bluuebunny/crossref_metadata_2025 huggingface dataset:
Recherches Axiomatiques sur un Théorème de Choquet concernant l’Effilement
Authors: Brelot M.
Published: July 2016

Il y a quelques années, CHOQUET a démontré [5], en théorie classique du potentiel (ou pour certains noyaux) que l’ensemble E des points où un ensemble e est effilé est contenu dans un ouvert ω, tel que ω∩e soit de capacité arbitrairement petite. Cela contient les résultats-elefs, connus depuis longtemps que E∩e est polaire et que si e est ouvert, p. ex. borné, E ∩ ∂e est de mesure harmonique nulle en tout point de e. La partie nouvelle du résultat général est que les points de Ce où e est effilé peuvent être enfermés dans un ouvert ω tel que ω∩e soit de capacité arbitrairement petite et l’effilement n’intervient plus pour un ensemble qu’aux points du complémentaire, d’une façon équivalente à la notion de topologie fine.
On a Class of Markov Processes Taking Values on Lines and the Central Limit Theorem
Authors: Fukushima Masatoshi , Hitsuda Masuyuki
Published: July 2016

We shall consider a class of Markov processes (n(t), x(t)) with the continuous time parameter t∈e[0, ∞), whose state space is {1, 2,..., N}×R1. We shall assume that the processes are spacially homogeneous with respect to X∈R1. In detail, our assumption is that the transition function

Fij(x,t) = P(n(t) = j, x(t)≦x|n(0) = i,x(0) = 0), t > 0, 1≦i, j,≦N, x∈R1satisfies following conditions (1, 1)~(1,4).
On the Pseudo-Periods of the Weierstrass Zeta Functions II
Authors: Heins Maurice
Published: July 2016

In a recent note bearing the same title (SIAM Journ. of Numerical Analysis, Vol. 3, 1966), I showed that there existed Weierstrass zeta functions having a vanishing pseudo-period. Cf. line 8, p. 376 of Saks-Zygmund, Analytic Functions. Professor Peter Henrici kindly pointed out to me that the mere existence of a Weierstrass zeta function with a vanishing pseudo-period was readily concluded from a classical formula of the theory of elliptic functions (Hurwitz-Courant, Funktionentheorie, 5th ed., p. 210) which reduces the question to the study of the zeros of
On Positive Solutions of the Heat Equation
Authors: Kato Masasumi
Published: July 2016

Consider the positive and twice continuously differentiable solutions u of the heat equation

in an open t-strip Ω = Rn×(0,T) for some T>0, where Rn is the n-dimensional Euclidean space.

In this note, we prove a theorem of Fatou type on u and, as its application, the uniqueness theorem for the Cauchy problem of ( 1 ).
Spiral Asymptotic Values of Functions Meromorphic in the Unit Disk
Authors: Stebbins J.L.
Published: July 2016

This paper contains part of the author’s Ph.D. dissertation directed by Frederick Bagemihl at Wayne State University. The research was supported by a grant from the Michigan Institute of Science and Technology.

Alice Roth has made an extensive study of entire meromorphic functions with prescribed behavior along half rays emanating from the origin (6). The question arose whether analogous results could be found for functions meromorphic in the unit disk with the same behavior prescribed along an exhaustive class of spirals emanating from the origin. In this paper, I present a class of spirals which satisfactorily fills this role. However, I make no claim to the effect that only this class will suffice.
Sur l’ensemble d’Adherence Fine des Fonctions Algebroides
Authors: Toda Nobushige
Published: July 2016

Dans ce mémoire, on fera pour les fonctions algébroïdes des études analogues à ceux des fonctions méromorphes dans |z|<∞ faits dans Doob [3], Toda [7].

Soit g(z) une fonction méromorphe dans |Z|<∞ ayant un point singulier essentiel isolé à l’infini. J.L. Doob a obtenu le théorème suivant en utilisant la topologie fine pour g(z).
Bayes Class and Wald Class
Authors: Kudō Hirokichi
Published: July 2016

In this paper we shall study relations among the class B of the Bayes solutions in the strict sense, the class W of the Bayes solutions in the wide sense and the closure c(B), in a certain sense, of the class B. For abbreviation, we shall use the word “Bayes class” for the class B and “Wald class” for the class W.
Transitive Extensions of Certain Permutation Groups of Rank 3
Authors: Tsuzuku Tosiro
Published: July 2016

We denote a permutation group H on a set Γ by (H, Γ). (H, Γ) is called a permutation group of rank 3 if (H, Γ) is transitive and (Ha, Γ), a ∈ Γ, has exactly three orbits, where Ha is the stabiliger of a point a, namely, {α ∈ H \aα = a}
A Remark on Peirce’s Rule in Many-Valued Logics
Authors: Ono Katuzi
Published: July 2016

Recently, S. Nagata gave an interesting series of rules beginning with Peirce’s rule introduced in [3], each rule in the series being really stronger than its successor in the intuitionistic logics. (See [1] Nagata.) Namely, let p0, p1, … be any series of mutually distinct propositional variables.
On a Class of Truth-Value Evaluations of the Primitive Logic
Authors: Ono Katuzi
Published: July 2016

Main purpose of the present paper is to exhibit a class of truth-value evaluations of the primitive logic LO and its sentential part LOS.
On Ramification Theory in Projective Orders
Authors: Endo Shizuo
Published: July 2016

The ramification theory in commutative rings, as a generalization of the classical one in maximal orders over a Dedekind domain, was established in [1], [13], [15] and etc.. For non-commutative algebras this was also studied in [3], [4], [9], [18] and etc.. However, the different theorem, which is a central part of ramification theory, has not been given in those, except for some special cases (cf. [12], [18]). The main object of this paper is to give the discriminant theorem and the different theorem for projective orders in a (non-commutative) separable algebra, in the most general form.
On ε-Entropy of Equivalent Gaussian Processes
Authors: Ihara Shunsuke
Published: July 2016

