bluuebunny/crossref_metadata_2025 huggingface dataset:
Integration in Locally Compact Spaces II
Authors: Hewitt Edwin , Zuckerman H. S.
Published: July 2016

The general problem of producing concrete representations for continuous linear functionals on normed linear spaces, ie., of identifying conjugate spaces, has of course attracted the attention of many mathematicians during the last five decades and has been solved in many cases [1, pp. 59-72]. Likewise, the problem of extending a linear functional defined on a linear subspace of a normed linear space may be regarded as solved by the Hahn-Banach theorem [1, p. 28], although problems involving “natural” extensions, like that yielding the Lebesgue integral from the Riemann integral, remain. In the present paper, we shall consider two “natural’ methods of extending a certain linear functional and show that they are in fact identical. As a by-product, we obtain a concrete representation both for the original functional and for its “natural” extension. In subsequent communications, the writers will consider topologies in certain families of linear functionals, canonical resolutions of linear functionals, and other extension problems.
Some Studies on Semi-local Rings
Authors: Nagata Masayoshi
Published: July 2016

The concept of semi-local rings was introduced by C. Chevalley [1], which the writer has generalized in a recent paper [7] by removing the chain condition. The present paper aims mainly at the study of completions of semi-local rings. First in § 1 we investigate semi-local rings which are subdirect sums of semi-local rings, and we see in § 2 that a Noetherian semi-local ringRis complete if (and only if)R/pis complete for every minimal prime divisorpof zero ideal, together with some other properties. Further we consider in § 3 subrings of the completion of a semi-local ring. § 4 gives some supplementary remarks to [7], Chapter II, Proposition 8.
Residue Rings of Semi-Primary Hereditary Rings*
Authors: Zaks Abraham
Published: July 2016

Throughout this paper we assume that all rings contain an identity. We say that R is a semi-primary ring if its (Jacobson) radical N is nilpotent, and R/N is an Artinian ring. We say that R admits a splitting, and we write R=A+B if A is a. subring of R, if B is a two-sided ideal in R, and if A∩B=0 .
A Lemma for Negationless Propositional Logics and its Applications
Authors: Tugué Tosiyuki
Published: July 2016

In this note, we treat the positive sentential logic LPS and the primitive sentential logic (the positive implicational calculus of Hilbert) LOS1). LOS has ‘implication’ as the only logical symbol and is a subsystem of LPS.
Superharmonic Functions in a Domain of a Riemann Surface
Authors: Kuramochi Zenjiro
Published: July 2016

Let R be a Riemann surface. Let G be a domain in R with relative boundary ∂G of positive capacity. Let U(z) be a positive superharmonic function in G such that the Dirichlet integral D(min(M,U(z))) < ∞ for every M. Let D be a compact domain in G.
On Algebras of Dominant Dimension One
Authors: Mueller Bruno J.
Published: July 2016

QF-3 algebras R are classified according to their second commutator algebras R′ with respect to the minimal faithful module, which satisfy dom.dim. R′ ≧ 2. The class C(S) of all QF-3 algebras whose second commutator is S, contains besides S only algebras R with dom.dim. R = 1. C(S) contains a unique (up to isomorphism) minimal algebra which can be represented as a subalgebra S0 of S describable in terms of the structure of S, and C(S) consists just of the algebras S0 ⊂ R ⊂ S (up to isomorphism).
On Multivariate Wide-sense Markov Processes
Authors: Mandrekar V.
Published: July 2016

The idea of multivariate wide-sense Markov processes has been recently used by F.J. Beutler [1], In his paper, he shows that the solution of a linear vector stochastic differential equation in a wide-sense Markov process. We obtain here a characterization of such processes and as its consequence obtain the conditions under which it satisfies Beutler’s equation. Furthermore, in stationary Gaussian case we show that these are precisely stationary Gaussian Markov processes studied by J. Doob [5].
Horocyclic Cluster Sets of Functions Defined in the Unit Disc
Authors: Dragosh Stephen
Published: July 2016

This paper contains in part the author’s Ph.D. dissertation written under the supervision of Professor F. Bagemihl at the University of Wisconsin-Milwaukee. This research was supported by grants from the National Science Foundation and the University of Wisconsin Graduate School.
Absolute Continuity of Markov Processes and Generators
Authors: Kunita Hiroshi
Published: July 2016

Let (x, ζ,ℬt,Px) be a (standard) Markov process with state space 5 defined on the abstract space Ω. Here, xt is the sample path, ζ is the terminal time and ℬt is the smallest α-field of Ω in which xs s ≤ t are measurable. Let P’x, x ∈ S be another family of Markovian measures defined on (ℬt, Ω).
Gaussian Measure on a Banach Space and Abstract Winer Measure
Authors: Sato Hiroshi
Published: July 2016

In this paper, we shall show that any Gaussian measure on a separable or reflexive Banach space is an abstract Wiener measure in the sense of L. Gross [1] and, for the proof of that, establish the Radon extensibility of a Gaussian measure on such a Banach space. In addition, we shall give some remarks on the support of an abstract Wiener measure.
A Characterization of the Finite Simple Groups PSp(4, q), G2(q), I
Authors: Fong Paul , Wong W.J.
Published: July 2016

Suppose that G is the projective symplectic groupPSp(4, q), the Dickson groupG2(q)>or the Steinberg “triality-twisted” groupwhereqis an odd prime power. Then G is a finite simple group, andGcontains an involutionjsuch that the centralizerC(j)inGhas a subgroup of index 2 which containsjand which is the central product of two groups isomorphic withSL(2,q1)andSL(2,q2)for suitableqlq2.We wish to show that conversely the only finite simple groups containing an involution with this property are the groupsPSp(4,q), G2(q)9.In this first paper we shall prove the following result.
Asymptotic Behavior of Solutions of Parabolic Equations with Unbounded Coefficients
Authors: Kuroda Tadashi
Published: July 2016

