bluuebunny/crossref_metadata_2025 huggingface dataset:
Meromorphic or Holomorphic Completion of a Reinhardt Domain
Authors: Sakai Eiichi
Published: July 2016

In the theory of functions of several complex variables, the problem about the continuation of meromorphic functions has not been much investigated for a long time in spite of its importance except the deeper result of the continuity theorem due to E. E. Levi [4] and H. Kneser [3], The difficulty of its investigation is based on the following reasons: we can not use the tools of not only Cauchy’s integral formula but also the power series and there are indetermination points for the meromorphic function of many variables different from one variable. Therefore we shall also follow the Levi and Kneser’s method and seek for the aspect of meromorphic completion of a Reinhardt domain in Cn.
Prolongations of G-Structures to Tangent Bundles of Higher Order
Authors: Morimoto Akihiko
Published: July 2016

In the previous paper [4] we have studied the prolongations of G-structures to tangent bundles. The purpose of the present paper is to generalize the previous prolongations and to look at them from a wide view as a special case by considering the tangent bundles of higher order. In fact, in some places, the arguments and calculations in [4] are more or less simplified. Since the usual tangent bundle T(M) of a manifold M considers only the first derivatives or first contact elements of M, the previous paper contains, in most parts, only the calculation of derivatives of first order.
On the Growth of Solutions of Algebraic Differential Equations Whose Coefficients are Arbitrary Entire Functions
Authors: Bank Steven
Published: July 2016

In this paper we treat the problem of determining the rate of growth of entire functions which are solutions of first order algebraic differential equations whose coefficients are arbitrary entire functions (i.e. equations of the form Ω(z, y, dy/dz) = 0, where Ω(z, y, dy/dz) = is a polynomial in y and dy/dz, whose coefficients fkJ(z) are entire functions).
Structure du Groupe des Similitudes Orthogonales
Authors: Yoshioka Akiko
Published: July 2016

1. Nous avons un théorème, ce qu’on appelle le théorème de Cartan-Dieudonné, sur les générateurs du groupe orthogonal: Toute transformation orthogonale ànvariables sur un corps de caractéristique ≠2 est un produit densymetries au plus, et sur un corps de caractéristique 2 elle est un produit au plus dentransvections orthogonales, sauf un seul cas, [1] ou [3]. C’est une généralisation d’un résultat obtenu par E. Cartan, relatif au corps des nombres réels ou au corps des nombres complexes [4].
On the Differentiability of Conformal Maps at the Boundary
Authors: Eke B.G.
Published: July 2016

Let S be a simply connected domain in the w + u + iv plane and let ∂S denote its boundary which we assume passes through w= ∞. Suppose that the segment L= {u ≧ u0; v = 0} of the real axis lies in S and that w∞ is the point of ∂ S accessible along L. Let z = z(w) = x(w) + iy(w) map S in a (1 — 1) conformal way onto ∑ = {z = x + iy: — ∞ < x < + ∞ } so that . The inverse map is w = w(z) = u(z) + iv(z). S is said to possess a finite angular derivative at w∞ if z(w) — w approaches a finite limit (called the angular derivative) as w→w∞ in certain substrips of S.
Invariants of Certain Groups I
Authors: Miyata Takehiko
Published: July 2016

Let G be a group and let k be a field. A K-representation ρ of G is a homomorphism of G into the group of non-singular linear transformations of some finite-dimensional vector space V over k. Let K be the field of fractions of the symmetric algebra S(V) of V, then G acts naturally on K as k-automorphisms. There is a natural inclusion map V→K, so we view V as a k-subvector space of K. Let v1, v2, · · ·, vn be a basis for V, then K is generated by v1, v2, · · ·, vn over k as a field and these are algebraically independent over k, that is, K is a rational field over k with the transcendence degree n. All elements of K fixed by G form a subfield of K. We denote this subfield by KG.
A Construction of Meromorphic Functions with Prescribed Asymptotic Behavior
Authors: Stebbins J.L.
Published: July 2016

Although there are several constructions of meromorphic functions with prescribed asymptotic sets [e.g., 5,6], it is usually difficult to determine or prescribe the nature of the asymptotic paths used in these constructions. On the other hand, there are several other constructions of meromorphic functions with prescribed asymptotic paths [e.g., 1, 10, 12], but the extent of the asymptotic values for these functions cannot always be restricted to the values approached along the given paths. Gross [3] has accomplished both results by prescribing paths for every value in the extended complex plane.
Sur Les Equations utt + tαuxx = f (α ≧ 0)
Authors: Matsuzawa Tadato
Published: July 2016

Le but principal de cette note est de démontrer les Théorème 4.2 et 6.1. Pour l’effectuer nous utiliserons la méthode de développement par les fonctions propres cf. [6]. Nous ne utilisons pas la méthode de la régularisation elliptique, mais les résultats de Baouendi [1] sont essentiels.
On Canonical Realizations of Bounded Symmetric Domains as Matrix-Spaces
Authors: Ise Mikio
Published: July 2016

It is the purpose of the present paper to give a natural method of realizing bounded symmetric domains as matrix-spaces. Our method yields, as special cases, the well-known bounded models of irreducible bounded symmetric domains of classical type (I)-(IV), as were already described in the original paper of E. Cartan [1] (see §3; we follow in this paper the classification table in [14], not in [1]). A direct application of this method will be to determine the canonical bounded models of the irreducible bounded symmetric domains of exceptional type; it will be published in another paper (see [6], [7] for the summary of the results).
An Integral Formula for the Chern from of a Hermitian Bundle
Authors: Omoto Hideo
Published: July 2016