Letbe a stochastic process, whereTis a finite interval. The ε-entropyis defined as the following quantity:

(1)
A Characterization of the Intuitionistic Propositional Logic
Authors: Muti Nobol
Published: July 2016

In this short note, is shown a necessary and sufficient condition for a logic to be an intermediate propositional logic in Umezawa’s sense (see the reference), under such an assumption that any logic in consideration (as a subclass of LK-provable propositions) contains at least the axioms of the positive propositional logic LPS (Curry’s LA) as its axioms and is closed with respect to the rules of detachment and substitution.
Über das Geschlecht und Die Klassenzahl Eines Relativ-Galoischen Zahlkörpers vom Primzahlpotenzgrade
Authors: Furuta Yoshiomi
Published: July 2016

Für einen relativ-galoischen Zahlkörper K über k bezeichnen wir mit G(K/k) die zugehörige galoische Gruppe und mit (K: k) dem Erweiterungsgrade. Ferner seien bzw. K* die gröBten, unverzweigten Erweiterungskörper von K, die beziehungsweise die folgenden Eigenschaften besitzen: die galoische Gruppe abelsch; die galoische Gruppe ist im Zentrum von enthalten; K* ist das Kompositum von K und einem über k abelschen Erweiterungskörper.
Note on the Infinite Dimensional Laplacian Operator
Authors: Hida Takeyuki
Published: July 2016

The infinite dimensional Laplacian operator can be discussed in connection with the infinite dimensional rotation group ([1]). Our interest centers entirely on observing how each one-parameter subgroup of the infinite dimensional rotation group contributes to the determination of the Laplacian operator.
On a Class of Metrical Automorphisms on Gaussian Measure Space
Authors: Nomoto Hisao
Published: July 2016

Let E be an infinite dimensional real nuclear space and H be its completion by a continuous Hilbertian norm ║ ║ of E. Then we have the relation

where E* is the conjugate space of E. Consider a function C(ξ) on E defined by the formula

(1)
Some Remarks on Evaluations of the Primitive Logic
Authors: Ono Hiroakira
Published: July 2016

In [4], K. Ono introduced the notion of evaluations of the primitive logic LO and proved that any semi-evaluation E is an evaluation of LO if E satisfies the following conditions:

(E1) p* → 0 = 0,

(E2) p* → p* = 0,

(E3) 0 → p* = p*,

(E4) p* → (p* → q*) = p* → q*,

(E5) p* → (q* → r*) = q* → (p* → r*),

(E6) p* → q* = 0 implies (r* → p*) → (r* → q*) = 0,

(E7) (x)p*(x) → p*(t) = 0 for any t, and

(E8) if u* → p*(t) = 0 for any t, then u* → (x)p*(x) = 0.
A Remark on the Moyal’s Construction of Markov Processes
Authors: Sirao Tunekiti
Published: July 2016

In the author’s previous paper [3], we used Theorem 1 of the present paper to assure the existence of a signed branching Markov process with age satisfying given conditions in [3], The purpose of this paper is to give a proof of Theorem 1.
Propriétés des Solutions Faibles Non Négatives de L’équation Parabolique
Authors: Chabrowski J.
Published: July 2016

Le but de cette communication est de prouver que la solution u(t, x) faible non négative dans (0,T]=En de l’équation

possède la limite presque partout dans En si t converge vers zéro, ainsi qu’elle représentable sous la forme d’une intégrale de la solution fondamentale faible de (1) par rapport à une mesure non négative. Ces problèmes ont été traités par M. Kato et M. Krzyzanski (voir [7] et [8]) pour les solutions au sens classiques. Nos démonstrations sont basées sur les méthodes utilisées dans leurs travaux.
On a Problem of Doob Concerning Multiply Superharmonic Functions
Authors: Gowrisankaran Kohur
Published: July 2016

The following is a well-known result due to A.P. Calderon [2], asserting the existence of non-tangential limits of multiply harmonic functions.
Integral Normal Bases in Galois Extensions of Local Fields
Authors: Ullom S.
Published: July 2016

Throughout this paper F denotes a field complete with respect to a discrete valuation, kF the residue field of F, K/F a finite Galois extension with Galois group G = G(K/F). The ring of integers 0K of K contains the (unique) prime ideal ; the collection of ideals n for all integers n are ambiguous ideals i.e. G-modules.
On Picard Values of Algebroid Functions in a Neighbourhood of A Totally Disconnected Compact Set
Authors: Suzuki Junji
Published: July 2016

1. Let E be a totally disconnected compact set in the 2-plane and Ω its complement with respect to the extended z-plane. Then Ω is a region. Let be an exhaustion of Ω satisfying the following conditions:
Prolongations of Connections to Tangential Fibre Bundles of Higher Order
Authors: Morimoto Akihiko
Published: July 2016

In the previous paper [3] we have studied the prolongations of G-structures to tangent bundles of higher order. The purpose of the present paper is to study the prolongations of connections to tangential fibre bundles of higher order, and to generalize the results due to S. Kobayashi [1] for the case of usual tangent bundle —— in fact, the arguments in [1] will be, in a sense, more or less simplified and clarified by using the notion of tangent bundles of higher order. In addition, as a consequence of our results, we shall obtain the prolongations of linear (affine) connections to tangent bundles of higher order.
An Elementary Proof of Abramov’s Result on the Entropy of a Flow
Authors: Ito Shunji
Published: July 2016

Let T be an automorphism on a probability space (Ω, B, P). Given a finite partition α of Ω, into disjoint measurable sets A1, A2, · · ·, An, its entropy is

(D.1)
The Cauchy Problem of Linear Parabolic Equations with Discontinuous and Unbounded Coefficients
Authors: Ikeda Yoshiaki
Published: July 2016

In this article we shall prove the uniqueness and existense of a weak solution for the Cauchy problem of linear parabolic equations with discontinuous and unbounded coefficients

