un nombre p > 0, Gp désigne le noyau de convolution de Dirichlet sur Rn vérifiant (Δ — p)Gp = — ε (au sens des distributions), où ε est la mesure de Dirac à l’origine. Si n ≧ 3, on note G = G0 le noyau newtonien avec ΔG = −ε.
Some remarks on angular ranges and sequences of ρ-points for holomorphic functions
Authors: Yoshida H.
Published: July 2016

In this paper, we will give examples of holomorphic functions in the unit disc having singular connections between the growth of maximum modulus and angular ranges (Theorem A) as well as singular connections between the growth of spherical derivative and sequences of ρ-points (Theorem B).
Coding theory in Gaussian channel with feedback II: evaluation of the filtering error
Authors: Ihara Shunsuke
Published: July 2016

The main purpose of this paper is to give a method to evaluate the actual value of the filtering error which arises in the transmission of a signal process, using the optimal coding, over a Gaussian channel. In his earier papers ([4] and [7]), the author has shown a method to construct an optimal causal coding for which the filtering error is minimized and at the same time the mutual information is maximized.
On moduli of stable quasi abelian varieties
Authors: Nakamura Iku
Published: July 2016

In [4] Deligne-Mumford introduced a concept of stable curves and proved the existence of the coarse moduli space of stable curves of given genus in the category of algebraic stacks. Thereafter Mumford has shown this coarse moduli space is a protective scheme. We can consider the coarse moduli space of stable curves as a geometric compactification of the coarse moduli space of non-singular curves.
Square of Brownian motion
Authors: Nomoto Hisao
Published: July 2016

Let Xt be a stochastic process and Yt be its square process. The present note is concerned with the solution of the equation assuming Yt is given. In [4], F. A. Grünbaum proved that certain statistics of Yt are enough to determine those of Xt when it is a centered, nonvanishing, Gaussian process with continuous correlation function. In connection with this result, we are interested in sample function-wise inference, though it is far from generalities. A glance of the equation shows that the difficulty is related how to pick up a sign of . Thus if we know that Xt has nice sample process such as the zero crossings are finite, no tangencies, in any finite time interval, then observations of these statistics will make it sure to find out sample functions of Xt from those of Yt (see [2]). The purpose of this note is to consider the above problem from this point of view.
On the Hopf fibration S7 → S4 Over Z
Authors: Ono Takashi
Published: July 2016

Let K be the classical quaternion field over the field Q of rational numbers with the quaternion units 1, i, j, k, with relations i2 = j2 = − 1, k = ij = −ji. For a quaternion x ∈ K, we write its conjugate, trace and norm by and Nx, respectively. Put

and consider the map h: A → B defined by
Sur quelques combinaisons lineaires exceptionnelles au sens de nevanlinna, IV
Authors: Toda Nobushige
Published: July 2016

Soit f(z) une fonction algébroïde transcendante à n(≧2) branches dans le plan |z| < ∞ définie par une équation irréductible
A relation between order and defects of meromorphic mappings of Cn into Pn(C)
Authors: Noguchi Junjiro
Published: July 2016

Let f be a meromorphic mapping of the n-dimensional complex plane Cn into the N-dimensional complex projective space PN(C). We denote by T(r,f) the characteristic function of f and by N(r,f*H) the counting function for a hyperplane H ⊂ PN(C). The purpose of this paper is to establish the following results.
Potential theoretic properties of the gradient of a convex function on a functional space
Authors: Kenmochi Nobuyuki , Mizuta Yoshihiro
Published: July 2016

In the previous paper [11], introducing the notions of potentials and of capacity associated with a convex function Φ given on a regular functional space we discussed potential theoretic properties of the gradient ∇Φ which were originally introduced and studied by Calvert [5] for a class of nonlinear monotone operators in Sobolev spaces. For example:

(i)

The modulus contraction operates.

(ii)

The principle of lower envelope holds.

(iii)

The domination principle holds.

