bluuebunny/crossref_metadata_2025 huggingface dataset:
Eigenspaces of the Laplace-Beltrami operator on a hyperboloid
Authors: Sekiguchi Jiro
Published: July 2016

Ever since S. Helgason [4] showed that any eigenfunction of the Laplace-Beltrami operator on the unit disk is represented by the Poisson integral of a hyperfunction on the unit circle, much interest has been arisen to the study of the Poisson integral representation of joint eigenfunctions of all invariant differential operators on a symmetric space X. In particular, his original idea of expanding eigenfunctions into K-finite functions has proved to be generalizable up to the case where X is a Riemannian symmetric space of rank one (cf. [4], [5], [11]). Presently, extension to arbitrary rank has been completed by quite a different formalism which views the present problem as a boundary-value problem for the differential equations. It should be recalled that along this line of approach a general theory of the systems of differential equations with regular singularities was successfully established by Kashiwara-Oshima (cf. [6], [7]).
Some analytic and geometric applications of the invariant theoretic method
Authors: Morikawa Hisasi
Published: July 2016

Determinant is a most useful tool in every branch of mathematics, especially in linear mathematics. What kind of quantities do take a similar universal important role as determinant, in advanced branches of mathematics? In the present articles, showing the usefulness of semi-invariants in the classical invariant theory, we shall give a partial answer of the above question.
Some notes on the theory of holomorphic curves
Authors: Suzuki Junji , Toda Nobushige
Published: July 2016

In this paper, we shall give some notes on the order functions of holomorphic curves and, applying these facts, we may formulate the theory of holomorphic curves more precisely than those in Ahlfors [2], Cowen and Griffiths [4], Weyl [7] or Wu [8] in several cases.
The canonical modules of graded rings defined by generic matrices
Authors: Yoshino Yuji
Published: July 2016

Let k be a field, and X = [xij] be an n × (n + m) matrix whose elements are algebraically independent over k.

We shall study the canonical module of the graded ring R, which is a quotient ring of the polynomial ring A = k[X] by the ideal αn(X) generated by all the n × n minors of X.
Some remarks about generalized functionals of complex white noise
Authors: Jondral Friedrich
Published: July 2016

Let us start with a short survey concerning complex white noise (for details see Hida [3]): Let be the space of real valued rapidly decreasing testing functions and its complexification.
Infinite dimensional Langevin equation and Fokker-Planck equation
Authors: Miyahara Yoshio
Published: July 2016

Stochastic processes on a Hilbert space have been discussed in connection with quantum field theory, theory of partial differential equations involving random terms, filtering theory in electrical engineering and so forth, and the theory of those processes has greatly developed recently by many authors (A. B. Balakrishnan [1, 2], Yu. L. Daletskii [7], D. A. Dawson [8, 9], Z. Haba [12], R. Marcus [18], M. Yor [26]).
A singular convolution kernel without pseudo-periods
Authors: Laub Jesper
Published: July 2016

Let G be a locally compact abelian group and N a non-zero convolution kernel on G satisfying the domination principle. We define the cone of N-excessive measures E(N) to be the set of positive measures ξ for which N satisfies the relative domination principle with respect to ξ. For ξ ∈ E(N) and Ω ⊆ G open the reduced measure of ξ over Ω is defined as

.
The moduli of a class of rank 2 vector bundles on P3
Authors: Wever G. Pete
Published: July 2016

Barth and others [1], [2], [5] have begun the study of stable algebraic vector bundles of rank 2 on projective space. Maruyama [7] has shown that stable rank 2 bundles have a variety of moduli which is the finite union of quasi-projective varieties.
On the holomorphical classification of spaces of holomorphic germs
Authors: Aragona Jorge
Published: July 2016

Let K be a compact set in a complex metrizable locally convex space E and F a complex Banach space. The study of the space of holomorphic germs ℋ(K; F) endowed with the Nachbin topology was undertaken by several authors.
Complex subspaces of homogeneous complex manifolds II—Homotopy Results
Authors: Sommese Andrew John
Published: July 2016

The Lefschetz hyperplane section theorem has roots going back at least to Picard, but it was Lefschetz [20] who first stated and proved it in the modern form for integer homology. Later it was improved up to the homotopy level by Andreotti-Frankel [1] and Bott [8] using an idea of Thorn. Numerous generalizations along the same lines have appeared, e.g. [14, Theorem H], [19], [24, App. II] etc.
A new characterization of the Bruhat decomposition
Authors: Kato Yoshifumi
Published: July 2016

By an algebraic homogeneous space, we mean the factor space X = G/P, where G is a simply-connected, complex, semi-simple Lie group and P is a parabolic subgroup of G. Many typical manifolds such as the projective spaces and the Grassmann varieties belong to this class of manifolds. For instance, the Grassmann variety G(k, n) can be expressed as SL(n + 1, C)/P, where P is a maximal parabolic subgroup of SL(n + 1, C) leaving a suitable k + 1 dimensional subspace invariant. In this paper, we devote ourselves to study the Bruhat decomposition of an algebraic homogeneous space X = G/P.
Curvature, geodesics and the Brownian motion on a Riemannian manifold I—Recurrence properties
Authors: Ichihara Kanji
Published: July 2016

LetMbe ann-dimensional, complete, connected and locally compact Riemannian manifold andgbe its metric. Denote byΔMthe Laplacian onM.
Modular forms of degree n and representation by quadratic forms II
Authors: Kitaoka Yoshiyuki
Published: July 2016