(1.1)
Solvability of a Class of Rank 3 Permutation Groups
Authors: Higman D.G.
Published: July 2016

1. Introduction. Let G be a rank 3 permutation group of even order on a finite set X, |X| = n, and let Δ and Γ be the two nontrivial orbits of G in X×X under componentwise action. As pointed out by Sims [6], results in [2] can be interpreted as implying that the graph = (X, Δ) is a strongly regular graph, the graph theoretical interpretation of the parameters k, l, λ and μ of [2] being as follows: k is the degree of , λ is the number of triangles containing a given edge, and μ is the number of paths of length 2 joining a given vertex P to each of the l vertices ≠ P which are not adjacent to P. The group G acts as an automorphism group on and on its complement = (X,Γ).
On the Trace of Hecke Operators for Certain Modular Groups
Authors: Yamauchi Masatoshi
Published: July 2016

The trace of Hecke operators with respect to a unit group of an order in a quaternion algebra has been given in Eichler [1], [2] in the case when the order is of square-free level. The purpose of this note is to study the order of type (q1, q2, q3) (see text 1.1), in the case, of cube-free level, and to give a formula for the trace of Hecke operators in the case q3 = 2.
On a Characterization of the First Ramification Group as the Vertex of the Ring of Integers
Authors: Miyata Yoshimasa
Published: July 2016

Letkbe a p-adic number field and o be the ring of all integers ink. Moreover, letK\kbe a finite Galois extension with the Galois groupG=G(K/k). Then the ringof all integers inKis an-module.
A Property of the Principal Cluster sets of a Class of Holomorphic Functions
Authors: Bagemihl F.
Published: July 2016

Let D be the open unit disk and Γ be the unit circle in the complex plane, and denote by Ω the Riemann sphere. If f(z) is a meromorphic function in D, and if ζ∈Г, then the principal cluster set of f at ζ is the set
Weak Formal Schemes
Authors: Meredith David
Published: July 2016

Throughout this paper, (R, m) denotes a (noetherian) local ring R with maximal ideal m.

In [5], Monsky and Washnitzer define weakly complete R-algebras with respect to m. In brief, an R-algebra A† is weakly complete if
Riemannian Manifolds with Discontinuous Metrics and the Dirichlet Integral
Authors: Glasner Moses , Nakai Mitsuru
Published: July 2016

Consider a relatively compact region Ω of a Riemann surface R. The term Dirichlet integral over Ω, DΩ(·), is used for the variation whose Euler-Lagrange equation is Δu = 0 on Ω and the term energy integral over Ω, , is used for the variation with Euler-Lagrange equation
Boundary Conditions for the Heat Equation in a Several-Dimensional Region
Authors: Gallavotti G. , McKean H. P.
Published: July 2016

The heat equation is to be solved in a severaldimensional region D with on the boundary B of D. The elementary solution (Green’s function) is interpreted as the transition density of an associated Brownian motion. The latter is built up pathwise from the free Brownian motion by simple geometric and probabilistic transformations.
On the Arithmetic of Pfaffians
Authors: Igusa Jun-Ichi
Published: July 2016

In this paper, we shall supply proofs to the results announced in [2], pp. 74-75: we shall prove the Siegel formula for the Pfaffian of degree n over an algebraic number field and also determine the zeta function of the Pfaffian. In the appendix, we shall briefly discuss the non-split case where the Pfaffian is replaced by the norm form of the simple Jordan algebra of quaternionic hermitian matrices of degree n.
Boundary Behaviour of Functions With Hadamard Gaps
Authors: Binmore K. G. , Hornblower R.
Published: July 2016

In this paper we discuss the boundary properties of a function f which is analytic in the open unit disc Δ and has Hadamard gaps—i.e.

(1)

where

. (2)
Comment on a Paper by Tahara on the Finite Subgroups of GL(3,Z)
Authors: Ascher E. , Grimmer H.
Published: July 2016

Tahara [1] has concretely determined the conjugate classes of finite subgroups of GL(3, Z). The group W5 in his list of groups of order 24 is in fact of order 12 and consists of the same matrices as the group W6 in his list of groups order 12. Hence, there are only 10 conjugate classes of subgroups of order 24 in GL(3, Z) and the total number of conjugate classes of finite subgroups is reduced to 73.
On Determining the Growth of Meromorphic Solutions of Algebraic Differential Equations Having Arbitrary Entire Coefficients
Authors: Bank Steven B.
Published: July 2016

In this paper, we treat the problem of determining the rate of growth of meromorphic functions on the plane, which are solutions of nth order algebraic differential equations whose coefficients are arbitrary entire functions (i.e., equations of the form, Ω(z,y,dy/dz, • • •, dny/dzn) — 0, where Ω is a polynomial in y, dy/dz, • • •, dny/dzn whose coefficients are arbitrary entire functions of z.)
Zur Isoperimetrischen Ungleichung für k-Dimensionale Konvexe Polyeder
Authors: Hadwiger H.
Published: July 2016

Für ein eigentliches konvexes Polyeder P des k-dimensionalen euklidischen Raumes gilt die isoperimetrische Ungleichung

(1)

wobei V das Volumen und F die Oberfläche von P bedeuten; die Grôsse wk bezeichnet das Volumen der k-dimensionalen Einheitskugel, also

(2)
Grouptheoretical Characterization of Projective Space and Conformal Space
Authors: Kurita Minoru
Published: July 2016

In this paper we characterize a projective space and a conformal space, namely a space of inversive geometry of point and sphere, from the standpoint of a homogeneous space. In such spaces a covariant differential of a vectorfield is not a vector, contrary to the case stated in my previous paper “On the vector in homogeneous spaces.” (This journal vol. 5. This paper will be referred to as [1] below.) But when we restrict a rotation about a point to a certain subgroup of the full rotation group, we get a covariant differential which is also a vector, and this situation holds good in a general homogeneous space.
Homotopy Classification of Mappings of a 4-Dimensional Complex into a 2-Dimensional Sphere
Authors: Shimada Nobuo
Published: July 2016

