bluuebunny/crossref_metadata_2025 huggingface dataset:
Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density
Authors: Rozovskii B. L. , Shimizu A.
Published: July 2016

In this paper, we shall discuss the smoothness of solutions of stochastic evolution equations, which has been investigated in N. V. Krylov and B. L. Rozovskii [2] [3], to establish the existence of a filtering transition density.
Counting the number of basic invariants for G ⊂ GL(2, k) Acting on k[X, Y]
Authors: Watanabe Junzo
Published: July 2016

The notations used in this paper without explicit mention are listed below. Here R is a positively graded Noetherian ring, a a homogeneous ideal of R, and f, g, …, h are homogeneous elements of R.
Définition des pseudogroupes infinitésimaux de Lie intransitifs—Théorème fondamental de réalisation en dimension deux
Authors: Quê Ngô van , Tho Vo van
Published: July 2016

Soit G un groupe de Lie opérant de manière localement effective sur une variété différentiable M. Pour tout sous-groupe à un paramètre {gt, t ∈ R} de G, on a le champ de vecteurs associé X dit de Killing sur M:

Le faisceau correspondant de tous les champs de vecteurs de Killing du groupe de transformations G sera noté par θ; il est démontré [7] qu’il existe un ouvert ^ partout dense dans M, dit de régularité tel que:
Definability theorem for the intuitionistic predicate logic with equality
Authors: Mizutani Chiharu
Published: July 2016

Svenonius’ definability theorem and its generalizations to the infinitary logic Lω1ω or to a second order logic with countable conjunctions and disjunctions have been studied by Kochen [1], Motohashi [2], [3] or Harnik and Makkai [4], independently. In this paper, we consider a (Svenonius-type) definability theorem for the intuitionistic predicate logic IL with equality.
Julia directions of entire functions of smooth growth
Authors: Yoshida H.
Published: July 2016

Let f(z) be entire i.e. analytic in the finite whole plane Z. The order of f(z) is defined as

where A ray χ(θ) = {z = r·eiθ : 0 < r < + ∞} is called a Julia direction of f(z) if, in any open sector containing the ray, f(z) takes all values of Z, with at most one finite exceptional value, infinitely often.
Irreducibility of some unitary representations of the Poincaré group with respect to the Poincaré subsemigroup, III
Authors: Kaneta Hitoshi
Published: July 2016

The aim of this paper is to prove that irreducible unitary representations of the Poincaré group P = R4 × SSL(2, C) are reducible as the representations of the Poincaré subsemigroup P+ = V+ × SSL(2, C) with
On the Lp bound for degenerate elliptic operators with two variables in the ill posed problem
Authors: Hasesaka Nobuo , Hayasida Kazuya
Published: July 2016

Let Ω be an open set in the upper half plane {y > 0}, whose boundary is denoted by ∂Ω. Let ∂Ω contain an open segment Γ lying on the x-axis.

We consider the following system of first order degenerating on y = 0:

where kj, μj are real constants and bjk are in L∞(Ω), further kj are non-negative integers.
On certain complex analytic cobordism between subvarieties realizing Chern classes of bundles
Authors: Morimoto Hiroshi
Published: July 2016

Cobordism invariants have been applied to both real and complex categories. For example, the index of 4k-dimensional manifolds was treated by Hirzebruch for the generalization of the Riemann-Roch theorem [3]. He also considered, in relation with this, virtual genus or virtual characteristics. But many invariants, such as virtual characteristics, have their origin in complex analytic category. In view of this, we consider certain complex analytic cobordism, i.e., quasilinear cobordism among quasilinear subvarieties in complex manifolds (see for the definition of quasilinear structure [4].) Quasilinear body has very simple type of singularities, as well as its quasilinear boundaries. Therefore, the theory of quasilinear cobordism can be reduced, through σ-processes, to that of non-singular cobordism theory.
Exceptionally ramified meromorphic functions with a non-enumerable set of essential singularities
Authors: Kurokawa Toshiko
Published: July 2016

In the complex function theory, Picard’s Great Theorem plays an essential and important role. It is well-known as generalizations of this theorem that in a neighborhood of an isolated essential singularity, a meromorphic function cannot be exceptionally ramified (see W. Gross [2]) and that even it cannot be normal (see O. Lehto and K. I. Virtanen [7]). We are therefore interested in the behaviour of meromorphic functions with non-isolated essential singularities as well as in generalizations of the Gross’ result. Several approaches in this direction have been made by G. af Hällström [3], S. Kametani [4], K. Noshiro [13], K. Matsumoto [8], [9], [10], [11], [12], S. Toppila [15], etc..
Pseudo-reflection group actions on local rings
Authors: Avramov Luchezar L.
Published: July 2016

In a classical paper [C] Chevalley considered the invariants of a finite group H ⊂ GLk(S1) generated by pseudo-reflections, acting on the graded polynomial ring S = k[X1,…,Xn] over a field k of characteristic zero. He proved that S is free as a graded SH-module, hence SH is a graded polynomial ring (Theorem A), and that the natural representation of H in is equivalent to the regular representation (Theorem B). On the other hand, a theorem of Shephard and Todd shows that when SH is a polynomial ring, the (finite) group H is generated by pseudo-reflections. These results have been extended by Bourbaki [Bo2] to fields whose characteristic may be positive, but does not divide the order |H| of the group.
The Bergman metric on a Thullen domain
Authors: Azukawa Kazuo , Suzuki Masaaki
Published: July 2016

In this paper we shall study the holomorphic sectional curvature of the Bergman metric on a domain
A note on modular forms mod p
Authors: Koike Masao
Published: July 2016