Let S(m), T(n) be positive definite integral matrices and suppose that T is represented by S over each p-adic integer ring Zp. We proved arithmetically in [3] that T is represented by S over Z provided that m ≥ 2n + 3 and the minimum of T is sufficiently large. This guarantees the existence of at least one representation but does not give any asymptotic formula for the number of representations. To get an asymptotic formula we must employ analytic methods.
Integrable derivations
Authors: Matsumura Hideyuki
Published: July 2016

Let A be a commutative ring and D be a derivation of A into itself. If there exists a homomorphism E: A → A[[t]] such that

then we say that D is integrable. Integrable derivations have many good properties. In fact, most of unpleasant phenomena of derivations in characteristic p disappear if we consider integrable derivations only.
Homeomorphisms without the pseudo-orbit tracing property
Authors: Aoki Nobuo
Published: July 2016

Recently, A. Morimoto [5] proved that every isometry of a compact Riemannian manifold of positive dimension has not the pseudo-orbit tracing property, and that if a homeomorphism of a compact metric space has the pseudo-orbit tracing property then Eφ— 0φ(see § 1 for definition). The purpose of this paper is to show that every distal homeomorphism of a compact connected metric space has not the pseudo-orbit tracing property.
The Cohen-Macaulayness of the Rees algebras of local rings
Authors: Ikeda Shin
Published: July 2016

Let (A, m, k) be a Noetherian local ring. We define

and call it the Rees algebra of A. Let X be an indeterminate over A, then R(A) can be identified with the A-subalgebra .
Proper morphisms and excellent schemes
Authors: Bellaccini Barbara
Published: July 2016

Let f: X → Y be a finite type morphism of locally noetherian schemes. It is well known ([3, IV, 7.8.6]) that the excellent property ascends from Y to X. On the other side there are counter-examples where X is excellent and Y is not. First of all it is easy to show that the condition on chains of prime ideals does not descend (see [3, IV, 7.8.4]), even by finite morphisms. Secondly in [2] it is produced an example where X is excellent while Y is not a G-scheme (i.e. it has not the good properties of formal fibers). However in [2] it is also proved that the property concerning the openness of regular loci (the so called “J-2”) descends by finite type surjective morphisms. Therefore we are led to the following question: When does the G-scheme property descend? I.e. what conditions do we need on f? A reasonable condition is conjectured (in [2]) as the following: f is proper surjective. The aim of the present paper is precisely to give an answer to such a question. What we really prove is the following. If X is a G-scheme and J-2 (quasi-excellent), then the same is true for Y, provided that f is proper surjective and moreover all the residue fields of Y have characteristic 0. We remark that the result is strongly based on Hironaka’s desingularization for quasi-excellent schemes defined over a field of characteristic 0.
Lévy’s functional analysis in terms of an infinite dimensional Brownian motion III
Authors: Hasegawa Yoshihei
Published: July 2016

The purpose of this paper is to define minimality of surfaces in an infinite dimensional space E by probabilistic methods with the description of the relation between minimal surfaces and harmonic functions on the space E, and to analyze purely analytic properties of a certain class of quadratic forms on the space E.
On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces
Authors: Kohno Toshitake
Published: July 2016

The purpose of this paper is to establish the following isomorphism of Lie algebras.

Main Theorem. Let X be the complement of a hypersurface S in the complex projective space PN. Then the tower of nilpotent complex Lie algebras associated with the fundamental group π1(X, *) and the holonomy Lie algebraattached to S are isomorphic.
On a generalization of Laplace integrals
Authors: Ono Takashi
Published: July 2016

Let Rn be the Euclidean space of dimension n ≧ 1 with the standard inner product and the norm be the unit sphere {x ∈ Rn; |x| = 1} and dωn-1 be the volume element of Sn-1 such that Sn-1 gets the volume 1. Let Ω be an open set of Rn containing Sn-1 and let f: Ω → Rm be a smooth map.
Extensions of number fields defined by cohomology groups
Authors: Opolka Hans
Published: July 2016

Letkbe a field of characteristic 0, letbe an algebraic closure ofkand denote byGk= G(/k) the absolute Galois group ofk. Suppose that for some natural numbern≥ 3 the cohomology groupHn(Gk) Z) is trivial.
On a dual relation for addition formulas of additive groups, I
Authors: Watanabe Toshihiro
Published: July 2016

This is the first in a series of papers concerned with a relation between a representation in the polynomial ring of additive groups and its translation invariant operators. The present study is to observe several properties of a polynomial sequence pa(x) satisfying the binomial identity:

by means of some translation invariant operators.
Non-linear predictors of transformed stationary processes
Authors: Kubo Izumi , Lee Sheu-San
Published: July 2016

One of the authors discussed the best non-linear predictor of the process X(t) = f(U(t)), which is obtained by transforming an Ornstein-Uhlenbeck process U(t) with a measurable function f(u) (see [5]).
Dirichlet series in the theory of Siegel modular forms
Authors: Kitaoka Yoshiyuki
Published: July 2016

We are concerned with Dirichlet series which appear in the Fourier expansion of the non-analytic Eisenstein series on the Siegel upper half space Hm of degree m. In the case of m = 2 Kaufhold [1] evaluated them. Here we treat the general cases by a different method.
Correction to: Topological stability of solenoidal automorphisms
Authors: Aoki Nobuo
Published: July 2016

