bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Studies on Kaehlerian Homogeneous Spaces
Authors: Hano Jun-Ichi , Matsushima Yozô
Published: July 2016

The present paper is devoted to the study of differential geometry of Kaehlerian homogeneous spaces. In section 1 we deal with the canonical decomposition of a simply connected complete Kaehlerian space and that of its largest connected group of automorphisms. We know that a simply connected complete Riemannian space V is the product of Riemannian spaces V0, V1, …, Vn, where V0 is a Euclidean space and V1, …,Vn are not locally flat and their homogeneous holonomy groups are irreducible [2]. Moreover, if V is homogeneous, so are all Vk [10]. We shall show that if V is Kaehlerian space with real analytic metric (resp. Kaehlerian homogeneous space), each factor Vk is also Kaehlerian (resp. Kaehlerian homogeneous) and that V is the product of V0, V1, …, Vn as Kaehlerian space. We call this decomposition the de Rham decomposition of the Kaehlerian space V. Although this result is supposedly known, there is no published proof as yet. Using this decomposition theorem we shall show that the largest connected group of automorphisms of a simply connected complete Kaehlerian space with real analytic metric is the direct product of those of the factors of the de Rham decomposition. In the Riemannian case this result has be been established in [3] by one of the authors of the present paper.
Canonical Connections and Pontrjagin Classes
Authors: Kobayashi Shoshichi
Published: July 2016

In the previous paper [7], we have studied the relationship between the Riemannian connection of an n-dimensional Riemannian space M imbedded into the (n + k)-dimensional Euclidean space Rn+k and the canonical connection in the bundle Pn, k = O(n + k)/{l} Х O(k) over the Grassmann manifold Mn, k = O(n + k)/O(n) Х O(k).

In the first half of the present paper, the relationship between the canonical connections in bundles and the invariant Riemannian connection on Mn, k will be discussed. We obtain the holonomy groups of these canonical connections.
On Automorphisms of A Kählerian Structure
Authors: Kobayashi Shoshichi , Nomizu Katsumi
Published: July 2016

Is every isometry, or more generally, every affine transformation of a Kählerian manifold a complex analytic transformation? The answer is certainly negative in the case of a complex Euclidean space. This question has been recently studied by Lichnerowicz [8] and Schouten-Yano [11] from the infinitesimal point of view; they have found some conditions in order that every infinitesimal motion of a Kählerian manifold preserve the complex structure. (As a matter of fact, [11] has dealt with the case of a pseudo-Kählerian manifold, which does not differ essentially from a Kählerian manifold as far as the question at hand is concerned.)

In the present paper, we generalize their results by a different approach. In order to explain our main idea, we shall first give a few definitions (1 and 2) and state our main results (3). The proofs are given in the subsequent sections.
Capacité d’Ensembles de Cantor Généralisés
Authors: Ohtsuka Makoto
Published: July 2016

D’abord nous définissons les ensembles de Cantor généralisés. Soient k1, k2, … des nombres entiers supérieurs à 1 et soient p1, p2, … des nombres finis quelconques également supérieurs à 1. On pose lq=l/(kqpq). Soit I un intervalle de longueur d > 0. On enlève de I (kq — l) intervalles de même longueur tels qu’il reste kq intervalles de même longueur lqd. On appelle cette opération la q-opération appliquée à I. On commence par appliquer l’1-opération à [0,1], on applique la 2-opération à chacun des intervalles qui restent, puis on applique la 3-opération à chacun des intervalles qui restent, et ainsi de suite. On appellera l’ensemble limite restant un ensemble de Cantor généralisé dans E1 et le notera F = F(kq, pq). Notre définition dans En = {(x1, …, xn)}, l’espace euclidien à n dimensions (n ≧ 2), est la suivante: Soit un ensemble de Cantor généralisé défini sur l’axe de xj; nous appellerons l’ensemble produit F = F1 × … × Fn un ensemble de Cantor généralisé dans En (n ≧ 2). II sera appelé symétrique si F1 = … =Fn.
On Frobenius Extensions I.
Authors: Nakayama Tadasi , Tsuzuku Tosiro
Published: July 2016

As a generalization of the notion of Frobenius algebras over a field Kasch [103 introduced that of Frobenius extensions of a ring. The present writers [13] recently freed one of Kasch’s main theorems from its rather strong S-ring assumption of the ground ring. However, even with the removal of the S-ring assumption of the ground ring the notion does not seem general enough, and we wish, in the present paper and its sequel, to develope the theory upon the basis of a more general notion of Frobenius extensions. Thus, we replace the free module property of the extension by the projective module property (according to a general tendency in algebra), which has been done in fact in case of Frobenius algebras over a commutative ring in a previous work by Eilenberg and one of the writers [4], and, further, take automorphisms of the ground ring into the definition of Frobenius extensions (which seems quite natural particularly in case of non-commutative rings). To such generalized notion of Frobenius extensions we may extend many of Kasch’s theorems, including those which are immediate extensions of classical theorems for Frobenius algebras and those which are essentially new, as the above alluded endomorphism ring theorem. Also homological properties of Frobenius extensions, as were developed in Hirata’s [6] recent paper in succession to Eilenberg-Nakayama [4], can be extended to our present generalized case; we shall also exceed [4], [6] somewhat in considering injective and weak dimensions.
A Generalization of the Ring of Triangular Matrices
Authors: Chase Stephen U.
Published: July 2016

Let R be a ring with unit, and e be an idem potent in R such that (1 - e)Re = 0. In this note we shall explore the relationships between homological properties of R and those of its subring eRe.

