bluuebunny/crossref_metadata_2025 huggingface dataset:
Liftings of Some Types of Tensor Fields and Connections to Tangent Bundles of pr-Velocities
Authors: Morimoto Akihiko
Published: July 2016

In the previous paper [6], we studied the liftings of tensor fields to tangent bundles of higher order. The purpose of the present paper is to generalize the results of [6] to the tangent bundles of pr-velocities in a manifold M— notions due to C. Ehresmann [1] (see also [2]). In §1, we explain the pr-velocities in a manifold and define the (Λ)-lifting of differentiable functions for any multi-index λ -(λ1, λ2,…,λp) of non-negative integers λi satisfying ΣΛi≤r. In § 2, we construct ‹Λ›-lifts of any vector fields and ‹Λ›-lifts of 1-forms. The ‹Λ›-lift is a little bit different from the ‹Λ›-lift of vector fields in [6].
Continuations of Analytic Functions of Class S and Class U
Authors: Yamashita Shinji
Published: July 2016

Let f be of class U in Seidel’s sense ([4, p. 32], = “inner function” in [3, p. 62]) in the open unit disk D. Then f has, by definition, the radial limit f(eiθ) of modulus one a.e. on the unit circle K. As a consequence of Smirnov’s theorem [5, p. 64] we know that the function
Quasi-Flows II Additive Functionals and TQ-Systems
Authors: Kubo Izumi
Published: July 2016

We have given in [3] the definition of the quasi-flow and discussed the representation and the time-change of the quasi-flow. Further we have defined the TQ-system and studied some properties of them using the time-change and the representation of the quasi-flow. These properties are very useful to study the ergodicity, the entropy and increasing partitions of the automorphism. We are now going to extend the definition of the TQ-system and to study the similar problems as the above.
On the Fundamental Group of a Simple Lie Group
Authors: Takeuchi Masaru
Published: July 2016

Let G be a simply connected simple Lie group and C the center of G, which is isomorphic with the fundamental group of the adjoint group of G. For an element c of C, an element x of the Lie algebra g of G is called a representative of c in g if exp x = c. Sirota-Solodovnikov [7] found a complete set of representatives of the center C in g and studied the group structure of C, and using their results Goto-Kobayashi [1] classified subgroups of the center C with respect to automorphisms of G. The group structure of C was also studied in Takeuchi [8],
Convergence of Isotropic Scattering Transport Process to Brownian Motion
Authors: Watanabe Shinzo , Watanabe Toitsu
Published: July 2016

Let us consider transporting particle in the n-dimensional Euclidian space Rn. It is assumed that a particle originating at a point x∈Rn moves in a straight line with constant speed c and continues to move until it suffers a collision. The probability that the particle has a collision between t and t + Δ is kΔ + o(Δ), where k is constant. When a particle has a collision, say at y in Rn, it moves afresh from y with an isotropic choice of direction independent of past history.
Ramification Theory for Extensions of Degree p
Authors: Williamson Susan
Published: July 2016

The notions of tame and wild ramification lead us to make the following definition.

Definition. The quotient field extension of an extension of discrete rank one valuation rings is said to be fiercely ramified if the residue class field extension has a nontrivial inseparable part.
On the Finite Subgroups of GL (3, Z)
Authors: Tahara Ken-Ichi
Published: July 2016

We should like to study three dimensional algebraic tori in the same way as Voskresenskiĭ does in [14] and [15]. To do so, it is necessary to determine all finite subgroups of GL(3,Z) up to conjugacy.
A Class of Riemannian Manifolds Satisfying R(X ,Y)·R = 0
Authors: Tanno Shûkichi
Published: July 2016

Let (M,g) be a Riemannian manifold and let R be its Riemannian curvature tensor. If (M, g) is a locally symmetric space, we have

(*) R(X,Y)·R = 0 for all tangent vectors X,Y

where the endomorphism R(X,Y) (i.e., the curvature transformation) operates on R as a derivation of the tensor algebra at each point of M. There is a question: Under what additional condition does this algebraic condition (*) on R imply that (M,g) is locally symmetric (i.e., ∇R = 0)? A conjecture by K. Nomizu [5] is as follows : (*) implies ∇R = 0 in the case where (M, g) is complete and irreducible, and dim M ≥ 3. He gave an affirmative answer in the case where (M,g) is a certain complete hypersurface in a Euclidean space ([5]).
Vector Bundles on an Elliptic Curve
Authors: Oda Tadao
Published: July 2016

Let k be an algebraically closed field of characteristic p≧ 0, and let X be an abelian variety over k.

The goal of this paper is to answer the following questions, when dim(X) = 1 and p≠0, posed by R. Hartshorne:

(1)

Is E(P) indecomposable, when E is an indecomposable vector bundle on X?

(2)

Is the Frobenius map F*: H1 (X, E) → H1 (X, E(p)) injective?