In this paper we shall study relations among the spaces of modular forms mod p attached to Sk(Np, ψχ) and Sk,(N, ψ) by using certain identities between dimensions of these spaces.
Parallel submanifolds of complex space forms I
Authors: Naitoh Hiroo
Published: July 2016

Complete parallel submanifolds of a real space form of constant sectional curvature k have been completely classified by Ferus [3] when k ≧ 0, and by Takeuchi [19] when k < 0. A complex space form is by definition a 2n-dimensional simply connected Hermitian symmetric space of constant holomorphic sectional curvature c and will be denoted by (c).
Topological stability of solenoidal automorphisms
Authors: Aoki Nobuo
Published: July 2016

In [10] A. Morimoto proved that every topologically stable homeomorphism of a compact manifold M has the pseudo-orbit tracing property in the case dim (M) ≥ 2. Further, in studying relation between the topological stability and other stability of diffeomorphisms, he showed the following

Theorem A. Let Rr be the r-dimensional vector group and φ be a group automorphism of Rr.
Central extensions and Schur’s multiplicators of Galois groups
Authors: Miyake Katsuya
Published: July 2016

When he developed the theory of central extensions of absolute abelian fields in [1], Fröhlich clearly pointed out a role of Schur’s multiplicators of the Galois groups in algebraic number theory. Another role of them was to be well known when the gaps between the everywhere local norms and the global norms of finite Galois extensions were cohomologically described by Tate [10]. The relation of two roles was investigated by Furuta [2], Shirai [9], Heider [3] and others.
On higher covariant derivatives of the curvature tensors of Kählerian C-spaces
Authors: Takagi Ryoichi
Published: July 2016

A compact simply connected complex homogeneous manifold is said briefly a C-space, which was completely classified by H. C. Wang [12]. A C-space is called to be Kählerian if it admits a Kählerian metric such that a group of isometries acts transitively on it. Hermitian symmetric spaces of compact type are typical examples of a Kählerian C-space. Let M be an arbitrary Kählerian C-space and R its curvature tensor. M. Itoh [6] expressed R in the language of Lie algebra and investigated various properties of R. In this paper, we study higher covariant derivatives of R.
On the fundamental inequality for degenerate systems of entire functions
Authors: Toda Nobushige
Published: July 2016

Let f═(f0, f1, …, fn) (n ≧ 1) be a transcendental system in ∣z∣ < ∞. That is, f0, f1,…, fn are entire functions without common zeros and the characteristic function of f defined by H.
On the diophantine equationx2−py2= ± 4qand the class number of real subfields of a cyclotomic field
Authors: Yokoi Hideo
Published: July 2016

LetH(m)denote the class number of the fieldwhereQis the rational number field and ζmis a primitive m-th root of unity for a positive rational integerm.
On the imaginary quadratic Doi-Naganuma lifting of modular forms of arbitrary level
Authors: Friedberg Solomon
Published: July 2016

In this paper, we use the theta function method [10] to give explicit Doi-Naganuma type maps associated to an imaginary quadratic field K, lifting cusp forms on any congruence subgroup of SL(2, Z) to forms on SL(2, C) automorphic with respect to an appropriate arithmetic discrete subgroup. The case of class number one, and form modular with respect to group Γ0(D) and character χ0 = (–D/*), where –D is the discriminant of K has been treated by Asai [1]. In order to complete his discussion, we must first introduce a more general theta function associated to an indefinite quadratic form (here of type (3, 1)), which we regard as a specialization of a symplectic theta function (see also [4]).
On positive vector superfunctions of elliptic systems
Authors: Hayasida Kazuya , Ikeda Yoshiaki
Published: July 2016

Let Ω be a bounded domain in Rn with coordinates x = (x1, …, xn) such that Ω contains the origin. We consider the elliptic operators

where are real valued and in C2(Ω).
On the Gorensteinness of Rees and form rings of almost complete intersections
Authors: Goto Shiro , Shimoda Yasuhiro
Published: July 2016

Let A be a Noetherian local ring and p a prime ideal in A. Let

and call them, respectively, the Rees ring and the form ring of p. The purpose of this paper is to clarify, provided p is an almost complete intersection in A (cf. (2.1) for definition), when the rings R(p) and G(p) are Gorenstein.
Remarks on lifting of Cohen-Macaulay property
Authors: Herrmann Manfred , Ikeda Shin
Published: July 2016

Let (R, m) be a local noetherian ring and I a proper ideal in R. Let (I) be the Rees-ring ⊕n≥0 In with respect to I. In this note we describe conditions for I and R in order that the Cohen-Macaulay property (C-M for short) of R/I can be lifted to R and (I), see Propositions 1.2, 1.3. and 1.4.
A note on local densities of quadratic forms
Authors: Kitaoka Yoshiyuki
Published: July 2016

Let L, M be regular quadratic lattices over Zp. The local density αp(L, M) is an important invariant in the theory of representation of quadratic forms and they appear naturally in Fourier coefficients of Eisenstein series. In spite of the importance we knew little except the case when either L = M or rk L = 1 and M is unimodular. Evaluating them is a laborious task.
On deformations of Hopf maps and hypergeometric series
Authors: Ono Takashi
Published: July 2016

Let Rn denote the Euclidean space of dimension n ≧> 1 with the standard inner product ‹x, y› and the norm Nx = ‹x, x›. We shall denote by dωn-i the volume element of the unit sphere normalized so that the volume of Sn-1 is 1.
On McKay’s conjecture
Authors: Koike Masao
Published: July 2016

Let η(z) be Dedekind’s η-function. For any set of integer g = (k1 …, Ks), k1 ≥ k2 ≥ … ≥ks ≥ 1, put . In this paper, we shall prove McKay’s conjecture which gives some combinatorial conditions about ki on which ηg(z) is a primitive cusp form. As to McKay’s conjecture, we refer [5].
On the topological structure of affinely connected manifolds
Authors: Higa Tatsuo
Published: July 2016

The purpose of the present paper is to investigate the relationship between the topological structure and differential geometric objects for affinely connected manifolds.