The paper with the above title (Vol. 90, 1983, 119-135) contains omissions. They are in the proof (p. 134) of uniform continuity and uniform convergence of maps hn stated in p. 133, l ↑ 3.
On the fundamental units and the class numbers of real quadratic fields
Authors: Azuhata Takashi
Published: July 2016

LetQbe the rational number field andh(m) be the class number of the real quadratic fieldwith a positive square-free integerm. It is known that ifh(m) = 1 holds, thenmis one of the following four types with prime numbersp≡ 1,pt≡ 3 (mod 4) (1 昤i≥ 4) : i)m= p, ii)m=p1, iii)m= 2 orm=2p2, iv)m=p3p4(see Behrbohm and Rédei [1]). The sufficient conditions forh(m) > 1 with thesemwere given by several authors: in all cases by Hasse [2], in case i) by Ankeny, Chowla and Hasse [3] and by Lang [4], in case ii) by Takeuchi [5] and by Yokoi [6].
Stable vector bundles on quadric hypersurfaces
Authors: Ein L. , Sols I.
Published: July 2016

Barth, Hulek and Maruyama have showed that the moduli of stable rank 2 vector bundles on P2 are nonsingular rational varieties. There are also many examples of stable rank 2 vector bundles on P3. On the other hand, there is essentially only one example of rank 2 bundles on P4, which is constructed by Horrocks and Mumford. We hope the study of rank 2 bundles on hypersurfaces in P4 may give more insight to the study of vector bundles on P4. In this paper, we establish some general properties of stable rank 2 bundles on quadric hypersurfaces. We show the restriction theorem (1.4), (1.6), the existence of the spectrum (2.2), and the vanishing theorem (2.4), are also true for the stable rank 2 reflexive sheaves on quadric hypersurfaces just as in the case when the base variety is Pn. Though the methods to prove such results are similar to those we use for projective spaces, there are some technical difficulties. We should also mention that we shall always assume the base field is characteristic 0 and algebraically closed, and we shall use the definition of stability introduced by Mumford and Takemoto.
Type II degenerations of K3 surfaces
Authors: Kondo Shigeyuki
Published: July 2016

A degeneration of K3 surfaces (over the complex number field) is a proper holomorphic map π: X→Δ from a three dimensional complex manifold to a disc, such that, for t ≠ 0, the fibres Xt = π-1(t) are smooth K3 surfaces (i.e. surfaces Xt with trivial canonical class KXt = 0 and dim H1(Xt, Oxt) = 0).
A note on quadratic fields in which a fixed prime number splits completely
Authors: Ichimura Humio
Published: July 2016

Throughout this note,pdenotes a fixed prime number andfdenotes a fixed natural number prime top.

It is easy to see and more or less known that for any natural numbern, there exists an elliptic curve overpwhosej-invariant is of degreenoverFpand whose endomorphism ring is isomorphic to an order of an imaginary quadratic field. In this note, we consider a more precise problem:for any natural number n, decide whether or not there exists an elliptic curve overpwhose j-invariant is of degree n over Fpand whose endomorphism ring is isomorphic to an order of an imaginary quadratic field with conductor f.
The application of the principal ideal theorem to p-groups
Authors: Miyake Katsuya
Published: July 2016

Let p be a fixed prime integer, and G a finite p-group. For a subgroup H of G, we denote the centralizer of H in G by CG(H). The commutator subgroup of G is denoted by [G, G].
The rank of syzygies under the action by a finite group
Authors: Goto Shiro
Published: July 2016

Let S be a Noetherian local ring with maximal ideal J and k the residue field of S. Let G be a finite group of order n and suppose that G acts on S as automorphisms. Let R = SG and I = JG. We denote by S[G] (resp. R[G]) the twisted group ring of G over S (resp. the group algebra of G over R). Recall that the multiplication of S[G] is defined as follows : sg · th = sg(t) · gh for s, t ∊ S and g, h ∊ G. Let tG(S) = {Σg ∈ Gg(s)/s ∈ S} and call it the trace ideal of S. Note that tG(S) = R if n is a unit of S. We say that S has a normal basis if S ≅ R[G] as R[G]-modules. This condition says that there is an element s of S so that {g(s)}g ∈ G forms an R-free basis of S.
A remark on the Grothendieck-Lefschetz theorem about the Picard group
Authors: Bădescu Lucian
Published: July 2016

Let K be an algebraically closed field of arbitrary characteristic. The term “variety” always means here an irreducible algebraic variety over K. The notations and the terminology are borrowed in general from EGA [4].
On global cluster sets for functions meromorphic on some Riemann surfaces
Authors: Segawa Shigeo
Published: July 2016

Consider a single-valued meromorphic function w = f(p) defined on an open Riemann surface R with an ideal boundary β. In [1], Collingwood and Cartwright introduced the global cluster set for a function meromorphic on the unit disk. Generalizing the definition of global cluster sets to our present setting, we define the global cluster set for w = f(p) as follows;

A value w in the extended complex plane is called a cluster value at β if there exists a sequence in R converging to β such that
On singular sets of flat holomorphic mappings with isolated singularities
Authors: Omoto Hideo
Published: July 2016

In [4] B. Iversen studied critical points of algebraic mappings, using algebraic-geometry methods. In particular when algebraic maps have only isolated singularities, he shows the following relation; Let V and S be compact connected non-singular algebraic varieties of dimcV = n, and dimc S = 1, respectively. Suppose f is an algebraic map of V onto S with isolated singularities. Then it follows that

where χ denotes the Euler number, μf(p) is the Milnor number of f at the singular point p, and F is the general fiber of f : V → S.
Examples of bad noetherian local rings
Authors: Marinari Maria Grazia
Published: July 2016