Examples of such rings are abundant, the most common being perhaps the ring R of all two-by-two upper triangular matrices over a field, where—
Examples of Weak Boundary Components
Authors: Akaza Tohru , Oikawa Kôtaro
Published: July 2016

Let D be a plane domain and Γ be a component of the boundary of D consisting of a single point. According to Sario [5] we shall call Γ a weak boundary component of D if its image under any conformal mapping of D consists of a single point. A weak boundary component has been introduced by Grötzsch [2], who called it “vollkommen punktförmig”. If Γ is not weak we shall say that it is unstable (Sario [5]). We know that the weakness depends merely on the configuration of D in a neighborhood of Γ (see [4], p. 274).
Corresponding Group and Module Sequences
Authors: Crowell R. H.
Published: July 2016

For convenience we consider throughout an arbitrary but fixed multiplicative group H. The integral group ring of H is denoted by ZH, and the homomorphism ε: ZH→Z is always the trivializer, or unit augmentation, defined by εh = 1 for all h ∈ H.
On Herstein’s Theorem Concerning Three Fields
Authors: Faith Carl
Published: July 2016

Let L > K ≧ Φ, LK, be three fields such that: (1) L/K is not purely inseparable, and (2) L/Φ is transcendental. Then Herstein’s theorem [2] asserts the existence of u ∈ L such that f(u) ∉ K for every non-constant polynomial f(X) ∈ Φ[X].
On Frobenius Extensions II
Authors: Nakayama Tadasi , Tsuzuku Tosiro
Published: July 2016

In Part I we introduced the notion of 2. Frobenius extensions of a ring, as a generalization of Kasch’s [10] Frobenius extensions and hence of classical Frobenius algebras. We proved, in I, bilinear (or sesqui-linear, rather, to follow Bourbaki’s terminology) form and scalar product characterizations of Frobenius extensions in such extended sense, generalizing Kasch’s and classical case, and then studied homological dimensions in them, generalizing and refining the results in Eilenberg-Nakayama [4] and Hirata [6]. Dual bases were considered in case of quasi-free (2.) Frobenius extensions Also the case of a semi-primary or S-ring ground ring was studied.
A Theorem on an Analytic Mapping of Riemann Surfaces
Authors: Kurita Minoru
Published: July 2016

Recently S. S. Chern [1] intended an aproach to some problems about analytic mappings of Riemann surfaces from a view-point of differential geometry. In that line we treat here orders of circular points of analytic mappings. The author expresses his thanks to Prof. K. Noshiro for his kind advices.
On Some Criteria for a Set to be of Class N
Authors: Suita Nobuyuki
Published: July 2016

Let D be a plane domain containing the point at infinity and E its complementary closed set. As to a sufficient condition for a compact set E to be of class N, Pfluger-Mori’s criterion is well-known (Pfluger [10], Mori [6]). Various relations between the conditions of this type and the Hausdorff measure of the set E have been investigated recently by Kuroda and Ozawa (Kuroda [5], Ozawa and Kuroda [8], Ozawa [7]). For example they showed that Pfluger-Mori’s condition implies that the set E is of one dimensional measure zero under some additional conditions (cf. [7], [8]). In the present paper we shall give an alternative proof of Pfluger-Mori’s criterion and another criterion using analytic module and, further, prove some criteria for the set E to be of one dimensional measure zero.
A Correction to My Paper “On the Non-Commutativity of Pontrjagin Rings mod 3 of Some Compact Exceptional Groups”
Authors: Araki Shôrô
Published: July 2016

This note is a correction of an error of the author’s paper mentioned in the title. (The reference [1]). The proof of the Prop. 6 of [1], Chap. II, p. 247, is an error. And the propositions and formulas in pp. 247-249 of [1] depending on this Prop. 6 must be corrected. All notations are referred to [1].
Spherical submanifolds which are of 2-type via the second standard immersion of the sphere
Authors: Barros Manuel , Chen Bang-Yen
Published: July 2016

Let Sm(r) be an m-sphere of constant sectional curvature 1/r2 and M an n-dimensional compact minimal submanifold of Sm(r). If Sm(r) is imbedded in Em+1 by its first standard imbedding, then, by a well-known result of Takahashi [11], the Euclidean coordinate functions restricted to M are eigenfunctions of Δ on M with the same eigenvalue n/r2. Moreover, the center of mass of M in Em+1 coincides with the center of the hypersphere Sm(r) in Em+1. Thus, M is mass-symmetric in Sm(r) ⊂ Em+\ Consequently, we see that if one wants to study the spectral geometry of a submanifold of Sm(r), it is natural to immerse Sm(r) by its k-th standard immersion, in particular, by its second standard immersion.
Congruences of Ankeny-Artin-Chowla type for pure quartic and sectic fields
Authors: Kamei Masato
Published: July 2016

Ankeny, Artin and Chowla [1] showed that there are congruences between class numbers of real quadratic fields and generalized Bernoulli numbers. Recently, Ito [3] has extended their results to the case of pure cubic fields using generalized Hurwitz numbers of Lichtenbaum [4]. In his paper, he suggested that similar results would be obtained for pure quartic and sectic fields. In this paper, we carry out this by following his idea. To give a congruence in an exact form, we need an idea due to Matthews [5]. As the argument in the sectic case is quite parallel to that in the quartic case, we shall discuss the former case briefly in the last two sections.
On Segre products of affine semigroup rings
Authors: Hoa Lê Tuân
Published: July 2016

Let N denote the set of non-negative integers. An affine semigroup is a finitely generated submonoid S of the additive monoid Nm for some positive integer m. Let k[S] denote the semigroup ring of S over a field k. Then one can identify k[S] with the subring of a polynomial ring k[t1, …, tm] generated by the monomials .
Projective varieties and rings of Thetanullwerte
Authors: Manni Riccardo Salvati
Published: July 2016

