bluuebunny/crossref_metadata_2025 huggingface dataset:
Rank Element of a Projective Module
Authors: Hattori Akira
Published: July 2016

In § 1 of this note we first define the trace of an endomorphism of a projective module P over a non-commutative ring A. Then we call the trace of the identity the rank element r(P) of P, which we shall illustrate by several examples. For a projective module P over the groupalgebra of a finite group G, the rank element of P is essentially the character of G in P. In § 2 we prove that under certain assumption two projective modules Pi and P2 over an algebra over a complete local ring o are isomorphic if and only if their rank elements are identical. This is a type of proposition asserting that two representations are equivalent if and only if their characters are identical, and in fact, when A is the groupalgebra, the above theorem may be considered as another formulation of Swan’s local theorem [9]).
Homomorphisms of Continuous Pseudogroups
Authors: D’atri Joseph E.
Published: July 2016

In this paper we attempt to set up a notion of homomorphism for continuous pseudogroups and show that the kernel exists (as a continuous pseudogroup) in the transitive case. This paper is really an extension of the paper by Kuranishi and Rodrigues [11] which essentially examines the question of the existence (as a continuous pseudogroup) of an image of a homomorphism. A certain amount of overlap in definitions and statements of results was unavoidable, especially in sections 2 and 3, but for many proofs and constructions the reader is referred to that paper. For the basic notions of the theory of continuous pseudogroups as used in section 4, see Kuranishi [9] and for the terminology of the Cartan-Kãhler theory used in section 5, see Kuranishi [6] Fuller expositions may be found in Cartan [I] Kàhler [4], Kumpera [5], Kuranishi [7], and Schouten and v.d. Kulk [13].
On Groups with Nilpotent Commutator Subgroups
Authors: Inagaki Nobuo
Published: July 2016

It is well known that a supersoluble group has the nilpotent commutator subgroup. But the converse does not hold in general. Therefore, it will be interesting to study the class of groups with nilpotent commutator subgroups. Some results were obtained by B. Huppert [1] and R. Baer [3] on this subject.

It is easily seen that the p-length of a group with the nilpotent commutator subgroup is 1 for every p dividing the order of this group. Theorem 1 of this paper may be considered as its local refinement, and is proved in a similar way as B. Huppert [2]. Theorem 2 gives a necessary and sufficient condition for a group to have the nilpotent commutator subgroup in terms of its Hall subgroups. In the last theorem 3 we shall study an interesting class of groups which have maximal subgroups of a certain nature. It turns out that these groups have nilpotent commutator subgroups and admit Sylowtowers.
Coherent Pairs of Extensions of Associative Algebras
Authors: Ramabhadran N.
Published: July 2016

Let K be a commutative ring with identity element and let Λi, i = 1, 2 be two K-projective associative algebras with identity element such that the map k → k · l of K into Λi is a monomorphism of K onto a K-direct summand of Λi, i = 1, 2. Let Λ = Λ1 ⊗ Λ2 and A be a two sided (Λ1, Λ2)-bimodule.
Une Generalisation des Lignes de Green
Authors: Lumer-Naim Linda
Published: July 2016

L’objet du présent travail est d’étudier, dans un espace de Green Ω, une généralisation des lignes de Green, à savoir les trajectoires orthogonales des surfaces de niveau de où G désigne la fonction de Green de pôle fixé y0 ∈ Ω, et h une fonction harmonique > 0 fixée dans Ω. Le cas h = 1, qui est celui des lignes de Green ordinaires, a été étudié en détail par M. Brelot et G. Choquet dans [4]. On montrera ici, moyennant l’introduction de notions convenablement appropriées, que les propriétés de ce cas initial s’étendent.
On the Grothendieck Ring of an Abelian p-Group
Authors: Obayashi Tadao
Published: July 2016

The Grothendieck ring of a finite group has been studied by Swan ([5], [6]). At the end of [6] he determined completely the structure of the Grothendieck ring G(Z) of a cyclic p-group over the ring of rational integers Z.
Unique Continuation for Parabolic Equations of Higher Order
Authors: Chen Lu-San , Kuroda Tadashi
Published: July 2016

Let x = (xl,…xn) be a point in the n-dimensional Euclidean space and let be the unit sphere In the (n + 1)-dimensional Euclidean space with coordinate (x, t), we put

and

where denotes the boundary of . We also use the following notation:
A Remark on the Intersection of Tow Logics
Authors: Miura Satoshi
Published: July 2016

The intuitionistic logic LJ and Curry’s LD (cf. [1], [2]) are logics stronger than Johansson’s minimal logic LM (cf. [3]) by the axiom schemes ⋏→x and y ∨ (y→⋏), respectively. However, LM can not be taken literally as the intersection of these two logics LJ and LD, which is stronger than LM by the axiom scheme (⋏ → x) VyV (y→⋏). In pointing out this situation, Prof. K. Ono suggested me to investigate the general feature of the intersection of any pair of logics. In this paper, I will show that the same situation occurs in general. I wish to express my thanks to Prof. K. Ono for his kind guidance.
Sur l’allure des Fonctions Meromorphes
Authors: Toda Nobushige
Published: July 2016

Récemment J. L. Doob [8] a trouvé quelques théorèmes intéressants sur l’allure des fonctions méromorphes au voisinage d’un point singulier essentiel isolé en utilisant la topologie fine c’est-à-dire la topologie la moins fine qui fait toutes les fonctions sous-harmoniques continues. A l’égard de ces résultats, on étudie dans ce mémoire quelques aspects de fonctions méromorphes au voisinage d’un point singulier essentiel isolé ou d’un point-frontière irrégulier.
A Formalism for Primitive Logic and Mechanical Proof-Checking
Authors: Ono Katuzi
Published: July 2016