Steenrod [1] solved the problem of enumerating the homotopy classes of maps of an (n + 1)-complex K into an n-sphere Sn utilizing the cup-i-product, the far-reaching generalization of the Alexander-Čech-Whitney cup product [7] and the Pontrjagin *-product [5].
Boundary Isomorphism between Dirichlet Finite Solutions of Δu = Pu and Harmonic Functions
Authors: Singer Ivan J.
Published: July 2016

Consider an open Riemann surface R and a density P(z)dxdy (z = x + iy), well defined on R. As was shown by Myrberg in [3], if P ≢ 0 is a nonnegative α-Hölder continuous density on R (0 < α ≤ 1) then there exists the Green’s functions of the differential equation

p>on R, where Δ means the Laplace operator. As a consequence, there always exists a nontrivial solution on R.
Contracted ideals from integral extensions of regular rings
Authors: Hochster M.
Published: July 2016

0. Introduction. The purpose of this paper is to consider the following question: if R is a regular Noetherian ring and S ⊃ R is a module-finite R-algebra, is R a direct summand of S as R-modules? An affirmative answer is given if R contains a field, and it is shown that if the completions of the local rings of S possess maximal Cohen-Macaulay modules in the sense of § 1 of [6] then the conclusion is valid in this case too. Hence, if Conjecture E of [6] is true then the question raised here has an affirmative answer without further restriction on the regular Noetherian ring R, and it will be shown here that only a greatly weakened version of Conjecture E is needed.
Sur une famille sous-ordonnée au noyau de convolution de Hunt donné
Authors: Itô Masayuki
Published: July 2016

Soient X un groupe abélien localement compact et dénombrable à l’infini, et ξ sa mesure de Haar. Dans la théorie du potentiel, un noyau de convolution N sur X signifie une mesure de Radon positive dans X. Pour une mesure de Radon réelle μ dans X, N* μ s’appelle le N-potentiel de μ dès que cette convolution a un sens.
Dirichlet finite biharmonic functions on the plane with distorted metrics
Authors: Nakai Mitsuru
Published: July 2016

The Laplace-Beltrami operator Δ on a smooth manifold M with a smooth Riemannian metric ds2 = ∑i,jgij(x)dxidxj applied to a smooth function φ takes the form Functions in the class H2(M) = {u∈ C4(M); Δ2u = 0} are called biharmonic.
Rigidity for elliptic isometric imbeddings
Authors: Tanaka Noboru
Published: July 2016

The main purpose of the present paper is to give the details of the results announced in the P. J. A. note [11], establishing some global theorems on rigidity for a certain class of isometric imbeddings.
Bäcklund transformations of the first kind associated with Monge-Ampère’s equations
Authors: Matsuda Michihiko
Published: July 2016

Due to Clairin and Goursat, a Bäcklund transformation of the first kind can be associated with Monge-Ampère’s equation. We shall consider Monge-Ampère’s equation of the form s + f(x, y, z, p, q) + g(x, y, z, p, q) t = 0, where p = ∂z/∂x, q = ∂z/∂y, s = ∂2z/∂x∂y, t = ∂2z/∂y2. The following theorems will be obtained:

1. The transformed equation takes on the same form s′ + f′ + g′t′ = 0 if and only if the given equation can be transformed to a Teixeira equation s + L(x, y, z, q)t + M(x, y, z, q)p + N(x, y, z, q) = 0 by a contact transformation.

2. Teixeira equation s + tL + pM + N = 0 is solved by integrable systems of order n if and only if the transformed equation is solved by integrable systems of order n — 1.
Restricted principal cluster sets of a certain holomorphic function
Authors: Gresser John T.
Published: July 2016

Let D be the open unit disk and let K be the unit circle. We say that α is an arc at ζ ∈ K if α is contained in D and is the image of a continuous function z = z(t) (0 ≤ t < 1) such that z(t) → ζ as t → 1. We call α a segment as ζ if the function z = z(t) is linear in t. If P is a property which is meaningful for each point of K, we say that nearly every point of K has property P if the exceptional set is a set of first Baire category in K. We assume that the reader is familiar with the rudiments of cluster set theory, and in particular with the terms ambiguous point, Meier point, and Plessner point of a function (cf. [4] or [7]).
Über gewisse Riemannsche Mannigfaltigkeiten mit positiver Krümmung
Authors: Tsukamoto Yôtaro
Published: July 2016

Es ist wichtig und interessant, die Beziehungen zwischen Krümmung, Volumen, Geodätischen und topologischen Strukturen von Riemannschen Mannigfaltigkeiten mit positiver Krümmung zu untersuchen.
Holomorphic extension of continuous, weakly holomorphic functions on certain analytic varieties
Authors: Mochizuki Nozomu
Published: July 2016

Let M, N be connected complex submanifolds of a neighborhood of the origin 0 ∈ Cd, the space of d complex variables, such that 0 ∈ M ∩ N. We shall suppose throughout that M ⊄ N and N ⊄ M in any neighborhood of 0. Let X = M ∪ N. X is an analytic subvariety with the irreducible branches M and N. Let Δ be a neighborhood of 0 in Cd.
Normal subgroups of finite multiply transitive permutation groups
Authors: Bannai Eiichi
Published: July 2016

Wagner [5] and Ito [2] proved the following theorems respectively.