Let Rn be the n-dimensional Euclidean space, each point of which is denoted by its coordinate x = (x1,...,xn). The variable t is in the real half line [0, ∞).
A Characterization of the Simple Group U3(5)
Authors: Harada Koichiro
Published: July 2016

In this note we consider a finite group G which satisfies the following conditions:

(0. 1) G is a doubly transitive permutation group on a set Ω of m + 1 letters, where m is an odd integer ≥ 3,

(0. 2) if H is a subgroup of G and contains all the elements of G which fix two different letters α, β, then H contains unique permutation h0 ≠ 1 which fixes at least three letters,

(0. 3) every involution of G fixes at least three letters,

(0. 4) G is not isomorphic to one of the groups of Ree type.
On a Necessary Condition for the Sample Path Continuity of Weakly Stationary Processes
Authors: Kubo Izumi
Published: July 2016

We shall discuss the sample path continuity of a stationary process assuming that the spectral distribution function F(λ) is given. Many kinds of sufficient conditions have been given in terms of the covariance function or the asymptotic behavior of the spectral distribution function.
On a Propositional Calculus Whose Decision Problem is Recursively Unsolvable
Authors: Nakamura Akira
Published: July 2016

The purpose of this paper is to present a propositional calculus whose decision problem is recursively unsolvable. The paper is based on the following ideas:

(1) Using Löwenheim-Skolem’s Theorem and Surányi’s Reduction Theorem, we will construct an infinitely many-valued propositional calculus corresponding to the first-order predicate calculus.

(2) It is well known that the decision problem of the first-order predicate calculus is recursively unsolvable.

(3) Thus it will be shown that the decision problem of the infinitely many-valued propositional calculus is recursively unsolvable.
Introduction of a Basic Theory of Objects
Authors: Ono Katuzi
Published: July 2016

In constructing various kind of mathematical theories on the basis of a common basic theory, it has been very usual to take up the set theory as the common basic theory. This approach has been already successful to a certain extent and looks like successfully developable in the future not only in constructing mathematical theories standing on the classical logic but also in constructing formal theories standing on weaker logics. In constructing mathematical theories standing on the classical logic, it has been successful in most cases only by interpreting mathematical notions in the set theory without defining any special interpretation of logical notions. In constructing any mathematical theory standing on weaker logics such as the intuitionistic logic, however, we have to give a special interpretation for logical notions, too.
Note on the Characters of Solvable Groups
Authors: Ito Noboru
Published: July 2016

Let be a solvable group of order g. Let p be a prime and let g = pa g′ with (p,g′) = 1. In [4] we have tried to find sufficient conditions for to possess an irreducible character of p-defect 0, that is, a character whose degree is divisible by pa.
C-Flows on a Lie Group for Euler Equations
Authors: Hasegawa Yoshihei
Published: July 2016

The purpose of this paper is to determine left-invariant vector fields on a Lie group G with a left-invariant Riemannian metric which induces C- flows on G.
Liftings of Tensor Fields and Connections to Tangent Bundles of Higher Order
Authors: Morimoto Akihiko
Published: July 2016

In the previous papers [1], [2] we have studied the prolongations of G-structures to tangent bundles of arbitrary order, and in [3] we have considered the prolongations of connections to the tangential fibre bundles of higher order. The purpose of the present paper is to study the liftings of tensor fields and affine connections to tangent bundles of higher order. In fact, most of results in [4], [5] will be generalized in a natural fashion and some of the formulas concerning vertical and complete lifts in [5] will be unified and generalized in our formulas concerning ‹Λ›-lifts (cf. §3).
Remarks on the Angular Derivative
Authors: Warschawski S. E.
Published: July 2016

Suppose that Ω is a simply connected domain in the w-plane, w = u + iv, and that w∞ is an accessible boundary point of Ω located at w = ∞.
Sur la Différentiabilité et la Continuité des Potentiels Associés en Valeur Principale À Noyaux Singuliers et M-Fois Régularisant
Authors: Ito Yoshifusa
Published: July 2016

D’après D. Courrège [1], l’opérateur de convolution associé en valeur principale à un noyau de Caldéron-Zygmund homogène de classe C0,μ(∑n) applique continûment dans Cp,λ(Rn) si 0 < λ < μ ≤ 1, et l’opérateur de convolution associé à un noyau homogène de degré m—n et de classe Cm,μ(∑n) applique continûment dans Cp+m,λ(Rn) si 0 < λ < μ ≤ 1.
A Note on Extended Ambiguous Points
Authors: Stebbins J.L.
Published: July 2016

Let f be an arbitrary function from the open unit disk D of the complex plane into the Riemann sphere S. If p is any point on the unit circle C, C(f, p) is the set of all points w such that there exists in D a sequence of points {Zj} such that zj→p and f(zj)→w. CΔ(f, p) is defined in the same way, but the sequence {Zj} is restricted to Δ⊂D. If α and β are two arcs in D terminating at p and Cα(f, p)∩Cβ(f, p) = Φ, p is called an ambiguous point for f.
On Projective Differential Equations on Complex Analytic Manifolds
Authors: Morikawa Hisasi
Published: July 2016

Linear differential equations have been studied more throughly than any other class. They posses a group of characteristic properties: the invariance of linearity by linear transformations, the linearly dependence of solutions on their initial values, e.t.c. The next simple type of differential equations is quadratic type
On the Block of Defect Zero
Authors: Tsushima Yukio
Published: July 2016

Let G be a finite group and let p be a fixed prime number. If D is any p-subgroup of G, then the problem whether there exists a p-block with D as its defect group is reduced to whether NG(D)/D possesses a p-block of defect 0. Some necessary or sufficient conditions for a finite group to possess a p-block of defect 0 have been known (Brauer-Fowler [1], Green [3], Ito [4] [5]). In this paper we shall show that the existences of such blocks depend on the multiplicative structures of the p-elements of G. Namely, let p be a prime divisor of p in an algebraic number field which is a splitting one for G, o the ring of p-integers and k = o/p, the residue class field.
Functional Equations of Generalized Epstein Zeta Functions in Several Complex Variables
Authors: Terras Audrey A.
Published: July 2016

LetS(n)be the matrix of a positive definite quadratic form and

Define

1.