We shall consider a Hermitian n-vector bundle E over a complex manifold X. When X is compact (without boundary), S.S. Chern defined in his paper [3] the Chern classes (the basic characteristic classes of E) Ĉi(E), i = 1, · · ·, n, in terms of the basic forms Φi on the Grassmann manifold H(n, N) and the classifying map f of X into H(n, N). Moreover he proved ([3], [4]) that if Ek denotes the k-general Stiefel bundle associated with E, the (n — k + 1)-th Chern class Ĉn-k+1(E) coincides with the characteristic class C(Ek) of Ek defined as follows: Let K be a simplicial decomposition of X and K2(n-k)+1 the 2(n — k) + 1 — shelton of K.
Riemann Domains with Boundary of Capacity Zero
Authors: Fujimoto Hirotaka
Published: July 2016

The well-known Thullen-Remmert-Stein’s theorem ([9], [7]) asserts that, for a domain D in CN and an n-dimensional irreducible analytic set S in D, a purely n-dimensional analytic set A in D — S has an essential singularity at any point in 5 if A has at least one essential singularity in S. In [1], E. Bishop generalized this to the case that A has the boundary of capacity zero in his sense. Afterwards, in [8], W. Rothstein obtained more precise informations on the essential singularities of A under the assumption dim A = 1. The main purpose in this paper is to generalize these Rothstein’s results to the case of arbitrary dimensional analytic sets.
Function-Theoretic Metrics and Boundary Behaviour of Functions Meromorphic or Holomorphic in the Unit Disk
Authors: Yamashita Shinji
Published: July 2016

The metrics to which the title of the present paper refers are expressed in the form of elements of arc length as follows:
On Prime Discriminants
Authors: Goldstein Larry Joel
Published: July 2016

Let be a quadratic field of discriminant d. We say that d is a prime discriminant if d is divisible by exactly one rational prime. It is classically known that the prime discriminants are given by

(p an odd prime).
Linear Imbeddings of Self-Dual Homogeneous Cones
Authors: Satake I.
Published: July 2016

Let G be a reductive algebraic Lie group acting linearly on a (finite-dimensional) real vector-space U with a maximal compact isotropy subgroup K and suppose that the quotient Ω = G/K is a self-dual homogeneous cone in U. Let (G′, K′) be another such pair corresponding to a self-dual homogeneous cone Ω′ in U′.
On Ramification Theory in Projective Orders, II
Authors: Endo Shizuo
Published: July 2016

Let R be a commutative ring and K be the total quotient ring of R. Let Σ be a separable K-algebra which is a finitely generated projective, faithful K-module and Λ be an R-order in DΛ/R. We denote by DΛ/R the Dedekind different of Λ and by NΛ/R the Noetherian different of Λ.
On Abstract Wiener Measure
Authors: Rajput Balram S.
Published: July 2016

In a recent paper, Sato [6] has shown that for every Gaussian measure n on a real separable or reflexive Banach space (X, ‖ • ‖) there exists a separable closed sub-space X〵 of X such that and is the σ-extension of the canonical Gaussian cylinder measure of a real separable Hilbert space such that the norm is contiunous on and is dense in The main purpose of this note is to prove that ‖ • ‖ x〵 is measurable (and not merely continuous) on .
Cosimplicial Cohomology of Coalgebras
Authors: Lee Keean
Published: July 2016

The interpretations of simplicial cohomology groups for associative commutative algebras and for Lie algebras were given by Beck [2], Iwai [9] and Shimada and others [15,16]. On the other hand, Jonah [10] gave a formulation and an interpretation of the second and third cohomology groups of an associative coalgebra after the Hochschild’s treatment [5 ∽ 8].
Azumaya’s Canonical Module and Completions of Algebras
Authors: Osterburg James
Published: July 2016

We are concerned with an algebra S over a commutative ring. Precisely S is a non-commutative ring with identity which is also a finitely generated unital R module such that r(xy) = (rx)y = x(ry) for r in R and x, y ∈ S. In section one, we assume A is a commutative, Artinian ring. Following Goro Azumaya (see (1, p. 273)), we define the canonical module F of A to be the injective hull of A modulo the Jacobson radical of A i.e. F = I(A/J(A)).
An Exact Sequence Associated with a Generalized Crossed Product
Authors: Miyashita Yôichi
Published: July 2016

The purpose of this paper is to generalize the seven terms exact sequence given by Chase, Harrison and Rosenberg [8]. Our work was motivated by Kanzaki [16] and, of course, [8], [9]. The main theorem holds for any generalized crossed product, which is a more general one than that in Kanzaki [16]. In §1, we define a group P(A/B) for any ring extension A/B, and prove some preliminary exact sequences. In §2, we fix a group homomorphism J from a group G to the group of all invertible two-sided B-submodules of A.
On the Quadratic Extensions and the Extended Witt Ring of a Commutative Ring
Authors: Kanzaki Teruo
Published: July 2016

Let B be a ring and A a subring of B with the common identity element 1. If the residue A-module B/A is inversible as an A-A- bimodule, i.e. B/A ⊗A HomA(B/A, A) ≈ HomA(B/A, A) ⊗A B/A ≈ A, then B is called a quadratic extension of A. In the case where B and A are division rings, this definition coincides with in P. M. Cohn [2]. We can see easily that if B is a Galois extension of A with the Galois group G of order 2, in the sense of [3], and if is a quadratic extension of A. A generalized crossed product Δ(f, A, Φ, G) of a ring A and a group G of order 2, in [4], is also a quadratic extension of A.
On the Existence of Various Bounded Harmonic Functions with given Periods
Authors: Hara Masaru
Published: July 2016

Consider a pair (R, Γ) of a Riemann surface R and a period Γ. By a period Γ we mean a real-valued function Γ(γ) on one-dimensional cycles {γ} of the Riemann surface R.
A Note on Gorenstein Rings of Embedding Codimension Three
Authors: Watanabe Junzo
Published: July 2016