We also partly answer the following question posed by D. Mumford:

(3)

Classify, or at least say anything about, vector bundles on X when dim (X) > 1.
Ample Vector Bundles on Curves
Authors: Hartshorne Robin
Published: July 2016

In our earlier paper [4] we developed the basic sheaftheoretic and cohomological properties of ample vector bundles. These generalize the corresponding well-known results for ample line bundles. The numerical properties of ample vector bundles are still poorly understood. For line bundles, Nakai’s criterion characterizes ampleness by the positivity of certain intersection numbers of the associated divisor with subvarieties of the ambient variety. For vector bundles, one would like to characterize ampleness by the numerical positivity of the Chern classes of the bundle (and perhaps of its restrictions to subvarieties and their quotients). Such a result, like the Riemann-Roch theorem, giving an equivalence between cohomological and numerical properties of a vector bundle, may be quite subtle. Some progress has been made by Gieseker [2], by Kleiman [8], and in the analytic case, by Griffiths [3].
Complex-Harmonic Meier’s Theorem
Authors: Yamashita Shinji
Published: July 2016

1. Fatou’s theorem is true for a bounded complex-valued harmonic function in the diskD: |z|<1. One asks naturally: “Is Meier’s topological analogue of Fatou’s theorem (simply, “MF theorem”; [14, p. 330, Theorem 6], cf. [10, p. 154, Theorem 8.9]) true for a bounded complex-valued harmonic function in D?” We shall give the affirmative answer to this question. Furthermore, the horocyclicMFtheorem [2, p. 14, Theorem 5] in the complex-harmonic form will be proved in parallel.
Sur les Principes Divers du Maximum et le Type Positif
Authors: Ito Masayuki
Published: July 2016

Dans la théorie du potentiel par rapport à la noyau-fonction continue (au sens large), les théorèmes de Ninomiya et ceux de Kishi sont très originels (cf. [9] et [7]). Dans cet article, en généralisant la notion du noyau, on se propose de discuter quelques théorèmes analoques.
Ramification Theory for Extensions of Degree p. II
Authors: Williamson Susan
Published: July 2016

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.
Oscillation Function of a Multiparameter Gaussian Process
Authors: Jain Naresh C. , Kallianpur G.
Published: July 2016

It is our object in this paper to show that the recent results of K. Ito and M. Nisio [4] on the oscillation function of Gaussian processes on [0,1] are valid for Gaussian processes with a general multiparameter “time” set T. Except in extending Theorem 4 of [4] where we assume T to be the d-dimensional cube, in all other cases we allow T to be a separable metric space. Despite the generality of the time set, the proofs are achieved essentially using the method of the above mentioned authors. However, in Theorem 1 below we find the use of Lemma 6 of [5] more convenient than the approach via orthogonal expansions and Kolmogorov’s zero-one law as is done in [4].
Families of K-3 Surfaces
Authors: Mayer Alan L.
Published: July 2016

Let V be a 2-dimensional compact complex manifold. V is called a K-3 surface if : a) the irregularity q = dim H1(V, θ) of V vanishes and b) the first Chern class c1 of V vanishes. The canonical sheaf (of holo-morphic 2-forms) K of such a surface is trivial, since q = 0 implies that the Chern class map cx : Pic (V) → H2(V, Z) is injective : thus V has a nowhere zero holomorphic 2-form.
Cores of Potential Operators for Processes With Stationary Independent Increments
Authors: Sato Ken-Iti
Published: July 2016

Let Xt(ω)) be a stochastic process with stationary independent increments on the N-dimensional Euclidean space RN, right continuous in t ≧ 0 and starting at the origin. Let C0(RN) be the Banach space of real-valued continuous functions on RN vanishing at infinity with norm . The process induces a transition semigroup of operators Tt on C0(RN) :

Ttf(x) = Ef(x + Xt).
Saturated Ideals in Boolean Extensions
Authors: Kakuda Yuzuru
Published: July 2016

0. Introduction. Let k be an uncountable cardinal, and let λ be a regular cardinal less than k. Let I be a λ-saturated non-trivial ideal on k. Prikry, in his thesis, showed that, in certain Boolean extensions, k has a λ-saturated non-trivial ideal on k.
Primeable entire functions
Authors: Gross Fred , Yang Chung-Chun , Osgood Charles
Published: July 2016

An entire function F(z) = f(g(z)) is said to have f(z) and g(z) as left and right factors respe2tively, provided that f(z) is meromorphic and g(z) is entire (g may be meromorphic when f is rational). F(z) is said to be prime (pseudo-prime) if every factorization of the above form implies that one of the functions f and g is bilinear (a rational function). F is said to be E-prime (E-pseudo prime) if every factorization of the above form into entire factors implies that one of the functions f and g is linear (a polynomial). We recall here that an entire non-periodic function f is prime if and only if it is E-prime [5]. This fact will be useful in the sequel.
A class of nonanalytic automorphic functions
Authors: Niebur Douglas
Published: July 2016

In this paper we consider a class of nonanalytic automorphic functions which were first mentioned to A. Selberg by C. L. Siegel. These functions have Fourier coefficients which are closely connected with the Fourier coefficients of analytic automorphic forms, and they are also eigenfunctions of the Laplace operator derived from the hyperbolic metric. We shall show how this latter property gives new results in the classical theory of automorphic forms.
Quaternary even positive definite quadratic forms of prime discriminant
Authors: Kitaoka Yoshiyuki
Published: July 2016

In this note we study quaternary even positive definite quadratic forms of prime discriminant. In § 1 we classify quaternary even positive definite quadratic forms of prime discriminant p = 1 mod 4 (called simply nice quaternary lattices in this note) which represent two. We note that the class number of such forms is closely related to the dimension of the space of certain automorphic forms. (Remark 4 in the text). By using the classification in § 1 and the theory of integral representations of cyclic groups we show that the orthogonal group of a nice quaternary lattice is generated by ±1 and symmetries (of the lattice). In § 3, we calculate the class number of nice quaternary lattices. Notations and terminologies will generally be those of O’Meara [5]. Any exceptions to this convention will be stated explicitly.
Stable vector bundles on algebraic surfaces II
Authors: Takemoto Fumio
Published: July 2016