Let r denote an even positive integer, m an element of Q2g such that r·m ≡ 0 mod 1 and ϑm the holomorphic function on the Siegel upper-half space Hg defined by

(1) ,

in which e(t) stands for exp and m′ and m″ are the first and the second entry vector of m. Let Θg(r) denote the graded ring generated over C by such Thetanullwerte; then it is a well known fact that the integral closure of Θg(r) is the ring of all modular forms relative to Igusa’s congruence subgroup Γg(r2, 2r2) cf. [6]. We shall denote this ring by A(Γg(r2, 2r2)).
A measure valued diffusion process describing an n locus model incorporating gene conversion
Authors: Shimizu Akinobu
Published: July 2016

Probability measure valued diffusion processes have been discussed by many authors, in connection with population genetics. Most papers studying probability measure valued diffusions are mainly concerned with the ones describing single locus models. In this paper, we will discuss a measure valued diffusion describing an n locus model. Random sampling, mutation and gene conversion, a kind of interaction between loci, which was introduced and investigated by T. Ohta in [5], [6], will be taken into consideration.
Hitting time distributions of single points for 1-dimensional generalized diffusion processes
Authors: Yamazato Makoto
Published: July 2016

In this paper, we will characterize the class of (conditional) hitting time distributions of single points of one dimensional generalized diffusion processes and give their tail behaviors in terms of speed measures of the generalized diffusion processes.
A note on ray class fields of global fields
Authors: Halter-Koch Franz
Published: July 2016

The notion of a ray class field, which is fundamental in Takagi’s class field theory, has no immediate analogon in the function field case. The reason for this lies in the lacking of a distinguished maximal order. In this paper I overcome this difficulty by a relative version of the notion of ray class fields to be defined for every holomorphy ring of the field. The prototype for this new notion is M. Rosen’s definition of a Hilbert class field for function fields [6].
Leopoldt kernels and central extensions of algebraic number fields
Authors: Miyake Katsuya
Published: July 2016

Let k be an algebraic number field of finite degree, and p be a fixed rational prime. We denote the set of all the non-Archimedian prime divisors of k by S0(k) and the set of all the real Archimedian ones by (k). Put and S = S0 ∪ S∞, and define a subgroup of the unit group (k) of k by
Holomorphic mapping into algebraic varieties of general type
Authors: Hu Peichu
Published: July 2016

We will study holomorphic mappings

from a connected complex manifold M of dimension m to a projective algebraic manifold N of dimension n. Assume first that N is of general type, i.e.

where KN→N is the canonical bundle of N. If KN is positive, then N is of general type.
On the class number and unit index of simplest quartic fields
Authors: Lazarus Andrew J.
Published: July 2016

The term “simplest” field has been used to describe certain totally real, cyclic number fields of degrees 2, 3, 4, 5, 6, and 8. For each of these degrees, the fields are defined by a one-parameter family of polynomials with constant term ±1. The regulator of these “simplest” fields is small in an asymptotic sense: in consequence, the class number of these fields tends to be large.
A generalization of Hubert’s theorem 94
Authors: Suzuki Hiroshi
Published: July 2016

In this paper we shall prove the following theorem conjectured by Miyake in [3] (see also Jaulent [2]).

THEOREM. Let k be a finite algebraic number field and K be an unramified abelian extension of k, then all ideals belonging to at least [K: k] ideal classes of k become principal in K.

Since the capitulation homomorphism is equivalently translated to a group-transfer of the galois group (see Miyake [3]), it is enough to prove the following group-theoretical verison:
On generalized Whittaker functions on Siegel’s upper half space of degree 2
Authors: Niwa S.
Published: July 2016

In [5], H. Maass showed that the dimension of a space of generalized Whittaker functions satisfying certain system of differential equations on Siegel’s upper half space H2 of degree 2 is three. First of all, we shall investigate the structure of a space of generalized Whittaker functions which are eigen functions for the algebra of invariant differential operators on H2. The theory of generalized Whittaker functions is discussed in Yamashita [12], [13], [14], [15] with full generality. But, we will get an outlook of the space of generalized Whittaker functions by using elementary calculus instead of representation theory of Lie groups.
A Characterization of White Noise Test Functionals
Authors: Kuo H.-H. , Potthoff J. , Streit L.
Published: July 2016

In a recent paper [PS 89], two of the present authors have found a characterization of a certain space (ℐ)* of generalized functionals of white noise, i.e. generalized functionals on ℐ′(R) equipped with the σ-algebra ℬ generated by its cyclinder sets and with the white noise measure μ given by
Analytic capacity for two segments
Authors: Murai Takafumi
Published: July 2016

The analytic capacity γ(E) of a compact set E in the complex plane C is defined by γ(E) = sup , where — f′(∞) is the 1/z-coeffieient of f(ζ) at infinity and the supremum is taken over all bounded analytic functions f(ζ) outside E with supremum norm less than or equal to 1. Analytic capacity γ(·) plays various important roles in the theory of bounded analytic functions.
Perturbation of the hope flow and transverse foliations
Authors: Matsumoto Shigenori , Sato Atsushi
Published: July 2016

Consider a nonsingular vector fieldXon a closed manifoldMn. As a matter of fact,Xalways admits a transverse codimension one plane field, which however may fail to be integrable. In fact it is well known that there are many examples of vector fields which do not admit transverse foliations.
Harmonic analysis on the quotient spaces of Heisenberg groups
Authors: Yang Jae-Hyun
Published: July 2016