Let A = R/, where R is a regular local ring of arbitrary dimension and is an ideal of R. If A is a Gorenstein ring and if height = 2, it is easily proved that A is a complete intersection, i.e., is generated by two elements (Serre [5], Proposition 3). Hence Gorenstein rings which are not complete intersections are of embedding codimension at least three. An example of these rings is found in Bass’ paper [1] (p. 29). This is obtained as a quotient of a three dimensional regular local ring by an ideal which is generated by five elements, i.e., generated by a regular sequence plus two more elements. In this paper, suggested by this example, we prove that if A is a Gorenstein ring and if height = 3, then is minimally generated by an odd number of elements. If A has a greater codimension, presumably there is no such restriction on the minimal number of generators for , as will be conceived from the proof.
Order of functions bounded on a spiral
Authors: Warren Joseph
Published: July 2016

The purpose of this paper is to improve a result of Schnitzer and Seidel [6] and to continue an analogy between entire functions and the class of functions which are holomorphic and unbounded in the unit disk, but bounded on a boundary spiral. The existence of such functions was established by Valiron [7].
Cohomological dimension of group schemes
Authors: Umemura Hiroshi
Published: July 2016

In Umemura [9], we calculated the invariants algcd (G), p(G), q(G) for a commutative algebraic group G. We remark that all the results hold for a group scheme which is not necessarily commutative.

To determine p(G), I cannot succeed in dropping the hypothesis “quasi-projective” but this assumption is satisfied in the characteristic 0 case.
Dedekind sums for a fuchsian group, II
Authors: Goldstein Larry Joel
Published: July 2016

In [1] we derived a generalization of Kronecker’s first limit formula. Our generalization was a limit formula for the Eisenstein series for an arbitrary cusp of a Fuchsian group Γ of the first kind operating on the complex upper half-plane H. In that work, we introduced Dedekind sums associated to the principal congruence subgroups Γ(N) of the elliptic modular group. The work of our preceding paper suggests a natural question: Is there a generalization of Kronecker’s second limit formula to the setting of a general Fuchsian group of the first kind? The answer to this question is the subject of this paper.
Geometric applications of critical point theory to submanifolds of complex projective space
Authors: Cecil Thomas E.
Published: July 2016

In a recent paper, [6], Nomizu and Rodriguez found a geometric characterization of umbilical submanifolds Mn ⊂ Rn+p in terms of the critical point behavior of a certain class of functions Lp, p ⊂ Rn+p, on Mn. In that case, if p ⊂ Rn+p, x ⊂ Mn, then Lp(x) = (d(x,p))2, where d is the Euclidean distance function.
On weak concepts of stability
Authors: Ikegami Gikö
Published: July 2016

The manifold in this paper is assumed to be connected differentiable of class C∞. Let Dr(M) and Ӿr(M) be the set of all diffeomorphisms and vector fields of class Cr on a manifold M with Whitney Cr topology, respectively. In [2], the concept of weak stability is defined. The definition is equivalent to the following ((2.1) of this paper); f∈Dr(M) or X ∈ Ӿr(M) is weakly (allowably) stable if and only if there is a neighborhood U of f or X in Dr(M) or Ӿr(M) such that for any (a suitable) g or Y ∈ U the set of all elements topologically equivalent to g or Y is dense in U, respectively. Here, f, g ∈ Dr(M) are said to be topologically equivalent if they are topologically conjugate and X, Y ∈ Ӿr(M) are said to be topologically equivalent if there is a homeomorphism mapping any trajectory of X onto a trajectory of Y preserving the orientations of the trajectories. Similarly, weak Ω-stability is defined for f and X.
A test for Picard principle
Authors: Nakai Mitsuru
Published: July 2016

A nonnegative locally Hölder continuous function P(z) on 0 < | z | ≤ 1 will be referred to as a density on 0 < | z | ≤ 1. The elliptic dimension of a density P(z) at z = 0, dim P in notation, is defined to be the dimension of the half module of nonnegative solutions of the equation Δu(z) = P(z)u(z) on the punctured unit disk Ω : 0 < | z | < 1 with boundary values zero on | z | = 1. After Bouligand we say that the Picard principle is valid for a density P at z = 0 if dim P = 1.
The Topological Support of Gaussian Measure in Banach Space
Authors: Vakhania N. N.
Published: July 2016

The main result of the present paper is the theorem 1, which describes the topological support of an arbitrary Gaussian measure in a separable Banach space. This theorem will be proved after some discussion of the notion of support itself. But we begin with the reminder of the notion of covariance operator of a probability measure. This notion has a great importance not only for the description of support of Gaussian measures but also for the study of other problems in the theory of probability measures in linear spaces (c.f. [1], [2]).
On symmetric Siegel domains
Authors: Takeuchi Masaru
Published: July 2016

Let V be a convex cone in a real vector space X, F: Y × Y → Xc a V-positive hermitian map on a complex vector space Y, and

the Siegel domain associated to V and F. D(V,F) is said to be symmetric, if for each point p ∈ D(V, F) there exists an involutive holomorphic automorphism σp of D(V,F) such that the fixed point set of σp consists of only the point p. Satake [6] showed that the symmetric Siegel domain D(V, F) is characterized by the following three conditions (i), (ii) and (iii).
The value distribution of harmonic mappings between Riemanniann-spaces
Authors: Imai Hideo
Published: July 2016

We are concerned with the value distribution of a mapping of an open Riemanniann-space (n≧ 3) into a Riemanniann-space. The value distribution theory of an analytic mapping of Riemann surfaces was initiated by S. S. Chern [1] and developed mainly by L. Sario [8], [9], [10], [11], and then by H. Wu [14], [15]. The most crucial part in Sario’s theory is the introduction of a kernel function on an arbitrary Riemann surface to describe appropriately the proximity of two points. His method indicates that the potential theoretic method is one of the powerful methods in the value distribution theory.
Ample vector bundles on a rational surface
Authors: Hosoh Toshio
Published: July 2016