THEOREM OF WAGNER. Let G be a triply transitive permutation group on a set Ω = {1,2, …, n}, and let n be odd and n > 4. If H is a normal subgroup (≠1) of G, then H is also triply transitive on Ω.
On a certain algebra associated with a polarized algebraic variety
Authors: Morikawa Hisasi
Published: July 2016

In the present note we associate a certain algebra of finite rank over Q to each non-singular polarized algebraic variety defined over C. For a surface the algebra is a Jordan algebra with identity, and for an abelian variety A the algebra is canonically isomorphic to the Jordan algebra of symmetric elements in EndQ(A) with respect to the involution induced by the polarization. This algebra may be important for a polarized algebraic variety as much as EndQ(A) for an abelian variety A.
On Lie algebras of vector fields with invariant submanifolds
Authors: Koriyama Akira
Published: July 2016

It is known (Pursell and Shanks [9]) that an isomorphism between Lie algebras of infinitesimal automorphisms of C∞ structures with compact support on manifolds M and M′ yields an isomorphism between C∞ structures of M and M’.

Omori [5] proved that this is still true for some other structures on manifolds. More precisely, let M and M′ be Hausdorff and finite dimensional manifolds without boundary. Let α be one of the following structures:
On some rationality properties of Hopf maps
Authors: Ono Takashi
Published: July 2016

As is well known, the Hopf fibrationS3→S2is the restriction of the maph:R4→R3given by, a system of three quadratic forms [2]. Since spheres and the map are defined by polynomials with coefficients inQ, the original setting can be considered as a localization at infinity of the underlying algebraic sets and morphism defined overQ. This makes one think of the arithmetic of the Hopf maps.
Über eine Klasse von L-Funktionen algebraischer Zahlkörper
Authors: Kuroda S.-N.
Published: July 2016

In der vorliegenden Arbeit konstruieren wir, indem wir die Schlüsse von Armitage [1] in einer für unseren Zweck geeigneten Form erbringen, eine andere Klasse von L-Funktionen als bei Armitage [1] und Fröhlich [5], welche an der Stelle s = 1/2 eine Nullstelle ungerader Ordnung haben.
Freely acting automorphisms of abelianC*-algebras
Authors: Enomoto Masatoshi , Tamaki Kazuhiro
Published: July 2016

Very recently, M. Choda, I. Kasahara and R. Nakamoto [3] extend the concept of free action of automorphisms forC*-algebras and prove several theorems which are hither to known for von Neumann algebras. In the present note, we shall concern with freely acting automorphisms on abelianC*-algebras. In § 2, several equivalent conditions for the free action are obtained. In §3, we shall apply them to an automorphism which has a transversal group.
On the distribution of zeros of a strongly annular function
Authors: Osada Akio
Published: July 2016

A functionf(z), regular in the unit diskD, is called annular ([1], p. 340) if there is a sequence of closed Jordan curvesJn⊂Dsatisfying

(A1)

Jnis contained in the interior ofJn+1for everyn,

(A2)

givenε> 0, there exists a positive numbern(ε)such that, for eachn > n(ε), Jnlies in the region 1 –ε< |z| < 1 and

(A3)

lim min {|f(z)|;z ∈ Jn} = + ∞.
On a problem of Bonar concerning Fatou points for annular functions
Authors: Osada Akio
Published: July 2016

The purpose of this paper is to study the distribution of Fatou points of annular functions introduced by Bagemihl and Erdös [1]. Recall that a functionf(z), regular in the open unit diskD: |z| < 1, is referred to as an annular function if there exists a sequence {Jn} of closed Jordan curves, converging out to the unit circleC: |z| = 1, such that the minimum modulus off(z)onJnincreases to infinity. If theJncan be taken as circles concentric withC, f(z)will be called strongly annular.
On the hopf fibration over Z
Authors: Ono Takashi
Published: July 2016

Let h: R4 → R3 be a quadratic map defined by

For a natural number t, put
A note on grade
Authors: Jothilingam P.
Published: July 2016

All rings that occur in this note will be assumed to be commutative with unity and all modules will be finitely generated and unitary.

The grade of a module M over a noetherian local ring R is defined to be the length of a maximal R-sequence contained in the annihilator of M. If M has finite projective dimension it is well-known that grade M ≤ proj. dim M. We can say more when R is a regular local ring.
On a function analogous to log η(τ)
Authors: Goldstein Larry , de la Torre Pilar
Published: July 2016

Let us denote by η(z) the classical η-function of Dedekind defined by
On some Formulas about Volume and Surface Area
Authors: Kurita Minoru
Published: July 2016

We prove in this paper some integral formulas about volume and surface area which are the extensions of the classical formulas such as Guldin-Pappus’s theorem about the solid of rotation and the surface of rotation and Holditch’s theorem about the area of the domains bounded by the loci of three points on a segment that moves on the euclidean plane. The formulas we prove are so elementary that they may be found in some literature, but the proofs here given are very simple by the use of moving frames and I assume that they are of some interest.
On Abelian Varieties
Authors: Morikawa Hisasi
Published: July 2016

In a Bourbaki seminary note, La Théorie des Fonctions Thêta, A. Weil has discussed two fundamental theorems of the general theory of Theta functions. The first, due to H. Poincaré, was proved very skilfully in the note by means of harmonic integrals on a torus and the second, due to Frobenius, was treated by the systematic use of the notion of analytic structure.
Cusps on boundaries of Teichmüller spaces
Authors: Sato Hiroki
Published: July 2016

We shall be concerned here with cusps on the boundaries of Teichmüller spaces.
Two theorems on excellent rings
Authors: Greco Silvio
Published: July 2016

Let f: A → B be a homomorphism of commutative noetherian rings. The main results of this paper are:

(a) Assume f is finite and induces a surjective map on the spectra. Then if B is quasi-excellent A is quasi-excellent and is excellent if it is universally catenarian (Th. 3.1); and

(b) If f is absolutely flat and A is excellent then B is excellent (Th. 5.3). In particular the strict henselization of an excellent local ring is excellent (Cor. 5.6.).
On area integrals and radial variations of analytic functions in the unit disk
Authors: Murai Takafumi
Published: July 2016

We are concerned with the behaviour of analytic functions near the boundary. Let T and D be the unit circle |z| = 1 and the unit disk |z| < 1, respectively. The element of T is denoted by θ (0 ≤ θ < 2π). Let be analytic in D. The area integral A(f, θ) of f at θ is defined by
The theory of Hecke integrals
Authors: Goldstein Larry Joel , Razar Michael
Published: July 2016