(iv)

The contraction Tk onto the real interval [0, k] (k > 0) operates.

(v)

The strong principle of lower envelope holds.

(vi)

The complete maximum principle holds.
Correction and comment concerning “on derivations and holomorphs of nilpotent Lie algebras”
Authors: Leger G. , Luks E.
Published: July 2016

The examples on p. 44 of metabelian Lie algebras L1 and L2 are isomorphic over certain base fields contrary to the claim in the paper. More specifically, the error lies in the incorrect statement that the rank of ad x for any x in L1 is either zero or is at least 3. This statement does hold over Q, but if τ is a scalar satisfying τ2 − τ − 1 = 0 then ad (x1 + τx2 + τ2x3 + x4 + τ2x5 has rank 2.
On Finite Groups with Given Conjugate Types I
Authors: Itô Noboru
Published: July 2016

LetGbe a finite group. Letn1, n2,…,nr, wheren1>n2>… >nr= 1, be all the numbers each of which is the index of the centralizer of some element of G in G. We call the vector (n1, n2,…, nr) the conjugate type vector of G. A group with the conjugate type vector (n1, n2,…, nr) is said to be a group of type (n1, n2,…, nr).
On Absolutely Segregated Algebras
Authors: Ikeda Masatoshi
Published: July 2016

Cohomology groups of (associative) algebras have been introduced (for higher dimensions) and studied by G. Hochschild in his papers [2], [3] and [4]. 1-, 2-, and 3-dimensional cohomology groups are in closest connection with some classical properties of algebras. In particular, an algebra is absolutely segregated. if and only if its 2-dimensional cohomology groups are all trivial. It is thus of use and importance to determine the structure of algebras with universally vanishing 2-cohomology groups, i.e. absolutely segregated algebras; they form a class which is wider than the class of all algebras with universally vanishing 1-cohomology groups, i.e. separable algebras in the sense of the Dickson-Wed-derburn theorem.
Monomiale Darstellung Endlicher Gruppen
Authors: Huppert Bertram
Published: July 2016

Eine wichtige Aufgabe der Darstellungstheorie ist die Aufstellung eines vollstandigen Systems von inäquivalenten irreduziblen Darstellungen einer endlichen GruppeObwohl man Verfahren kennt, die dies theoretisch leisten (etwa die Reduktion der regularen Darstellung), ist die praktische Durchführung nur in wenigen Fallen möglich. Die Aufgabe vereinfacht sich jedoch wesentlich, wenn sich alle irreduziblen Darstellungen vonauf monomiale Gestalt transfor-mieren lassen; denti alle monomialen Darstellungen einer endlichen Gruppe kann man nach einem sehr einfachen Verfahren gewinnen (siehe [4], S. 140).
On Absolutely Segregated Algebras and Relative 3-Cohomology Groups of an Algebra
Authors: Nakayama Tadasi
Published: July 2016

Recently M. Ikeda [1] succeeded in determining the structure of absolutely segregated algebras, i.e. algebras whose 2-cohomology groups all vanish. His beautiful result reads : an algebra A, of finite rank over its ground field, is absolutely segregated if and only if i) the residue-algebra A/N modulo the radical N is separable and, moreover, ii) the A-left-module N is an (Mo)-module. A. simplification was given by H. Nagao [5], who obtained, besides an interesting-result on algebras with vanishing 3-(or higher) cohomology groups, an elegant short proof to the fact that under the assumption of i), the property ii) is necessary, and sufficient, for the absolute segregation of A.
Mappings of nonpositively curved manifolds
Authors: Goldberg Samuel I.
Published: July 2016

In recent papers with S. S. Chern [3] and T.Ishihara [4], the author studied both the volume—and distance—decreasing properties of harmonic mappings thereby obtaining real analogues and generalizations of the classical Schwarz-Ahlfors lemma, as well as Liouville’s theorem and the little Picard theorem. The domain M in the first case was the open ball with the hyperbolic metric of constant negative curvature, and the target was a negatively curved Riemannian manifold with sectional curvature bounded away from zero. In this paper, it is shown that M may be taken to be any complete Riemannian manifold of non-positive curvature.
A few theorems on completion of excellent rings
Authors: Valabrega Paolo
Published: July 2016

In [2], chap. IV, 2me partie, (7.4.8), Grothendieck considered the following problem: is any m-adic completion of an excellent ring A also excellent?