The universal character of the primitive logic LO in the sense that popular logics such as the lower classical predicate logic LK, the intuitionistic predicate logic LJ, Johansson’s minimal predicate logic LM, etc. can be faithfully interpreted in LO is very remarkable even from the view point of mechanical proof-checking. Since LO is very simple, deductions in LO could be mechanized in a simple form if a suitable formalism for LO is found out. Main purpose of this paper is to introduce a practical formalism for LO, practical in the sense that it is suitable at least for mechanical proof-checking business.
On the Explicite Defining Relations of Abelian Schemes of Level Three
Authors: Morikawa Hisasi
Published: July 2016

It is known classically that abelian varieties of dimension one over the field of complex numbers may be expressed by non-singular Hesse’s canonical cubic plane curves, The purpose of the present paper is to generalize this idea to higher dimensional case.
Transitive Extensions of a Class of Doubly Transitive Groups
Authors: Suzuki Michio
Published: July 2016

1. When a permutation group G on a set Ω is given, a transitive extension G of G is defined to be a transitive permutation group on the set Γ which is a union of Ω and a new point ∞ such that the stabilizer of ∞ in G1 is isomorphic to G as a permutation group on Ω. The purpose of this paper is to prove that many known simple groups which can be represented as doubly transitive groups admit no transitive extension. Precise statement is found in Theorem 2. For example, the simple groups discovered by Ree [5] do not admit transitive extensions. Theorem 2 includes also a recent result of D. R. Hughes [3] which states that the unitary group U3(q) q>2 does not admit a transitive extension. As an application we prove a recent theorem of H. Nagao [4], which generalizes a theorem of Wielandt on the non-existence of 8-transitive permutation groups not containing the alternating groups under Schreier’s conjecture.
A Theorem on Finite Generation of a Ring
Authors: Nagata Masayoshi
Published: July 2016

The fourteenth problem of Hilbert asked finite generation of a certain class of rings and had a counter-example (cf. [4]). On the other hand, many mathematicians gave various sufficient conditions for finite generation of such rings (see, for instance, [9], [5] and [8]). The purpose of the present paper is to give a new sufficient condition. The class of rings to be treated is much more general than those treated before, except for the one in [8].
A Cohomological Investigation of the Discriminant of a Normal Algebraic Number Field
Authors: Yokoi Hideo
Published: July 2016

1. Let F be an algebraic number field of finite degree, and let K/F be a normal extension of degree n. Denote by OK the ring of all integers in K. In we proved the following:
On Quasinormal Subgroups II
Authors: Deskins W. E.
Published: July 2016

A subgroup was defined by O. Ore to be quasinormal in a group if it permuted with all subgroups of the group, and he proved [5] that such a subgroup is subnormal (= subinvariant = accessible) in a finite group. Finite groups in which all subgroups are quasinormal were classified by K. Iwasawa [3], and more recently N. Ito and J. Szép [2] and the author [1] proved that a quasi-normal subgroup is an extension of a normal subgroup by a nilpotent group. Similar results were obtained by O. Kegel [4] and in [1] for subgroups which permute not necessarily with all subgroups but with those having some special property.
Global Norm-Residue Map over Quasi-Finite Field
Authors: Rim D. S. , Whaples G.
Published: July 2016

A field k is called quasi-finite if it is perfect and if Gk≈Ż where Gk is the Galois group of the algebraic closure kc over k and Ż is the completion of the additive group of the rational integers. The classical reciprocity law on the local field with finite residue field is well-known to hold on local fields with quasi-finite residue field ([4] [5]). Thus it is natural to ask if the global reciprocity law should hold in the ordinary sense (see § 1 below) on the function-fields of one variable over quasi-finite field. We consider here two basic prototypes of non-finite quasi-finite fields:
On Regular Sequences
Authors: Dieudonné J.
Published: July 2016

The concept of regular sequence of elements of a ring A (first introduced by Serre under the name of A-sequence [2]), has far-reaching uses in the theory of local rings and in algebraic geometry. It seems, however, that it loses much of its importance when A is not a noetherian ring, and in that case, it probably should be superseded by the concept of quasi-regular sequence [1].
A Remark on Differentiable Structures on Real Projective (2n-1)-Spaces
Authors: Shiraiwa Kenichi
Published: July 2016

The main objective of this paper is to study the action of the group of differentiate structures Γ2n-1 on the (2n-1)-sphere S2n-1 on the diffeomorphism classes on the real projective (2n-1)-space P2n-1 by connected sum. This is done by considering universal covering spaces of the connected sum where Σ is an exotic (2n-1)-sphere.
Integrability of the Backward Diffusion Equation in a Compact Riemannian Space
Authors: Yosida Kôsaku
Published: July 2016

Let R be an orientable, compact Riemannian space with the metric ds2=gij(x)dxidxj and consider the backward diffusion equation
Some Theorems on Open Riemann Surfaces
Authors: Tsuji Masatsugu
Published: July 2016

Let F be an open Riemann surface spread over the z-plane. We say that F is of positive or null boundary, according as there exists a Green’s function on F or not, Let u(z) be a harmonic function on F

and be its Dirichlet integral As R. Nevanlinna proved, if F is of null boundary, there exists no one-valued non-constant harmonic function on F5 whose Dirichlet integral is finite, This Nevanlinna’s theorem was proved very simply by Kuroda.
Sur le Théorème de Produit Relatif au Degré Topologique d’une Application dans l’Espace Vectoriel Topologique
Authors: Hukuhara Masuo
Published: July 2016