Let H denote the complex upper half-plane and let η(z) denote Dedekind’s η-function
Representations of quadratic forms and their application to Selberg’s zeta functions
Authors: Kitaoka Yoshiyuki
Published: July 2016

Let M and L be quadratic lattices over the maximal order of an algebraic number field. In case of dealing with representations of M by L, they sometimes assume certain indefiniteness and the condition rank L-rank M ≥ 3. In this case, representation problems are reduced not to global but to local problems by virtue of the strong approximation theorem for rotations and of the fact that for regular quadratic spaces U, V over a non-archimedian local field there is an isometry from U to V if dim V — dim U ≥ 3.
A note on holomorphic matric automorphic factors with respect to a lattice in a complex vector space
Authors: Morikawa Hisasi
Published: July 2016

A holomorphic n × n-matric automorphic factor with respect to a lattice L in Cg means a system of holomorphic n × n-matrices {μα(z) | α ∈ L} such that
Hypoellipticity for a class of the second order partial differential equations
Authors: Matsuzawa Tadato
Published: July 2016

In this paper, we shall investigate the hypoellipticity for a class of degenerate equations of the second order with complex coefficients as a direct extension of the results obtained in [8]. As is well known, the satisfactory general results about hypoellipticity of real operators of the second order have been obtained in [3] and [9], where the assumption that the operators are real plays a crucial role and our aim of this paper is to study the operators with complex coefficients. Our method may be considered as a generalization of the usual variational method replacing the Gårding inequality by the estimate (2.15), (cf. [3], [5]).
Curves in Grassmann varieties
Authors: Papantonopoulou Aigli
Published: July 2016

The following question was the main motivation of this paper : which are the necessary and sufficient conditions for a non-singular subvariety of a Grassmann variety to have an ample normal bundle. Knowing that a non-singular subvariety of a Grassmann variety has an ample normal bundle we can apply on it several well-known theorems.
Note on class number factors and prime decompositions
Authors: Furuta Yoshiomi
Published: July 2016

LetKbe a Galois extension of an algebraic number fieldkof finite degree with Galois groupg,be a congruent ideal class group ofK, andMbe the class field overKcorresponding to. Assume thatMis normal overk. Thengacts onas a group of automorphisms. Donote bylgthe augmentation ideal of the group ringZgover the ring of integers Z.
On Shimura’s trace formula
Authors: Niwa Shinji
Published: July 2016

In [1], G. Shimura gave a very practical formula of the traces of the Hecke operators acting on the space of cusp forms of rational weight and there he emphasized that the traces are effectively computable. We shall practice the computation in some special cases and discuss the structure of the Hecke algebra, which is not necessarily semi-simple.
Quasi-coefficient rings of a local ring
Authors: Matsumura Hideyuki
Published: July 2016

In this note we will make a few observations on the structure of fields and local rings. The main point is to show that a weaker version of Cohen structure theorem for complete local rings holds for any (not necessarily complete) local ring. The consideration of non-complete case makes the meaning of Cohen’s theorem itself clearer. Moreover, quasi-coefficient fields (or rings) are handy when we consider derivations of a local ring.
The fourth dimension subgroups and polynomial maps, II
Authors: Tahara Ken-Ichi
Published: July 2016

In our previous paper [3] we proved the following ([3, Theorem 16]) :

THEOREM A. Let G be a 2-group of class 3. Let G2 and G/G2 be direct products of cyclic groups 〈yq〉 of order αq (1 ≦ q ≦ m), and of cyclic groups 〈hi〉 of order βi (1 ≦ i ≦ n) with β1 ≧ β2 ≧ · · · βn, respectively. Let xi be representatives of hi (1 ≦ i ≦ n), and put Then a homomorphism ψ:G3→T can be extended to a polynomial map from G to T of degree ≦ 4 if and only if there exists an integral solution in the following linear equations of Xiq (1 ≦ i ≦ n, 1 ≦ q ≦ m) with coefficients in T:

(I)

where δij is the Kronecker symbol for βi: i.e. δij = 1 or 0 according to βi = βj or βi > βj, respectively.
Ultrametric theta functions and abelian varieties
Authors: Tapia-Recillas Horacio
Published: July 2016

Let k be a field complete with respect to a non-trivial, non-archimedean valuation and let g be a positive integer. Consider the following question : if Γ is a multiplicative subgroup of Gg = (k*)g satisfying certain “Riemann conditions”, can one construct in a natural way an abelian variety defined over k having Gg/Γ as its set of k-rational points? This problem was first considered by Morikawa [3]. J. Tate provided a complete solution for g = 1 (cf. for example [6]). J. McCabe [2] gave a partial solution for g > 1. He showed how to attach to Γ a graded ring R of theta functions such that A = Proj. R is g-dimensional abelian variety over k.
La Notion D’anneau de Décomposition
Authors: Chevalley C.
Published: July 2016

Soit un domaine d’intégrité intégralement clos dans son corps des quotients, et soit m un idéal premier de . Soit un domaine d’intégrité intégralement clos dans son corps des quotients et dont est sous-anneau; soit un idéal premier de tel que
A Note on Euler Numbers and Polynomials
Authors: Carlitz L.
Published: July 2016

Let Em denote the Euler number in the even suffix notation so that

(1.1)

where, as usual, after expansion of the left member Er is replaced by Er. Nielsen [4, p. 273] has proved that

(1.2)
Algebras With Vanishing n-Cohomology Groups
Authors: Ikeda Masatoshi , Nagao Hiroshi , Nakayama Tadashi
Published: July 2016

Cohomology theory for (associative) algebras was first established in general higher dimensionalities by G. Hochschild [3], [4], [5]. Algebras with vanishing 1-cohomology groups are separable semisimple algebras ([3], Theorem 4.1). On extending and refining our recent results [6], [8], [12], we establish in the present paper the following:

Let n ≧ 2. Let A be an (associative) algebra (of finite rank) possessing a unit element 1 over a field Ω, and N be its radical.
On the Group Structure in Homotopy Groups
Authors: Kuranishi Masatake
Published: July 2016

Usually the group structure in a homotopy group is defined directly and explicitly. But the algebraic approach to the topology, now common, seems to raise the following question : is that the only group sturcture which is natural from the algebraic topological point of view? On the other hand, several algebraists have begun to feel a necessity to construct a “homotopy or cohomotopy theory of groups,” and it may be allowed to say that one of the first steps to the problem is the axiomatization of homotopy groups. Our first question is of course a special case of the latter problem.
On Associative Compositions in Finite Nilpotent Groups
Authors: Iwahori Nagayosi , Hattori Akira
Published: July 2016

Let

(1)

be a word in two variables X, Y, i.e. an element in the free group F2 on two generators X, Y. Let us say that f defines an associative composition for a group G if for arbitrary elements a, b, c in G we have

(2)

where a ° b is defined by

(3)
Les equations differentielles invariantes par les pseudo-groupes
Authors: Higa Tatsuo
Published: July 2016

S. Lie a étudié méthodiquement, pour la première fois, des propriétés des équations différentielles invariantes par les groupes continus de transformations locales (pseudo-groupes continus). Après avoir étudié la structure des pseudo-groupes, Lie a esquissé la méthode générale d’intégration des équations différentielles, [9]. Un de ses idées fondamentales est celle de réduire les équations différentielles aux autres équations faciles à étudier : par exemple, les systèmes de Pfaff complètement intégrables.
Form rings and regular sequences
Authors: Valabrega Paolo , Valla Giuseppe
Published: July 2016

Hironaka, in his paper [H1] on desingularization of algebraic varieties over a field of characteristic 0, to deal with singular points develops the algebraic apparatus of the associated graded ring, introducing standard bases of ideals, numerical characters ν* and τ* etc. Such a point of view involves a deep investigation of the ideal b* generated by the initial forms of the elements of an ideal A of a local ring, with respect to a certain ideal a.
Equations de Lie invariantes par un pseudogroupe de Lie
Authors: Abib Odinete Renée
Published: July 2016

Soit (ℒ, M) un pseudogroupe de Lie infinitesimal [4] transitif d’ordre h sur une variété M différentiate, Jhℒ son équation de définition et L son algèbre formelle au point a de M.
The structure of the multiplicative group of residue classes modulo
Authors: Nakagoshi Norikata
Published: July 2016

Letkbe an algebraic number field of finite degree andbe a prime ideal ofk, lying above a rational primep. We denote byG() the multiplicative group of residue classes modulo(N≧ 0) which are relatively prime to. The structure ofG() is well-known, whenN= 0, orkis the rational number fieldQ. Ifkis a quadratic number field, then the direct decomposition ofG() is determined by A. Ranum [6] and F.H-Koch [4] who gives a basis of a group of principal units in the local quadratic number field according to H. Hasse [2]. In [5, Theorem 6.2], W. Narkiewicz obtains necessary and sufficient conditions so thatG() is cyclic, in connection with a group of units in the-adic completion ofk.
On zeta functions associated with quadratic forms of variable coefficients
Authors: Suzuki Toshiaki
Published: July 2016

In 1938, C. L. Siegel studied zeta functions of indefinite quadratic forms ([6], c). On the other hand, M. Sato and T. Shintani constructed the general theory of zeta functions of one complex variable associated with prehomogeneous vector spaces in 1974 ([1]). Moreover T. Shintani studied several zeta functions of prehomogeneous vector spaces, especially, “Dirichlet series whose coefficients are class-numbers of integral binary cubic forms” ([3]) and “Zeta functions associated with the vector space of quadratic forms” ([2]).
Tensor products of positive definite quadratic forms IV
Authors: Kitaoka Yoshiyuki
Published: July 2016

Let L, M, N be positive definite quadratic lattices over Z. We treated the following problem in [5], [6]:

If L ⊗ M is isometric to L ⊗ N, then is M isometric to N?

We gave a condition (**) in [6] such that the answer is affirmative for an indecomposable lattice L satisfying (**), and we gave some examples. In this paper we introduce a certain apparently weaker condition (A) than the condition (**), and we show that the condition (A) implies the condition (**) and more on integral orthogonal groups than a result in [6].
Groups with a (B, N)–pair and locally transitive graphs
Authors: Weiss Richard
Published: July 2016

Let Γ be an undirected graph and G a subgroup of aut (Γ). We denote by ∂(x, y) the distance between two vertices x and y, by E(Γ) the edge set of Γ, by V(Γ) the vertex set of Γ, by Γ(x) the set of neighbors of the vertex x and by G(x)Γ(x) the permutation group induced by the stabilizer G(x) on Γ(x).
On algebraic groups defined by Jordan pairs
Authors: Loos Ottmar
Published: July 2016

Let G be an algebraic group over a field k, and let ψ be an action of the multiplicative group km of k on G by automorphisms. We say ψ is an elementary action if it has only the weights 0, ±1; more precisely, if there exist subgroups H, U+, U- of G such that (i) H is fixed under ψ, (ii) U+ and U+ are vector groups and (iii) Ω = U+. H . U+ is open in G, and (iv) G is generated by H, U+, U+. This situation is characteristic for the complexifications of the automorphism groups of bounded symmetric domains (see, e.g., [9, 16]). A typical example is G = GLnwith (matrices being decomposed into 4 blocks) ψ given by
Modular forms of degree n and representation by quadratic forms
Authors: Kitaoka Yoshiyuki
Published: July 2016