On a complete non-singular curve defined over the complex number field C, a stable vector bundle is ample if and only if its degree is positive [3]. On a surface, the notion of the H-stability was introduced by F. Takemoto [8] (see § 1). We have a simple numerical sufficient condition for an H-stable vector bundle on a surface S defined over C to be ample; let E be an H-stable vector bundle of rank 2 on S with Δ(E) = c1(E)2 - 4c2(E) ≧ 0, then E is ample if and only if c1(E) > 0 and c2(E) > 0, provided S is an abelian surface, a ruled surface or a hyper-elliptic surface [9]. But the assumption above concerning Δ(E) evidently seems too strong. In this paper, we restrict ourselves to the projective plane P2 and a rational ruled surface Σn defined over an algebraically closed field k of arbitrary characteristic. We shall prove a finer assertion than that of [9] for an H-stable vector bundle of rank 2 to be ample (Theorem 1 and Theorem 3). Examples show that our result is best possible though it is not a necessary condition (see Remark (1) §2).
Remarks on the Differential Forms of the First Kind on Algebraic Varieties
Authors: Kawahara Yûsaku
Published: July 2016

A differential form co on a complete variety Un is said to be of the first kind if it is finite at every simple point of any variety which is birationally equivalent to U. Let k be a common field of definition for Uand ω, and let Pbe a generic point of Uover k. If ω is of the first kind, then ω(P) is of course a differential form of the first kind belonging to the extension k(P) of k.
Some Remarks on Local Rings
Authors: Nagata Masayoshi
Published: July 2016

Previously C. Chevalley [1] proved the followings:

1. Let x1,…, Xn be algebraically independent elements over a field t which has infinitely many elements. Then :

a) If y is an element of [x1,…, xn] and if y is not in , then there exist elements y2…, yn of [x1,…, xn] such that [x1,…, xn] is integral over [y1, y2,…, yn]
On some Asymptotic Properties Concerning Homogeneous Differential Processes
Authors: Sirao Tunekiti
Published: July 2016

About the behaviour of brownian motion at time point ∞ there are many results by P. Levy and A. Khintchine etc. The method of W. Feller is applicable to a similar discussion about a homogeneous differential process. In this paper we shall study, applying his method, the properties of a homogeneous differential process.
A Generalization of the Hahn-Banach Theorem
Authors: Ono Takashi
Published: July 2016

Recently the Hahn-Banach theorem for normed spaces over non-archimedean valued fields was treated by A. F. Monna [1], L S. Cohen [2], A. W. Ingleton [3], and the writer [4]. In [3] and [4] very essential use was made of an idea of L. Nachbin [5]
A characterization of the Veronese varieties
Authors: Nomizu Katsumi
Published: July 2016

Let Pm(C) be the complex projective space of dimension m. In a previous paper [2] we have proved

THEOREM A. Let f be a Kaehlerian immersion of a connected, complete Kaehler manifold Mn of dimension n into Pm(C). If the image f(τ) of each geodesic τ in Mn lies in a complex projective line P1(C) of Pm(C), then f(Mn) is a complex projective subspace of Pm(C), and f is totally geodesic.
Small Random perturbation of dynamical systems with reflecting boundary
Authors: Anderson Robert F. , Orey Steven
Published: July 2016

Consider a diffusion process in Rd satisfying the stochastic differential equation

.
A relation between biharmonic Green’s functions of simply supported and clamped bodies
Authors: Ralston James , Sario Leo
Published: July 2016

The deflection, under a point load, of a thin elastic plate clamped at the edges is the biharmonic Green’s function β with the boundary data β = ∂β/∂n = 0. If the boundary of the region is reasonably smooth, the construction of β offers no difficulty. In contrast, nothing is known about the existence of β in the general case. The purpose of our study is to give a sufficient condition for the existence of β on a given Riemannian manifold of arbitrary dimension and to construct β. Our results will have, apart from their physical meaning in elasticity, consequences in the biharmonic classification theory of Riemannian manifolds.
A geometrical characterization of a class of holomorphic vector bundles over a complex torus
Authors: Hano Jun-Ichi
Published: July 2016

This note is to be a supplement of the preceeding paper in the journal by Matsushima, settling a question raised by him. In his paper he associates a holomorphic vector bundle over a complex torus to a holomorphic representation of what he calls Heisenberg group. We shall show that a simple holomorphic vector bundle is determined in this manner if and only if the associated projective bundle admits an integrable holomorphic connection. A theorem by Morikawa ([3], Theorem 1) is the motivation of this problem and is somewhat strengthened by our result.
On certain isolated normal singularities
Authors: Bădescu Lucian
Published: July 2016

In the following we shall fix an algebraically closed fieldKof arbitrary characteristic. The term variety will mean an algebraic scheme overKwhich is integral. In general we shall use the notations and the terminology of Éléments de Géométrie Algébrique of A. Grothendieck and J. Dieudonné. For instance, ifZis a variety andx ∈ Zis a point, thenOZ, xmeans the local ring ofZatxandmx– the maximal ideal of0Z, x.
Character formulas for discrete series on semisimple Lie groups
Authors: Herb Rebecca A.
Published: July 2016

Let G be a connected, semisimple real Lie group with finite center, K a maximal compact subgroup of G. Assume rank G = rank K. Let be the Lie algebra of G, its complexification. If Gc is the simplyconnected complex analytic group corresponding to assume G is the real analytic subgroup of Gc corresponding to .
Scalar extension of quadratic lattices
Authors: Kitaoka Yoshiyuki
Published: July 2016