Soit E un espace vectoriel topologique localement convexe, E un ensemble fermé dans E et f une application complètement continue de E dans E. M. Nagumo a montré, après avoir défini le degré topologique d(b, E, I—f) de l’application I—f de E en un point b ∉ (I—f)(∂E), la validité des propriétés importantes dont jouit le degré topologique. Mais dans sa démonstration du théorème de produit, il reste encore une lacune à combler.
Über Einige Allgemeine Konvexitätssätze in der Theorie der Partiellen Differentialgleichungen
Authors: Dinghas Alexander
Published: July 2016

Es bezeichne Rn(n≥2) den durch den Alexandroff-Punkt kompaktifizierten n-dimensionalen euklidischen Raum, [xl,......,xn], ein Koordinatensystem von Rn, x = (x1,......,xn) einen (endlichen) Punkt von Rn und

dessen Norm. Wir betrachten ein im Endlichen liegendes Gebiet G von Rn, definieren auf G einen linearen Operator
On Some Families of Analytic Functions on Riemann Surfaces
Authors: Yamashita Shinji
Published: July 2016

Throughout this paper all functions are single-valued. Let R be a Riemann surface. We shall denote by φ∧ the least harmonic majorant of a function φ defined in R if it has the meaning.
Über einige Beispiele der Quasinormal—teiler einer p-Gruppe
Authors: Nakamura Kirio
Published: July 2016

In dieser Note soil die Struktur des Quasinormalteilers vom Exponenten p der endlichen p-Gruppe untersucht werden. Ferner sollen einige Beispiele sowohl im regularen Falle als auch im nicht regulären Falle angeführt werden, die zeigen, daß das erst gesagte Ergebnis im allgemeinen Quasinormalteiler nicht immer zutrifft.
Certain Method for Generating a Series of Logics
Authors: Miura Satoshi , Nagata Shûrô
Published: July 2016

At first, we define three relations ⊇, =, and ⊃ in connection with a pair of logics L and L* as follows:

L ⊇ L*, if and only if every proposition provable in L* is also provable in L;

L = L*, if and only if L ⊇ L* and L* ⊇ L;

L ⊃ L*, if and only if L, ⊇ L* but not L* ⊇ L.
Equivalence Classes of Maximal Orders
Authors: Williamson Susan
Published: July 2016

Let k denote the quotient field of a complete discrete rank one valuation ring R. The purpose of this paper is to establish a relationship between the Brauer group of k and the set of maximal orders over R which are equivalent to crossed products over tamely ramified extensions of R.
A Characterization of the Zassenhaus Groups
Authors: Harada Koichiro
Published: July 2016

A doubly transitive permutation group on the set of symbols Ω is called a Zassenhaus group if satisfies the following condition: the identity is the only element leaving three distinct symbols fixed.
Corrections to “Algebraic Deformations of Polarized Varieties”, Nagoya Math. J. 31 (1968), pp. 185–245
Authors: Matsusaka T.
Published: July 2016

p. 187, line 20: Delete “—s” from the formula.

p. 228, line 4: Delete “—1” from the formula.

p. 228, lines 18 and 21: Delete “—s” from the formulas.
On the Sum of Homological Dimension and Codimension of Modules over a Semi-local Ring
Authors: Young Samuel S.H.
Published: July 2016

Let M be a finitely generated module over a regular local ring R. It is well known that the sum of homological dimension and codimension of M is equal to the global dimension of R. For modules over an arbitrary ring, this is in general not true. The purpose of this paper is to investigate the properties of such sums in the semi-local case.
Green’s Functions For Generalized Schroedinger Equations
Authors: Beekman John A.
Published: July 2016

I. Introduction. The purpose of this paper is to discuss functions defined on the continuous sample paths of Gaussian Markov processes which serve as Green’s functions for pairs of generalized Schroedinger equations. The results extend the author’s earlier paper [2] to a forward time version, and consider different boundary conditions.
Second Order Itô Processes
Authors: Goldstein Jerome A.
Published: July 2016

A first order stochastic differential equation is any equation which can be expressed symbolically in the form

(1. 1)

m and σ are called the drift and diffusion coefficients and z( · ) is usually a Brownian motion process.
On a Method of Describing Formal Deductions Convenient for Theoretical Purposes
Authors: Ono Katuzi
Published: July 2016

In my paper [2], I have proposed a method of describing formal deductions which seems to be convenient for practical purposes. In my paper [3], I have employed an index-system to exactly express tree-form configurations of proofs in Gentzen’s formalism for sequents. In the present paper, I would like to propose a method of describing formal deductions which seems to be convenient for theoretical purposes. The device employed for this purpose relies mostly on an index-system. Just as in [2] as well as in [3], I propose here also to denote every proposition and every denomination of a variable, or every sequent in Gentzen’s formalism, by an index-word.
Unitary Equivalence in Pairwise Spectral Analysis
Authors: Barankin Edward W.
Published: July 2016

It is a privilege to share in the honoring of Professor Katuzi Ono on this occasion, It would be enough to be simply putting in evidence my high regard for a good and dear friend. But there is so very much more than that here. It is an opportunity for me to declare my esteem for the kind of mathematician who looks at his field from the outside as well as the inside; who sees the richness of all experience and seeks its instruction to know better and better the meaning of mathematics ; who by the example of his own life urges young, coming scientists to the more productive path of an uncompartmentalized personality. Katuzi Ono is all of these.