A certain nilpotent Lie group plays an important role in the study of the foundations of quantum mechanics ([Wey]) and of the theory of theta series (see [C], [I] and [Wei]). This work shows how theta series are applied to decompose the natural unitary representation of a Heisenberg group.
Mansfield and Solovay type results on covering plane sets by lines
Authors: Fujita Hiroshi P.
Published: July 2016

F. van Engelen, K. Kunen, and A. W. Miller proved, in [EKM], that for every analytic set A on the plane, either A can be covered by a countable family of lines or else there is a perfect subset P of A such that no three points of P are collinear. In this paper, we present some generalizations of their result. In particular, a question which was raised by van Engelen et al. in the last paragraph of [EKM] is answered (see Section 3).
On nilpotent extensions of algebraic number fields I
Authors: Miyake Katsuya , Opolka Hans
Published: July 2016

The lower central series of the absolute Galois group of a field is obtained by iterating the process of forming the maximal central extension of the maximal nilpotent extension of a given class, starting with the maximal abelian extension. The purpose of this paper is to give a cohomological description of this central series in case of an algebraic number field. This description is based on a result of Tate which states that the Schur multiplier of the absolute Galois group of a number field is trivial. We are in a profinite situation throughout which requires some functorial background especially for treating the dual of the Schur multiplier of a profinite group. In a future paper we plan to apply our results to construct a nilpotent reciprocity map.
Some types of regularity for the Dirichlet problem
Authors: Sadi Amar
Published: July 2016

The question of whether the existence of a harmonic majorant in a relative neighbourhood of each point of a boundary of a domain D implies the existence of a harmonic majorant in the whole of D has received great attention in recent years and has been dealt with by several authors in different settings. The most general results to date have been achieved in [10] with the Martin boundary. In [9], the author arrives, by independent means, at the conclusions of [10] in the particular case where D is a Lipschitz domain.

In this paper, we answer the question in domains with suitably regular topological frontiers. Our methods rely heavily on the possibility of obtaining an extented-representation for nonnegative superharmonic functions defined near a frontier point. This naturally led to the introduction and the study of new types of regularity for the generalised Dirichlet problem. As well as their suitability in dealing with the question of harmonic majorisation, they present an intrinsic importance as natural extensions of the (classical) regularity. For simplicity reasons, we will treat the finite boundary points and the point at infinity separately.
On the spectrum of periodic elliptic operators
Authors: Brüning Jochen , Sunada Toshikazu
Published: July 2016

It was observed in [Su5] that the spectrum of a periodic Schrödinger operator on a Riemannian manifold has band structure if the transformation group acting on the manifold satisfies the Kadison property (see below for the definition). Here band structure means that the spectrum is a union of mutually disjoint, possibly degenerate closed intervals, such that any compact subset of R meets only finitely many. The purpose of this paper is to show, by a slightly different method, that this is also true for general periodic elliptic self-adjoint operators.
Limit theorems for stochastic difference-differential equations
Authors: Fujiwara Tsukasa , Kunita Hiroshi
Published: July 2016

There are extensive works on the limit theorems for sequences of stochastic ordinary differential equations written in the form:

where is a stochastic process and is a deterministic function, both of which take values in the space of vector fields. The case where {ftn} n satisfies certain mixing conditions has been studied by Khas’minskii [7], Kesten-Papanicolaou [6] and others.
A construction of q-analogue of Dedekind sums
Authors: Satoh Junya
Published: July 2016

If one looks back the classical proof (cf. Carlitz [4]) of the reciprocity law for Dedekind sums in order to construct q-analogue of Dedekind sums which also have the reciprocity law, one can soon see that the following elementary equation is essential in the proof:

for any distinct complex numbers u and v, where means the generating function of Euler numbers associated to u. So we must extend the above equation to the generating function of q-Euler numbers for our purpose.
Mukai-Umemura’s example of the Fano threefold with genus 12 as a compactification of C3
Authors: Furushima Mikio
Published: July 2016

Let (X, Y) be a smooth projective compactification with the non-normal irreducible boundary Y, namely, X is a smooth projective algebraic threefold and Y a non-normal irreducible divisor on X such that X – Y is isomorphic to C3. Then Y is ample and the canonical divisor Kx on X can be written as Kx = - r Y (1 ≦ r ≦ 4).
Infinite dimensional rotations and Laplacians in terms of white noise calculus
Authors: Hida Takeyuki , Obata Nobuaki , Saitô Kimiaki
Published: July 2016

The theory of generalized white noise functionals (white noise calculus) initiated in [2] has been considerably developed in recent years, in particular, toward applications to quantum physics, see e.g. [5], [7] and references cited therein. On the other hand, since H. Yoshizawa [4], [23] discussed an infinite dimensional rotation group to broaden the scope of an investigation of Brownian motion, there have been some attempts to introduce an idea of group theory into the white noise calculus. For example, conformal invariance of Brownian motion with multidimensional parameter space [6], variational calculus of white noise functionals [14], characterization of the Levy Laplacian [17] and so on.
Rational double points on a normal octicK3 surface
Authors: Tang Li-Zhong
Published: July 2016

LetSbe a normal surface of degreenin, where (n, k) = (4,3), (6,4) or (8,5). People try to describe all possible combinations of singularities on such surfaces. The case (4,3) is already very complicated. Using properties ofK3 surface and elementary transformations of Dynkin Graphs effectively, Urabe [17] was able to solve the problem partially when all singularities are rational double points.
Polyhedricity of convex sets in sobolev space
Authors: Rao Murali , Sokołowski Jan
Published: July 2016