Let E/F be a finite extension of algebraic number fields, OE, OF the maximal orders of E, F respectively. A classical theorem of Springer [6] asserts that an anisotropic quadratic space over F remains anisotropic over E if the degree [E: F] is odd. From this follows that regular quadratic spaces U, V over F are isometric if they are isometric over E and [E : F] is odd. Earnest and Hsia treated similar problems for the spinor genera [2, 3]. We are concerned with the quadratic lattices. Let L, M be quadratic lattices over OF in regular quadratic spaces U, V over F respectively.
On the Compacity of the Orthogonal Groups
Authors: Ono Takashi
Published: July 2016

It is a well known fact on Lorenz groups that a quadratic form f is definite if and only if the corresponding orthogonal group On(R∞, f) where R∞ is the real number field, is compact. In this note, we shall show that the analogue of this holds for the case of the p-adic orthogonal group On(Rp, f), where Rp is the rational p-adic number field, as a special result of the more general statement on the completely valued fields.
Theta functions and modular jets
Authors: Fegan H. D.
Published: July 2016

Let⌈be a subgroup of the modular groupPSL(2,Z) then⌈acts on the upper half planeH={zЄC: Imz> 0} and we can form the Riemann surfaceM=H/⌈, see [3]. The complex line bundles on a Riemann surfaceMform a groupH1(M,*), see [4], and whenever we raise a line bundle to a power it will be in this group. Letκdenote the canonical bundle onMthen a modular form of weightνis a section of the bundle. A modularn-jet is then a section ofJnthen-th jet bundle, see [7]. We can reformulate these ideas in the following terms. A modular form can be viewed as a functionΦ: H→Cand a modularn-jet as a vector valued functionΦ: H → Cn+1both of which satisfy a transformation law under the elements ofΓ.
Super-Łukasiewicz implicational logics
Authors: Komori Yuichi
Published: July 2016

In the traditional study of Łukasiewicz propositional logic, the finite-valued or infinite-valued linearly ordered model exists at the start, and then the axiomatization of the set of all formulas valid in its model are studied. On the other hand, we are in a point of view such that the set of provable formulas is important and models are no more than means to characterize the set.
Distributions with automorphy and Dirichlet series
Authors: Suzuki Toshiaki
Published: July 2016

In [1], Maass proved that the Dirichlet series associated with Siegel modular form satisfies a function equation. In this paper, we try to generalize the above fact to the indefinite case.
Courbes elliptiques ayant bonne réduction en dehors de 3
Authors: Ligozat Gérard
Published: July 2016

Le résultat principal de ce travail est le suivant: les courbes elliptiques définies sur Q, et ayant bonne réduction en dehors de 3, vérifient la conjecture de Weil (cf. [2], Th. 2).
Komplettierung semilokaler quasiausgezeichneter Ringe
Authors: Rotthaus Christel
Published: July 2016

In [4] EGA IV (7.4.8) hat Grothendieck die folgende Frage gestellt: “A sei ein noetherscher Ring, I⊆ A ein Ideal, so daß A separiert und komplett in der I-adischen Topologie ist. A/I sei ein P-Ring. 1st dann A ebenfalls ein P-Ring?″ In dieser Arbeit beschäftigen wir uns mit dem Fall, daß A ein semilokaler noetherscher Ring ist und P die Eigenschaft “die formellen Fasern von A sind geometrisch regulär” bezeichnet. Wir wollen zeigen: “A sei ein semilokaler noetherscher I-adisch kompletter Ring, wobei I ein im Jacobsonradikal von A enthaltenes Ideal ist. Sind die formellen Fasern von A/I geometrisch regulär, so sind auch die formellen Fasern von A geometrisch regulär.”
On a conjecture of M. P. Murthy
Authors: Boratyński M.
Published: July 2016

In [M] Murthy asked if every subvariety V of kn (k-any field) with a trivial conormal bundle is a (scheme theoretic) complete intersection.

In [B] we were able to prove that all such subvarieties of kn are at least set theoretic complete intersections. Mohan Kumar has shown in [MK] that if one assumes moreover that n ≥ 2 dim V + 2 then V is a complete intersection. The aim of this paper is to prove the following result which extends the Mohan Kumar Theorem in the nonsingular (and connected) case and moreover sheds some light on his bound for n.
Hyperbolic affine hyperspheres
Authors: Sasaki Takeshi
Published: July 2016

A locally strongly convex hypersurface in the affine space Rn + 1 is called an affine hypersphere if the affine normals (§ 1) through each point of the hypersurface either all intersect at one point, called its center, or else are all mutually parallel. It is called elliptic, parabolic or hyperbolic according to whether the center is, respectively, on the concave side of the hypersurface, at infinity or on the convex side. This class of hypersurfaces was first studied systematically by W. Blaschke ([1]) in the frame of affine geometry. In his paper [3] E. Calabi redefined it and proposed a problem of determining all complete hyperbolic affine hyperspheres and raised a conjecture that these hypersurfaces are asymptotic to the boundary of a convex cone and every non-degenerate cone V determines a hyperbolic affine hypersphere, asymptotic to the boundary of V, uniquely by the value of its mean curvature.
Finite arithmetic subgroups of GLn, II
Authors: Kitaoka Yoshiyuki
Published: July 2016

In [1] ∼ [6] the following question was treated: Let k be a totally real Galois extension of the rational number field Q, O the maximal order of k and G a finite subgroup of GL(n, O) which is stable under the operation of G(k/Q). Then does G ⊂ GL(n, Z) hold?
On the composition series of principal series representations of a three-fold covering group of SL(2, K)
Authors: Aritürk Haluk
Published: July 2016

In this paper, we study the composition series of certain principal series representations of the three-fold metaplectic covering group of SL(2, K), where K is a non-archimedean local field. These representations are parametrized by unramified characters μ(x) = |x|s of K× and characters ω of the group of third roots of unity.
Decomposition of representations of SL(2, C) induced by the continuous series of E(2)
Authors: Kaneta Hitoshi
Published: July 2016