In this paper we use a general technique, due to Larfeldt-Lech [9], to show that there exist local noetherian rings which are “bad” with respect to some properties which are obviously verified in the algebro-geometric case. In particular we show that there exist local Gorenstein rings which are not homomorphic images of regular (local) rings and that there exist local rings which do have canonical module but do not have canonical algebra.
On Holonomy and Homogeneous Spaces
Authors: Kostant Bertram
Published: July 2016

In general a homogeneous space admits many invariant affine connections. Among these are certain connections which appear in many ways to be more natural than the others. We refer to the connections which K. Nomizu in [4] calls canonical affine connections of the first kind. When G is a compact connected Lie group and K a closed subgroup we called an invariant Riemannian metric on G/K, natural (in [2]) when it induced such a connection.
On Pseudo-Analytic Functions
Authors: Storvick D. A.
Published: July 2016

Many of the properties of analytic functions can be proved in a purely topological manner, so that such properties are then valid for the larger class of functions which are topologically equivalent to analytic functions. The importance of such functions has been recognized fairly recently, particularly in the theory of partial differential equations, where certain solutions have been shown to possess the topological properties of analytic functions, i.e., interiority and continuity, but not necessarily the analytic properties of complex differentiability and integrability.
Unit Groups of Cyclic Extensions
Authors: Kubota Tomio
Published: July 2016

LetΩbe an algebraic number field of finite degree, which we fix once for all, and letKbe a cyclic extension overΩsuch that the degree ofK/Ωis a powerof a prime numberl. It is obvious that the norm groupNK/ΩeKof the unit group ekofK, being a subgroup of the unit group e of Ω contains the groupconsisting of all-th powersof ε∈e.
Dynamical construction of Kähler-Einstein metrics
Authors: Tsuji Hajime
Published: July 2016

In this article, we give a new construction of a Kähler-Einstein metric on a smooth projective variety with ample canonical bundle. As a consequence, for a dominant projective morphismf:X→Swith connected fibers such that a general fiber has an ample canonical bundle, and for a positive integerm, we construct a canonical singular Hermitian metrichE,monwith semipositive curvature in the sense of Nakano.
Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone
Authors: Xu Gang , Yin Huicheng
Published: July 2016

In this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the bookSupersonic Flow and Shock Wavesby Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.
Sharp estimates of the potential kernel for the harmonic oscillator with applications
Authors: Nowak Adam , Stempak Krzysztof
Published: July 2016

We prove qualitatively sharp estimates of the potential kernel for the harmonic oscillator. These bounds are then used to show that theLp–Lqestimates of the associated potential operator obtained recently by Bongioanni and Torrea are in fact sharp.
Divisor class groups and graded canonical modules of multisection rings
Authors: Kurano Kazuhiko
Published: July 2016

We describe the divisor class group and the graded canonical module of the multisection ringT(X;D1,…,Ds) for a normal projective varietyXand Weil divisorsD1,…,DsonXunder a mild condition. In the proof, we use the theory of Krull domain and the equivariant twisted inverse functor.
Hartman’s theorem for hyperbolic sets
Authors: Kurata Masahiro
Published: July 2016

Hartman proved that a diffeomorphism is topologically conjugate to a linear map on a neighbourhood of a hyperbolic fixed point ([3]). In this paper we study the topological conjugacy problem of a diffeomorphism on a neighbourhood of a hyperbolic set, and prove that for any hyperbolic set there is an arbitrarily slight extension to which a sub-shift of finite type is semi-conjugate.
Analytic torsion of space forms of certain compact symmetric spaces
Authors: Urakawa Hajime
Published: July 2016

Let M be a compact, oriented Riemannian manifold of dimension dr and let Γ be the fundamental group of M. For a finite dimensional representation ρ of Γ on a vector space F, Ray and Singer [10] have defined the analytic torsion T(M, ρ) as follows: We denote by E the vector bundle over M with typical fibre F defined by the representation ρ.
Markov families for Anosov flows with an involutive action
Authors: Adachi Toshiaki
Published: July 2016

The aim of this note is to construct “involutive” Markov families for geodesic flows of negative curvature. Roughly speaking, a Markov family for a flow is a finite family of local cross-sections to the flow with fine boundary conditions. They are basic tools in the study of dynamical systems. In 1973, R. Bowen [5] constructed Markov families for Axiom A flows. Using these families, he reduced the problem of counting periodic orbits of an Axiom A flow to the case of hyperbolic symbolic flows.
On polarized normal varieties, I
Authors: Matsusaka T.
Published: July 2016

In this paper, we deal with the first part of an application of our Riemann-Roch type inequalities (cf. [13], [23]) toward deformations of polarized normal varieties. In Chapter I, we discuss the problem of eliminating fixed components from complete linear systems defined by multiples of a given divisor. Let Un be a complete normal variety and Y0 an ample Cartier divisor on U. The main result of the chapter is that there is a positive integer c0, predicted by the first two leading coefficients of the polynomial X(U, O(m Y0)), such that the complete linear system Λ(rc0Y0) has no fixed component whenever r is a positive integer (which is essentially contained in Theorem 1.1 (cf. [13], Lemma 5.2)). An easy consequence of this result is that when n = 2, we can find another positive integer c1 predicted by the same coefficients as above, such that rc1c0Y0 is very ample on U whenever r is a positive integer. Even though this has been generalized to n = 3 by J. Kollár (cf. [12]), we have included this in Section 3 since it is very simple.
Fibre Bundles over Spheres
Authors: Shizuma Ryoji
Published: July 2016

This note is concerned with homotopy relations in fibre bundles over spheres, in connection with my previous note.