This paper is a continuation of “Stable vector bundles on algebraic surfaces” [10]. For simplicity we deal with non-singular projective varieties over the field of complex numbers. LetWbe a variety whose fundamental group is solvable, letHbe an ample line bundle onW, and letf: V → Wbe an unramified covering. Then we show in section 1 that ifEis anf*H-stable vector bundle onVthenf*Eis a direct sum ofH-stable vector bundles. In particularf*Lis a direct sum of simple vector bundles ifLis a line bundle onV.
On a certain poisson formula
Authors: Igusa Jun-Ichi
Published: July 2016

Let G denote a locally compact commutative group with a lattice Γ, G* its dual, and for every (g, g*) in G × G*; let Γ* denote the annihilator of Γ in G* and dg the Haar measure on G such that G/Γ is of measure 1.
The extension of G-foliations to Tangent bundles of higher order
Authors: Cordero Luis A.
Published: July 2016

In this paper we describe a canonical procedure for constructing the extension of a G-foliation on a differentiable manifold X to its tangent bundles of higher order and by applying the Bott-Haefliger’s construction of characteristic classes of G-foliations ([2], [3]) we obtain an infinite sequence of characteristic classes for those foliations (Theorem 4.8).
On p-adic L-functions and cyclotomic fields
Authors: Greenberg Ralph
Published: July 2016

Let p be a prime. If one adjoins to Q all pn-th roots of unity for n = 1, 2, 3, …, then the resulting field will contain a unique subfield Q∞ such that Q∞ is a Galois extension of Q with Gal the additive group of p-adic integers. We will denote Gal(Q∞/Q) by Γ.
Non-linear elliptic operators on a compact manifold and an implicit function theorem
Authors: Sunada Toshikazu
Published: July 2016

Many problems in differential and analytic geometry seem to have something to do with the study of non-linear partial differential equations of elliptic type. For instance, the classical Weyl and Minkowski problems for a convex surface have been studied by H. Weyl, H. Lewy, and L. Nirenberg using the iteration method for the construction of solutions of certain non-linear equations of elliptic type (see [6]). Also, M. Kuranishi [3] constructed the effective complete family of deformations of complex analytic structures on a given compact complex manifold as the solution space of another non-linear equation of elliptic type; whereby the basic idea in his work is to apply an implicit function theorem to the non-linear operator of a Banach space, and to construct the bifurcation of solutions explicitly.
Stable vector bundles on an algebraic surface
Authors: Maruyama Masaki
Published: July 2016

Let X be a non-singular projective algebraic curve over an algebraically closed field k. D. Mumford introduced the notion of stable vector bundles on X as follows;

DEFINITION ([7]). A vector bundle E on X is stable if and only if for any non-trivial quotient bundle F of E,

where deg ( • ) denotes the degree of the first Chern class of a vector bundles and r( • ) denotes the rank of a vector bundle.
Stable vector bundles with numerically trivial Chern classes over a hyperelliptic surface
Authors: Umemura Hiroshi
Published: July 2016

In [17], Weil studied the space of representations of certain Fuchsian groups as a generalization of Jacobian variety. The theory of stable vector bundles over a curve developed by Mumford, Seshadri and others are the theory of unitary representations of Fuchsian groups. The moduli space of stable vector bundles over a curve is the space of the irreducible unitary representations of a Fuchsian group. The moduli space is studied in detail. Recently Mumford (unpubished) and Takemoto [12] introduced the notion of H-stable vector bundle over a non-singular projective algebraic surface. In this paper, we study the space of the irreducible unitary representations of the fundamental group of a hyperelliptic surface. Our view point is based on the theory of H-stable vector bundles of Takemoto [12] and [13]. We deal only with hyperelliptic surfaces. Our results should be generalized to the vector bundles over some other surfaces (See §3).
One-Valued Mappings of Groups into Fields
Authors: Masuda Katsuhiko
Published: July 2016

The aim of this article is to investigate algebraic nature of systems of one-valued mappings of given group into given field and to apply it to the theory of Galois algebras and duality of compact T0-groups. The results obtained in the following are those; factor systems of Galois algebras with finite Galois groups are defined without any restrictions on the orders of Galois groups and the coefficient fields, a necessary and sufficient condition for them to be associated with Galois fields is obtained, dualities of finite groups are obtained very simply without any restrictions for coefficient field of representations, and Tannaka’s duality of compact T0-groups is proved without the use of the compactness of Tannaka representation groups of representations of compact T- groups and the use of Kampen’s theorem.
On an Existence Lemma in Valuation Theory
Authors: Nagata Masayoshi , Nakayama Tadasi , Tuzuku Tosiro
Published: July 2016

Recently one of the writers used, in proving a theorem on the commutativity of certain division rings, the following lemma :

I. Let L be a field and K be its proper subfield. Except either when L is of characteristic p ≠ O and absolutely algebraic or ivhen L is algebraic and purely inseparable over K, there exists a pair of distinct (special exponential) valuations in L which coincide on K.

II. Let K be a field which is either of characteristic 0 or not absolutely algebraic, and L be its separable finite extension. There exist then infinitely many valutions in L which are of 1st degree over K.
On the triad Excision Theorem of Blakers and Massey
Authors: Araki Shôrô
Published: July 2016

The purpose of the present paper is to give a new proof to the triad excision theorem of Blakers and Massey [1], in case m≦2 and n≦2, by the aid of path spaces and in connection with a recent work of J. P. Serre [2].
Theory of Meromorphic Functions on an Open Riemann Surface with Null Boundary
Authors: Tsuji Masatsugu
Published: July 2016