In the pairwise spectral analysis of two projections F and G (see [1, §4] of the References) there are determined two resolutions of the identity, EF-and EG, which are spectral measures on the Borel interval [0, 1], and which are, in fact, the spectral measures of the Hermitian operators SF and SG of (1. 6) below.
On the Uniqueness in Cauchy’s Problem for Elliptic Systems with Double Characteristics
Authors: Hayashida Kazunari
Published: July 2016

We consider in the 2 dimensional space with the coordinate (x,y). Let Γ be a segment of the y-axis containing the origin in its interior and let Ω be a domain whose boundary contains Γ.
Sur les Fonctions Polyharmoniques et le Probleme de Riquier
Authors: Ito Masayuki
Published: July 2016

Soit Ω un ouvert de l’espace euclidien Rn à n(≧2) dimensions. Les recherches des fonctions harmoniques dans Ω sont essentielles dans la théorie classique du potentiel. A ce moment-là, il est bien connu que le balayage pour le noyau de Green dans Ω joue un grand rôle (par example, cf. M. Brelot [1]).
The Centers of Semi-Simple Algebras Over a Commutative Ring, II
Authors: Endo Shizuo , Watanabe Yutaka
Published: July 2016

In this note we assume that all rings have identities and denote by R a commutative ring. All R-algebras considered are assumed to be finitely generated faithful R-modules. An R-algebra Λ is said to be semi-simple ([5]), if any finitely ‘generated Λ-module is (Λ, R)-projective.
On Holomorphic Families of Holomorphic Maps
Authors: Orth Donald
Published: July 2016

Let D be the unit disk {z: | z | < l} in the complex plane C with boundary ∂D and closure and denote by R the image of the canonical embedding r → r + iO of the real line into C. The symbol ε will be used throughout to denote a complex parameter; the unit disk in the complex ε-plane will be denoted by Dp.
The Behaviour of Meromorphic Functions with a Set of Singularities of the Class N0B
Authors: Sagawa Akira
Published: July 2016

Let E be a totally disconnected compact set in the complex z-plane and let G be the complementary domain of E with respect to the extended z-plane. Consider a domain in G whose relative boundary consists of at most a countable number of analytic curves clustering nowhere in G. Such a domain is called a subregion in G.
Normal Light Interior Functions Defined in the Unit Disk
Authors: Mathews J.H.
Published: July 2016

Let D be the unit disk, C the unit circle, and f a continuous function from D into the Riemann sphere W. We say that f is normal if f is uniformly continuous with respect to the non-Euclidean hyperbolic metric in D and the chordal metric in W.
Elementary Quotients of Abelian Groups, and Singular Homology on Manifolds
Authors: Morse Marston , Cairns Stewart Scott
Published: July 2016

Let there be given a compact topological manifold Mn. If Mn admits a “triangulation” it is known that the fundamental invariants, namely the connectivities of Mn over fields, the Betti numbers and torsion coefficients over Z of the singular homology groups of Mn, are finite and calculable. However it is not known that a “triangulation” of Mn always exists when n > 3.
On Trace for Modules
Authors: Beckwith Howard B.
Published: July 2016

Classically, trace was defined as the sum of the diagonal entries of a square matrix with entries in a field. This notion played an important role in classical mathematics, e.g. in the theory of algebras over a field of characteristic zero, and in the theory of group characters (as in [1]). A generalization to endomorphisms of a finitely generated projective module over any ring R with unit is well-known. For such a module P the canonical homomorphism Ψ: P* ⊗ P→ EndR(P) is an isomorphism. Then the composite ε˚Ψ-1: EndR(P) → P* ↗ P→ R, where e denotes “evaluation”, is a homomorphism which coincides with the classical trace whenever P is free. This version of trace has been used by Hattori [3] and others to study projective modules. However, this approach to trace is limited to the finitely generated projective modules, since it can be shown that Ψ is an isomorphism if and only if P is finitely generated and projective.
On Tangential Principal Cluster Sets of Normal Meromorphic Functions
Authors: Vessey Theodore A.
Published: July 2016

Let w = f(z) be a normal meromorphic function defined in the upper half plane U = {Im(z) >0}. We recall that a meromorphic function f(z) is normal in U if the family {f(S(z))}, where z′ = S(z) is an arbitrary one-one conformal mapping of U onto U, is normal in the sense of Montel. It is the purpose of this paper to state some results on the behavior of f(z) on curves which approach a point x0 on the real axis R with a fixed (finite) order of contact q at x0.
On Holomorphic Maps into a Real Lie Group of Holomorphic Transformations
Authors: Fujimoto Hirotaka
Published: July 2016

1. Introduction. Let M, N be complex manifolds and G be a group of holomorphic automorphisms of N. In [3] (c.f. p. 74) W. Kaup introduced the notion of holomorphic maps into a family of holomorphic maps between complex spaces. By definition, a map g: M→G is holomorphic if and only if the induced map g̃(x, y): = g(x) (y) (x∈M, y∈N) of M×N into N is holomorphic in the usual sense. The purpose of this note is to give a description of a holomorphic map of a connected complex manifold M into G. We show first the existence of the maximum connected Lie subgroup G0 of G which is a complex Lie transformation group of N.
Intersections of Arc-Cluster Sets for Meromorphic Functions
Authors: Belna Charles L.
Published: July 2016

Let D and C denote the open unit disk and the unit circle in the complex plane, respectively; and let f be a function from D into the Riemann sphere Ω. An arc γ⊂D is said to be an arc at p∈C if γ∪{p} is a Jordan arc; and, for each t (0<t<1), the component of γ∩{z: t≤|z|<1} which has p as a limit point is said to be a terminal subarc of γ. If γ is an arc at p, the arc-cluster set C(f, p,γ) is the set of all points a∈Ω for which there exists a sequence {zk}a⊂γ with zk→p and f(zk)→a.
A Note on Holomorphic Vector Bundles Over Complex Tori
Authors: Morikawa Hisasi
Published: July 2016