Let R be a fibre boundle, with the n-dimensional sphere Sn as the base space and with fibres which are connected and simple in n − 1 dimension. Let further π denote the projection of R onto Sn. We take a simplicial decomposition K of Sn which is so fine that the star of each simplex lies in a coordinate neighborhood of Sn.
On the Structure of Complete Local Rings
Authors: Nagata Masayoshi
Published: July 2016

The concept of a local ring was introduced by Krull [2], who defined it as a Noetherian ringR(we say that a commutative ringRis Noetherian if every ideal inRhas a finite basis and ifRcontains the identity) which has only one maximal idealm. If the powers of m are defined as a system of neighbourhoods of zero, thenRbecomes a topological ring satisfying the first axiom of countability, And the notion was studied recentlybyC. Chevalley and I. S. Cohen. Cohen [1] proved the structure theorem for complete rings besides other properties of local rings.
Über die Restklassenkörper bewerteter perfekter Körper
Authors: Moriya Mikao
Published: July 2016

Die Struktur diskret bewerteter perfekter Körper ist bisher von H. Hasse, F. K. Schmidt, O. Teichmüller und E, Witt eingehend untersucht worden. Es ist schon von diesen Autoren bewiesen worden, dass der Restklassenkörper eines diskret perfekten Körpers K stets in K ein mit multiplikativ isomorphes Repräsentantensystem besitzt, und sogar, dass es im charakteristikgleichen Fall ein Reprasentantensystem R von gibt, welches einen mit isomorphen Körper bildet. Dabei lässt sich K ais Potenzreihenkörper eines Primelementes aus K mit Koeffizienten aus R darstellen.
On Krull’s Conjecture concerning Valuation Rings
Authors: Nagata Masayoshi
Published: July 2016

Previously W. Krull conjectured that every completely integrally closed primary domain of integrity is a valuation ring, The main purpose of the present paper is to construct in §1 a counter example against this conjecture. In § 2 we show a necessary and sufficient condition that a field is a quotient field of a suitable completely integrally closed primary domain of integrity which is not a valuation ring.
Note on A-Groups
Authors: Itô Noboru
Published: July 2016

Let us consider soluble groups whose Sylow subgroups are all abelian. Such groups we callA-groups, following P. Hall.A-groups were investigated thoroughly by P. Hall and D. R. Taunt from the view point of the structure theory. In this note, we want to give some remarks concerning representation theoretical properties ofA-groups.
Espaces à Connexions Affines et Riemanniennes Symétriques
Authors: Kobayashi Shôshichi
Published: July 2016

Le but de la présente note est de clarifier la notion de variété riemanien-ne ou affine symétrique (et plus généralement, localement reductive) du point de vue de la théorie de connexions dans les espaces fibres. Nous donnerons quelques caractérisations des espaces localement symétriques, ou réductives (Th. 1. 2 et 3). On trouvera la définition de dérivation covariante de tenseurs de courbure et de torsion dans la terminologie de la théorie de connexions dans les espaces fibres. Cette définition peut être généralisée à la dérivation covariante d’un tenseur quelconque. Les résultats concernant la dérivation covariante seront publiés ailleurs. Enfin on retrouvera des résultats de Borel-Lichnerowicz. Même si l’on ne trouvera pas de résultats nouveaux dans cette note, on comprendra mieux les espaces symétriques par la théorie de connexion de Cartan.
An Example of Normal Local Ring which is Analytically Ramified
Authors: Nagata Masayoshi
Published: July 2016

Previously the following question was offered by Zariski [6]:

Is any normal Noetherian local ring analytically irreducible?

In the present note, we will construct a counter-example against the question.

TERMINOLOGY. A ring (integrity domain) means always a commutative ring (integrity domain) with identity. A normal ring is an integrity domain which is integrally closed in its field of quotients. When 0 is an integrity domain, the integral closure of 0 in its field of quotients is called the derived normal ring of 0.
A Note on Units of Algebraic Number Fields
Authors: Kubota Tomio
Published: July 2016

We shall prove in the present note a theorem on units of algebraic number fields, applying one of the strongest formulations, be Hasse [3], of Grunwald’s existence theorem.
A Global Formulation of the Fundamental Theorem of the theory of Surfaces in three Dimensional Euclidean Space
Authors: Sasaki Shigeo
Published: July 2016

Let us consider a surface S of class C3 in Euclidean space E3 and

(1.1) xi = xi(u1, u2) (i, j, k = 1, 2, 3)

be its parametric representation of class C3.
Theta Functions and Abelian Varieties over Valuation Fields of Rank one I
Authors: Morikawa Hisasi
Published: July 2016

We shall denote by the Z-module of integral vectors of dimension r, by T a symmetric complex matrix with positive definite imaginary part and by g the variable vector. If we put and
the fundamental theta function is expressed in the form: as a series in q and u. Other theta functions in the classical theory are derived from the fundamental theta function by translating the origin and making sums and products, so these theta functions are also expressed in the form: as series of q and u. Moreover the coefficients in the relations of theta functions are also expressed in the form: as series in q.
A Theory of Mathematical Objects as a Prototype of Set Theory
Authors: Ono Katuzi
Published: July 2016