In the former paper, I have developped a theory of meromorphic functions in a neighbourhood of a bounded closed set E of logarithmic capacity zero, by means of Evans’ potential fnnction u(z), which tends to ∞, when z tends to any point of E. It is not known, whether such a potential function exists on an open Riemann surface with null boundary, but by a substitute of Evans’ function. we shall develop the similar theory of meromorphic functions on an open Riemann surface with null boundary.
Some relations between differential geometric invariants and topological invariants of submanifolds
Authors: Chen Bang-Yen
Published: July 2016

Let M be an n-dimensional manifold immersed in an m-dimensional euclidean space Em and let ∇ and ∇̃ be the covariant differentiations of M and Em, respectively. Let X and Y be two tangent vector fields on M. Then the second fundamental form h is given by

(1.1) ∇̃XY = ∇XY + h(X,Y).
The ring of algebraic correspondences on a generic curve of genus g
Authors: Ikeda Yoshiaki
Published: July 2016

0. Let p be a prime number or zero and let g be a non-negative integer. Then there is a coarse moduli space Mg for complete non-singular irreducible curves of genus g defined over fields of characteristic p, which is an irreducible variety over the algebraic closure F̅p of the prime field Fp. (Especially, F0 is also denoted by Q as usual.) ([8], [2]). The curve corresponding to a generic point of Mg over F̅p is called a generic curve of genus g.
Perturbed billiard systems, I. The ergodicity of the motion of a particle in a compound central field
Authors: Kubo I.
Published: July 2016

The ergodicity of classical dynamical systems which appear really in the statistical mechanics was discussed by Ya. G. Sinai [9]. He announced that the dynamical system of particles with central potential of special type in a rectangular box is ergodic. However no proofs have been given yet. Sinai [11] has given a proof of the ergodicity of a simple one-particle model which is called a Sinai billiard system.
Some properties of complete intersections in “good” projective varieties
Authors: Robbiano Lorenzo
Published: July 2016

In [10] it was proved that, if X denotes a non singular surface which is a complete intersection in (k an algebraically closed field of characteristic 0) and C an irreducible curve on X, which is a set-theoretic complete intersection in X, then C is actually a complete intersection in X; the key point was to show that Pic (X) modulo the subgroup generated by the class of is torsion-free.
The three-separated-arc property of the modular function
Authors: Bagemihl Frederick
Published: July 2016

Let D be the open unit disk and Γ be the unit circle in the complex plane, and denote the Riemann sphere by Ω. If f(z) is a function defined on D with values belonging to Ω, if ζ ∈Γ, and if Λ is an arc at ζ then C∈(f, ζ) denotes the cluster set of f at ζ along Λ. If there exist three mutually exclusive arcs Λ1, Λ2, Λ3 at ζ such that
Congruences between cusp forms and linear representations of the Galois group
Authors: Koike Masao
Published: July 2016

Let f(z) be a cusp form of type (l,ε) on Γ0(N) which is a common eigenfunction of all Hecke operators. For such f(z), Deligne and Serre [1] proved that there exists a linear representation

such that the Artin L-function for p is equal to the L-function associated to f(z).
On p-adic properties of the Eichler-Selberg trace formula II
Authors: Koike M.
Published: July 2016

Let be the space of cusp forms of weight k with respect to SL(2, Z). Let p be a prime number and let Tk(p) be the Hecke operator of degree p acting on as a linear endomorphism. Put Hk(X) = det (I – Tk(p)X + pk-lX2I), where I is the identity operator on . Hk(X) is a polynomial with coefficients of rational integers, which is called the Hecke polynomial.
Sur quelques combinaisons linéaires exceptionnelles au sens de Nevanlinna, V.
Authors: Toda Nobushige
Published: July 2016

Soit un système transcendant dans le plan c’est-à-dire, les fonctions f0,...,fnsont entières sans zéros communs à toutes et
On certain examples of surfaces with pg = 0 Due to Burniat
Authors: Peters C. A. M.
Published: July 2016

Let Sbe a compact complex protective and smooth variety of dimc2, shortly a surface. We employ the following standard notations:

Os: structure sheaf of S.

Ks: the canonical bundle on S.
Non-degenerate real hypersurfaces in complex manifolds admitting large groups of pseudo-conformal transformations II
Authors: Yamaguchi Keizo
Published: July 2016

This is the continuation of our previous paper [3], and will complete, without homogeneity assumption, the classification of non-degenerate real hypersurfaces S of complex manifolds M for which the groups A(S) of pseudo-conformal transformations of S have either the largest dimension n2 + 2n or the second largest dimension.
C3-Actions and algebraic threefolds with ample tangent bundle
Authors: Mabuchi Toshiki
Published: July 2016

One of the most challenging problems in complex differential geometry is the following conjecture of Frankel [3].

(F-n) A compact Kaehler manifold M of dimension n with positive sectional (or more generally, positive holomorphic bisectional) curvature is biholomorphic to the complex projective space Pn(C).
Boundary Components of Riemann Surfaces
Authors: Ohtsuka Makoto
Published: July 2016

The boundary components of an abstract Riemann surface were defined by B. v. Kérékjértó [7] and utilized in the book [14] written by S. Stoïlow. It is the purpose of the present paper to investigate their images under conformal mapping and to solve the Dirichlet problem with boundary values distributed on them.
Baire Sets, Borel Sets and Some Typical Semi-Continuous Functions
Authors: Nagami Keiô
Published: July 2016

Recently Hing Tong [3], M. Katētov [4] and C. H. Dowker [2] have established two sorts of insertion theorems for semi-continuous functions defined on normal and countably paracompact normal spaces. The purpose of this paper is to give the insertion theorem for some typical semi-continuous functions defined on a T-space. The relations between Baire sets and Borel sets in some topological spaces are also studied.
On the module structure in a cyclic extension over a -adic number field
Authors: Miyata Yoshimasa
Published: July 2016

Let p be a prime. Let k be a -adic number field and be the ring of all integers of k. Let K/k be a cyclic totally ramified extension of degree pn with Galois group G. Clealy the ring of all integers of K is an [G]-module, and the purpose of this paper is to give a necessary and sufficient condition for the [G]-module to be indecomposable.
Distance functions and umbilic submanifolds of hyperbolic space
Authors: Cecil Thomas E. , Ryan Patrick J.
Published: July 2016

In 1972, Nomizu and Rodriguez [5] found the following characterization of the complete umbilic submanifolds of Euclidean space.