In [8] I proved that, if A is an algebra of finite type over an arbitrary field k, the answer is positive.
Heisenberg groups and holomorphic vector bundles over a complex torus
Authors: Matsushima Yozo
Published: July 2016

Let V be a complex vector space of dimension n, L a lattice of V and E = V/L a complex torus. Let H be a Hermitian form on V. We introduce a multiplication in L × C* by
Deformations of real analytic functions and the natural stratification of the space of real analytic functions
Authors: Fukuda Takuo
Published: July 2016

Let A be a real analytic set, M be a compact real analytic manifold and f : A × M → R be a real analytic function. Then we have a family of real analytic functions fa, a ∈ A, on M defined by fa(X) = f(a, x).
Expansive flows and their centralizers
Authors: Oka Masatoshi
Published: July 2016

R. Bowen and P. Walters [2] have defined expansive flows on metric spaces which generalized the similar notion by D. Anosov [1]. On the other hand, P. Walters [4] investigated continuous transformations of metric spaces with discrete centralizers and unstable centralizers and proved that expansive homeomorphisms have unstable centralizers.
Differential equations and an analog of the Paley-Wiener theorem for linear semisimple Lie groups
Authors: Johnson Kenneth D.
Published: July 2016

Let G be a noncompact linear semisimple Lie group. Fix G = KAN an Iwasawa decomposition of G. That is, K is a maximal compact subgroup of G, A is a vector subgroup with AdA consisting of semisimple transformations and A normalizes N, a simply connected nilpotent subgroup of G.
On a certain type of vector bundles over an abelian variety
Authors: Umemura Hiroshi
Published: July 2016

It seems to the author that the theory of vector bundles of rank r over an abelian variety of dimension g is not sufficiently developed except for the two cases r = 1 and g = 1. The case r = 1 is the theory of theta functions and is one of the richest branches of mathematics. It is quite natural to try to explore vector bundles in the higher rank case as we did in the case r = 1.
A uniqueness theorem of algebraically non-degenerate meromorphic maps into PN(C)
Authors: Fujimoto Hirotaka
Published: July 2016

In the previous paper [3], the author generalized the uniqueness theorems of meromorphic functions given by G. Pólya in [5] and R. Nevanlinna in [4] to the case of meromorphic maps of Cn into the N- dimensional complex projective space PN(C).
On some analogues of Titchmarsh divisor problem
Authors: Fujii Akio
Published: July 2016

In [15] Titchmarsh posed and solved under the generalized Riemann Hypothesis, the problem of an asymptotic behavior of the number of the solutions of the equation 1 = p — n1n2 for a prime p ≦ x and natural numbers n1 and n2. When we put then the above problem is to get an asymptotic law for the sum
Holomorphic mappings into a compact quotient of symmetric bounded domain
Authors: Sunada Toshikazu
Published: July 2016

In this paper, we shall be concerned with the finiteness property of certain holomorphic mappings into a compact quotient of symmetric bounded domain.

Let be a symmetric bounded domain in n-dimensional complex Euclidean space Cn and Γ\ be a compact quotient of S by a torsion free discrete subgroup Γ of automorphism group of . Further, we denote by l() the maximum value of dimension of proper boundary component of , which is less than n (=dim).
Sur l’unicité du cône convexe divisible relatif au noyau de convolution de Hunt défini par l’opérateur différentiel
Authors: Itô 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 note |x| = et la coordonnée sphérique dans Rn désignera (r, α).