Here the sum is over unimodular matriceswhich lie in a complete set of representatives for the equivalence relationwithPunimodular and having block form
A Characterization of Odd Order Extensions of the Finite Simple Groups PSp(4, q), G2(q),
Authors: Harris Morton E.
Published: July 2016

Let p denote an odd prime integer and let q = pf where f is a positive integer. Let ℋ denote the projective symplectic group PSp(4,q), the Dickson group G2(q), or the Steinberg “triality twisted” group over a field Fq of q elements. Then ℋ is simple and the Sylow 2-subgroups of ℋ have centers of order 2 so that involutions which centralize a Sylow 2-subgroup of ℋ form a single conjugacy class of ℋ.
On the Field of Rationality for an Abelian Variety
Authors: Shimura Goro
Published: July 2016

The purpose of this paper is to prove the following two facts:

I

Every generic polarized abelian variety of odd dimension has a model rational over its field of moduli.

II

No generic principally polarized abelian variety of even dimension has a model rational over its field of moduli.
Gaussian Sample Functions: Uniform Dimension and Hölder Conditions Nowhere
Authors: Berman Simeon M.
Published: July 2016

Let X(t), t≥0, be a real Gaussian process with mean 0, stationary increments, and a2(t) = E|X(t) - X(0)|2. Here dH(λ), for some bounded monotone H. We summarize the main results.
Tangential Boundary Properties of Arbitrary Functions in the Unit Disc
Authors: Yoshida Hidenobu
Published: July 2016

1. By the method of Dolzhenko’s paper, we studied relations between non-tangetial (angular) boundary behaviors and horocyclic boundary behaviors of arbitrary functions defined in the open unit disc of the complex plane in [8]. Vessey [5], [6] investigated the behavior of arbitrary functions on paths which are “more tangential” than horocycles. The purpose of the present paper is to prove the fact that is sharper than the results in Vessey [5], [6], and generalize the results in [8] to obtain the connection between behaviors on two “more tangential” angles.
Remarks on Kähler-Einstein Manifolds
Authors: Matsushima Yozo
Published: July 2016

The main purpose of this note is to characterize a compact Káhler-Einstein manifold in terms of curvature form. The curvature form Q is an EndT valued differential form of type (1,1) which represents the curvature class of the manifold. We shall prove that the curvature form of a Káhler metric is the harmonic representative of the curvature class if and only if the Káhler metric is an Einstein metric in the generalized sense (g.s.), that is, if the Ricci form of the metric is parallel. It is well known that a Káhler metric is an Einstein metric in the g. s. if and only if it is locally product (globally, if the manifold is simply connected and complete) of Kàhler-Einstein metrics. We obtain an integral formula, involving the integral of the trace of some operators defined by the curvature tensor, which measures the deviation of a Káhler-Einstein metric from a Hermitian symmetric metric. In the final section we shall prove the uniqueness up to equivalence of Kãhler-Einstein metrics in a simply connected compact complex homogeneous space. This result was proved by Berger in the case of a complex projective space and our proof is completely different from Berger’s.
Stable Vector Bundles on Algebraic Surfaces
Authors: Takemoto Fumio
Published: July 2016

Let k be an algebraically closed field, and X a nonsingular irreducible protective algebraic variety over k. These assumptions will remain fixed throughout this paper. We will consider a family of vector bundles on X of fixed rank r and fixed Chern classes (modulo numerical equivalence). Under what condition is this family a bounded family? When X is a curve, Atiyah [1] showed that it is so if all elements of this family are indecomposable. But when I is a surface, he showed also that this condition is not sufficient. We give the definition of an H-stable vector bundle on a variety X. This definition is a generalization of Mumford’s definition on a curve. Under the condition that all elements of a family are H-stable of rank two on a surface X, we prove that the family is bounded. And we study H-stable bundles, when X is an abelian surface, the protective plane or a geometrically ruled surface.
Separating Function Algebras
Authors: Csordas G. L. , Reiter H. B.
Published: July 2016

Recent results of Hoffman and Singer [7], Weiss [10] and Wilken [11] indicate that the study of separation properties play a central rôle in the theory of function algebras. Our purpose in this paper is to investigate a natural separation property of function algebras.
Neo-Normal Functions in Arbitrary Regions
Authors: Tse Kam-Fook
Published: July 2016

It is well known that many properties possessed by functions holomorphic and bounded in a region are also possessed by functions meromorphic and omitting three values. Noshiro [14] in 1938 and Lehto and Virtanen [12] in 1957 independently defined the notion of “normal functions” ; they and many others subsequently discovered that most properties concerning boundary behavior and value distribution acquired by meromorphic functions omitting three values in the unit disk (or more general, in a simply-connected region) are also valid properties of “normal functions” defined there. In their research on the problems of value distribution of normal functions, Lange [9], Gavrilov [5] and Gauthier [4] have discovered that functions normal in the disk are exactly those which omit three values “locally,” i.e., they do not possess any “p-sequence” (see above references). However, the definition of a function being normal in a region depends on the simply-connectedness of the region or its universal covering surface. It is thus difficult to judge if a function defined in an arbitrary region is normal.
On the Behavior of Extensions of Vector Bundles Under the Frobenius Map
Authors: Tango Hiroshi
Published: July 2016