Theorem A. Let Mn, n ≥ 2, be a connected, complete Riemannian manifold isometrically immersed in a Euclidean space Em. Every Morse function of the form Lp has index 0 or n at all of its critical points if and only if Mnis embedded as a Euclidean n-subspace or a Euclidean n-sphere in Em.
Trace formula of certain Hecke operators for Γ0(qν)
Authors: Saito Hiroshi , Yamauchi Masatoshi
Published: July 2016

Let SK(Γo(qν)) be the space of cusp forms of weight K with respect to the congruence subgroup Γ0(qν), and SK(Γ0(qν)) its subspace of all new forms in SK(Γ0(qν)), where q is a prime such that q ≥ 3. Now for f ∈ SK(Γ(qν)), put Then it is known that W induces an automorphism of SK(Γ0(qν)). On the other hand, for the character χ of (Z/qZ)× of order 2, let δx denote the “twisting operator” with respect to χ which was defined in [15] by Shimura, namely, for .
A contribution to the theory of formal meromorphic functions
Authors: Faltings Gerd
Published: July 2016

In my paper [F3] I more or less explicitly conjectured that if A is a complete local integral domain with maximal ideal and if I = (t1, …, tn) is an ideal in A with n ≤ dim (A) – 2, then Spec (A/I) – is G3 in Spec (A) – . This will be proved in this paper.
Einstein hypersurfaces of Kählerian C-spaces
Authors: Sakane Yusuke , Takeuchi Masaru
Published: July 2016

A compact simply connected homogeneous complex manifold is called a C-space. A C-space is said to be kählerian if it carries a Kähler metric. It is known (Matsushima [7]) that a kählerian C-space has always an Einstein Kähler metric which is essentially unique.
On the nonwandering sets of diffeomorphisms of surfaces
Authors: Koike Tokihiko
Published: July 2016

Let M be a compact manifold without boundary. Let f: M → M be a C1 diffeomorphism. Then the nonwandering set Ω(f) is defined to be the closed invariant set consisting of x ∈ M such that for any neighborhood U of x, there exists an integer n ≠ 0 satisfying fn(U) ∩ U ≠ ø. In particular, the set Per (f) of all periodic points is included in Ω(f).
Extended f-orbits are approximated by orbits
Authors: Sawada Ken
Published: July 2016

Let f be a Cr-diffeomorphism, r ≦ 1, on a compact differentiable manifold M with dim M ≧ 2. In [9] F. Takens introduced the concept of extended f-orbits and conjectured the following.
Sur les sous-groupes algebriques primitifs du groupe de cremona a trois variables
Authors: Umemura Hiroshi
Published: July 2016

Au 19e siècle le terme de géométrie algébrique désignait exclusivement la géométrie birationnelle. Aujourd’hui on n’accepterait pas cette définition, parce que l’objet de la géométrie algébrique est celui des invariants biréguliers plutôt que birationnels. Quelle que soit la définition adoptée, il est intéressant de connaître la structure de groupes des automorphismes birationnels. Mais celle-ci est très peu connue (Mumford [10]). La question suivante a été posée depuis longtemps; déterminer à conjugaison près tous les sous-groupes algébriques connexes et maximaux du groupe de Cremona Crn. Le groupe Crn est, par définition, le groupe des automorphismes du corps des fonctions rationnelles à n indéterminées. Si n = 1. Cr1 coïncide avec le groupe des automorphismes de P1 Enriques a résolu ce problème pour n = 2 (Enriques [5]). On croit généralement (par exemple Godeaux [8]) que Enriques et Fano l’ont fait pour n = 3 (Enriques et Fano [6]). Après avoir collaboré avec Enriques, G. Fano a travaillé seul sur ce problème et il a laissé des résultats très intéressants dont la plupart des démonstrations ne semble pas rigoureuse. Demazure [4] a étudie les; sous-groupes algébriques de rang maximum n de Crn. Il a démontré qu’il y a une correspondence bijective entre les sous-groupes algébriques de rang maximum n de Crn et les systèmes d’Enriques. Puisque les derniers sont de nature combinatoire, c’est un dictionaire géométrique-combinatoire.
Cusp forms of weight 3/2
Authors: Kojima Hisashi
Published: July 2016

In this paper we deal with the problem (C) in § 4 of [4]. Let Ik be the Shimura mapping in [4] of Sk(4N, χ) into k-1(N′ χ2) (see p. 458). The problem (C) can be stated as follows: I3(f) is a cusp form if and only if ‹f, h› = 0 for all h ∈ U, where U is the vector space spanned by every theta series of S3(4N, χ) associated with some Dirichlet character.
Topologically stable homeomorphisms of the circle
Authors: Yano Koichi
Published: July 2016

In this paper, we study topologically stable homeomorphisms of the circle. Our results are the following:

Theorem 1. A homeomorphism of the circle is topologically stable if and only if it is topologically conjugate to some Morse-Smale diffeomorphism.