We provide results on differential stability of metric projection in Sobolev space onto convex set

(1.1)

where Ω ⊂ Rd is open, bounded domain.
L2-boundedness of the cauchy transform on smooth non-Lipschitz curves
Authors: Kang Hyeonbae , Seo Jin Keun
Published: July 2016

Let Γ be a curve defined by y = A(x) in R2. The Cauchy transform on the curve Γ is a singular integral operator defined by the singular integral kernel

(1.1)
Central extensions and rational quadratic forms
Authors: Furuta Yoshiomi , Kubota Tomio
Published: July 2016

The purpose of this paper is to characterize by means of simple quadratic forms the set of rational primes that are decomposed completely in a non-abelian central extension which is abelian over a quadratic field. More precisely, let L = Q be a bicyclic biquadratic field, and let K = Q. Denote by the ray class field mod m of K in narrow sense for a large rational integer m. Let be the maximal abelian extension over Q contained in and be the maximal extension contained in such that Gal(/L) is contained in the center of Gal(/Q). Then we shall show in Theorem 2.1 that any rational prime p not dividing d1d2m is decomposed completely in /Q if and only if p is representable by rational integers x and y such that x ≡ 1 and y ≡ 0 mod m as follows

where a, b, c are rational integers such that b2 − 4ac is equal to the discriminant of K and (a) is a norm of a representative of the ray class group of K mod m.

Moreover is decomposed completely in if and only if .
Generators for a maximally differential ideal in positive characteristic
Authors: Maloo Alok Kumar
Published: July 2016

In this note we give the structure of maximally differential ideals in a Noetherian local ring of prime characteristic p > 0, in terms of their generators. More precisely, we prove the following result:

THEOREM 4. Let A be a Noetherian local ring of prime characteristic p > 0 with maximal ideal m. Let I be a proper ideal of A. Suppose n= emdim(A) and r = emdim(A/l). If I is maximally differential under a set of derivations of A then there exists a minimal set xl,…,xn of generators of m such that I = (xρl, …,xρr, xr+1,…xn).
New invariants and class number problem in real quadratic fields
Authors: Yokoi Hideo
Published: July 2016

In recent papers [10, 11, 12, 13, 14], we defined some new ρ-invariants for any rational prime ρ congruent to 1 mod 4 and D-invariants for any positive square-free integer D such that the fundamental unit εD of real quadratic field Q(√D) satisfies NεD = –1, and studied relationships among these new invariants and already known invariants.

One of our main purposes in this paper is to generalize these D-invariants to invariants valid for all square-free positive integers containing D with NεD = 1. Another is to provide an improvement of the theorem in [14] related closely to class number one problem of real quadratic fields. Namely, we provide, in a sense, a most appreciable estimation of the fundamental unit to be able to apply, as usual (cf. [3, 4, 5, 9, 12, 13]), Tatuzawa’s lower bound of L(l, XD) (Cf[7]) for estimating the class number of Q(√D) from below by using Dirichlet’s classical class number formula.
On a q-analogue of the log-Γ-function
Authors: Tsumura Hirofumi
Published: July 2016

For complex numbers q and u, Carlitz defined the q-Bernoulli numbers {βk(q)} and the q-Euler numbers {Hk(u, q)} associated to u by

and
On vanishing of the twisted rational de Rham cohomology associated with hypergeometric functions
Authors: Kita Michitake
Published: July 2016

Recent development in hypergeometric functions in several variables has made the importance of studying twisted rational de Rham cohomology clear to many specialists. Roughly speaking, a hypergeometric function in our sense is the integral of a product of complex powers of polynomials Pj(u1, . . . . ,un) : ∫ U du1 ∧ · · · ∧ dun, U = Π , integration being taken over some cycle. So we are led naturally to consider the twisted rational de Rham cohomology, which is a direct generalization of the usual de Rham cohomology to multivalued case.
The WeitzenbÕck formula for the Bach operator
Authors: Itoh Mitsuhiro
Published: July 2016

(Anti-)self-dual metrics are 4-dimensional Riemannian metrics whose Weyl conformai tensor W half vanishes. The Weyl conformai tensor W of an arbitrary metric on an oriented 4-manifold has in general the self-dual part W+ and the anti-self-dual part W− with respect to the Hodge star operator * and one says that a metric is self-dual or anti-self-dual if W− = 0 or W+ = 0, respectively.
Behnke-Stein theorem on complex spaces with singularities
Authors: Colţoiu M. , Silva A.
Published: July 2016

Let X be a non-compact Riemann surface and D ⊂ X an open subset. By a classical result due to Behnke and Stein [2] D is Runge in X (i.e. the restriction map has dense image) iff X\D has no compact connected components. In other words the obstruction to holomorphic approximation is purely topological. This result has been generalized to 1-dimensional Stein spaces by Mihalache in [11].
Errata for “L2-boundedness of the Cauchy transform on smooth non-Lipschitz curves”, Nagoya Math J. 130 (1993), 123–147
Authors: Kang Hyeonbae , Seo Jinkeun
Published: July 2016

Note that an extra condition of symmetry of f, namely, the boundedness of f(x) = f(− x) is added to the hypothesis of the Lemma. Lemma 2.1 was used in three places in the paper to prove that the functions F, G*, and f given in pages 140, 141, and 144, respectively, belong to BMO. It can be checked by a standard argument that these functions satisfy the symmetry condition.
Microscopic asymptotics for solutions of some semilinear Elliptic equations
Authors: Ogawa Takayoshi , Suzuki Takashi
Published: July 2016