The theory of mathematical objects, developed in this work, is a trial system intended to be a prototype of set theory. It concerns, with respect to the only one primitive notion “proto-membership”, with a field of mathematical objects which we shall hereafter simply call objects, it is a very simple system, because it assumes only one axiom scheme which is formally similar to the aussonderung axiom of set theory. We shall show that in our object theory we can construct a theory of sets which is stronger than the Zermelo set-theory [1] without the axiom of choice.
A Theorem on Factorizable Groups of Odd Order
Authors: Nagai Osamu
Published: July 2016

Recently, W. Feit [2] obtained some results on factorizable groups of odd order. By using his procedure and applying the theory of R. Brauer [1], we can prove the following theorem similar to that of W. Feit [2]:

Theorem. Let G be a factorizable group of odd order such that

G = HM

where H is a subgroup of order 3p, p being a prime greater than 3, and M is a maximal subgroup of G. Then G contains a proper normal subgroup which is contained either in H or in M.
Finite Groups which Contain a Selfcentralizing Subgroup of Order 3
Authors: Feit Walter , Thompson John G.
Published: July 2016

The polyhedral group (l, m, n) is defined in [3] by the presentation
On the Clifford Collineation, Transform and Similarity Groups (IV): An Application to Quadratic Forms
Authors: Wall G. E.
Published: July 2016

E. S. Barnes and I recently constructed a series of positive quadratic forms fN in N = 2n variables (n = 1, 2,…) with relative minima of order for large N. I continue this investigation by determining the minimal vectors of fN and showing that, for its group of automorphs is the Clifford group This suggests a generalization. Replacing by where p is an odd prime, I derive a new series of positive forms in N =(p−1)pn variables (§4). The relative minima are again of order (p fixed, N → ∞ ), the “best” forms being those for p = 3, 5. All forms are eutactic though only those for p = 3,5 are extreme.
Group Characters and Normal Hall Subgroups
Authors: Gallagher P. X.
Published: July 2016

1. Introduction

Let G be a finite group and let ψ be an (ordinary) irreducible character of a normal subgroup N. If ψ extends to a character of G then ψ is invariant under G, but the converse is false. In section 3 it is shown that if ψ extends coherently to the intermediate groups H for which H/N is elementary, then ψ extends to G. If N is a Hall subgroup, then in order for ψ to extend to G it is sufficient that ψ be invariant under G. This leads to a construction of the characters of G from the characters of N and the characters of the subgroups of G/N in this case.
On Theta Functions and Abelian Varieties over Valuation Fields of Rank One: (II) Theta Functions and Abelian Functions of Characteristicp(>0)
Authors: Morikawa Hisasi
Published: July 2016

It may safely said that one of the most important problems in modern algebraic geometry is to elevate theory of abelian functions to the same level as theory of elliptic functions beyond the modern formulation of classical results. Being concerned in such a problem, we feel that one of the serious points is the lack of knowladge on the explicit expressions of abelian varieties and their law of compositions by means of their canonical systems of coordinates: Such expressions correspond to the cubic relationof Weierstrass’-functions and their addition formulae in theory of elliptic functions.
Crossed Products and Ramification
Authors: Williamson Susan
Published: July 2016

Introduction. Let S be the integral closure of a complete discrete rank one valuation ring R in a finite Galois extension of the quotient field of R, and let G denote the Galois group of the quotient field extension. Auslander and Rim have shown in [3] that the trivial crossed product Δ (1, S, G) is an hereditary order if and only if 5 is a tamely ramified extension of R. And the author has proved in [7] that if the extension S of R is tamely ramified then the crossed product Δ(f, 5, G) is a Π-principal hereditary order for each 2-cocycle f in Z2(G, U(S)). (See Section 1 for the definition of Π-principal hereditary order.) However, the author has exhibited in [8] an example of a crossed product Δ(f, S, G) which is a Π-principal hereditary order in the case when S is a wildly ramified extension of R.
Finite Dimensional Approximations to Some Flows on the Projective Limit Space of Spheres
Authors: Nomoto Hisao
Published: July 2016

LetΩbe the projective limit space of a sequence of probability spaceΩnwhich is a certain subset of (n− 1)-dimensional sphere with the usual uniform probability distribution on it. T. Hida [2], starting from a sequence of finite dimensional flowswhich are derived from some one-parameter subgroups of rotations of spheres, constructed a flow {Tt} onΩas the limit of them. Observing his method, the concept ofconsistencyof flowswhich approximate {Tt} seems to play an essential role in his work [2]. As will be made clear in the following sections, the concept of consistency is closely related to the projective limiting structure of our basic spaceΩ. The purpose of this paper is to determine all the flows onΩwhich can be approximated in the sense of [2] by finite dimensional flows.
On a Theorem of Schwarz Type for Quasiconformal Mappings in Space
Authors: Ikoma Kazuo
Published: July 2016

A space ring R is defined as a domain whose complement in the Moebius space consists of two components. The modulus of R can be defined in variously different but essentially equivalent ways (see e.g. Gehring [3] and Krivov [5]), which is denoted by mod R. Following Gehring [2], we refer to a homeomorphism y(x) of a space domain D as a k-quasiconformal mapping, if the modulus condition

is satisfied for all bounded rings R with their closure , where y(R) denotes the image of R by y = y(x). Then, it is evident that the inverse of a k-quasi-conformal mapping is itself k-quasiconformal and that a k1-quasiconformal mapping followed by a k2-quasiconformal one is k1k2-quasiconformal. It is also well known that the restriction of a Moebius transformation to a space domain is equivalent to a 1-quasiconformal mapping of its domain.
Finite Dimensional Approximations to Some Flows on the Projective Limit Space of Spheres II
Authors: Nomoto Hisao
Published: July 2016