Theorem 2. There exists a homeomorphism of the circle which has the pseudo-orbit-tracing-property but is not topologically stable.
On the Cohen-Macaulayfication of certain Buchsbaum rings
Authors: Goto Shiro
Published: July 2016

Let A be a Noetherian local ring of dimension d and with maximal ideal m. Then A is called Buchsbaum if every system of parameters is a weak sequence. This is equivalent to the condition that, for every parameter ideal q, the difference is an invariant I(A) of A not depending on the choice of q. (See Section 2 for the detail.) The concept of Buchsbaum rings was introduced by Stückrad and Vogel [8], and the theory of Buchsbaum singularities is now developing (cf. [6], [7], [9], [10], and [12]).
On some types of geodesics on Riemannian manifolds
Authors: Kurogi Tetsunori
Published: July 2016

For a given Riemannian manifold M and its submanifold N, one can find various types of geodesies on M starting from any point of N and ending in any point of N. For example, geodesies which start perpendicularly from N and end perpendicularly in N are treated by many mathematicians. K. Grove has stated a condition in a general case for the existence of such a geodesic ([4]), where he has used the method of the infinite dimensional critical point theory. This method is very useful for the study of geodesies and many geometricians have used it successfully. It has two aspects: one is an existence theory and the other is a quantitative theory, which one can find, for instance, in the excellent theory for closed geodesies of W. Klingenberg ([1], [7]) and so on.
Annulation de groupes de classes réelles
Authors: Oriat Bernard
Published: July 2016

Il est bien connu que le groupe des classes relatives d’une extension abélienne du corps des rationnels est annulé par tout êlément entier de l’idéal de Stickelberger. Soit l un nombre premier impair. Nous montrons dans les pages qui suivent qu’un certain groupe de l-classes réelles associé à un caractère x d’ordre g et considéré comme -module est annulé par la valeur en 1 de la fonction L l-adique: ou bien par un multiple bien défini de cette valeur.
On functions which satisfy some differential inequalities on Riemannian manifolds
Authors: Motomiya Kanji
Published: July 2016

Most of the problems in differential geometry can be reduced to problems in differential equations and differential inequalities on Riemannian manifolds. Our main purpose of this paper is to study such differential inequalities on complete Riemannian manifolds. In [5], H. Omori proved a very important theorem. S. Y. Cheng and S. T. Yau gave a simplification and a generalization of it which was called the generalized maximum principle in [2] and [7], and many interesting applications in differential geometry in [2], [3], [7], and [8].
On Buchsbaum rings obtained by gluing
Authors: Goto Shiro
Published: July 2016

Let A be a Noetherian local ring with maximal ideal m. In 1973 J. Barshay [1] showed that, if A is a Cohen-Macaulay ring, then so is the Rees algebra R(q) = ⊕n≧0qn for every parameter ideal q of A (cf. p. 93, Corollary). Recently the author and Y. Shimoda [5] have proved that the Rees algebra R(q) is a Cohen-Macaulay ring for every parameter ideal q of A if and only if

(#) A is a Buchsbaum ring and for i ≠ 1, dim A.
Weakly normal varieties: The multicross singularity and some vanishing theorems on local cohomology
Authors: Leahy John V. , Vitulli Marie A.
Published: July 2016

The foundations for this paper were developed in [5], “Seminormal rings and weakly normal varieties”, where the historical framework and fundamental properties of weakly normal varieties were presented in detail. Here we devote our attention to the study of the multicross singularity and the role of local cohomology in the theory of weakly normal varieties.
Theb-functions and holonomy diagrams of irreducible regular prehomogeneous vector spaces
Authors: Kimura Tatsuo
Published: July 2016

The purpose of this paper is to investigate the micro-local structure and to calculate, by constructing the holonomy diagrams, theb-functions (See [2]) of irreducible regular prehomogeneous vector spaces (See [1]).
Projective summands in generators
Authors: Eisenbud David , Vasconcelos Wolmer , Wiegand Roger
Published: July 2016

An R-module M is a generator (of the category of modules) provided every module is a homomorphic image of a suitable direct sum of copies of M. Equivalently, some M(k) has R as a summand. Except in the last section, all rings are assumed to be commutative, Noetherian domains, and modules are usually finitely generated. In this context generators are exactly those modules that have non-zero free summands locally. Of course, generators can fail to have free summands (e.g., over Dedekind domains), and we ask whether they necessarily have non-zero projective summands. The answer is “yes” for rings of dimension 1, as we point out in § 3, and for the polynomial ring in one variable over a Dedekind domain. In § 1 we show that for 2-dimensional rings the answer is intimately connected with the structure of projective modules. Our main result in the positive direction, Theorem 1.3, grew out of the attempt, in conversations with T. Stafford, to understand the case R = k[x, y]. In § 2 we give examples of rings having generators with no projective summands. The last section contains miscellaneous observations, some of them on rings without chain conditions.
The central limit theorem for trigonometric series
Authors: Murai Takafumi
Published: July 2016

We denote by Z+ the semi-group of positive integers. For a subset E of Z+, we denote by |E| (≦ + ∞) its cardinal number and by E(n) the intersection of E and an interval [1, n) (n ≧ 1). We shall identify a subset E of Z+ with a sequence, arranging elements of E according to their order.
A note on universally catenary rings
Authors: Greco Silvio
Published: July 2016

The following two related problems in Commutative Algebra are certainly very popular:

1. Study the permanence of properties from a ring A to an idealadic completion of A; and

2. Study the lifting of properties from A/I to A where A is a ring which is complete and separated in the I-adic topology.
Rees rings and form rings of almost complete intersections
Authors: Brodmann Markus
Published: July 2016