Rappelons qu’un noyau de convolution N sur Rn est une mesure (de Radon) positive dans Rn dans la théorie du potentiel. Pour une mesure réelle μ dans Rn, N * μ s’appelle le N-potentiel de μ dès que cette convolution est définie au sens des mesures. On connaît bien que, dans la théorie du potentiel, les noyaux de convolution de Hunt possédent les propriétés définitives.
Construction of a solution of a certain evolution equation
Authors: Shimizu Akinobu
Published: July 2016

Let us consider the stochastic differential equation,

with initial condition,

where Bt, t ≧ 0,is a one-dimensional Brownian motion, and Lxis a second order uniformly elliptic partial differential operator satisfying some additional conditions that will be described in §2. The existence and the uniqueness of solutions of the Cauchy problem have been established by B. L. Rozovskii [8].
Class numbers of quadratic forms over real quadratic fields
Authors: Kitaoka Yoshiyuki
Published: July 2016

Let k be an algebraic number field, let K be a Galois extension of k of finite degree, and let OK, Ok be the maximal orders of K, k, respectively. We consider the conjugate operation: for a given quadratic lattice M over OK equipped with a bilinear form B and for an automorphism σ ∈ G(K/k), we define a new quadratic lattice Mσ over OK. Here Mσ has the same underlying abelian group as M, but a new OK-action ; the new bilinear form Bσ on Mσ is defined by
Analytic structure of Schläfli function
Authors: Aomoto Kazuhiko
Published: July 2016

In this note it is shown that Schläfli function can be simply expressed in terms of hyperlogarithmic functions, namely iterated integrals of forms with logarithmic poles in the sense of K. T. Chen (Theorem 1). It is also discussed the relation between Schläfli function and hypergeometric ones of Mellin-Sato type (Theorem 2). From a combinatorial point of view the structure of hyperlogarithmic functions seem very interesting just as the dilog log (so-called Abel-Rogers function) has played a crucial part in Gelfand-Gabriev-Losik’s formula of 1st Pontrjagin classes. See also [3].
Algebras and differential equations
Authors: Röhrl Helmut
Published: July 2016

One purpose of this paper is a purely algebraic study of (systems of) ordinary differential equations of the type

where the coefficients are taken from a fixed associative, commutative, unital ring R, such as the field R of real or C of complex numbers or a commutative, unital Banach algebra. The right hand sides of D are considered to be elements in the polynomial ring R[X1, …, Xn] of associating but non-commuting variables X1, …, Xn. An algebraic study calls for maps between such differential equations and, in fact, morphisms are defined between differential equations having the same arity m but not necessarily the same dimension n. These morphisms are rectangular matrices with entries in R which satisfy certain relations. This leads to a category RDiffm whose objects are precisely the differential equations of arity m and in which the composition of the morphisms is the usual matrix multiplication.
Representations of quadratic forms
Authors: Kitaoka Yoshiyuki
Published: July 2016

We have shown in [1]

Theorem A. Let L be a lattice in a regular quadratic space U over Q; then L has a submodule M satisfying the following conditions 1),2):

1)

dM ≠ 0, rank M = rank L — 1, and M is a direct summand of L as a module.

2)

Let L′ be a lattice in some regular quadratic space U′ over Q satisfying dL′ = dL, rank L′ — rank L, tp(L′) ≥ tp(L) for any prime p. If there is an isometry α from M into L′ such that α(M) is a direct summand of L′ as a module, then L′ is isometric to L.
Sur le Prolongement D’un Pseudogroupe D’isomorphismes Locaux D’une Variété Différentiable
Authors: Matsushima Yozô
Published: July 2016

Dans leurs mémoires classiques sur les groupes de transformations continus et infinis, MM. É. Cartan et E. Vessiot ont introduit la notion de prolongement des groupes de transformations pour définir l’isomorphisme et l’homomorphisme entre deux groupes de transformations.
Completions of rings of invariants and their divisor class groups
Authors: Griffith Phillip
Published: July 2016