Let (ω: Z2r→Cr be an isomorphism of the free additive group of rank 2r into the complex vector n-space such that the quotient group T = Crω/(Z2r) is compact, i.e., Tω is a complex torus.
Sur le Principe Classique du Maximum Pour les Noyaux de Convolution Symétriques
Authors: Ito Masayuki
Published: July 2016

Soit X un groupe abélien localement compact, et on désigne par dx sa mesure de Haar. On notera respectivement CK et MK les ensembles des fonctions finies, continues dans X, à support compact, et des fonctions mesurables, bornées dans X, à valeurs réelles et à support compact. (resp. ) est le sous-ensemble des fonctions non-négatives de CK (resp. MK).
The P-Harmonic Boundary and Energy-Finite Solutions of Δu = Pu
Authors: Kwon Y.K. , Sario L. , Schiff J.
Published: July 2016

The P-harmonic boundary ΔP and the P-singular point s of a Riemannian manifold R have been shown to play an important role in the study of bounded energy-finite solutions of Δu = Pu (Nakai-Sario [7], Kwon-Sario [4], Kwon-Sario-Schiff [5]). The objective of the present paper is to establish, in terms of ΔP and s, properties of unbounded energy-finite solutions (PE-functions) and of limits of decreasing sequences of positive PE-functions (-functions). Also, PE- and -minimal functions will be discussed.
Simultaneous Asymptotic Diophantine Approximations to a Basis of a Real Number Field
Authors: Adams William W.
Published: July 2016

The purpose of this paper is to prove the following result.

Theorem 1. Let K be a real algebraic number field of degree m = n + 1. Let 1, β1, …, βn be a basis of K.
A Generalization of Epstein’s Zeta Function
Authors: Terras Audrey
Published: July 2016

Koecher defined in [3] the following zeta function associated with the matrixS(n)of a positive quadratic form and one complex variableρ

(1)
A Note on Hecke Operators and Theta-Series
Authors: Kitaoka Yoshiyuki
Published: July 2016

As typical examples of modular forms there are theta series and Eisenstein series. We can easily see the behaviour of the Hecke operator on the Eisenstein series but it is very difficult to know that on the theta series.
Algebras of Finite Cohomological Dimension
Authors: Wehlen Joseph A.
Published: July 2016

The cohomology theory of an associative algebra has been shown to be valuable in the study of the structure of algebras of finite cohomological dimension, especially those of dimension less than or equal to one over a field. M. Harada [9] has shown that every semi-primary hereditary algebra A (for example, A is finitely generated over a field R and has dimension < 1) is isomorphic to a generalized triangular matrix algebra. The concept of a central separable algebra over a commutative ring has been shown to be a useful generalization of the concept of a central simple algebra over a field, where a separable algebra is defined to be an algebra having cohomological dimension zero.
Noyaux de Convolution Réguliers et Noyaux de Convolution Singuliers
Authors: Ito Masayuki
Published: July 2016

Soient X un groupe abélien localement compact et non-compact, et dx sa mesure de Haar. Rappelons qu’un noyau de convolution N sur X est une mesure de Radon positive dans X. Il est symétrique s’il est symétrique par rapport à l’origine. Notons MK la totalité de fonctions mesurables, bornées dans X, à valeurs réelles et à support compact. On dit que N est de type positif si, quelle que soit f une fonction de et la signe * est la convolution sur X.
Puissance Fractionnaire d’un Noyau Positif dont le Carré est Encore un Noyau
Authors: Kishi Masanori
Published: July 2016

Le noyau de Riesz-Frostman dans l’espace euclidien à d(≥3) dimensions est à la puissance fractionnaire du noyau de Newton. On trouve la conformité dans la théorie des espaces de Dirichlet; on construit un noyau à la puissance fractionnaire d’un noyau associé à l’espace de Dirichlet spécial, qui détermine à nouveau un espace de Dirichlet spécial [2]. En notant que le noyau de Dirichlet est positif et symétrique, et satisfait au principe complet du maximum, on s’interroge: est-il possible de construire de bons noyaux à la puissance fractionnaire pour des noyaux de genre plus large?
Relations between Non-Compact Transformation Groups and Compact Transformation Groups
Authors: Chu Hsin
Published: July 2016

In this paper certain relations between non-compact transformation groups and compact transformation groups are studied. The notion of re-ducibility and separability of transformation groups is introduced, several necessary and sufficient conditions are established: (1) A separable transformation group to be locally weakly almost periodic, (2) A reducible and separable transformation group to be a minimal set and (3) A reducible and separable transformation group to be a fibre bundle. As applications we show, among other things, that (1) for certain reducible transformation groups its fundamental group is not trivial which is a generalization of a result in [4].
Representations of Chevalley Groups in Characteristic p
Authors: Wong W.J.
Published: July 2016

If GK is a Chevalley group over a field K of prime characteristic p, the irreducible representations of GK over K form a natural object of study. The basic results have been obtained by Steinberg [15], who showed that, if K is perfect, then each irreducible rational representation of GK over K is a tensor product of representations obtained from certain basic representations by composing them with field automorphisms. These basic representations were obtained by “integrating” the irreducible restricted representations of a restricted Lie algebra associated with the group, which had been studied earlier by Curtis [7]. The present author had obtained the main results previously for the groups SL(n, K), Sp(2n, K) by different means, involving reduction (mod p) from the characteristic 0 case [16]. In this paper we extend this method to the other types of groups, in the hope that some additional insight may be gained.
Isometric Immersions of Constant Mean Curvature and Triviality of the Normal Connection
Authors: Erbacher Joseph
Published: July 2016