Let k be an algebraically closed field of characteristic p > 0, and let X be a curve defined over k. The aim of this paper is to study the behavior of the Frobenius map F*: H1(X, E) → H1(X, F*E) for a vector bundle E.
Umbilical Submanifolds and Morse Functions
Authors: Nomizu Katsumi , Rodríguez Lucio
Published: July 2016

Let Mn be a differentiable manifold (of class C∞). By a Morse function on Mn we mean a differentiable function whose critical points are all non-degenerate. If f is an immersion of Mn into a Euclidean space Rm, we may obtain Morse functions on Mn in the following way.
Long Exact Sequences and the Transgression Relation
Authors: Berkson A. , McConnell Alan
Published: July 2016

Throughout what follows, let H be a normal subgroup of the group G, be G/H, M a left G module, and HomH(G,M) = a left G module via (τϕ(σ) = (ϕ(στ)

In [1] the present authors compared the 5-term Hochschild Serre sequence to the long exact sequence arising from the short exact

sequence of modules
On the Distribution of Values of Functions in the Unit Disk
Authors: Choike James R.
Published: July 2016

Let f(z) be a function analytic and bounded, |f(z)| < 1, in |z| < 1. Then, by Fatou’s theorem the radial limit f*(eiθ) = limr→1f(reiθ) exists almost everywhere on |z| = 1. Seidel [8, p. 208] and Calderón, González- Domínguez, and Zygmund [1] (see also [9, pp. 281-282]) proved the following: if f*(eiθ) is of modulus 1 almost everywhere on an arc a < θ < b of |z| = 1, then either f(z) is analytically continuable across this arc or the values f*(eiθ), a < d < b, cover the circumference |w| = 1 infinitely many times.
On the Theory of Henselian Rings
Authors: Nagata Masayoshi
Published: July 2016

The notion of Henselian rings was introduced by G. Azuma-ya [l]. We concern ourselves in the present paper mainly with Henselizations of integrally closed integrity domains. Chapter I deals with general integrally closed integrity domains. As a preparation of our studies, we introduce the notion of decomposition rings analogously as in the case of fields (§1). And then we define the notions of (local) Henselian rings and Henselizations of integrally closed integrity domains, and obtain several results concerning characterizations of Henselian rings and the uniqeness of Henselizations (§2).
Unitary Representations of Some Linear Groups II
Authors: Itô Seizô
Published: July 2016

§0. Introudction. In his preceding paper [2], the author determined the types of irreducible unitary representations and cyclic unitary representations of the group of all euclidean motions in 2-space E2. The purpose of the present paper is to determine the types of irreducible unitary representations and cyclic ones of the group of all euclidean motions in n-space En for n≥3. In this paper, we shall make use of the results of the preceding paper [2], but notations are independent of those in [2].
Dedekind Sums for a Fuchsian Group, I
Authors: Goldstein Larry Joel
Published: July 2016

The well-known first limit formula of Kronecker asserts that

where z = x + iy is contained in the complex upper halfplane H, C = the Euler-Mascheroni constant, and η(z) is the Dedekind eta-function defined by
On the Grobal Dimension of Ore-Extensions
Authors: Bhatwadekar S. M.
Published: July 2016

Let S be a ring and d be a derivation of S. The Oreextension S(X,d) is the ring generated by S and an indeterminate X satisfying the ralation Xa — aX = da for all a in S.
An operator valued function space integral applied to multiple integrals of functions of class L1
Authors: Cameron R. H. , Storvick D. A.
Published: July 2016

In a recent paper [2], an operator valued function space integral was defined by the authors as follows.
On stochastic optimal control laws
Authors: Nisio Makiko
Published: July 2016

Let us begin by recalling the existence of optimal controls for a class of stochastic differential equations

with given initial condition X(0) = x, where B is an n-dimensional Brownian motion and the control U is a stochastic process. As admissible controls, let us allow all non-anticipative process U(t) = (U1(t),…Um(t)) ∈ Γ where Γ is a compact subset of Rm. We call Γ a control region. Assume that the matrix valued functional β and the n-vector valued α satisfy a Lipscitz condition in X and some growth condition. Then we have a unique solution Xu for an admissible control U.
On some degenerate parabolic equations II
Authors: Matsuzawa Tadato
Published: July 2016

In the article I: [8], we have proved the hypoellipticity of a degenerate parabolic equation of the form:

where the coefficients a(x, t), b(x,t) and c(x, t) are complex valued smooth functions. The fundamental assumption on the coefficients is that Re a(x, t) satisfies the condition of Nirenberg and Treves ([8], (1.5)). To prove the hypoellipticity we have constructed recurcively the parametrices as pseudodifferential operators with parameter. This method may be viewed as an improvement of that of [9] and [7]. We have analyzed the properties of these parametrices by estimating the symbols with parameter associated with the given operator. We shall summerize these results in §3.
A problem of complete intersections
Authors: Robbiano Lorenzo
Published: July 2016

Let X be a non-singular projective surface in (k an algebraically closed field of characteristic 0) and C an irreducible curve, which is a set-theoretically complete intersection in X; is it true that C is actually a complete intersection in X?
Classification of homogeneous bounded domains of lower dimension
Authors: Kaneyuki Soji , Tsuji Tadashi
Published: July 2016