Recently different authors have studied the conormal modules I/I2 of almost complete intersections in local Gorenstein rings (c. t. Aoyama [1], Herzog [8], Kunz [13], Matsuoka [16]). An essential tool in these papers is the theory of canonical modules and the fact that these modules are easy to handle in the case of almost complete intersections.
On the maximal connected algebraic subgroups of the Cremona group I
Authors: Umemura Hiroshi
Published: July 2016

This paper is a continuation of the two preceding papers [12], [13] where the classification of the de Jonquières type subgroups in the Cremona group of 3 variables is promised. However the classification of such subgroups is postponed until the article in preparation “On the maximal connected algebraic subgroups of the Cremona group II”. The purpose of this paper is to establish a general method to study algebraic subgroups in the Cremona group of n variables and to illustrate how it works and leads to the classification of Enriques (Theorem (2.25)) when applied to the 2 variable case. This method gives us also the classification of the maximal connected algebraic subgroups of the Cremona group of 3 variables.
On existence of tolerance stable diffeomorphisms
Authors: Ikegami Gikō
Published: July 2016

We consider a compact smooth manifold M. Diff1 (M) denotes the space of C1-diffeomorphisms of M onto itself with the usual C1-topology. In the research of the qualitative theory of dynamical systems there is a desire to find a concept of stability of geometric global structure of orbits such that this stable systems are dense in the space of dynamical systems on M. Structural stability does not satisfy the density condition in Diff1 (M). Tolerance stability (see Section 2 for definition) is a candidate for the density property [7, p. 294]. Concerning tolerance stability there are researches as [6], [7], [8], and [2].
Parallel submanifolds of complex space forms II
Authors: Naitoh Hiroo
Published: July 2016

This is a continuation of Part I, which appeared in this journal.

In the previous paper I we have defined the following notions: orthogonal Jordan triple system (OJTS), orthogonal symmetric graded Lie algebra (OSGLA), orthogonal Jordan algebra (OJA), Hermitian symmetric graded Lie algebra (HSGLA). And we have shown that equivalent classes of OJTS naturally correspond to equivalent classes of OSGLA and through this correspondence we have naturally constructed HSGLA’s from the OJTS’s associated with OJA’s with unity.
Threefolds with negative Kodaira dimension and positive irregularity
Authors: Beltrametti Mauro , Francia Paolo
Published: July 2016

The purpose of this paper is to study threefolds X, with negative Kodaira dimension k(X) and positive irregularity q(X), defined over the complex field C.
The corona problem on finitely sheeted covering surfaces
Authors: Nakai Mitsuru
Published: July 2016

The purpose of this paper is to show that the corona theorem is valid on any unbounded finitely sheeted covering surface if and only if the corona theorem is valid on its base surface.
On stochastic relaxed control for partially observed diffusions
Authors: Fleming W. H. , Nisio M.
Published: July 2016

In this paper we are concerned with stochastic relaxed control problems of the following kind. Let X(t), t ≥ 0, denote the state of a process being controlled, Y(t), t ≥ 0, the observation process and p(t, ·) a relaxed control, that is a process with values probability measures on the control region Г. The state and observation processes are governed by stochastic differential equations

and

where B and W are independent Brownian motions with values in Rn and Rm respectively, (put m = 1 for simplicity).
Fourier coefficients of Siegel cusp forms of degree two
Authors: Kitaoka Yoshiyuki
Published: July 2016

Our purpose is to prove the following

Theorem. Let k be an even integer ≥ 6. Let

be a Siegel cusp form of degree two, weight k. Then we have
On maximal spacelike hypersurfaces in a Lorentzian manifold
Authors: Nishikawa Seiki
Published: July 2016

We prove a Bernstein-type property for maximal spacelike hypersurfaces in a Lorentzian manifold.
The Hausdorff dimension of general Sierpiński carpets
Authors: McMullen Curt
Published: July 2016

In this note we determine the Hausdorff dimension of a family of planar sets which are generalizations of the classical Cantor set.
Completely operator-selfdecomposable distributions and operator-stable distributions
Authors: Sato Ken-Iti , Yamazato Makoto
Published: July 2016

Urbanik introduces in [16] and [17] the classes Lm and L∞ of distributions on R1 and finds relations with stable distributions. Kumar-Schreiber [6] and Thu [14] extend some of the results to distributions on Banach spaces. Sato [7] gives alternative definitions of the classes Lm and L∞ and studies their properties on Rd. Earlier Sharpe [12] began investigation of operator-stable distributions and, subsequently, Urbanik [15] considered the operator version of the class L on Rd. Jurek [3] generalizes some of Sato’s results [7] to the classes associated with one-parameter groups of linear operators in Banach spaces. Analogues of Urbanik’s classes Lm (or L∞) in the operator case are called multiply (or completely) operator-selfdecomposable. They are studied in relation with processes of Ornstein-Uhlenbeck type or with stochastic integrals based on processes with homogeneous independent increments (Wolfe [18], [19], Jurek-Vervaat [5], Jurek [2], [4], and Sato-Yamazato [9], [10]). The purpose of the present paper is to continue the preceding papers, to give explicit characterizations of completely operator-selfdecomposable distributions and operator-stable distributions on Rd, and to establish relations between the two classes. For this purpose we explore the connection of the structures of these classes with the Jordan decomposition of a basic operator Q.
Quotient complete intersections of affine spaces by finite linear groups
Authors: Nakajima Haruhisa
Published: July 2016