Since the representations of SL(2, C) induced by irreducible unitary representations of appear as the restriction to the Lorentz group of some irreducible unitary representations of the inhomogeneous Lorentz group, the decomposition of the induced representations deserves our investigation. For the representations of SL(2, C) induced by irreducible unitary representations with discrete spin of E(2), the decomposition has been obtained by Mukunda [9]. We hope that our analysis will justify the calculations by Chakrabarti [1], [2] and [3].
On the group of automorphisms of a Hopf map
Authors: Ono Takashi
Published: July 2016

Let K be an infinite field of characteristic not 2. Let qx, qY be nonsingular quadratic forms on vector spaces X, Y over K, respectively. Assume that there is a bilinear map B:X × Y → Y such that qY(B(x, y)) = qx(x)qY(y). To each such triple {qx, qY, B} one associates the Hopf map h: Z = X × Y → W = K × Y by h(z) = (qx(x) – qY(y), 2B(x, y)), z = (x, y).
On the structure of the idele group of an algebraic number field
Authors: Miyake Katsuya
Published: July 2016

The purpose of this paper is to present the results of E. Artin and Furtwängler, with which they proved the principal ideal theorem, as a structure theorem of the idele group of an algebraic number field. Such treatment may be helpful to clarify the Arithmetic nature these results possess.
Holomorphic automorphisms and cancellation theorems
Authors: Urata Toshio
Published: July 2016

Let X be a complex analytic space of positive dimension and A a complex analytic subvariety of X. We call A a direct factor of X if there exist a complex analytic space B and a biholomorphic mapping f: A × B → X such that, for some b ∊ B, f(a, b) = a on A, and a complex analytic space X to be primary if X has no direct factor, not equal to X itself, of positive dimension.
Ternary quadratic forms and Shimura’s correspondence
Authors: Ponomarev Paul
Published: July 2016

In his paper [11] Shimura defined a correspondence between modular forms of half integral weight and modular forms of integral weight. To each pair (t, f(z)), consisting of a square-free integert≥ 1 and a cusp formof weightk/2 (kodd, ≥ 3), levelN(divisible by 4) and characterϰ, he associated a certain functionf(t)(z) (Ft(z) in Shimura’s notation).
The principle of limiting absorption for uniformly propagative systems with perturbations of long-range class
Authors: Tamura Hideo
Published: July 2016

The aim of this paper is to establish the principle of limiting absorption for uniformly propagative systems Λ(x, Dx) = E(x)-1AjDj, Dj = — i∂/∂xj, with perturbations of long-range class, where the perturbation of long-range class, roughly speaking, means that E(x) approaches to E0, E0 being the N × N identity matrix, as | x | → ∞ with order O(| x |-δ), 0 < δ ≦ 1. (The more precise assumptions will be stated below and we require some additional assumptions on the derivatives of E(x).) The spectral and scattering problem for uniformly propagative systems was first formulated by Wilcox [10]. Since then, the principle of limiting absorption has been proved by many authors ([5], [7], [8], [11] etc.). The perturbations discussed in their works belong to the short-range class with δ > 1.
Ergodic properties of the equilibrium measure of the stepping stone model in population genetics
Authors: Itatsu Seiichi
Published: July 2016

We shall present in this paper some ergodic properties of the stepping stone model. The model has been proposed by M. Kimura [2], to describe the evolution of a genetical population with mating and geographical structures. It has been investigated and developed by M. Kimura and G. H. Weiss [3], G. H. Weiss and M. Kimura [6], W. Fleming and C.-H. Su [1], S. Sawyer [5], and others.
Algebraic degeneracy theorem for holomorphic mappings into smooth projective algebraic varieties
Authors: Aihara Yoshihiro , Mori Seiki
Published: July 2016

The famous Picard theorem states that a holomorphic mapping f: C → P1(C) omitting distinct three points must be constant. Borel [1] showed that a non-degenerate holomorphic curve can miss at most n + 1 hyperplanes in Pn(C) in general position, thus extending Picard’s theorem (n = 1). Recently, Fujimoto [3], Green [4] and [5] obtained many Picard type theorems using Borel’s methods for holomorphic mappings.
Continuous valuation and logic
Authors: Yasugi Mariko
Published: July 2016

We consider the continuous valuation of logic, where the certainty of a statement is measured with a number in the closed unit interval I =[0, 1].

The idea originates in continuous logics, which have been investigated from various standpoints, in [1] ~ [4] and [8] ~ [10], for example. More comprehensive information can be seen in [4] and others.
An elimination theorem of uniqueness conditions in the intuitionistic predicate calculus
Authors: Motohashi Nobuyoshi
Published: July 2016

This paper is a sequel to Motohashi [4]. In [4], a series of theorems named “elimination theorems of uniqueness conditions” was shown to hold in the classical predicate calculus LK. But, these results have the following two defects : one is that they do not hold in the intuitionistic predicate calculus LJ, and the other is that they give no nice axiomatizations of some sets of sentences concerned. In order to explain these facts more explicitly, let us introduce some necessary notations and definitions. Let L be a first order classical predicate calculus LK or a first order intuitionistic predicate calculus LJ. n-ary formulas in L are formulas F(ā) in L with a sequence ā of distinct free variables of length n such that every free variable in F occurs in ā.
Irreducibility of some unitary representations of the poincaré group with respect to the Poincaré subsemigroup, II
Authors: Kaneta Hitoshi
Published: July 2016

Let P+(3) and P+(3) be the 3-dimensional space-time Poincaré group and the Poincaré subsemigroup, that is, P(3) = R3 × sSU(1, 1) and P+(3) = V+(3)=SSU(1, 1) where The multiplication is defined by the formula (x, g)(x′, g′) = (x + g*−1x′g−1, gg′) for x, x′ ∈ R3 and g, g′ ∈ SU(l, 1). Here x = (x0, x1, x2) is identified with the matrix
On the fields of rationality for curves and for their jacobian varieties
Authors: Sekiguchi Tsutomu
Published: July 2016