In the previous paper [6], we have considered flows on the measure space (Ω, ℬ, P), which was the projective limit of a certain subspace (Ωn, ℬn, Pn) of the measure space (Sn,ℬ(Sn), Pn), where Snis the (n− 1) · sphere with radiusandPnis the uniform probability distribution overSn.
Some Results on Value Distribution of Meromorphic Functions in the Unit Disk
Authors: Tse Kam-Fook
Published: July 2016

Let C and D be the unit circle and the open unit disk respectively. We shall use p(z,z′) to represent the non-Euclidean distance [3, p. 263] between the two points z and z′ in D, and X(w, w′) to represent the chordal distance between the two points w and w′ on the Riemann Sphere Ω.
On Uniform Approximation by Rational Functions with an Application to Chordal Cluster Sets
Authors: Gresser J.T.
Published: July 2016

For a closed and bounded set E in the complex plane, let A(E) denote the collection of all functions continuous on E and analytic on E°, its interior; let R(E) denote the collection of all functions which are uniform limits on E of rational functions with poles outside E. Then let A denote the collection of all closed, bounded sets for which A(E) = R(E). The purpose of this paper is to formulate a condition on a set, which is essentially of a geometric nature, in order that the set belong to A. Then using approximation techniques, we shall construct a meromorphic function having a certain boundary behavior on a perfect set; this answers a question raised in [1].
On families of meromorphic maps into the complex projective space
Authors: Fujimoto Hirotaka
Published: July 2016

In [10], P. Montel defined the notion of a quasinormal family of meromorphic functions and obtained several results relating to this. Afterwards, in [13], H. Rutishauser generalized some of them to the case of meromorphic functions of several variables. By definition, a quasi-normal family of meromorphic functions on a domain D in Cn is a family such that any sequence in has a subsequence which converges compactly outside a thin analytic subset of D.
On the multiple Markov property of Lévy-Hida for Gaussian processes
Authors: Mandrekar V.
Published: July 2016

The purpose of this note is to clarify relations between multiple Markov properties (MMP) defined by Lévy ([8], [9]) and Hida [5] for Gaussian processes and to extend some work in Lévy [8] and Hida [5]. In the stationary Gaussian case it has been shown ([5], [4]) that these notions of MMP coincide. Interesting examples of (non-stationary) processes satisfying MMP can be found in [5], [8].
An application of the Morse theory to foliated manifolds
Authors: Fukui Kazuhiko
Published: July 2016

In [5], R. Thorn has started the study of the foliated structures by using the Morse theory. Recently K. Yamato [7] has studied the topological properties of leaves of a codimension one foliated manifold by investigating the “critical points” of variation equation of the given one-form.
Sur les noyaux de convolution conditionnellement sous-médians II
Authors: Itô Masayuki
Published: July 2016

Dans toute la suite X désignera un groupe abélien localement compact, séparé et dénombrable à l’infini et ξ désignera la mesure de Haar sur X. Un noyau de convolution N sur X est une mesure de Radon positive dans X et, pour une mesure de Radon réelle μ dans X, le N-potentiel de μ est la convolution N*μ dès qu’elle a un sens.
On the central ideal class group of cyclotomic fields
Authors: Shirai Susumu
Published: July 2016

Let Q be the rational number field, K/Q be a finite Galois extension with the Galois group G, and let CK be the ideal class group of K in the wider sense. We consider CK as a G-module. Denote by I the augmentation ideal of the group ring of G over the ring of rational integers. Then CK/I(CK) is called the central ideal class group of K, which is the maximal factor group of CK on which G acts trivially. A. Fröhlich [3, 41 rationally determined the central ideal class group of a complete Abelian field over Q whose degree is some power of a prime. The proof is based on Theorems 3 and 4 of Fröhlich [2]. D. Garbanati [6] recently gave an algorithm which will produce the l-invariants of the central ideal class group of an Abelian extension over Q for each prime l dividing its order.
Remarks on Fujiwara’s stationary phase method on a space of large dimension with a phase function involving electromagnetic fields
Authors: Tsuchida Tetsuo
Published: July 2016

We consider an oscillatory integral of the form

Here each xj, j = 0, 1,…, L, runs in Rd, ν > 1 is a constant and tj, j = 1,…,L, are positive constants. Fujiwara [5] discussed this integral for L large and developed the stationary phase method with an estimate of the remainder term for the phase function S(xL,…, x0) coming from the action integral for a particle in an electric field. But his results cannot be applied to the integral which naturally arises in the discussion of quantum mechanics of a charged particle moving in a magnetic field. In this paper we extend his results to the case for the phase function involving both electric and magnetic fields.
Bounded realization ofl-groups over global fields
Authors: Geyer Wulf-Dieter , Jarden Moshe
Published: July 2016

We use the method of Scholz and Reichardt and a transfer principle from finite fields to pseudo finite fields in order to prove the following result. THEOREMLet G be a group of order ln, where l is a prime number. Let K0be either a finite field with |K0| >l4n+4or a pseudo finite field. Suppose that l≠ char(K0)and that K0does not contain the root of unity ζlof order l. Let K=K0(t),with t transcendental over K0.Then K has a Galois extension L with the following properties:(a)(L/K) ≅G; (b)L/K0is a regular extension; (c) genus(L) <; (d)K0[t]has exactly n prime ideals which ramify in L; the degree of each of them is[K0:K0]; (e) (t)∞totally decomposes in L; (f)L=K(x),withanddeg(ai(t)) < deg(a1(t))for i= 1,…,ln.
Solutions of the third Painlevé equation I
Authors: Umemura Hiroshi , Watanabe Humihiko
Published: July 2016