Let G be a finite subgroup of GLn(C) acting naturally on an affine space Cn of dimension n over the complex number field C and denote by Cn/G the quotient variety of Cn under this action of G. The purpose of this paper is to determine G completely such that Cn/G is a complete intersection (abbrev. CI.) i.e. its coordinate ring is a C.I. when n > 10. Our main result is (5.1). Since the subgroup N generated by all pseudo-reflections in G is a normal subgroup of G and Cn/G is obtained as the quotient variety of without loss of generality, we may assume that G is a subgroup of SLn(C) (cf. [6, 16, 24, 25]).
On 3-dimensional terminal singularities
Authors: Mori Shigefumi
Published: July 2016

Canonical and terminal singularities are introduced by M. Reid [5], [6]. He proved that 3-dimensional terminal singularities are cyclic quotient of smooth points or cDV points [6].
On the dimension of the vector space C[θm]4
Authors: Manni Riccardo Salvati
Published: July 2016

Let τ denote a point of the Siegel upper-half space be a (column) vector in Cg and m a vector with m′ resp. m″ in Zg as its first resp. second entry vectors, then the series

in which , represents an holomorphic function on the product and it is called the theta function of characteristic m.
Mathieu group M24 and modular forms
Authors: Koike Masao
Published: July 2016

In [6], Mason reported some connections between sporadic simple group M24 and certain cusp forms which appear in the ‘denominator’ of Thompson series assigned to Fisher-Griess’s group F1. In this paper, we discuss the ‘numerator’ of these Thompson series.
Picard principle for finite densities
Authors: Nakai Mitsuru
Published: July 2016

A nonnegative locally Holder continuous function P(z) on 0<|z |≤1 will be referred to as a density on Ω 0 < |z | < 1 with singularity at δ : z = 0, removable or genuine. A density P on Ω is said to be finite if it is integrable over Ω :

(1) ∫ Ω P(z)dxdy < ∞.
On the Dimension of Modules and Algebras, VIII. Dimension of Tensor Products
Authors: Eilenberg Samuel , Rosenberg Alex , Zelinsky Daniel
Published: July 2016

The questions concerning the dimension of the tensor product of two K-algebras have turned out to be surprisingly difficult. In this paper we follow a method using spectral sequences (§§1-3) which in some concrete cases yields complete results (§§4-5). In particular, complete results are obtained when r is a ring of matrices, triangular matrices, polynomials or rational functions, so that in the first three cases is respectively the ring of matrices, triangular matrices or polynomials with coefficients in the arbitrary algebra A.
Capacité des Ensembles Produits
Authors: Ohtsuka Makoto
Published: July 2016

SiXest un ensemble mesurable au sens de Lebesgue dans un espace euclidienEnetYest un ensemble mesurable au sens de Lebesgue dans un autre espace euclidienEm, alorsX× Y est mesurable dansEn+m=Enx Emet sa mesure est égale au produit de la mesure deXet celle deY. Mais il n’existe pas de telle relation simple ni pour la capacité d’ordre général ni pour la mesure de Hausdorff de dimension générale. Dans le présent mémoire nous essayons d’évaluer la capacité des ensembles produits au moyen de la capacité ou de la mesure de Hausdorff des ensembles composants.
Über die Ordnung Gewisser Untergruppen von GL(q, p)
Authors: Nakamura Kirio
Published: July 2016

Es ist wohlbekannt (Burnside [1]), dass(Sp1(GL(m, p)) < pm für ein belie-biges m und für eine von p(≠2)verschiedene ungerade Primzahl p1.
On the extension of L2 holomorphic functions V-Effects of generalization
Authors: Ohsawa Takeo
Published: July 2016

A general extension theorem for L2 holomorphic bundle-valued top forms is formulated. Although its proof is based on a principle similar to Ohsawa-Takegoshi’s extension theorem, it explains previous L2 extendability results systematically and bridges extension theory and division theory.
Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces
Authors: Shimada Ichiro , Zhang De-Qi
Published: July 2016

We present a complete list of extremal elliptic K3 surfaces (Theorem 1.1). As an application, we give a sufficient condition for the topological fundamental group of complement to an ADE-configuration of smooth rational curves on a K3 surface to be trivial (Proposition 4.1 and Theorem 4.3).
Weak Bloch property for discrete magnetic Schrödinger operators
Authors: Higuchi Yusuke , Shirai Tomoyuki
Published: July 2016

For a magnetic Schröodinger operator on a graph, which is a generalization of classical Harper operator, we study some spectral properties: the Bloch property and the behaviour of the bottom of the spectrum with respect to magnetic fields. We also show some examples which have interesting properties.
On stabilization of partial differential equations by noise
Authors: Caraballo Tomás , Liu Kai , Mao Xuerong
Published: July 2016

Some results on stabilization of (deterministic and stochastic) partial differential equations are established. In particular, some stability criteria from Chow [4] and Haussmann [6] are improved and subsequently applied to certain situations, on which the original criteria commonly do not work, to ensure almost sure exponential stability. This paper also extends to infinite dimension some results due to Mao [9] on stabilization of differential equations in finite dimension.
The norm of a Ree group
Authors: Medts Tom De , Weiss Richard M.
Published: July 2016

We give an explicit construction of the Ree groups of typeG2as groups acting on mixed Moufang hexagons together with detailed proofs of the basic properties of these groups contained in the two fundamental papers of Tits on this subject (see [7] and [8]). We also give a short proof that the norm of a Ree group is anisotropic.
Birational classification of curves on rational surfaces
Authors: Calabri Alberto , Ciliberto Ciro
Published: July 2016

In this paper we consider the birational classification of pairs (S, ℒ), withSa rational surface andℒa linear system onS. We give a classification theorem for such pairs, and we determine, for each irreducible plane curveB, itsCremona minimalmodels, that is, those plane curves which are equivalent toBvia a Cremona transformation and have minimal degree under this condition.