The theory of classification of homogeneous bounded domains in the complex number space Cn has been developed mainly in the recent papers [10], [6], [3] and [7]. As a result, the classification is reduced to that of S-algebras due to Takeuchi [7] which correspond to irreducible Siegel domains of type I or type II (For the definition of irreducibility see § 1). On the other hand Pjateckii-Sapiro [5] found large classes of homogeneous Siegel domains obtained from classical self-dual cones. Even in lower-dimensional cases, however, there are still homogeneous Siegel domains which do not appear in his results.
The scheme of Lie sub-algebras of a Lie algebra and the equivariant cotangent map
Authors: Haboush William J.
Published: July 2016

The main object of this paper is to develop techniques for investigating the local properties of actions of an algebraic group on an algebraic variety. Our main tools are certain schemes which may be associated to Lie algebras.
On the conductor of an elliptic curve with a rational point of order 2
Authors: Hadano Toshihiro
Published: July 2016

Let C be an elliptic curve (an abelian variety of dimension one) defined over the field Q of rational numbers. A minimal Weierstrass model for C at all primes p in the sense of Néron [3] is given by a plane cubic equation of the form

where aj belongs to the ring Z of integers of Q, the zero of C being the point of infinity.
On the semisimplicity of the algebra associated to a polarized algebraic variety
Authors: Kato Yoshifumi
Published: July 2016

Let V be a compact nonsingular algebraic variety of dimension n with a Hodge structure ω and let Hi,i(V,C) be the subgroup of 2i-th cohomology group H2i(V,C) represented by harmonic (i,i)-forms on V with respect to ω.
Sur les cônes convexes de Riesz et les noyaux de convolution complètement sous-harmoniques
Authors: Itô Masayuki
Published: July 2016

Soit X un groupe abélien localement compact et dénombrable à l’infini; ζ sera sa mesure de Haar. Dans les articles précédents [10] et [11], pour un noyau de convolution de Hunt N sur X, nous avons défini la famille sous-ordonnée H(N; X) au noyau N, qui est une large classe de noyaux de convolution de Hunt sur X définie par N et la totalité des noyaux de convolution de Hunt bornés sur la droite réelle R portés par R+ = {t ∈ R; t ≧ 0}.
On some p-adic properties of the eichler-selberg trace formula
Authors: Koike Masao
Published: July 2016

In this paper we shall prove some congruence relations mod pα between the traces of Hecke operators T(pm) which act on the space of cusp forms of different weights satisfying some congruences mod pα – pα-1. The method of the proof is very simple and is applicable to all the cases where the trace formula for Hecke operators are already known.
Large increments of Brownian motion
Authors: Kaufman R.
Published: July 2016

Let X(t) denote Brownian motion on the line 0 ≤ t < ∞, let and let 0 < α < 1. Orey and Taylor [5] have investigated the random set defined by the inequalities

and proved that P{dim Eα = 1 – α2} = 1. Here we prove two theorems on Eα that reflect more subtle properties of Eα than its Hausdorff dimension alone.
Modular forms of half integral weight and the integral of certain theta-functions
Authors: Niwa Shinji
Published: July 2016

Recently G. Shimura [1] constructed modular forms of integral weight from the forms of half integral weight. His construction is rather indirect. Indeed, he proved that the Dirichlet series, obtained from a form of half integral weight, multiplied by a certain L-function, corresponds to a modular form of an integral weight by means of the characterization of modular forms due to Weil.
On the Transitive Domination Principle for Continuous Function-Kernels
Authors: Higuchi Isao
Published: July 2016

One of the interesting problems in the potential theory for a function-kernel is to investigate the relation between the domination principle and the balayage principle.
Negative Vector Bundles and Complex Finsler Structures
Authors: Kobayashi Shoshichi
Published: July 2016

A complex Finsler structure F on a complex manifold M is a function on the tangent bundle T(M) with the following properties. (We denote a point of T(M) symbolically by (z, ζ), where z represents the base coordinate and ζ the fibre coordinate.)
Hida-Cramér Multiplicity Theory for Multiple Markov Processes and Goursat Representations
Authors: Pitt Loren D.
Published: July 2016

This work grew out of an attempt to prove the false result that ann-ple Markov process in the sense of Hida (1960) or Lévy (1956a) has multiplicity one. Instead we proved the representation theorem (Theorem III. 1.) that a centered Gaussian processx(t)isn-ple Markov iff it can be written in the form

(I.1)

whereis a Gaussian martingale with

(I.2) sp {x(s):s≤t} ≡sp{ai(s):s≤tand 1 ≤i≤n}

andA(t) and {ei(t)} satisfy some non-degeneracy condition. We also show (Corollary IV. 13.) that for any Gaussian martingaleA(t) with simple left innovation spectrum, continuousei(t) may be found so that the processx(t) given in (I.1) will satisfy (I.2).
An equality of distributions associated to families of theta series
Authors: Haris Stephen J.
Published: July 2016

Let G be a connected algebraic group, p a finite dimensional representation of G in a vector space V, all defined over a number field fc. To the pair (G, p) we can associate the family of theta series
Correction to My Paper “On Titchmarsh-kodaira’s Formula Concerning Weyl-Stone’s Eigenfunction Expansion” in Nagoya Mathematical Journal, Vol. 1 (1950), 49–58
Authors: Yosida Kôsaku
Published: July 2016

Recently Mr. Seizô Itô kindly called the author’s attention to the fact that the derivation of (4.15) in the above referred paper is insufficient since the paper does not contain the proof of the compactness condition:

(1)

uniformaly in a and b
The asymptotic distribution of eigenvalues of the Laplace operator in an unbounded domain
Authors: Tamura Hideo
Published: July 2016