Let M be a compact, connected and oriented Riemannian manifold, Pr(M) the vector space of all parallel r-forms on M and br(M) the r-th Betti number of M.
A decomposition theorem on differential polynomials of theta functions
Authors: Morikawa Hisasi
Published: July 2016

Let τ = (τij) be a symmetric complex g = g matrix with the positive definite imaginary part. A theta function of level n means an entire function f(z) in g complex variables z = (zl …, zg) satisfying the difference relations:
On degrees and genera of curves on smooth quartic surfaces in P3
Authors: Mori Shigefumi
Published: July 2016

Our result is motivated by the results [GP] of Gruson and Peskin on characterization of the pair of degree d and genus g of a non-singular curve in P3. In the last step, they construct the required curve C on a singular quartic surface when Here we consider curves on smooth quartic surfaces.
Conformal invariance of white noise
Authors: Hida Takeyuki , Lee Ke-Seung , Lee Sheu-San
Published: July 2016

The remarkable link between the structure of the white noise and that of the infinite dimensional rotation group has been exemplified by various approaches in probability theory and harmonic analysis. Such a link naturally becomes more intricate as the dimension of the time-parameter space of the white noise increases. One of the powerful method to illustrate this situation is to observe the structure of certain subgroups of the infinite dimensional rotation group that come from the diffeomorphisms of the time-parameter space, that is the time change. Indeed, those subgroups would shed light on the probabilistic meanings hidden behind the usual formal observations. Moreover, the subgroups often describe the way of dependency for Gaussian random fields formed from the white noise as the time-parameter runs over the basic parameter space.

The main purpose of this note is to introduce finite dimensional subgroups of the infinite dimensional rotation group that have important probabilistic meanings and to discuss their roles in probability theory. In particular, we shall see that the conformal invariance of white noise can be described in terms of the conformal group which is a finite dimensional Lie subgroup of the infinite dimensional rotation group.
Higher reciprocity law, modular forms of weight 1 and elliptic curves
Authors: Koike Masao
Published: July 2016

In this paper, we study higher reciprocity law of irreducible polynomials f(x) over Q of degree 3, especially, its close connection with elliptic curves rational over Q and cusp forms of weight 1. These topics were already studied separately in a special example by Chowla-Cowles [1] and Hiramatsu [2]. Here we bring these objects into unity.
Relative invariants and b-functions of prehomogeneous vector spaces
Authors: Teranishi Yasuo
Published: July 2016

Let G be a connected linear algebraic group, p a rational representation of G on a finite-dimensional vector space V, all defined over C.
Some results on harmonic analysis on compact quotients of heisenberg groups
Authors: Morikawa Hisasi
Published: July 2016

Heisenberg group H2g+1(R) of dimension 2g + 1 is a real nilpotent group defined on R × Rg × Rg by the law of composition

which is isomorphic to the unipotent matrix group
On the central class field mod of Galois extensions of an algebraic number field
Authors: Shirai Susumu
Published: July 2016

Letkbe the rational number field,K/kbe an Abelian extension defined modwhose degree is some power of a primel, and letbe the module ofKbelonging toin the sense of Fröhlich [1, p. 239].
Some examples of stochastically stable homeomorphisms
Authors: Sasaki Takeshi
Published: July 2016

Recently A. Morimoto [1] has proved the Takens conjecture in the tolerance stability by using the notion of pseudo-orbits and the stochastic stability. He also characterized group automorphisms of a torus to be stochastically stable and clarified the relations to other stabilities.

In this paper we shall give the condition for spherical or projective linear transformations to be stochastically stable.
On the decay of the local energy for wave equations with a moving obstacle
Authors: Tamura Hideo
Published: July 2016

Recently the decay of the local energy for wave equations with a moving obstacle has been studied by Cooper [1] and Cooper and Strauss [2] etc. In their works it has been assumed that the obstacle is uniformly bounded in time t and that the origin is contained in for all t > 0 and is star-shaped with respect to the origin. (The second condition has been assumed implicitly in [2] (see Assumption (B), [2]).)
An example on canonical isomorphism
Authors: Nakai Mitsuru
Published: July 2016

A nonnegative locally Hölder continuous second order differential P = P(z)dxdy (z = x + iy) on a Riemann surface R is referred to as a density on R. A density P is said to be finite if P is integrable over R, i.e.

(1) ∫ R P(z)dxdy < ∞.
Innovation processes associated with stationary Gaussian processes with application to the problem of prediction
Authors: Okabe Yasunori
Published: July 2016

As a continuation of the previous paper [7], we shall consider in this paper the problem of prediction given bounded intervals and obtain integral representations of predictors and prediction errors. For that purpose we shall introduce innovation processes well matched with bounded intervals. We follow the notation and terminology in [6].
Some properties of ordinal diagrams
Authors: Yasugi Mariko
Published: July 2016

The theory of ordinal diagrams has been a most powerful means for consistency proofs of some systems of second order arithmetic. The last existing result in this line is the consistency proofs of the systems with the provably -comprehension axiom and the -comprehension axiom respectively (cf. [6]). In order to pursue the consistency problem further, one needs investigate the theory of ordinal diagrams in two directions—refinement and strengthening of the theory.