Let k be a field and let A = be a normal graded subring of the full ring of polynomials R = k[X1, · · ·, Xn] (where R always is graded via total degree and A0 = k). R. Fossum and the author [F-G] observed that the completion Â at the irrelevant maximal ideal of A is isomorphic to the subring of the formal power series ring R̂ = k[[X1, · ·., Xn]] and, moreover, that Â is a ring of invariants of an algebraic group whenever A is.
A decomposition of additive functionals of finite energy
Authors: Fukushima Masatoshi
Published: July 2016

The celebrated Ito formula for the n-dimensional Brownian motion Xt and for u ∈ C2(Rn) runs as follows:

(0.1)

In § 6 of this paper we extend this to the case where u is any element of the Sobolev space H1R(n) and accordingly Δu is a tempered distribution which is not even a signed measure in general. As a consequence the second term of the right hand side of (0.1) may not be of bounded variation in t.
On the module structure of a p-extension over a -adic number field
Authors: Miyata Yoshimasa
Published: July 2016

Throughout this paper, let p be an odd prime. Let k be a -adic number field and be the ring of all integers in k. Let K/k be a finite totally ramified Galois p-extension of degree pn with the Galois group G. Clearly the ring of all integers in K is an [G]-module. In the previous paper [4], we studied [G]-module structure of in a cyclic totally ramified p-extension, and we have obtained the condition for to be an indecomposable [G]-module.
On differential invariants of holomorphic projective curves
Authors: Morikawa Hisasi
Published: July 2016

Let (φ1(u), …, φn(u)) be a system of holomorphic functions whose Wronskian does not vanish at origin, where holomorphic functions mean functions holomorphic around origin.
Some examples of integral definite quaternary quadratic forms with prime discriminant
Authors: Hashimoto Ki-Ichiro
Published: July 2016

In the theory of integral quadratic forms or the related theory such as modular forms, it is important to give examples of forms with given discriminant for various computational purposes. However, little is known about this problem even in the case where the explicit formula for the class number has been given. Among the works that deal with satisfactorily many examples or give a constructive method of them, there are [1] for ternary forms, and [5] for quaternary forms with square discriminants. As for quaternary forms with prime discriminant, P. Ponomarev [8] gave an explicit way to construct such forms from ternary forms with discriminant 2q. It was based on the result of his previous work [7] and that of Y. Kitaoka [6], but was rather complicated.
Spectral properties of first order ordinary differential operators with short range potentials
Authors: Itatsu S. , Kaneta H.
Published: July 2016

The purpose of the present paper is to give a complete proof of the theorem which will be used in a paper of the second author [4].

We will discuss certain spectral properties of selfadjoint ordinary differential operators of the form iA(d/dx) + V acting in L2(R)n = Σ ⊕ L2(R)n, where A is a real diagonal constant matrix and V an Hermitian matrix valued function on R which satisfies some conditions to be stated in the sequel.
On a criterion for the class number of a quadratic number field to be one
Authors: Kutsuna Masakazu
Published: July 2016

G. Rabinowitsch [3] generalized the concept of the Euclidean algorithm and proved a theorem on a criterion in order that the class number of an imaginary quadratic number field is equal to one:

Theorem.It is necessary and sufficient for the class number of an imaginary quadratic number fieldD= 1 — 4m, m> 0,to be one that x2—x+m is prime for any integer x such that1 ≤x≤m— 2.
On the upper semi-lattice of -degrees
Authors: Shinoda Juichi
Published: July 2016

S. C. Kleene developed the theory of recursive functionals of finite types in Kleene [5]. He proved that a set A of natural numbers is recursive in E if and only if A is hyperarithmetical, where E is the type 2 object defined by
On a decomposition of spaces of cusp forms and trace formula of Hecke operators
Authors: Saito Hiroshi
Published: July 2016