This paper is devoted to the study of the asymptotic distribution of eigenvalues of the Laplace operator with zero boundary conditions in a quasi-bounded domain contained in Euclidean space R2.
The Cameron-Storvick function space integral: An L(Lp, Lp′) theory
Authors: Johnson G. W. , Skoug D. L.
Published: July 2016

In [3] Cameron and Storvick introduced a very general operator-valued function space “integral”. In [3-5, 8, 9, 11, 13-20] the existence of this integral as an operator from L2 to L2 was established for certain functions. Recently the existence of the integral as an operator from L1 to L∞, has been studied [6, 7, 21]. In this paper we study the integral as an operator from Lp to Lp′, where 1 < p ≤ 2. The resulting theorems extend the theory substantially and indicate relationships between the L2-L2 and L1-L∞ theories that were not apparent earlier. Even in the most studied case, p = p′ = 2, the results below strengthen the theory.
A classification of irreducible prehomogeneous vector spaces and their relative invariants
Authors: Sato M. , Kimura T.
Published: July 2016

LetGbe a connected linear algebraic group, andpa rational representation ofGon a finite-dimensional vector spaceV, all defined over the complex number fieldC.

We call such a triplet (G, p, V) aprehomogeneous vector spaceifVhas a Zariski-denseG-orbit. The main purpose of this paper is to classify all prehomogeneous vector spaces whenpis irreducible, and to investigate their relative invariants and the regularity.
Sur les noyaux de convolution conditionnellement sous-medians
Authors: Itô Masayuki
Published: July 2016

Dans toute la suite Xdésignera un groupe abélien localement compact et séparé, et ξdésignera la mesure de Haar sur X.Pour simplifier la discussion, on supposera toujours que Xest à base dénombrable.
Elliptic curves with a torsion point
Authors: Hadano Toshihiro
Published: July 2016

Let E be an elliptic curve defined over the field Q of rational numbers, then the torsion subgroup of the Mordell-Weil group E(Q) is finite and it is known that there exist the elliptic curves whose torsion subgroups E(Q)t are of the following types: (1), (2), (3), (2, 2), (4), (5), (2, 3), (7), (2, 4), (8), (9), (2, 5), (2, 2, 3), (3, 4) and (2, 8). It has been conjectured from various reasons that E(Q)t is exhausted by the above types only. If E has a torsion point of order precisely n, then it is known that E has an n-isogeny, that is to say, an isogeny of degree n.
An application of Ritt’s low power theorem
Authors: Matsuda Michihiko
Published: July 2016

Consider an algebraic differential equation F = 0 of the first order. A rigorous definition will be given to the classical concept of “particular solutions” of F = 0. By Ritt’s low power theorem we shall prove that a singular solution of F = 0 belongs to the general solution of F if and only if it is a particular solution of F = 0.
Theta-functions and Hilbert modular forms
Authors: Kudla Stephen S.
Published: July 2016

The purpose of this note is to show how the theta-functions attached to certain indefinite quadratic forms of signature (2, 2) can be used to produce a map from certain spaces of cusp forms of Nebentype to Hilbert modular forms. The possibility of making such a construction was suggested by Niwa [4], and the techniques are the same as his and Shintani’s [6]. The construction of Hilbert modular forms from cusp forms of one variable has been discussed by many people, and I will not attempt to give a history of the subject here. However, the map produced by the theta-function is essentially the same as that of Doi and Naganuma [2], and Zagier [7]. In particular, the integral kernel Ω(τ, z1, z2) of Zagier is essentially the ‘holomorphic part’ of the theta-function.
Stochastic stability of Anosov diffeomorphisms
Authors: Kato Kazuhisa
Published: July 2016

R. Bowen [1] introduced the notion of pseudo-orbit for a homeomorphism f of a metric space X as follows: A (double) sequence {xi}i∈Z of points Xi in X is called a δ-pseudo-orbit of f iff

d(fxi, xi+1) ≤ δ

for every i ∈ Z, where d denotes the metric in X. We say f is stochastically stable if for every ε > 0 there exists δ > 0 such that every δ pseudo-orbit {Xi}i∈Z of f is ε-traced by some x ∈ X, i.e.,

d(fix, xi) ≤ ε

for every i ∈ Z. He proved in [1] that if a compact hyperbolic set Λ for a diffeomorphism f of a compact manifold M has local product structure then the restriction f | Λ of f to Λ is stochastically stable, using stable and unstable manifolds.
On a theorem of Ramanan
Authors: Umemura Hiroshi
Published: July 2016

Let G be a simply connected Lie group and P a parabolic subgroup without simple factor. A finite dimensional irreducible representation of P defines a homogeneous vector bundle E over the homogeneous space G/P. Ramanan [2] proved that, if the second Betti number b2 of G/P is 1, the inequality in Definition (2.3) holds provided F is locally free. Since the notion of the H-stability was not established at that time, it was inevitable to assume that b2 = 1 and F is locally free. In this paper, pushing Ramanan’s idea through, we prove that E is H-stable for any ample line bundle H. Our proof as well as Ramanan’s depends on the Borel-Weil theorem. If we recall that the Borel-Weil theorem fails in characteristic p > 0, it is interesting to ask whether our theorem remains true in characteristic p > 0.
On the Theory of Henselian Rings, II
Authors: Nagata Masayoshi
Published: July 2016

In a previous paper, we studied a general theory of integrally closed Henselian integrity domains and some properties of Henselian valuation rings. The present paper is its continuation. The main aim of the present paper is to study a general theory of Henselian local integrity domains in the present paper we call a ring o a local ring if o is a quasi-local ring and if the intersection of all powers of the maximal ideal of o is zero, and in this case we introduce a topology by taking the system of all powers of the maximal ideal as a system of neighbourhoods of zero.
On a theorem of Lichnerowicz
Authors: Hano Jun-Ichi
Published: July 2016