Let A(m), B(n) be positive definite integral matrices and suppose that B is represented by A over each p-adic integers ring Zp. Using the circle method or theory of modular forms in case of n = 1, B, if sufficiently large, is represented by A provided that m ≥ 5. The approach via the theory of modular forms has been extended by [7] to Siegel modular forms to obtain a partial result in the particular case when n = 2, m ≥ 7.
Universell japanische Ringe mit night offenem regulärem ort
Authors: Rotthaus Christel
Published: July 2016

Im Zusammenhang mit dem von Grothendieck in [2] Chap. IV (7.4.8) gestellten Problem “1st die ideal-adische Komplettierung eines ausgezeichneten Ringes wieder ausgezeichnet?” scheint aufgrund der Arbeiten von Marot [3] und Valabrega [8] im lokalen Fall die folgende Frage intéressant zu sein: “R sei ein lokaler universell japanischer Ring. 1st der singuläre Ort jeder endlich erzeugten R- Algebra A abgeschlossen in Spec (A)?” Diese Frage wird hier negativ beantwortet, d.h. wir werden einen lokalen universell japanischen Ring A konstruieren, dessen singulärer Ort nicht abgeschlossen in der Zariski-Topologie von Spec (A) ist.
Construction of arithmetic automorphic functions for special Clifford groups
Authors: Shih Kuang-Yen
Published: July 2016

An important problem in the theory of arithmetic automorphic functions is to construct, for a reductive algebraic group overQwhich defines a bounded symmetric domain, a system of canonical models [2], [6], [18]. For the similitude group of a hermitian form over a quaternion algebra whose center is a totally real field, this is solved by Shimura [17], and for the similitude group of a hermitian form with respect to an involution of the second kind of a central division algebra over aCM-field, by Miyake [8], In this paper, we show that this also can be done for the special Clifford group of a quadratic formQover a totally real algebraic number field. (We have to impose certain conditions on the signature ofQin order thatGdefines a bounded symmetric domain, see 1.1.)
First Chern class and holomorphic tensor fields
Authors: Kobayashi Shoshichi
Published: July 2016

Let M be an n-dimensional compact Kaehler manifold, TM its (holomorphic) tangent bundle and T*M its cotangent bundle. Given a complex vector bundle E over M, we denote its m-th symmetric tensor power by SmE and the space of holomorphic sections of E by Γ(E).
Some properties of weakly normal varieties
Authors: Manaresi Mirella
Published: July 2016

In this paper we give a new characterization of weak normalization and we use it to discuss some questions about weakly normal varieties formulated by A. Andreotti and E. Bombieri in [1] and studied by S. Greco and C. Traverso in [8] for seminormality.
N-ary algebras
Authors: Carlsson Renate
Published: July 2016

N-ary algebras are modules with a n-fold multiplication which we assume to be associative if nothing else is stated. They are a canonical generalization of binary and ternary associative algebras. Ternary rings were first investigated by Lister [8]. The aim of this note is to show that the Wedderburn structure theory and the usual cohomology for binary associative algebras can be extended to n-ary algebras. For ternary algebras this has been done in [8] and [1]. Moreover analogous results are wellknown for Lie and alternative triple systems, and for ternary Jordan pairs.
On compact minimal hypersurfaces in a sphere with constant scalar curvature
Authors: Doi Naoya
Published: July 2016

Let M be an n-dimensional hypersurface immersed in the (n + 1)-dimensional unit sphere Sn+1 with the standard metric by an immersion f. We denote by A the second fundamental form of the immersion / which is considered as a symmetric linear transformation of each tangent space TXM, i.e. for an arbitrary point x of M and the unit normal vector field ξ defined in a neighborhood of x, A is given by where is the covariant differentiation in Sn+i and Thus, A depends on the orientation of the unit normal vector field ξ and, in general, it is locally defined on M.
A note on Thom classes in general cohomology
Authors: Haas Ronald Kirk , Uehara Hiroshi
Published: July 2016

This note is dedicated to the second author’s teacher, Professor Atsuo Komatsu, in celebration of his seventieth birthday.

It is well known [4], [7] that the theory of characteristic classes in general cohomology is essentially based upon one theorem, the Leray-Hirsch Theorem. We further claim [8] that the entire theory could be developed merely from the Künneth Formula if under suitable conditions a truly relative version of the Meyer-Vietoris sequence exists in the general cohomology theory. In his lectures delivered at Aarhus in 1968, Dold [6] set up the necessary machinery including the Leray-Hirsch Theorem to define Chern Classes with values in general cohomology. However, he then stated [6, p. 47] that he “found a difficulty here in choosing adequate orientations (Thorn Classes) for the bundles involved”, and proceeded differently, discarding the “classical” approach used in both ordinary cohomology [9] and K-theory [3]. Later, he [7] published a more categorical work, although the approach to Chern Classes was basically unchanged from his previous work. Consequently, the possibility of the classical direct approach to the theory has remained open.
A prime decomposition symbol for a non-abelian central extension which is abelian over a bicyclic biquadratic field
Authors: Furuta Yoshiomi
Published: July 2016

In a previous paper [6] we had some criteria for the prime decomposition in certain non-abelian extensions over the rational number fieldQ, and as its special case we had a reciprocity of the biquadratic residue symbol. The reciprocity was obtained by using a descent method of the prime decomposition for a central extension overQwhich is abelian over a biquadratic fieldIn the present paper we study on the case over a biquadratic fieldin general. We define a symbol [d1,d2,p] which expresses the decomposition law of a rational primepin a central extension mentioned above.
Solution of the congruence subgroup problem for solvable algebraic groups
Authors: Chahal Jasbir Singh
Published: July 2016

Let k be an algebraic number field of finite degree over the field Q of rational numbers. We denote by o the ring of integers in k. In general, for a subring A, containing 1, of a universal domain Ω we denote by GL(n, A) the subgroup of GL(n, Ω) consisting of matrices x = (xij) with xij ∈ A and det x ∈ A×, the group of units of A. Now, we consider an algebraic group G in GL(n, Ω) defined over k.