For a positive integerN, put
Duality between D(X) and with its application to picard sheaves
Authors: Mukai Shigeru
Published: July 2016

As is well known, for a real vector space V, the Fourier transformation

gives an isometry between L2(V) and L2(Vv), where Vv is the dual vector space of V and < , >: V×Vv → R is the canonical pairing.
A generalization of a theorem of marotto
Authors: Shiraiwa Kenichi , Kurata Masahiro
Published: July 2016

In 1975, Li and Yorke [3] found the following fact. Let f: I→ I be a continuous map of the compact interval I of the real line R into itself. If f has a periodic point of minimal period three, then f exhibits chaotic behavior. The above result is generalized by F.R. Marotto [4] in 1978 for the multi-dimensional case as follows. Let f: Rn → Rn be a differentiate map of the n-dimensional Euclidean space Rn (n ≧ 1) into itself. If f has a snap-back repeller, then f exhibits chaotic behavior.

In this paper, we give a generalization of the above theorem of Marotto. Our theorem can also be regarded as a generalization of the Smale’s results on the transversal homoclinic point of a diffeomorphism.
Tensor products of positive definite quadratic forms, V
Authors: Kitaoka Yoshiyuki
Published: July 2016

Our aim is to prove

THEOREM. Let L be a positive lattice of E-type such that [L: L̃] < ∞ and L̃ is indecomposable.

(i)

If L ≅ L1 ⊗ L2for positive lattices L1, L2, then L1, L2 are of E-type and [L1: L̃1], [L2:L̃2] < ∞ and L̃1, L̃2 are indecomposable.

(ii)

If L is indecomposable with respect to tensor product, then for each indecomposable positive lattice X we have

(1)

L ⊗ X ≅ L ⊗ Y implies X ≅ Y for a positive lattice Y,

(2)

If X= ⊗t L ⊗ X′ where X′ is not divided by L, then O(L ⊗ X) is generated by O(L), O(X′) and interchanges of L’s, and

(3)

L ⊗ X is indecomposable.
On the norm continuity of -valued Gaussian processes
Authors: Mitoma Itaru
Published: July 2016

Let be the Schwartz space of all rapidly decreasing functions on Rn, be the topological dual space of and for each positive integer p, be the space of all elements of which are continuous in the p-th norm defining the nuclear Fréchet topology of . The main purpose of the present paper is to show that if {Xt, t ∈ [0, + ∞]} is an -valued Gaussian process and for any fixed φ ∈ the real Gaussian process {Xt(φ), t ∈ [0, + ∞)} has a continuous version, then for any fixed T > 0 there is a positive integer p such that {Xt, t ∈ [0, T]} has a version which is continuous in the norm topology of .
On algebra with universal finite module of differentials
Authors: Yamauchi Norio
Published: July 2016

Let k be a field and A a noetherian k-algebra. In this note, we shall study the universal finite module of differentials of A over k, which is denoted by Dk(A). When the characteristic of k is zero, detailed results have been obtained by Scheja and Storch [8]. So we shall treat the positive characteristic case. In § 1, we shall study differential modules of a local ring over subfields. We obtain a criterion of regularity (Theorem (1.14)). In § 2, we shall study the formal fibres and regular locus of A with Dk(A). Our main result is Theorem (2.1) which shows that, if Dk(A) exists, then A is a universally catenary G-ring under a certain assumption. In the local case, this is a generalization of Matsumura’s theorem ([5] Theorem 15), where regularity of A is assumed.
The index of elliptic operators over V-manifolds
Authors: Kawasaki Tetsuro
Published: July 2016

Let M be a compact smooth manifold and let G be a finite group acting smoothly on M. Let E and F be smooth G-equivariant complex vector bundles over M and let be a G-invariant elliptic pseudo-differential operator. Then the kernel and the cokernel of the operator P are finite-dimensional representations of G. The difference of the characters of these representations is an element of the representation ring R(G) of G and is called the G-index of the operator P.