For this purpose we have begun to search for some properties concerning ordinal diagrams and some variations of the theory of ordinal diagrams. The reader is requested to refer to §26 of [7] for the basic knowledge of ordinal diagrams.
A Remark on (π, n)-Type CW-Complexes
Authors: Shiraiwa Kenichi
Published: July 2016

Let X be a space whose i-th homotopy group πi(X)vanishes for every i ≧ 0 except i = n ≧ 1, and whose n-th homotopy group is isomorphic to a group π. Then it is well known that the polyhedral homotopy type of X is completely determined by π and n. We call such a space a (π, n)-type space. Also it is well known that the minimal complex of the singular complex of a (π, n)-type space is isomorphic to the complex K(π, n)defined by S. Eilenberg and S. MacLane [1]. We know also that for any n ≧ 1 and any group π(abelian if n > 1) there exists a (π, n)-type space (See [6]).
The Conformal Mapping of Simply Connected Riemann Surfaces II
Authors: Heins Maurice
Published: July 2016

On reviewing recently the proof which I gave for the Riemann mapping theorem for simply-connected Riemann surfaces several years ago [2], I observed that the argument which I used could be so modified that the assumption of a countable base could be completely eliminated. The problem of treating the Riemann mapping theorem without this assumption has been current for some time. The object of the present note is to give an account of a solution of this question. Of course, the classical theorem of Radó permits us to dispense with an attack on the Riemann mapping theorem which does not appeal to the countable base assumption. In this connection, we recall that Nevanlinna [4] has given a straightforward potential-theoretic treatment of the Radó theorem in which neither the Riemann mapping theorem (nor the notion of a universal covering) enters as they do in Radó’s proof. Nevertheless, a certain technical interest attaches to a direct treatment of the Riemann mapping theorem without the countable base assumption. An immediate byproduct of such a treatment is a simple proof of the Radó theorem which invokes the notion of a universal covering but in a manner different from that of Radó’s proof. Indeed, it suffices to note that a manifold has a countable base if the domain of a universal covering does.
On Some Properties of Binary Relations
Authors: Ono Katuzi
Published: July 2016

Some important notions in the theory of binary relations such as the relative product of two relations and the converse of a relation are defined in Whitehead and Russell’s “Principia mathematica” ([1]). McKinsey ([2]) and Tarski ([3]) gave their systems of postulates for the calculus of relations. Ore studied on equivalence relations ([4]) and Riguet on closures (fermeture) of relations ([5] and [6]), and they obtained remarkable results on the structure of these relations. The purpose of this paper is to examine the relative properties of some relations to each other, whose notions are closely related to the notions given by Riguet.
Analytic discs in symplectic spaces
Authors: Baracco Luca , Zampieri Giuseppe
Published: July 2016

We develop some symplectic techniques to control the behavior under symplectic transformation of analytic discs A of X = ℂn tangent to a real generic submanifold R and contained in a wedge with edge R.

We show that if A* is a lift of A to T* X and if χ is a symplectic transformation between neighborhoods of po and qo, then A is orthogonal to po if and only if Ã:= πχA* is orthogonal to qo. Also we give the (real) canonical form of the couples of hypersurfaces of ℝ2n ⋍ ℂn whose conormal bundles have clean intersection. This generalizes [10] to general dimension of intersection.

Combining this result with the quantized action on sheaves of the “tuboidal” symplectic transformation, we show the following: If R, S are submanifolds of X with R ⊂ S and then the conditions can be characterized as opposite inclusions for the couple of closed half-spaces with conormal bundles

In §3 we give some partial applications of the above result to the analytic hypoellipticity of CR hyperfunctions on higher codimensional manifolds by the aid of discs (cf. [2], [3] as for the case of hypersurfaces).
The Calogero-Moser partition for G(m, d, n)
Authors: Bellamy Gwyn
Published: July 2016

We show that it is possible to deduce the Calogero-Moser partition of the irreducible representations of the complex reflection groups G(m,d, n) from the corresponding partition for G(m,1,n). This confirms, in the case W = G(m,d,n), a conjecture of Gordon and Martino relating the Calogero-Moser partition to Rouquier families for the corresponding cyclotomic Hecke algebra.
Alternative polarizations of Borel fixed ideals
Authors: Yanagawa Kohji
Published: July 2016

For a monomial idealIof a polynomial ringS, apolarizationofIis a square-free monomial idealJof a larger polynomial ringsuch thatS/Iis a quotient of/Jby a (linear) regular sequence. We show that a Borel fixed ideal admits a nonstandard polarization. For example, while the usual polarization sendsours sends it tox1y2y3Using this idea, we recover/refine the results onsquare-free operationin the shifting theory of simplicial complexes. The present paper generalizes a result of Nagel and Reiner, although our approach is very different.
Functions with finite Dirichlet sum of orderpand quasi-monomorphisms of infinite graphs
Authors: Hattori Tae , Kasue Atsushi
Published: July 2016

In this paper, we study some potential theoretic properties of connected infinite networks and then investigate the space ofp-Dirichlet finite functions on connected infinite graphs, via quasi-monomorphisms. A main result shows that if a connected infinite graph of bounded degrees possesses a quasi-monomorphism into the hyperbolic space form of dimensionnand it is notp-parabolic forp > n -1, then it admits a lot ofp-harmonic functions with finite Dirichlet sum of orderp.
A generalization of the Levinson-Massera’s equalities
Authors: Shiraiwa Kenichi
Published: July 2016

In his study of non-linear differential equations of the second order, N. Levinson [3] defined the dissipative systems (D-systems) which arise in many important cases in practice. To a dissipative system a transformation T: R2 → R2 called the Poincaré transformation is associated. Levinson used the Poincaré transformation in the qualitative study of dissipative systems, and he [3] and Massera [5] obtained certain equalities between the number of subharmonic solutions of a dissipative systems under suitable conditions. We call these the Levinson-Massera’s equalities.
Onp-adicL-functions and cyclotomic fields. II
Authors: Greenberg Ralph
Published: July 2016