In our previous work [8], we picked up the elliptic equation

(1)

with the nonlinearity f(u) ⊇ 0 in C1. We studied the asymptotics of the family {(λ, u(x))} of classical solutions satisfying

(2)
A question of Gross and the uniqueness of entire functions
Authors: yi Hong-Xun
Published: July 2016

For any set S and any entire function f let

where each zero of f — a with multiplicity m is repeated m times in Ef(S) (cf. [1]). It is assumed that the reader is familiar with the notations of the Nevanlinna Theory (see, for example, [2]). It will be convenient to let E denote any set of finite linear measure on 0 < r < ∞, not necessarily the same at each occurrence. We denote by S(r, f) any quantity satisfying .
Class-number problems for cubic number fields
Authors: Louboutin Stéphane
Published: July 2016

Let M be any number field. We let DM, dM, hu, , AM and RegM be the discriminant, the absolute value of the discriminant, the class-number, the Dedekind zeta-function, the ring of algebraic integers and the regulator of M, respectively.

we set
If q is any odd prime we let (⋅/q) denote the Legendre’s symbol.
On compactness of isospectral conformal, metrics of 4-manifolds
Authors: Xu Xingwang
Published: July 2016

In this paper, we are interested in the compactness of isospectral conformal metrics in dimension 4.

Let us recall the definition of the isospectral metrics. Two Riemannian metricsg, g′on a compact manifold are said to be isospectral if their associated Laplace operators on functions have identical spectrum. There are now numeruos examples of compact Riemannian manifolds which admit more than two metrics such that they are isospectral but not isometric. That is to say that the eigenvalues of the Laplace operatorΔon the functions do not necessarily determine the isometry class of (M, g). If we further require the metrics stay in the same conformal class, the spectrum of Laplace operator still does not determine the metric uniquely ([BG], [BPY]).
Scalar curvatures of conformal metrics on Sn
Authors: Kawai Shigeo
Published: July 2016

In this paper we consider the following problem: Given a smooth function K on the n-dimensional unit sphere Sn(n ≥ 3) with its canonical metric g0, is it possible to find a pointwise conformal metric which has K as its scalar curvature? This problem was presented by J. L. Kazdan and F. W. Warner. The associated problem for Gaussian curvature in dimension 2 had been presented by L. Nirenberg several years before.
The minimum and the primitive representation of positive definite quadratic forms II
Authors: Kitaoka Yoshiyuki
Published: July 2016

We are concerned with representation of positive definite quadratic forms by a positive definite quadratic form. Let us consider the following assertion

Am, n : Let M, N be positive definite quadratic lattices over Z with rank(M) = m and rank(N) = n respectively. We assume that the localization Mp is represented by Np for every prime p, that is there is an isometry from Mp to Np. Then there exists a constant c(N) dependent only on N so that M is represented by N if min(M) > c(N), where min(M) denotes the least positive number represented by M.
Conformal immersions of compact Riemann surfaces into the 2n-sphere (n ≥ 2)
Authors: Hano Jun-Ichi
Published: July 2016

The purpose of this article is to prove the following theorem:

Let n be a positive integer larger than or equal to 2, and let S be the unit sphere in the 2n + 1 dimensional Euclidean space. Given a compact Riemann surface, we can always find a conformal and minimal immersion of the surface into S whose image is not lying in any 2n — 1 dimensional hyperplane.

This is a partial generalization of the result by R. L. Bryant. In this papers, he demonstrates the existence of a conformal and minimal immersion of a compact Riemann surface into S2n, which is generically 1:1, when n = 2 ([2]) and n = 3 ([1]).
On the series for L(1, x)
Authors: Leu Ming-Guang , Winnie Li Wen-Ch’ing
Published: July 2016

Let k be a positive integer greater than 1, and let X(n) be a real primitive character modulo k, The series

can be divided into groups of k consecutive terms.
Global generation of adjoint bundles
Authors: Tsuji Hajime
Published: July 2016

In 1988, I. Reider proved that for a smooth projective surface X and an ample line bundle L on X, Kx + 3L is globally generated and Kx + 4L is very ample ([12]). In fact his theorem is much stronger than this (see [12] for detail). Recently a lot of results have been obtained about effective base point freeness (cf. [1, 3, 8, 13, 14, 15]). In particular J. P. Demailly proved that 2KX + 12nnL is very ample for a smooth projective n-fold X and an ample line bundle L on X. [2] will give a good overview for these recent results. The motivation of these works is the following conjecture posed by T. Fujita.
On Ramified Riemann Domains
Authors: Togari Yoshio
Published: July 2016

Let ϕ be a holomorphic mapping of an n-dimensional analytic space E into Cn. If ϕ is non-degenerate at every point of E, we call the pair (E, ϕ) a Riemann domain. The notion of a Riemann domain is a generalization of the notion of a concrete Riemann surface. A Riemann domain (E, ϕ) is said to be unramified if ϕ is a local homeomorphism, and to be ramified if otherwise.
Rigidité des plongements des quotients primitifs minimaux de Ug(sl(2)) dans l’algebre quantique de Weyl-Hayashi
Authors: Alev J. , Dumas F.
Published: July 2016

Ce travail est consacré aux groupes d’automorphismes de certaines algebres quantiques de dimension 2 ou 3. Dans la théorie classique des algebres enveloppantes, si désigne l’algèbre de Lie de Heisenberg de dimension 3, U() admet l’algèbre de Weyl A1 comme seul quotient primitif de dimension 2, avec les propriétés suivantes: d’ une part tout automorphisme de A1 se relève en un automor-phisme de U(), d’autre part U() admet des automorphismes non modérés (cf. [A1], [Di1], [ML]). On retrouve la même situation pour les quotients primitifs minimaux de U(sl(2)) paramétrés par C (cf. [Di2], [Jo]). En outre, dans ce cas, on dispose des plongements de Conze de ces quotients dans A1 (cf. [Di2], [Co], [Ro]); bien que les groupes d’automorphismes soient comparables, la restriction correspondant à un tel plongement est seulement définie sur le sous-groupe des automorphismes triangulaires de A1 (cf. annexe).
Exponential asymptotics in the small parameter exit problem
Authors: Sugiura Makoto
Published: July 2016