In a recent paper [2] Nomizu and Smyth have determined the hypersurfaces Mn of non-negative sectional curvature iso-metrically immersed in the Euclidean space Rn+1 or the sphere Sn+1 with constant mean curvature under the additional assumption that the scalar curvature of Mn is constant. This additional assumption is automatically satisfied if Mn is compact. In this paper we extend these results to codimension p isometric immersions. We determine the n-dimensional submanifolds Mn of non-negative sectional curvature isometrically immersed in the Euclidean Space Rn+P or the sphere Sn+P with constant mean curvature under the additional assumptions that Mn has constant scalar curvature and the curvature tensor of the connection in the normal bundle is zero. By constant mean curvature we mean that the mean curvature normal is paral lel with respect to the connection in the normal bundle. The assumption that Mn has constant scalar curvature is automatically satisfied if Mn is compact. The assumption on the normal connection is automatically sa tisfied if p = 2 and the mean curvature normal is not zero.
On Nilpotent Groups of Algebra Automorphisms
Authors: Leger G. , Luks E.
Published: July 2016

The main purpose of this paper is to derive conclusions about the structure of a nilpotent group of algebra automorphisms and, in the case of a Lie algebra, about the influence of this nilpotence on the structure of the algebra. A motivation for this study is a well known theorem due to Kolchin: A unipotent linear group can be triangularized and is thus nilpotent. The converse is manifestly false, but we have (as an immediate consequence of Theorem 2.7):
Sur les Noyaux de Dirichlet Continus
Authors: Itô Masayuki
Published: July 2016

Soit X un espace localement compact et dénombrable à l’infini, et supposons qu’il existe une mesure de Radon positive ξ partout dense dans X. Dans toute la suite X et ξ seront fixés.
Sur L’existence et la Non-existence des Algèbres de Dirichlet
Authors: Itô Masayuki
Published: July 2016

Cette mémoire sera consacrée à l’etude sur l’existence et la nonexistence des alg’bres de Dirichlet sur un ouvert de l’espace euclidien Rn à n(≧1) dimensions. La notion des algèbres de Dirichlet a été introduite par A. Beurling et J. Deny (cf. [1]).
Prime Entire Functions with Prescribed Nevanlinna Deficiency
Authors: Gross Fred , Osgood Charles , yang Chung-Chun
Published: July 2016

According to [4] a meromorphic function h(z) = f(g)(z) is said to have f(z) and g(z) as left and right factors respectively, provided that f(z) is non-linear and meromorphic and g(z) is non-linear and entire (g may be meromorphic when f(z) is rational). h(z) is said to be E-prime (E-pseudo prime) if every factorization of the above form into entire factors implies that one of the functions f, or g is linear (polynomial). h(z) is said to be prime (pseudo-prime) if every factorization of the above form, where the factors may be meromorphic, implies that one of f or g is linear (a polynomial or f is rational).
On Non-Anticipative Linear Transformations of Gaussian Processes with Equivalent Distributions
Authors: Rozanov YU. A.
Published: July 2016

Let ξ(t), t ∈ T, be a Gaussian process on a set T, and H = H(ξ) be the closed linear manifold generated by all values ξ(t), t ∈ T, with the inner product
Positiveness of the Reproducing Kernel in the Space PD(R)
Authors: Singer Ivan J.
Published: July 2016

An important problem in the study of the Hilbert space PD(R) of Dirichlet finite solutions of Δu = Pu on a Riemann surface R is to know the behavior of the reproducing kernel in PD(R). The main result of this paper is that the reproducing kernel is strictly positive.
Remark on the Tricomi Equation
Authors: Matsuzawa Tadato
Published: July 2016

As an application of the Garleman-type estimation Hörmander [4], p. 221, has proved the following:

A solution (distribution) of the Tricomi equation

in an open set Ω in belongs to C∞(Ω) if it is in C∞(Ω-) where .
Periodic Orbits of Isometric Flows
Authors: Ozols V.
Published: July 2016

Let M be a compact C∞ Riemannian manifold, X a Killing vector field on M, and φt its 1-parameter group of isometries of M. In this, paper, we obtain some basic properties of the set of periodic points of φt. We show that the set of least periods is always finite, and the set P(X, t) of points of M having least period t for the vector field X is a totally geodesic submanifold, with possibly non-empty boundary. Moreover, we show there are at least m geometrically distinct closed geodesic orbits of φt, where m is the number of least periods which are not integral multiples of any other least period.
A Note on Holomorphic Vector Bundles Over Quotient Manifolds With Respect to Nilpotent Groups
Authors: Morikawa Hisasi
Published: July 2016

A holomorphic vector bundle E over a complex analytic manifold is said to be simple, if its global endomorphism ring Endc (E) is isomorphic to C. Projectifying the fibers of E, we get the associated projective bundle P(E) of E, If we can choose a system of constant transition functions of P(Exs), the projective bundle P(E) is said to be locally flat.
An Example of a Positive Non-Symmetric Kernel Satisfying the Complete Maximum Principle
Authors: Kishi Masanori
Published: July 2016

One of the main problems in potential theory is to determine the class of kernels satisfying the domination principle or the complete maximum principle. As to positive symmetric kernels this is settled to a certain extent, but as to non-symmetric kernels we have not yet obtain satisfactorily large explicit classes. In this note we shall give a class of positive non-symmetric convolution kernels on the real line satisfying the complete maximum principle.
Circle Means of Green’s Functions
Authors: Nakai Mitsuru
Published: July 2016

Consider the polar coordinate differentials (dr, dθ) on a hyperbolic Riemann surface R with center z0 ∈ R which are given by

where GR(z, ζ) is the Green’s function on R with pole ζ ∈ R.
Some Consequences of Martin’s Axiom and the Negation of the Continuum Hypothesis
Authors: Shinoda Juichi
Published: July 2016