Throughout the paper, a scheme means a noetherian scheme. By a curve C over a scheme S of genus g, we mean a proper and smooth S-scheme with irreducible curves of genus g as geometric fibres. In the previous paper [15], the author showed that the field of moduli for a non-hyperelliptic curve over a field coincides with the one for its canonically polarized jacobian variety, and in [16], he gave a partial result on the coincidence of the fields of rationality for a hyperelliptic curve and for its canonically polarized jacobian variety. In the present paper, we will discuss the isomorphy of the isomorphism schemes of two curves over a scheme and of their canonically polarized jacobian schemes, by using Oort-Steenbrink’s result [12].
The boundary behaviour of Hadamard lacunary series
Authors: Murai Takafumi
Published: July 2016

A convergent power series f(z) in the open unit disk D is called Hadamard lacunary if it is expressed as follows:
Exterior powers of fields and subfields
Authors: Saltman David J.
Published: July 2016

Let D be a division algebra of finite dimension n2 over it’s center F. Suppose D has an involution, τ, of the first kind, of symplectic type (e.g. [1], p. 169). By the theory of the pfaffian, τ symmetric elements have degree less than n/2 over F. On the other hand, Tamagawa has shown (unpublished) that involutions like τ are closely related to minimal symmetric idempotents in D ⊗ F D. This author began by examining and trying to generalize these relationships. But before any theory seemed possible for division algebras, a theory relating subfields and symmetric idempotents was required. This investigation gave rise to the results presented here, especially the main theorem in Section Two.
On a certain homology of finite projective spaces
Authors: Morikawa Hisasi
Published: July 2016

We denote by Pn(q) the projective space of dimension n over a finite field GF(q) with q elements, and we mean by an i-flat a linear subspace of dimension i in Pn(q).
Riemannian foliations with parallel curvature
Authors: Blumenthal Robert A.
Published: July 2016

Let M be a smooth compact manifold and let be a smooth codimension q Riemannian foliation of M. Let T(M) be the tangent bundle of M and let E ⊂ T(M) be the subbundle tangent to . We may regard the normal bundle Q = T(M)/E of as a subbundle of T(M) satisfying T(M) = E ⊕ Q. Let g be a smooth Riemannian metric on Q invariant under the natural parallelism along the leaves of .
Non-Linear prediction problems for Ornstein-Uhlenbeck process
Authors: Lee Sheu-San
Published: July 2016

We shall discuss in this paper some problems in non-linear prediction theory. An Ornstein-Uhlenbeck process {U(t)} is taken to be a basic process, and we shall deal with stochastic processes X(t) that are transformed by functions f satisfying certain condition. Actually, observed processes are expressed in the form X(t) = f(U(t)). Our main problem is to obtain the best non-linear predictor X̂(t, τ) for X(t + τ), τ > 0, assuming that X(s), s ≤t, are observed. The predictor is therefore a non-linear functional of the values X(s), s ≤ t.
Transient Markov convolution semi-groups and the associated negative definite functions
Authors: Itô Masayuki
Published: July 2016

Let X be a locally compact and σ-compact abelian group and be the dual group of X. We denote by ξ a fixed Haar measure on X and by the Haar measure on associated with ξ.
Some results on the variety of complexes
Authors: Yoshino Yuji
Published: July 2016

Let R be a (commutative) Noetherian ring, and let {n0, n1 …, nm} {k1 k2, …, km} be two sequences of integers satisfying m > 0, ki ≧ 0 (i = 1, 2, …, m) and ni ≧ ki ki + 1 (i = 1, 2, …, m) with k0 = km + 1 = 0.
A connection between blowing-up and gluings in one-dimensional rings
Authors: Tamone Grazia
Published: July 2016

Let C be an affine curve, contained on a non-singular surface X as a closed 1-dimensional subscheme. If P is a closed point on C, the blowing-up C′ of C with center P (induced by the blowing-up of X with center P) is an affine curve. It is known that there is a sequence:

where C is the normalization of C, and each Ci + 1 is the blowing-up of Ci with center a singular point Pt on Ci (i = 0, …, k – 1).
Normal holomorphic mappings and classical theorems of function theory
Authors: Funahashi Ken-Ichi
Published: July 2016

In [7], O. Lehto and K. I. Virtanen introduced the concept of normal meromorphic functions in connection with the study of boundary behaviour of meromorphic functions of one complex variable.

In this paper, we generalize the theory of normal meromorphic functions to the case of holomorphic mappings into higher dimensional complex spaces in connection with the theory of hyperbolic manifolds and Nevanlinna theory.

The main concern of this paper is the generalizations of the big Picard theorem and Lindelöf’s theorem which appear in the classical function theory.
Lévy’s Brownian motion; Total positivity structure of M(t)-process and deterministic character
Authors: Noda Akio
Published: July 2016

Let X = {X(A); A ∈ Q} be a Lévy’s Brownian motion with the basic time parameter space Q, where Q is taken to be the n-dimensional metric space Qn,k of constant curvature (2 ≤ n ≤ ∞, — ∞ < k: < ∞), i.e., Q is one of

(a) Euclidean space for k = 0, (b) sphere for k > 0 and

(c) real hyperbolic space for K < 0.