Let M be a d-dimensional Riemannian manifold of class C∞ with Riemannian metric and let D be a connected domain in M having a non-empty smooth boundary and a compact closure . Suppose that are given and that converges uniformly to on D′ as for some neighborhood D′ of D. Consider the diffusion process on D′ with a small parameter generated by

(1.1)
Hyponormal Toeplitz operators on H2(T) with polynomial symbols
Authors: Yu Dahai
Published: July 2016

Let T be the unit circle on the complex plane, H2(T) be the usual Hardy space on T, Tø be the Toeplitz operator with symbol Cowen showed that if f1 and f2 are functions in H such that is in Lø, then Tf is hyponormal if and only if for some constant c and some function g in H∞ with Using it, T. Nakazi and K. Takahashi showed that the symbol of hyponormal Toeplitz operator Tø satisfies and and they described the ø solving the functional equation above. Both of their conditions are hard to check, T. Nakazi and K. Takahashi remarked that even “the question about polynomials is still open” [2]. Kehe Zhu gave a computing process by way of Schur’s functions so that we can determine any given polynomial ø such that Tø is hyponormal [3]. Since no closed-form for the general Schur’s function is known, it is still valuable to find an explicit expression for the condition of a polynomial á such that Tø is hyponormal and depends only on the coefficients of ø, here we have one, it is elementary and relatively easy to check. We begin with the most general case and the following Lemma is essential.
Finite arithmetic subgroups of GLn, V
Authors: Kitaoka Yoshiyuki
Published: July 2016

Let K be a finite Galois extension of the rational number field Q and G a Gal(K/Q)-stable finite subgroup of GLn(OK). We have shown that G is of A-type in several cases under some restrictions on K. In this paper, we show that it is true for n = 2 without any restrictions on K.
On relative base point freeness of adjoint bundle
Authors: Takayama Shigeharu
Published: July 2016

We give an effective result on the relative base point freeness of an adjoint bundle for a pair of a projective morphism and a relatively ample line bundle.
On the stability of pseudoconvexity for certain covering spaces
Authors: Ohsawa Takeo
Published: July 2016

It is proved that, if is a proper holomorphic map with one-dimensional fibers and a covering map, a point t ∈ T has a neighbourhood U such that is holomorphically convex if and only if is holomorphically convex.
Sobolev and Lipschitz estimates for weighted Bergman projections
Authors: Chang Der-Chen , Li Bao Qin
Published: July 2016

Let Ω be a bounded, decoupled pseudo-convex domain of finite type in ℂn with smooth boundary. In this paper, we generalize results of Bonami-Grellier [BG] and Bonami-Chang-Grellier [BCG] to study weighted Bergman projections for weights which are a power of the distance to the boundary. We define a class of operators of Bergman type for which we develop a functional calculus. Then we may obtain Sobolev and Lipschitz estimates, both of isotropic and anisotropic type, for these projections.
The genus of curves on the three dimensional quadric
Authors: De Cataldo Mark Andrea A.
Published: July 2016

By means of an ad hoc modification of the so-called “Castelnuovo-Harris analysis” we derive an upper bound for the genus of integral curves on the three dimensional nonsingular quadric which lie on an integral surface of degree 2/c, as a function of k and the degree d of the curve. In order to obtain this we revisit the Uniform Position Principle to make its use computation-free. The curves which achieve this bound can be conveniently characterized.
On differential polynomials I
Authors: Morikawa Hisasi
Published: July 2016

The content of Part I is nothing else than, the theory of binomial polynomial sequences in infinite variables (u(1), u(2), u(3), …) with weight u(1) = l. However, sometimes we are concerned with specialization therefore, we call the elements in K[u(1), u(2), u(3), …] differential polynomials. As analogies of special polynomials with binomial property, we may construct special differential polynomials with binomial property.
On differential polynomials, II
Authors: Morikawa Hisasi
Published: July 2016

In Part II, we shall be concerned with applications of classical invariant theory, to statistic physics and to theta functions. Main theorem in Chapter 2 is stated as follows:

For a partition function

satisfying γl ≥ 0 (l ≥ 1) and α > 0, the 2n-apolar of ξ(s)

has the expansion

such that βn,1 ≥ 0 (l ≥ 2). This means, for a given partition function ξ(s) with nonnegative relative probabilities, we construct a sequence of partition functions A2n (ξ(s), ξ(s))n≥1 with the same properties, which may be considered a sequence of symbolical higher derivative of ξ(s). The main theorem in Chapter 3 is stated as follows: For given theta functions φ1(z) and φ2(z) of level n1 and n2 respectively, in g variables z = (z1, z2,…, zg), then r = (r1, r2,…, rg-apolar

is a theta function of level n1 + n2, and
On the centralizer algebra of the unitary reflection group G(m,p,n)
Authors: Tanabe Kenichiro
Published: July 2016

The imprimitive unitary reflection group G(m, p, n) acts on the vector space V =Cn naturally. The symmetric group Sk acts on ⊗kV by permuting the tensor product factors. We show that the algebra of all matrices on ⊗kV commuting with G(m, p, n) is generated by Sk and three other elements. This is a generalization of Jones’s results for the symmetric group case [J].
Bounded p.s.h. functions and pseudoconvexity in Kähler manifold
Authors: Ohsawa Takeo , Sibony Nessim
Published: July 2016