We classify transcendental classical solutions of the third Painlevé equation. This result combined with the list of algebraic solutions in [11] gives a complete table of classical solutions of the third Painlevé equation.
Geodesics and Killing vector fields on the tangent sphere bundle
Authors: Konno Tatsuo , Tanno Shukichi
Published: July 2016

We show that any Killing vector field on the unit tangent sphere bundle with Sasaki metric of a space of constant curvaturek≠ 1 is fiber preserving by studying some property of geodesies on the bundle. As a consequence, any Killing vector field on the unit tangent sphere bundle of a space of constant curvaturek≠ 1 can be extended to a Killing vector field on the tangent bundle.
Algebres nucleaires de fonctions entières et equations aux derivées partielles stochastiques
Authors: Ouerdiane H.
Published: July 2016

En analyse du bruit blanc (W.N.A) on utilise usuellement le triplet de Gelfand (S(R) ⊂ L2(R, dt) ⊂ S′(R), μ) où S′(R) est l’espace de L. Schwartz des distributions tempérées et μ la mesure Gaussienne donnée par sa fonction caractéristique:

(1)
Hyperconvexity and Bergman completeness
Authors: Blocki Zbigniew , Pflug Peter
Published: July 2016

We show that any bounded hyperconvex domain is Bergman complete.
Landen inequalities for hypergeometric functions
Authors: Qiu S.-L. , Vuorinen M.
Published: July 2016

A generalization of the Landen identity, in the form of an inequality, is proved for hypergeometric functions. Some well-known asymptotic formulas are refined.
On proper holomorphic mappings from domains with T-action
Authors: Coupet Bernard , Pan Yifei , Sukhov Alexandre
Published: July 2016

We describe the branch locus of a proper holomorphic mapping between two smoothly bounded pseudoconvex domains of finite type in under the assumption that the first domain admits a transversal holomorphic action of the unit circle. As an application we show that any proper holomorphic self-mapping of a smoothly bounded pseudoconvex complete circular domain of finite type in is biholomorphic.
Symplectic Capacities of Toric Manifolds and Related Results
Authors: Lu Guangcun
Published: July 2016

In this paper we give concrete estimations for the pseudo symplectic capacities of toric manifolds in combinatorial data. Some examples are given to show that our estimates can compute their pseudo symplectic capacities. As applications we also estimate the symplectic capacities of the polygon spaces. Other related results are impacts of symplectic blow-up on symplectic capacities, symplectic packings in symplectic toric manifolds, the Seshadri constant of an ample line bundle on toric manifolds, and symplectic capacities of symplectic manifolds withS1-action.
The Fourth-OrderQ-Curvature Flow on Closed 3-Manifolds
Authors: Chang Shu-Cheng , Wu Chin-Tung
Published: July 2016

Let the Paneitz operatorP0be strictly positive on a closed 3-manifoldMwith a fixed conformal class. It is proved that the solution of a fourth-orderQ-curvature flow exists onMfor all time and converges smoothly to a metric of constantQ-curvature.
The Carathéodory–Cartan–Kaup–Wu Theorem on an Infinite-Dimensional Hilbert Space
Authors: Cima Joseph A. , Graham Ian , Kim Kang Tae , Krantz Steven G.
Published: July 2016

This paper treats a holomorphic self-mapping f: Ω → Ω of a bounded domain Ω in a separable Hilbert space with a fixed point p. In case the domain is convex, we prove an infinite-dimensional version of the Cartan-Carathéodory-Kaup-Wu Theorem. This is basically a rigidity result in the vein of the uniqueness part of the classical Schwarz lemma. The main technique, inspired by an old idea of H. Cartan, is iteration of the mapping f and its derivative. A normality result for holomorphic mappings in the compact-weak-open topology, due to Kim and Krantz, is used.
Hilbert-Kunz Multiplicity and Reduction Mod p
Authors: Trivedi V.
Published: July 2016

We show that the Hilbert-Kunz multiplicities of the reductions to positive characteristics of an irreducible projective curve in characteristic 0 have a well-defined limit as the characteristic tends to infinity.
Large Deviations for Radial Random Walks on Homogeneous Trees
Authors: Ichihara Kanji
Published: July 2016

Donsker-Varadhan’s type large deviation will be discussed for the pinned motion of a radial random walk on a homogeneous tree. We shall prove that the rate function corresponding to the large deviation is associated with a new Markov chain constructed from the above random walk through a harmonic transform based on a positive principal eigenfunction for the generator of the random walk.
Linear Differential Equations with Solutions in the Dirichlet Type Subspace of the Hardy Space
Authors: Heittokangas J. , Korhonen R. , Rättyä J.
Published: July 2016

Sufficient conditions for the analytic coefficients of the linear differential equation

are found such that all solutions belong to a given -space, or to the Dirichlet type subspace Dp of the classical Hardy space Hp, where 0 < p ≤ 2. For 0 < q < ∞, the space consists of those functions f, analytic in the unit disc D, for which |f(z)|(1 – |z|2)q is uniformly bounded in D, and f ∈ Dp if the integral ∫D |f′(z)|p(1 – |z|2)p–1dσz converges.