Letpbe a prime. If one adjoins toQallpn-th roots of unity forn= 1,2,3, …, then the resulting field will contain a unique subfieldQ∞such thatQ∞is a Galois extension ofQwith Gal (Q∞/Q)Zp, the additive group ofp-adic integers. We will denote Gal (Q∞/Q) byΓ. In a previous paper [6], we discussed a conjecture relatingp-adicL-functions to certain arithmetically defined representation spaces forΓ. Now by using some results of Iwasawa, one can reformulate that conjecture in terms of certain other representation spaces forΓ. This new conjecture, which we believe may be more susceptible to generalization, will be stated below.
Bounds of modes and unimodal processes with independent increments
Authors: Sato Ken-Iti
Published: July 2016

A probability measure μ is called unimodal if there is a point α such that the distribution function of μ is convex on (− ∞, α) and concave on (α, ∞). The point α is called a mode of μ. When μ is unimodal, the mode of μ is not always unique; the set of modes is a one point set or a closed interval. If μ is a unimodal distribution with finite variance, Johnson and Rogers [6] give a bound

where m and v are mean and variance of μ (see also [11]).
Construction and Characterization of Galois Algebras with Given Galois Group
Authors: Nakayama Tadasi
Published: July 2016

Recently H. Hasse has given an interesting theory of Galois algebras, which generalizes the well known theory of Kummer fields; an algebra over a field Ω is called a Galois algebra with Galois group G when possesses G as a group of automorphisms and is (G, Ω)-operator-isomorphic to the group ring G(Ω) of G over Ω. On assuming that the characteristic of Ω does not divide the order of G and that absolutely irreducible representations of G lie in Ω, Hasse constructs certain Ω-basis of , called factor basis, in accord with Wedderburn decomposition of the group ring and shows that a characterization of is given by a certain matrix factor system which defines the multiplication between different parts of the factor basis belonging to different characters of G. Now the present work is to free the theory from the restriction on the characteristic. We can indeed embrace the case of non-semisimple modular group ring G(Ω).
Distortion Theorems in the Theory of Schlicht Functions
Authors: Nagura Shohei , Komatu Yusaku
Published: July 2016

Let be the family of analytic functions F(z) which are regular and schlicht in the circle E: |z| < 1 and normalized at the origin such that F(0) = 0 and F′(0) = 1. Let be the subfamily of consisting of all functions, each of which possesses, as boundary of its image-domain., a closed Jordan curve which is supposed to be regular analytic. Then is everywhere dense in the original family . Hence, by an approximation theorem of Carathéodory on the kernel of sequence of domains, we may restrict ourselves within , so far as we concern the estimation of continuous functionals on .
On Conditions of Differentiability of Locally Compact Groups
Authors: Kuranishi Masatake
Published: July 2016

A formulation of the differentiability of the product function of a locally compact group at the identity may be given in the following way: In a sufficiently small euclidean neighborhood of the identity product satisfies the condition:

where M(λ) is a function such that M(λ) → 0 as λ → 0, From this we can deduce easily

.
Note on p-Groups
Authors: Itô Noboru
Published: July 2016

In connection with the class field theory a problem concerning p-groups was proposed by W. Magnus: Is there any infinite tower of p-groups G1, G2,…, Gn, Gn+1,…such that G1 is abelian and each Gn is isomorphic to Gn+1/θn(Gn+1), θn(Gn+1) ≠ 1, n = 1,2,…, where θn(Gn+1) denotes the n-th commutator subgroup of Gn+1? The present note is, firstly, to construct indeed such a tower, to settle the problem, and also to refine an inequality for p-groups of P. Hall.
On the Imbedding Problem of Normal Algebraic Number Fields
Authors: Inaba Eizi
Published: July 2016

LetGandHbe finite groups. If a groupG̅has an invariant subgroupH̅, which is isomorphic withH, such that the factor groupG̅/H̅is isomorphic with G. then we say thatG̅is an extension ofHby G. Now letGbe the Galois group of a normal extensionKover an algebraic number fieldkof finite degree. The imbedding problem concerns us with the question, under what conditionsKcan be imbedded in a normal extensionLoverksuch that the Galois group ofLoverkis isomorphic withG̅andKcorresponds toH̅. Brauer connected this problem with the structure of algebras overk, whose splitting fields are isomorphic withK.
On the Existence of the Resolvent Kernel for Elliptic Differential Operator in a Compact Riemann Space
Authors: Yosida Kôsaku
Published: July 2016

We consider the differential operator

in an n-dimensional (n≧2), orientiable, compact Riemann space R with the metric ds2 = gij(x)dxidxj. Here bij(x) is a contravariant tensor such that the quadratic form and ai(x) changes, by the coordininates transformation x → x̅, as follows:

.
On the Dimension of Paracompact Hausdorff Spaces
Authors: Nagami Keiô
Published: July 2016

This short note gives the generalized sum theorem for Lebesgue dimension of paracompact Hausdorff spaces. Our theorem, though it is a generalization of Mr. Morita’s sum theorem for fully normal spaces [3, Theorem 3. 2] which is essentially based on his generalized sum theorem for normal spaces [3, Theorem 3.1], is obtained by very brief arguments, using only the usual sum theorem for normal spaces.
Paracompactness and Strong Screenability
Authors: Nagami Keiô
Published: July 2016