It is proved that the C2-smoothly bounded pseudoconvex domains in Pn admit bounded plurisubharmonic exhaustion functions. Further arguments are given concerning the question of existence of strictly plurisubharmonic functions on neighbourhoods of real hypersurfaces in Pn.
Optimalities for random functions Lee-Wiener’s network and non-canonical representation of stationary Gaussian processes
Authors: Htay Win Win
Published: July 2016

Representation of a Gaussian process in terms of a Brownian motion is a powerful tool in the investigation of its structure. Among various representations is the canonical representation which is viewed as the best one from the viewpoint of the prediction theory. We have discovered some significance of non-canonical representations and discuss their optimality in an information theoretical approach.
On Relative Homological Algebra of Frobenius Extensions
Authors: Hirata Kazuhiko
Published: July 2016

In this paper we study two features of relative homological algebra of Frobenius extensions, the one is the relative dimension and the other is the relative complete resolution. The theory of Frobenius extensions was developed by F. Kasch [4] as a generalization of Frobenius algebras. We deal with only Frobenius extensions of finite rank (see §2 for the definition).
Sur Certains Espaces Fibrés Principaux Différentiables Et Holomorphes
Authors: Murakami Shingo
Published: July 2016

Le but principal de ce mémoire est d’étudier les espaces fibres principaux différentiables et holomorphes de groupe abelien connexe ayant pour base une C-variété au sens de Wang [12]. Une C-variété X étant une variété complexe compacte simplement connexe et homogène, X est la base d’un espace fibre principal qui est un groupe de Lie où opère un sous-groupe fermé par les translations à droite comme groupe structural. Pour cette raison, on considère d’abord dans le § 1 les espaces fibres principaux différentiables de groupe abelien connexe A ayant pour base la base X d’un certain espace fibre principal differentiate Y de groupe B. Parmi ces espaces fibres principaux les plus simples sont ceux qui sont associés à Y par les homomorphismes du groupe B dans le groupe A.
On standard L-functions attached to automorphic forms on definite orthogonal groups
Authors: Murase Atsushi , Sugano Takashi
Published: July 2016

We show an explicit functional equation of the standard L-function associated with an automorphic form on a definite orthogonal group over a totally real algebraic number field. This is a completion and a generalization of our previous paper, in which we constructed standard L-functions by using Rankin-Selberg convolution and the theory of Shintani functions under certain technical conditions. In this article we remove these conditions. Furthermore we show that the L-function of f has a pole at s = m/2 if and only if f is a constant function.
Degree bounds for generators of cohomology modules and Castelnuovo-Mumford regularity
Authors: Nagel Uwe , Schenzel Peter
Published: July 2016

By extending Mumford’s result on the generating by global sections there are estimates on the degree for generators of local cohomology modules. These arguments provide bounds on the Castelnuovo-Mumford regularity, in particular for Cohen-Macaulay varieties. As an application they imply a few more cases of varieties that satisfy a conjecture posed by Eisenbud and Gôto.
The martingale problem for pseudo-differential operators on infinite-dimensional spaces
Authors: Bogachev V. , Lescot P. , Röckner M.
Published: July 2016

A martingale problem for pseudo-differential operators on infinite dimensional spaces is formulated and the existence of a solution is proved. Applications to infinite dimensional “stable-like” processes are presented.
Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations
Authors: Chae Dongho , Kim Sung-Ki , Nam Hee-Seok
Published: July 2016

In this paper we prove the local existence and uniqueness of C1+γ solutions of the Boussinesq equations with initial data υ0, θ0 ∈ C1+γ, ω0, ∇θ0 ∈ Lq for 0 < γ < 1 and 1 < q < 2. We also obtain a blow-up criterion for this local solutions. More precisely we show that the gradient of the passive scalar θ controls the breakdown of C1+γ solutions of the Boussinesq equations.
On the rank of the first radical layer of ap-class group of an algebraic number field
Authors: Yamashita Hiroshi
Published: July 2016

Letpbe a prime number. LetMbe a finite Galois extension of a finite algebraic number fieldk. Suppose thatMcontains a primitive pth root of unity and that thep-Sylow subgroup of the Galois groupG= Gal(M/k) is normal. LetKbe the intermediate field corresponding to thep-Sylow subgroup. Let= Gal(K/k). Thep-class groupCofMis a module over the group ringZpG, whereZpis the ring ofp-adic integers. LetJbe the Jacobson radical ofZpG. C/JCis a module over a semisimple artinian ringFp. We study multiplicity of an irreducible representation Φ apperaring inC/JCand prove a formula giving this multiplicity partially. As application to this formula, we study a cyclotomic fieldMsuch that the minus part ofCis cyclic as aZpG-module and a CM-fieldMsuch that the plus part ofCvanishes for oddp.

To show the formula, we apply theory of central extensions of algebraic number field and study global and local Kummer duality between the genus group and the Kummer radical for the genus field with respect toM/K.
Linearizations of ordinary differential equations by area preserving maps
Authors: Ozawa Tetsuya , Sato Hajime
Published: July 2016

We clarify the class of second and third order ordinary differential equations which can be tranformed to the simplest equations Y″ = 0 and Y‴ = 0. The coordinate changes employed to transform the equations are respectively area preserving maps for second order equations and contact form preserving maps for third order equations. A geometric explanation of the results is also given by using connections and associated covariant differentials both on tangent and cotangent spaces.