The increment X(A) — X(B) is, by definition, Gaussian in distribution and has mean 0 and variance d(A, B), the distance between A and B. The existence of such a Gaussian random field is well known ([3], [4], [16] and [23]).
Evaluating symplectic Gauss sums and Jacobi Symbols
Authors: Styer Robert
Published: July 2016

Stark [9] has explicitly evaluated some symplectic Gauss sums when the “denominator” matrix has odd prime level. This result is useful in computing the exact tranformation formulas of multivariable theta functions (see Stark [10], Friedberg [3] and Styer [11]). It is particularly useful when considering theta functions with quadratic forms having an odd number of variables, often a troublesome case (see Eichler [2] and Andrianov-Maloletkin [1]).
Isometry invariant closed geodesic on a nonpositively curved manifold
Authors: Kurogi Tetsunori
Published: July 2016

In this paper we wish to study the isometry invariant geodesic on a non-positively curved manifold from a point of view of the displacement function.
Smoothness of Noetherian rings
Authors: Tanimoto Hiroshi
Published: July 2016

In [16] we studied the following problems which had been asked by H. Matsumura (cf. [11]):

(I)

What is the difference between smoothness and J-smoothness? In particular, concerning the characterization of smoothness,

(II)

When is a ring A[X1 …, Xn]/a smooth over A?

In this paper, according to these problems, we will study J-smoothness further when rings are noetherian as in [16].
Congruence relations of Ankeny-Artin-Chowla type for pure cubic fields
Authors: Ito Hiroshi
Published: July 2016

Ankeny, Artin and Chowla [1] proved a congruence relation among the class number, the fundamental unit of real quadratic fields, and the Bernoulli numbers. Our aim of this paper is to prove similar congruence relations for pure cubic fields. For this purpose, we use the Hurwitz numbers associated with the elliptic curve defined byy2= 4x3— 1 instead of the Bernoulli numbers (§ 3).
Sur les variétés canoniques de dimension 3 d’indice positif
Authors: Benveniste X.
Published: July 2016

Dans tout ce qui suit, les varietés qui interviendront seront définies sur le corps des nombres complexes C. L’objet de cet article est de préciser le résultat suivant obtenu dans [B-2] et [K-1]:

Théorème 0. Soit X une variété protective normale de dimension 3, dont les singularités sont canoniques au sens de [R-1]. Soient e le p.p.c.m. des indices des points singuliers de X. Soit R un diviseur de Cartier sur X, tel que le bidual de soit isomorphe à Supposons que R soit numériquement positif et que R3 > 0. Alors il existe un entier n0 > 0 tel que pour tout le système linéaire |nR| soit sans point base; en particulier l’anneau est de type fini sur C.
Gauss’s ternary form reduction and its application to a prime decomposition symbol
Authors: Furuta Yoshiomi
Published: July 2016

We defined a prime decomposition symbol [d1 d2, p] in a previous paper [3], and characterized in [4] the set of rational primes p which are decomposed completely in a non-abelian central extension which is of degree 8 in substance. The explicit value of the symbol was determined by using a solution of certain ternary quadratic diophantine equation. The solution corresponds to a square root of an ideal class of the principal genus of a quadratic field. This is translated to a problem in classes of integral quadratic forms, namely to find a form whose duplication is a given one contained in a principal genus. An explicit method to find the form is given by Gauss in [5, Art. 286], which is due to his ternary form reduction.
Rings of Modular Forms on Eichler’s Problem
Authors: Tsuyumine Shigeaki
Published: July 2016

In his paper [4] or lecture note [3], Eichler asked the problem when the ring of modular forms is Cohen-Macaulay. We shall try to investigate it for the Hilbert or Siegel modular case.
The semi-balayability of real convolution kernels
Authors: Itô Masayuki , Suzuki Noriaki
Published: July 2016

Let X be a locally compact, σ-compact and non-compact abelian group. Throughout this paper, we shall denote by ξ a fixed Haar measure on X and by δ the Alexandroff point of X.
The functional equation of zeta distributions associated with prehomogeneous vector spaces
Authors: Teranishi Yasuo
Published: July 2016

Let (G, ρ, V) be a triple of a linear algebraic group G and a rational representation ρ on a finite dimensional vector space V, all defined over the complex number field C.
Remarks on the curvature of hypersurfaces in Cn
Authors: Sasaki Takeshi , Shiga Kiyoshi
Published: July 2016

In this paper we shall study the global condition of curvatures of hypersurfaces in the complex Euclidean space. S. Bochner ([1]) and E. Calabi ([2]) have already investigated kähler embeddings (i.e. holomorphic and isometric embeddings) of a kähler manifold into the complex Euclidean space. However, it seems that they did not discuss the relation between the embeddability and the curvature.
On the Doi-Naganuma lifting associated with imaginary quadratic fields
Authors: Asai Tetsuya
Published: July 2016

Similarly to the real quadratic field case by Doi and Naganuma ([3], [9]) there is a lifting from an elliptic modular form to an automorphic form on SL2(C) with respect to an arithmetic discrete subgroup relative to an imaginary quadratic field. This fact is contained in his general theory of Jacquet ([6]) as a special case. In this paper, we try to reproduce this lifting in its concrete form by using the theta function method developed first by Niwa ([10]); also Kudla ([7]) has treated the real quadratic field case on the same line. The theta function method will naturally lead to a theory of lifting to an orthogonal group of general signature (cf. Oda [11]), and the present note will give a prototype of non-holomorphic case.
Functions meromorphic on some Riemann surfaces
Authors: Segawa Shigeo
Published: July 2016

Consider an open Riemann surface R and a single-valued meromorphic function w = f(p) defined on R. A value w0 in the extended complex plane is said to be a cluster value for w = f(p) if there exists a sequence {pn } in R accumulating at the ideal boundary of R such that
On the Behaviour of Analytic Functions in the Neighbourhood of the Boundary of a Riemann Surface
Authors: Cornea A.
Published: July 2016

Mr. Z. Kuramochi has recently obtained the following very interesting result concerning the classification of Riemann surfaces [1]:

If we delete from a Riemann surface belonging to the class an arbitrary compact set, the resulting surface remains in the class .

In the present paper we indicate a new method of proving this theorem, simultaneously for the cases B and D.