Throughout this paper, a space means a T1-space. A space is called fully normal if every open covering of it has a Δ-refinement , that is, an open covering for which the stars (x, ) form a covering which refines . A space is called paracompact if every open covering of it has a locally finite (= neighborhood finite) open covering which refines . It is well known that paracompactness is identical with full normality in a Hausdorff space ([3], [7]).
On the Dimension of Modules and Algebras, II: (Frobenius Algebras and Quasi-Frobenius Rings)
Authors: Eilenberg Samuel , Nakayama Tadasi
Published: July 2016

In this paper we study Frobenius algebras and quasi-Frobenius rings with particular emphasis on their cohomological dimensions. For definitions of these cohomological dimensions we refer the reader to Cartan-Eilenberg [3] or Eilenberg [4].
A Remark on Finitely Generated Modules, II
Authors: Nakayama Tadasi
Published: July 2016

The following small remark on the relationship of the (quasi-)regularity and the zero-divisor property may be more or less known but does not seem to the writer to have been explicitly stated in a literature.
Studies on Riemannian Homogeneous Spaces
Authors: Nomizu Katsumi
Published: July 2016

The purpose of the present paper is to give the details of the results announced in the C. R. notes [7], [8] and [9].

In I which corresponds to [7], we shall develop a method for the study of affine transformations of a Riemannian manifold and prove Lemma 5 which is fundamental for the results in I and II. This part of our work has been motivated by a result of K. Yano [12] stating that the largest connected group of affine transformations of a compact orientable Riemannian manifold consists of isometries. Our method will have further applications to some other problems concerning or involving the connected group of isometries of a Riemannian manifold (for example, [10]).
Reduction Theorem for Connections and its Application to the Problem of Isotropy and Holonomy Groups of a Riemannian Manifold
Authors: Nomizu Katsumi
Published: July 2016

The present paper constitutes, together with [13], a continuation of the study of differential geometry of homogeneous spaces which we started in [11]. Our main result states that if the homogeneous holonomy group of a complete Riemannian manifold is contained in the linear isotropy group at each point, then the Riemannian manifold is symmetric. The converse is of course one of the well known properties of a Riemannian symmetric space [4]. Besides the results already sketched in [12], we add a few applications of the main theorem.
On the Dimension of Modules and Algebras (III): Global Dimension
Authors: Auslander Maurice
Published: July 2016

Let Λ be a ring with unit. If A is a left Λ-module, the dimension of A (notation: 1.dimΛA) is defined to be the least integer n for which there exists an exact sequence

0 → Xn → … → X0 → A → 0

where the left Λ-modules X0, …, Xn are projective. If no such sequence exists for any n, then 1. dimAA = ∞. The left global dimension of Λ is

1. gl. dim Λ = sup 1. dimAA

where A ranges over all left Λ-modules, The condition 1. dimA A < n is equivalent with (A, C) = 0 for all left Λ-modules C. The condition 1.gl. dim Λ < n is equivalent with = 0. Similar definitions and theorems hold for right Λ-modules.
On Exceptional Values of a Meromorphic Function
Authors: Ohtsuka Makoto
Published: July 2016

M. Brelot [1] has shown that if u(z) is subharmonic in an open set D in the z-plane with boundary C and is bounded from above in a neighborhood of a boundary point z0, which is contained in a set E ⊂ C of inner harmonic measure zero with respect to D, and such that z0 is a regular point for Dirichlet problem in D, then

(1) .
On Invariant Connections over a Principal Fibre Bundle
Authors: Wang Hsien-Chung
Published: July 2016

The invariant affine connection over a coset space G/J of a Lie group G have been discussed by various authors. Recently, Nomizu [8] gave a systematic study of this problem when J is reductible in G. Among other results, he established a 1-1 correspondence between the invariant affine connections and certain multilinear mappings, and calculated the torsion and curvature. For canonical affine connection of the second kind, the holonomy group was also given.
On the Groups of Cobordism Ωk
Authors: Adachi Masahisa
Published: July 2016

In the papers [11] and [18] Rohlin and Thom have introduced an equivalence relation into the set of compact orientable (not necessarily connected) differentiable manifolds, which, roughly speaking, is described in the following manner: two differentiable manifolds are equivalent (cobordantes), when they together form the boundary of a bounded differentiable manifold. The equivalence classes can be added and multiplied in a natural way and form a graded algebra Ω relative to the addition, the multiplication and the dimension of manifolds. The precise structures of the groups of cobordism Ωk of dimension k are not known thoroughly. Thom [18] has determined the free part of Ω and also calculated explicitly Ωk for 0 ≦ k ≦ 7.
Strongly Regular Extensions of Rings
Authors: Faith Carl
Published: July 2016

As defined by Arens and Kaplansky [2] a ring A is strongly regular (s.r.) in case to each a∊ A there corresponds x = xa
∊A depending on a such that a
2
x = a. In the present article a ring A is defined to be a s.r. extension of a subring B in case each a>∊A satisfies a
2
x-a∊B with x = xa
∊A. S.r. rings are, then, s.r. extensions of each subring. A ring A which is a s.r. extension of the center has been called a ξ-ring (see Utumi [13], Drazin [3], Martindale [11], and their bibliographies).
R-Sequences and Homological Dimension
Authors: Kaplansky Irving
Published: July 2016

The motivation for the results in this note comes from a theorem of Macaulay. Let f
1, …, fn
be elements of a polynomial ring R over a field, and let I be the ideal they generate. Assume I

R and rank (I) = n. Then the theorem of Lasker and Macaulay asserts that I is unmixed (all prime ideals belonging to I have rank n). Macaulay [1, p. 51] proved further that any power of I is unmixed.
Classes of Equations of the Type y2 = x3 + k Having No Rational Solutions
Authors: Edgar Hugh M.
Published: July 2016