W. Sierpisnki [3] demonstrated 82 propositions, called C1-C82, with the aid of the continuum hypothesis. D. A. Martin and R. M. Solovay remarked in [2] that 48 of these propositions followed from Martin’s axiom (MA), 23 were refuted by and three were independent of But the relation of the remaining eight propositions to has been unsettled.
On the Vector in Homogeneous Spaces
Authors: Kurita Minoru
Published: July 2016

The main purpose of this paper is to investigate the parallelism of vectors in homogeneous spaces. The definition of a vector and the condition for spaces under which a covariant differential of a vector is also a vector were given by E. Cartan [4] in a very intuitive way. Here I formulate this in a stricter way by his method of moving frame. Even if a homogeneous space has the property that the covariant differential of a vector is of the same kind, another definition of covariant differential may also have the required property. I will give a necessary and sufficient condition under which the definition of covariant differential is unique. Once the covariant differential has been defined it is easy to introduce a parallelism of vectors in the space. But the parallelism depends in general on the path along which we translate a vector. The condition for the spaces with an absolute parallelism can be obtained.
On a Theorem of H. F. Blichfeldt
Authors: Itô Noboru
Published: July 2016

In 1903 H. F. Blichfeldt proved the following brilliant theorem : Let G be a matrix group of order g and of degree n. Let p be a prime divisor of g such that Then G contains the abelian normal p-Sylow subgroup. In 1941 applying his modular theory of the group representation, R. Brauer improved this theorem in the case in which p divides g to the first power only. Further in 1943 H. F. Tuan improved this result of R. Brauer one step more.
Cohomology Relations in Spaces with a Topological Transformation Group
Authors: hu Sze-Tsen
Published: July 2016

Let Q be a topological transformation group operating on the left of a topological space X. Let us denote by. B the orbit space and p : X → B the projection, p is a continuous and open map of X onto B. For an arbitrary abelian coefficient group G, the continuous map p induces homomorphisms
Corrections to My Paper “On the Structure of Complete Local Rings”
Authors: Nagata Masayoshi
Published: July 2016

The proof of Proposition 2 and that of Corollary to Proposition 3 in my previous paper “On the structure of complete local rings” are not correct Here we want to correct them.
Stochastic Integrals in Abstruct Wiener Space II: Regularity Properties
Authors: Kuo Hui-Hsiung
Published: July 2016

This paper continues the study of stochastic integrals in abstract Wiener space previously given in [14]. We will present, among other things, the detailed discussion and proofs of the results announced in [16]. Let H ⊂ B be an abstract Wiener space.
Noyaux Réguliers et Noyaux Singuliers
Authors: Itô Masayuki
Published: July 2016

Dans l’article précédent [6], nous définissions deux classes des noyaux de convolution symétriques sur un groupe abélien localement compact et dénombrable à l’infini; l’une est régulière et l’autre est singulière.
Characterization of Relative Domination Principle
Authors: Higuchi Isao , Itô Masayuki
Published: July 2016

Let X be a locally compact and σ-compact Abelian group and ξ be the Haar measure of X. A positive Radon measure N on X is called a convolution kernel when we regard it as a kernel of potentials of convolution type. M. Itô [4], [6] characterized the convolution kernel which satisfies the domination principle. The purpose of this paper is to characterize the relative domination principle for the convolution kernels.
Operators on Tensor Products of ℒ1, ℒ2 and ℒ∞ Spaces
Authors: Ichinose Takashi
Published: July 2016

Let A and B be densely defined closed linear operators in complex Banach spaces X, Y, respectively, with nonempty resolvent sets.
Holomorphic Mappings into Projective Space with Lacunary Hyperplanes
Authors: Kiernan Peter , Kobayashi Shoshichi
Published: July 2016

In this note, we shall examine some results of Bloch [2] and Cartan [3] concerning complex projective space minus hyperplanes in general position. The purpose is to restate their results in a more general setting by using the intrinsic pseudo-distance defined on a complex space [16] and the concept of tautness introduced by Wu in [18]. In the process we shall generalize some results of Dufresnoy [4] and Fuj imoto [7].
Uniform densities on hyperbolic Riemannl surfaces
Authors: Nakai Mitsuru
Published: July 2016

We are interested in the question how the spaces of solutions of elliptic equations vary according to the variations of underlying regions and coefficients of the equation. We will discuss this question for the case of equations Δu = Pu considered on noncompact Riemann surfaces R. Typically we ask the properties of mappings τx: (R,P) → dim PX(R) from the space Φ of pairs (R, P) of noncompact Riemann surfaces R and densities P on R, i.e. P(z)dxdy are 2-forms on R such that P(z)dxdy ≢ 0 and P(z) ≥ 0 are Hölder continuous with respect to local parameters z = x + iy, into cardinals, where PX(R) are the linear spaces of solutions of Δu = Pu on R with certain boundedness properties X.
A heterogeneous interpolant
Authors: Taylor Walter
Published: July 2016

In this note we exhibit an interpolant for a certain valid implication ╞ φ → ψ, where φ and ψ come from the infinitary language Lω1ω1. The existence of this interpolant follows from Takeuti’s heterogeneous interpolation theorem [5], but unfortunately the proof in [5] is not explicit enough to allow one to find the interpolant explicitly. Takeuti’s theorem asserts the existence of an interpolant in the class Lω1ω1 of heterogeneous formulas, which admits the rules of formation of Lω1ω1 plus the following additional rule:
Some results in the theory of vector bundles
Authors: Umemura Hiroshi
Published: July 2016