In his study on the structure of the complex Lie algebra of holomorphic vector fields on a compact Kähler manifold, Lichnerowicz ([3] Theorem 2, see also [1] and [4]) shows that if the first Chern class of the manifold is positive semi-definite, then to each harmonic (O.l)-form (i.e. anti-holomorphic 1-form) η, there exists a holomorphic vector field X such that the (O.1)-form i(X)k is d″-cohomologous to η, where k is the Kähler form. The purpose of this note is to indicate that this result is a consequence of an existence theorem for solutions of a certain self-adjoint elliptic partial differential equation.
On the decay of solutions for some nonlinear evolution equations of second order
Authors: Yamada Yoshio
Published: July 2016

In this paper we consider nonlinear evolution equations of the form

(E) u″(t) + Au(t) + B(t)u′(t) = f(t), 0 ≦ t < ∞,

(u′(t) = d2u(t)/dt2, u′(t) = du(t)/dt), where A and B(t) are (possibly) nonlinear operators. Various examples of equations of type (E) arise in physics; for instance, if Au = –Δu and B(t)u′ = | u′ | u′, the equation represents a classical vibrating membrane with the resistance proportional to the velocity.
A numerical criterion of quasi-abelian surfaces
Authors: Iitaka Shigeru
Published: July 2016

At first, we fix the notation. Letk=Cand we shall work in the category of schemes overk. For an algebraic varietyVof dimensionn, we have the following numerical invariants:

Pm(V) = them-genus ofV,

q(V) = the irregularity ofV,

k(V) = the Kodaira dimension ofV;

= the logarithmicm-genus ofV,

= the logarithmic irregularity ofV,

= the logarithmic Kodaira dimension ofV.
On the geometry of some Siegel domains
Authors: Zelow Rune
Published: July 2016

In his book [2], Pyatetskii-Shapiro describes representations of classical domains as certain “fibrations” over their boundary components. The fibers are quasi-symmetric Siegel domains of the second kind [3]. Professor Kobayashi asked “how symmetric” these fibers are, or more precisely, he asked for totally geodesic directions in the fiber. The object of this paper is to determine at least a totally geodesic sub-manifold of the fiber, and it turns out to be complex.
The group of automorphisms of a differential algebraic function field
Authors: Matsuda Michihiko
Published: July 2016

Consider a one-dimensional differential algebraic function field K over an algebraically closed ordinary differential field k of characteristic 0. We shall prove the following theorem:

Suppose that the group of all automorphisms of K over k is infinite. Then, K is either a differential elliptic function field over k or K = k(ν) with ν′ = ξ or ν′ = ην, where ξ, η ϵ k.
An effective method of counting the number of limit cycles
Authors: Yamato Kazuo
Published: July 2016

We are interested in determining, after a finite number of procedures, the number and the approximate positions of limit cycles for a given system.
On the integer ring of the compositum of algebraic number fields
Authors: Kataoka Toshitaka
Published: July 2016

Let k be an algebraic number field of finite degree. For a finite extension L/k we denote by L/k the different of L/k, and by L the integer ring of L. Let K1 and K2 be finite extensions of k.
Invariant subrings which are complete intersections, I: (Invariant subrings of finite Abelian groups)
Authors: Watanabe Keiichi
Published: July 2016

Let G be a finite subgroup of GL(n, C) (C is the field of complex numbers). Then G acts naturally on the polynomial ring S = C[X1, …, Xn]. We consider the following

Problem. When is the invariant subring SG a complete intersection?

In this paper, we treat the case where G is a finite Abelian group. We can solve the problem completely. The result is stated in Theorem 2.1.
Weil type representations and automorphic forms
Authors: Suzuki Toshiaki
Published: July 2016

During 1934-1936, W. L. Ferrar investigated the relation between summation formulae and Dirichlet series with functional equations, inspired by Voronoi’s works (1904) on summation formula with respect to the numbers of divisors. In [11] A. Weil showed that the automorphic properties of theta series are expressed by generalized Poisson summation formulae with respect to the so-called Weil representation. On the other hand, T. Kubota, in his study of the reciprocity law in a number field, defined a generalized theta series and a generalized Weil type representation of SL(2, C) and obtained similar results to those of A. Weil (1970-1976, [5], [6], [7]). The methods, used by W. L. Ferrar and T. Kubota, to obtain (generalized Poisson) summation formulae depend similarly on functional equations of Dirichlet series (attached to the generalized theta series).
Zum Begriff der Borelmessbarkeit
Authors: Zobel Robert
Published: July 2016

In dieser Arbeit werden die Voraussetzungen untersucht, die an einen topologischen Raum (X, ) mit dem System offener Mengen zu stellen sind, damit einige der in der Literatur geläufigen Begriffe der Borelmeβbarkeit reellwertiger Funktionen äquivalent sind.
Boundedness of semi-stable sheaves of small ranks
Authors: Maruyama Masaki
Published: July 2016

As for the construction of moduli spaces of stable sheaves, the boundedness of semi-stable sheaves is one of the most important questions which are left unanswered. In the case of dimension one, the boundedness was proved by M. F. Atiyah [1]. When the dimension of the base variety is two and the rank is two, F. Takemoto and D. Mumford showed the boundedness independently ([13]). The author proved in [7] that the boundedness holds for every rank in the case of dimension two, and then D. Gieseker gave another proof of it in [3].
Irreducibility of some unitary representations of the Poincaré group with respect to the Poincaré subsemigroup, I
Authors: Kaneta Hitoshi
Published: July 2016

Since E. Wigner set up a framework of the relativistically covariant quantum mechanics, several aspects of unitary representations of the Poincaré group have been investigated (see [8], [16]). In this paper it will be shown that some unitary representations of the Poincaré group are irreducible, even if they are restricted to the Poincaré semigroup (Theorem 1, 2 and 3).
On the least positive eigenvalue of the Laplacian for the compact quotient of a certain Riemannian symmetric space
Authors: Urakawa Hajime
Published: July 2016

Let (, g) be the standard Euclidean space or a Riemannian symmetric space of non-compact type of rank one. Let G be the identity component of the Lie group of all isometries of (, g). Let Γ be a discrete subgroup of G acting fixed point freely on whose quotient manifold MΓ is compact.
Corrigenda On a classification of the function fields of algebraic tori: (Nagoya Math. J. 56 (1975), 85–104)
Authors: Endo Shizuo , Miyata Takehiko
Published: July 2016

There are some errors in Theorems 3.3 and 4.2 in [2]. In this note we would like to correct them.