The equation y2 = x3 + k, k an integer, has been discussed by many authors. Mordell [1] has found many classes of k values for which the equation has no integral solutions. Fueter [2], Mordell [3] and Chang [4] have found classes of k values for which the equation has no rational solutions. The following two theorems exhibit two more sets of conditions which give rise to classes of k values for which the corresponding equations have no rational solutions.
Equicontinuity on Harmonic Spaces
Authors: Constantinescu Corneliu
Published: July 2016

G. Mokobodzki proved [5] that on any harmonic space with countable basis satisfying the axioms 1, 2, T+, K0 [2] [1] any equally bounded set of harmonic functions is equicontinuous. P. Loeb and B. Walsh showed [4] that the same property holds on a harmonic space without countable basis, if Brelot’s axiom 3 is fulfilled. The aim of this paper is to generalize these results to a harmonic space X satisfying only the axioms 1, 20, K1, [2] [1] where 20 is a weakened form of axiom 2. As a corollary we get: if any point of X possesses two open neighbourhoods U, V such that the set of harmonic functions on U separates the points of U∩V, then X has locally a countable basis.
Note on the Uniqueness Proprety of Weak Solutions of Parabolic Equations
Authors: Kuroda Tadashi
Published: July 2016

Aronson proved, in his paper [1], the existence and the uniqueness property of weak solutions of the initial boundary value problem for parabolic equations of second order with measurable coefficients. On the uniqueness of solutions of the Cauchy problem for such equations he also gave some interesting results in [2].
Regular Tsuji Functions with Infinitely Many Julia Points
Authors: Hayman W. K.
Published: July 2016

Let D denote the unit disk | z | < 1, and C the unit circle | z | = 1. Corresponding to any function f meromorphic in D we denote by f* the spherical derivative
On Mean Distortion for Analytic Functions with Positive Real Part in a Circle
Authors: Komatu Yûsaku
Published: July 2016

Let be the class of analytic functions Ф(z) which are regular and of positive real part in the unit circle | z | <1 and normalized by Ф(0) = 1. Several distortion theorems have been obtained on various functionals in this class. In a previous paper [4] we have dealt with mean distortion which generalizes a classical theorem of Rogosinski [6].
Planar Coverings of Closed Riemann Surfaces
Authors: Tamura Jiro
Published: July 2016

Several years ago, K. Oikawa, my colleague, investigated the properties of Schottky coverings of closed Riemann surfaces, leaving an interesting problem as open [3]:

Does exist a Schottky covering between the basic surface and a given planar covering?
Continua Which are Curvilinear Cluster Sets
Authors: Lappan Peter
Published: July 2016

Let D be the unit disk | z | < 1 and let f be a complex-valued function continuous in D. The cluster set C(f, eiθ) of f at eiθ is defined by
On the Continuity of Stationary Gaussian Processes
Authors: Nisio Makiko
Published: July 2016

Let us consider a stochastically continuous, separable and measurable stationary Gaussian process X = {X(t), − ∞ < t < ∞} with mean zero and with the covariance function p(t) = EX(t + s)X(s). The conditions for continuity of paths have been studied by many authors from various viewpoints. For example, Dudley [3] studied from the viewpoint of ε-entropy and Kahane [5] showed the necessary and sufficient condition in some special case, using the rather neat method of Fourier series.
On the module structure of the ring of all integers of a p-adic number field
Authors: Miyata Yoshimasa
Published: July 2016

Let k be a p-adic number field and o be the ring of all integers of k. Let K/k be a cyclic ramified extension of prime degree p with Galois group G. Then the ring of all integers of K is o[G]-module. The purpose of this paper is to give a necessary and sufficient condition for o[G]-modale to be indecomposable.
A theorem of Matsushima
Authors: Umemura Hiroshi
Published: July 2016

In [7], Matsushima studied the vector bundles over a complex torus. One of his main theorems is: A vector bundle over a complex torus has a connection if and only if it is homogeneous (Theorem (2.3)). The aim of this paper is to prove the characteristic p > 0 version of this theorem. However in the characteristic p > 0 case, for any vector bundle E over a scheme defined over a field k with char, k = p, the pull back F*E of E by the Frobenius endomorphism F has a connection. Hence we have to replace the connection by the stratification (cf. (2.1.1)). Our theorem states: Let A be an abelian variety whose p-rank is equal to the dimension of A. Then a vector bundle over A has a stratification if and only if it is homogeneous (Theorem (2.5)).
Addendum: Π-principal hereditary orders (Nagoya Math. J. 32 (1968), 41–65)
Authors: Williamson Susan
Published: July 2016

Let R denote a complete discrete rank one valuation ring of unequal characteristic, and let p denote the characteristic of the residue class field R̅ of R. Consider the integral closure S of R in a finite Galois extension K of the quotient field k of R. Recall (see Prop. 1.1 of [3]) that the inertia group G0 of K over k is a semi-direct product G0 = J × Gp, where J is a cyclic group of order relatively prime to p and Gp is a normal p-subgroup of G.
On certain abelian varieties obtained from new forms of weight 2 on Γ0(34) and Γ0(35)
Authors: Koike Masao
Published: July 2016

Let N be a positive integer and let Γ0(N) be the subgroup of SL(2, Z) defined by all matrices with c ≡ 0 (mod N). Let S2(Γ0(N)) be the space of holomorphic cusp forms of weight 2 with respect to Γ0(N) and let be the “essential part” of S2(Γ0(N)), which is defined in [1].
Symmetric ladders
Authors: Conca Aldo
Published: July 2016