We have several definitions of the positivity of a vector bundle, differentiate definitions, an algebro-geometric definition, a topological definition etc. In § 1 we review the definitions and the relations between them. For a line bundle all the definitions are equivalent and every one agrees that they are reasonable. For a vector bundle, however, the definitions are not necessarily equivalent. One of the main results of this paper is the equivalence of the definitions over a complete non-singular curve. The proof is given in §2. We proved this over an elliptic curve in Umemura [18]. In this case the proof was based on Atiyah’s classification. To prove the equivalence over a curve of genus ≥ 2, the fundamental lemma is; A stable bundle of positive degree is positive in the sense of Nakano. The tool used to prove this lemma is the theory of stable bundles due to Narasimhan and Seshadri [11] —they establish a correspondence between stable bundles and certain types of irreducible unitary representations of a Fuchsian group.
On a θ-Weyl sum
Authors: Nakai Yoshinobu
Published: July 2016

We treat the sum , where α and γ are real with α positive. This sum was treated first by Hardy and Littlewood [4], and after them, by Behnke [1] and [2], Mordell [9], Wilton [11] and others. The reader will find its history in [7] and in the comments of the Collected Papers [4]. Here we show that the sum can be expressed explicitly, together with an error term O(N1/2), using the regular continued fraction expansion of α. As the statements have complications we will divide them into two theorems. In the followings all letters except ϑ, i, σ, ζ, χ and those in 3° are real, N is a positive real, and always k, n, a, A, B, C, D and E denote integers. The author expresses his thanks to Professor Tikao Tatuzawa and Professor Tomio Kubota for their encouragements.
On the canonical holomorphic map from the Moduli space of stable curves to the Igusa monoidal transform
Authors: Namikawa Yukihiko
Published: July 2016

LetMgbe the coarse moduli space of complete non-singular curves of genusgandthe coarse moduli space of principally polarized abelian varieties of dimensiong. There is a canonical map:
Finite groups of conjugate rank 2
Authors: Camina Alan R.
Published: July 2016

In 1953 N. Itô defined the conjugate rank of a finite group as the number of distinct sizes, not equal to 1, of the conjugacy classes of the group [7].
Lipeomorphisms close to an Anosov diffeomorphism
Authors: Takaki Kentaro
Published: July 2016

It is well-known that an Anosov diffeomorphism f on a compact manifold is structurally stable in the space of all C1-diffeomorphisms, with the C1-topology (Anosov [1]). In this paper we show that f is also structurally stable in the space of all lipeomorphisms, with a lipschitz topology. The proof is similar to that of the C1-case by J. Moser [4].
Sur la famille sous-ordonnée au noyau de convolution de hunt II
Authors: Itô Masayuki
Published: July 2016

Dans toute la suite X désignera un groupe abélien localement compact et dénombrable à l’infini; ξ sera sa mesure de Haar. Un noyau de convolution N sur X signifie une mesure de Radon positive dans X, et, 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.
Banach spaces of bounded solutions of Δu = Pu (P ≥ 0) on hyperbolic riemann surfaces
Authors: Nakai Mitsuru
Published: July 2016

Consider a nonnegative Hölder continuous 2-form P(z)dxdy on a hyperbolic Riemann surface R (z = x + iy). We denote by PB(R) the Banach space of solutions of the equation Δu = Pu on R with finite supremum norms. We are interested in the question how the Banach space structure of PB(R) depends on P. Precisely we consider two such 2-forms P and Q on R and compare PB(R) and QB(R). If there exists a bijective linear isometry T of PB(R) to QB(R), then we say that PB(R) and QB(R) are isomorphic.
Optimal control of ultimately bounded stochastic processes
Authors: Miyahara Yoshio
Published: July 2016

We shall consider the optimal control for a system governed by a stochastic differential equation

where u(t, x) is an admissible control and W(t) is a standard Wiener process. By an optimal control we mean a control which minimizes the cost and in addition makes the corresponding Markov process stable.
A characterization of unitary operators induced by nonsingular transformations and its applications
Authors: Sato Hiroshi , Oka Yukimasa
Published: July 2016

In this paper we give a necessary and sufficient condition for a unitary operator on an L2-space to be induced by a nonsingular transformation and its applications.
Siegel domains over self-dual cones and their automorphisms
Authors: Tsuji Tadashi
Published: July 2016

The Lie algebra gr of all infinitesimal automorphisms of a Siegel domain in terms of polynomial vector fields was investigated by Kaup, Matsushima and Ochiai [6]. It was proved in [6] that gr is a graded Lie algebra; gr = g-1 + g-1/2 + g0 + g1/2 + g1 and the Lie subalgebra ga of all infinitesimal affine automorphisms is given by the graded subalgebra; ga = g-1 + g-1/2 + g0. Nakajima [9] proved without the assumption of homogeneity that the non-affine parts g1/2 and g1 can be determined from the affine part ga.
On a class of degenerate elliptic equations
Authors: Hashimoto Yoshiaki , Matsuzawa Tadato
Published: July 2016

We shall prove in Chapter I the hypoellipticity for a class of degenerate elliptic operators of higher order. Chapter II will be devoted to the consideration of the regularity at the boundary for the solutions of general boundary problems for the equations considered in Chapter I being restricted to the second order.
Solutions to extremal problems in Ep space
Authors: Vinge Vernor
Published: July 2016

Let Ω be a bounded domain (in the complex plane) whose boundary, C, consists of finitely many disjoint, rectifiable, closed Jordan curves.
On a distance function between Differentiable structures
Authors: Shikata Yoshihiro
Published: July 2016

In this note, we investigate a relation between the connected sum of manifolds and the distance of manifolds ([2]). Since the smoothing of a piecewise linear equivalence is given by connected sum of exotic spheres ([1]), we have a certain estimate of the smoothing obstruction using the distance of manifolds (Proposition 3). In § 3, an application is given to show the impossibility of the 0.64-pinching of an exotic sphere.