1) In Theorem 3.3 (and [IV]), the condition (1) must be replaced by the following one;

(1) П is (i) a cyclic group, (ii) a dihedral group of order 2m, m odd, (iii) a direct product of a cyclic group of order qf, q an odd prime, f ≧ 1, and a dihedral group of order 2m, m odd, where each prime divisor of m is a primitive qf-1(q — 1)-th root of unity modulo qf, or (iv) a generalized quaternion group of order 4m, m odd, where each prime divisor of m is congruent to 3 modulo 4.
Deformations and equitopological deformations of strongly pseudoconvex manifolds
Authors: Yau Stephen S.-T.
Published: July 2016

One of the main problems in complex analysis has been to determine when two open sets D1, D2 in Cn are biholomorphically equivalent. In [26] Poincaré studied perturbations of the unit ball B2 in C2 of a particular kind, and found necessary and sufficient conditions on a first order perturbation that the perturbed domain be biholomorphically equivalent to B2. Recently Burns, Shnider and Wells [7] (cf. also Chern-Moser [9]) have studied the deformations of strongly pseudoconvex manifolds. They proved that there is no finite-dimensional deformation theory for M if one keeps track of the boundary.
Completely superharmonic measures for the infinitesimal generator A of a diffusion semi-group and positive eigen elements of A
Authors: Itô Masayuki , Suzuki Noriaki
Published: July 2016

Let X be a locally compact Hausdorff space with countable basis. We denote by

M(X) the topological vector space of all real Radon measures in X with the vague topology,

MK(X) the topological vector space of all real Radon measures in X whose supports are compact with the usual inductive limit topology.
Remarks to the uniqueness problem of meromorphic maps into PN(C), IV
Authors: Fujimoto Hirotaka
Published: July 2016

Let H1, H2, …, HN+2 be hyperplanes in PN(C) located in general position and v1v2, … νN+2 divisors on Cn. We consider the set ℱ(Hi, νi) of all non-degenerate meromorphic maps of Cn into PN(C) such that the pull-backs ν(f, Hi) of the divisors (Hi) on PN(C) by f are equal to νi for any i = 1, 2, …, N + 2. In the previous paper [6], the author showed that =:= ℱ(Hi, νi) cannot contain more than N+ 1 algebraically independent maps. Relating to this, the following theorem will be proved.
Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties
Authors: Noguchi Junjiro
Published: July 2016

Nevanlinna’s lemma on logarithmic derivatives played an essential role in the proof of the second main theorem for meromorphic functions on the complex plane C (cf., e.g., [17]). In [19, Lemma 2.3] it was generalized for entire holomorphic curves f: C → M in a compact complex manifold M (Lemma 2.3 in [19] is still valid for non-Kähler M). Here we call, in general, a holomorphic mapping from a domain of C or a Riemann surface into M a holomorphic curve in M, and sometimes use it in the sense of its image if no confusion occurs. Applying the above generalized lemma on logarithmic derivatives to holomorphic curves f: C → V in a complex projective algebraic smooth variety V and making use of Ochiai [22, Theorem A], we had an inequality of the second main theorem type for f and divisors on V (see [19, Main Theorem] and [20]). Other generalizations of Nevanlinna’s lemma on logarithmic derivatives were obtained by Nevanlinna [16], Griffiths-King [10, § 9] and Vitter [23].
The principle of limiting absorption for propagative systems in crystal optics with perturbations of long-range class
Authors: Tamura Hideo
Published: July 2016

The present paper is a continuation of [10] where we have proved the principle of limiting absorption for uniformly propagative systems with perturbations of long-range class. In this paper, we consider the Maxwell equation in crystal optics as an important example of non-uniformly propagative systems and, under the same assumptions on perturbations as in [10], we prove the principle of limiting absorption for the stationary problem associated with this equation by using a way similar to that in [10]. We here restrict our consideration to a very special class of non-uniformly propagative systems, but the method developed in this paper will be applicable to more general systems for which non-zero roots of characteristic equations of unperturbed systems are at most double. For another works on the spectral and scattering problems for non-uniformly propagative systems with perturbations of short-range class, see [1], [5], [6], [7] and [8], etc.
Strictly localizable measures
Authors: Guerra P. Jiménez , Rodríguez-Salinas B.
Published: July 2016

In this paper it is proved that every locally strictly localizable Radon measure of type (ℋ) is strictly localizable, from where it follows immediately the existence of lifting for these measures.
On ample divisors
Authors: Bădescu Lucian
Published: July 2016

In this paper we are dealing with the following problem: determine all normal (or smooth) projective varieties X over an algebraically closed field k supporting a given variety Y as an ample Cartier divisor.
On some quasilinear wave equations with dissipative terms
Authors: Yamada Yoshio
Published: July 2016

In this paper we consider the initial value problems for the following quasilinear wave equations with dissipative terms

with initial conditions

where