In this paper we define and study ladder determinantal rings of a symmetric matrix of indeterminates. We show that they are Cohen-Macaulay domains. We give a combinatorial characterization of their h-vectors and we compute the a-invariant of the classical determinantal rings of a symmetric matrix of indeterminates.
Un raffinement du théorème de Golod-Safarevic
Authors: Maire Christian
Published: July 2016

Soientkun corps de nombres,pun nombre premier, etLlap-tour de Hilbert dek; G= Gal(L/k). Dans ce papier, on se propose de donner un raffinement du critère de Golod-Safarevic appliqué àG, construit en filtrant le groupe de nombres Λ = {x∈k×/(x) =}. Ce raffinement permettra alors de montrer qu’un corps quadratique réel dont le groupe des classes contient un sous-groupe de la forme (4, 4, 4, 4), possède une 2-tour de Hilbert infinie.
On the classification theorem for CR mappings
Authors: Hayashimoto Atsushi
Published: July 2016

Let f: M → M′ be a real analytic CR mapping between hyper-surfaces with f(p) = q, where p ∈ M and q ∈ M′. In this paper, the relation between the type at p and the one at q is considered. As a corollary of the type condition theorem (Theorem 1.1), a classification theorem, which states that under certain type condition, any real analytic CR mapping as above is constant, is proved.
Fano 4-Folds with scroll structure
Authors: Langer Adrian
Published: July 2016

We classify smooth Fano 4-folds with second betti number b2 = 2, possesing adjunction theoretic scroll structure. These manifolds occur to be projectivisations of coherent sheaves over Fano manifolds. The paper deals mainly with projectivisations of non-locally free rank 2 Fano sheaves over Fano 3-folds with b2 = 1, using Mori theory. By the way, we classify nef and big rank 2 bundles over P2 with the first Chern class (3).
On the determinism of the distributions of multiple Markov non-Gaussian symmetric stable processes
Authors: Kojo Katsuya
Published: July 2016

Consider a non-Gaussian SαS process X = {X(t); t ∈ T} which is expressed as a canonical representation , and is continuous in probability. If X is n-ple Markov, then X has determinism of dimension n + 1. That is, any SαS process having the same (n + l)-dimensional distributions with X is identical in law with X.
Pesin’s entropy formula for endomorphisms
Authors: Liu Pei-Dong
Published: July 2016

In this paper we prove Pesin’s entropy formula for general C2 (or C1+α) (non-invertible) endomorphisms of a compact manifold preserving a smooth measure.
Representations and interpolations of harmonic Bergman functions on half-spaces
Authors: Choe Boo Rim , Yi Heungsu
Published: July 2016

On the setting of the half-space of the euclidean n-space, we prove representation theorems and interpolation theorems for harmonic Bergman functions in a constructive way. We also consider the harmonic (little) Bloch spaces as limiting spaces. Our results show that well-known phenomena for holomorphic cases continue to hold. Our proofs of representation theorems also yield a uniqueness theorem for harmonic Bergman functions. As an application of interpolation theorems, we give a distance estimate to the harmonic little Bloch space. In the course of the proofs, pseudohyperbolic balls are used as substitutes for Bergman metric balls in the holomorphic case.
On the Gauss mean-value formula for class number
Authors: Chamizo Fernando , Iwaniec Henryk
Published: July 2016

In his masterworkDisquisitiones Arithmeticae, Gauss stated an approximate formula for the average of the class number for negative discriminants. In this paper we improve the known estimates for the error term in Gauss approximate formula. Namely, our result can be written asfor every ∊ > 0, whereH(−n) is, in modern notation,h(−4n). We also consider the average ofh(−n) itself obtaining the same type of result.

Proving this formula we transform firstly the problem in a lattice point problem (as probably Gauss did) and we use a functional equation due to Shintani and Dirichlet class number formula to express the error term as a sum of character and exponential sums that can be estimated with techniques introduced in a previous work on the sphere problem.
The blowup of solutions for 3-D axisymmetric compressible Euler equations
Authors: Yin Huicheng , Qiu Qingjiu
Published: July 2016

In this paper, for three dimensional compressible Euler equations with small perturbed initial data which are axisymmetric, we prove that the classical solutions have to blow up in finite time and give a complete asymptotic expansion of lifespan.
On the average of central values of symmetric square L-functions in weight aspect
Authors: Kohnen Winfried , Sengupta Jyoti
Published: July 2016

It is proved that the central values of symmetric square L-functions of normalized Hecke eigenforms for the full modular group on average satisfy an analogue of the Lindelöf hypothesis in weight aspect, under the assumption that these values are non-negative.
Dirichlet series and automorphic functions associated to a quadratic form
Authors: Peter Manfred
Published: July 2016

Starting from the reciprocity law for Gaussian sums attached to an integral quadratic form we prove functional equations for a new kind of Dirichlet series in two variables. For special values of one variable they are of Hecke type with respect to the other variable. With Weil’s converse theorem we derive automorphic functions which generalize Siegel’s genus invariant and the automorphic functions of Cohen and Zagier.
Galois Sections in Absolute Anabelian Geometry
Authors: Mochizuki Shinichi
Published: July 2016

We show that isomorphisms between arithmetic fundamental groups of hyperbolic curves over p-adic local fields preserve the decomposition groups of all closed points (respectively, closed points arising from torsion points of the underlying elliptic curve), whenever the hyperbolic curves in question are isogenous to hyperbolic curves of genus zero defined over a number field (respectively, are once-punctured elliptic curves [which are not necessarily defined over a number field]). We also show that, under certain conditions, such isomorphisms preserve certain canonical “integral structures” at the cusps [i.e., points at infinity] of the hyperbolic curve.