bluuebunny/crossref_metadata_2025 huggingface dataset:
Certain Unitary Representations of the Infinite Symmetric Group, I
Authors: Obata Nobuaki
Published: July 2016

LetXbe the set of all natural numbers and letbe the group of all finite permutations ofX.The groupequipped with the discrete topology, is called theinfinite symmetric group.It was discussed in F. J. Murray and J. von Neumann as a concrete example of an ICC-group, which is a discrete group with infinite conjugacy classes. It is proved that the regular representation of an ICC-group is a factor representation of type II1. The infinite symmetric group is, therefore, a group not of type I. This may be the reason why its unitary representations have not been investigated satisfactorily. In fact, only few results are known. For instance, all indecomposable central positive definite functions on, which are related to factor representations of typeIIl, were given by E. Thoma. Later on, A. M. Vershik and S. V. Kerov obtained the same result by a different method in and gave a realization of the representations of type II1in. Concerning irreducible representations, A. Lieberman and G. I. Ol’shanskii obtained a characterization of a certain family of countably many irreducible representations by introducing a particular topology inHowever, irreducible representations have been studied not so actively as factor representations.
On the Cubic Theta Function
Authors: Yoshimoto Akinori
Published: July 2016

The generalized theta function of a totally imaginary field including n-th roots of unity, which was defined by T. Kubota [2], was introduced in his investigation of the reciprosity law of the n-th power residue. If n = 2, it reduces to the classical theta function. In the case n = 3 for the Eisenstein field, the Fourier coefficients of the cubic theta function, which were explicitly expressed by S.J. Patterson, are essentially cubic Gauss sums [3], Furthermore in the case n = 4 for the Gaussian field those of the biquadratic theta functions, which have been investigated by T. Suzuki [4], haven’t been obtained completely yet.
Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions
Authors: Srivastava H. M. , Owa Shigeyoshi
Published: July 2016

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disk are introduced and studied systematically. The various results presented here include, for example, a number of coefficient estimates and distortion theorems for functions belonging to these subclasses, some interesting relationships between these subclasses, and a wide variety of characterization theorems involving a certain functional, some general functions of hypergeometric type, and operators of fractional calculus. Some of the coefficient estimates obtained here are fruitfully applied in the investigation of certain subclasses of analytic functions with fixed finitely many coefficients.
The Dirichlet problem at infinity and complex analysis on Hadamard manifolds
Authors: Yasuoka Takashi
Published: July 2016

In this paper we shall study hyperbolicity of Hadamard manifolds.

In Section 1 we shall define and solve the Dirichlet problem at infinity for Laplacian J, which gives a partial extension of the result of Anderson and Sullivan in Theorem 1 (cf.). In Section 2 we apply the solution of the Dirichlet problem at infinity to a complex analysis on a Kâhler Hadamard manifold whose metric restricted to every geodesic sphere is conformai to that of the standard sphere. It seems that the sphere at infinity of such a manifold admits a CR-structure. In fact we can define a CR-function at infinity on the sphere at infinity. We shall show in Theorem 2 that there exists a holomorphic extension from the sphere at infinity and it coincides with the solution of the Dirichlet problem at infinity, if the Dirichlet problem at infinity is solvable. So we see that such a manifold admits many bounded holomorphic functions. By the similar method we shall show in Theorem 3 that such a manifold is biholomorphic to a strictly pseudoconvex domain in Cn, if the holomorphic sectional curvature Kh(x) is less than −1/(1 + r(x)2), where r(x) is a distance function from a pole. Theorem 3 is a partial answer to a conjecture raised by Green and Wu.
Quasi-Anosov diffeomorphisms and pseudo-orbit tracing property
Authors: Sakai Kazuhiro
Published: July 2016

Let M be a compact boundaryless C∞-manifold, and let Diff (M) be the space of C1-diffeomorphisms of M endowed with the C1-topology. An Axiom A diffeomorphism is said to satisfy the strong transversality condition if for every x∊M, TxM = TxW3(x) + TxWu(x).
The dimension formula of the space of cusp forms of weight one for Γ0(p)
Authors: Tanigawa Yoshio , Ishikawa Hirofumi
Published: July 2016

The purpose of this paper is to study the dimension formula for cusp forms of weight one, following the series of Hiramatsu [2] and Hiramatsu-Akiyama [3]. We define as usual the subgroup Γ0(N) of SL2(Z) by

.
A modification of Grothendieck’s spectral sequence
Authors: Enochs Edgar
Published: July 2016

Let C, C′ and C″ be abelian categories where C and C′ have enough injectives and let F: C → C′, G: C′ → C″ be additive covariant functors. Then for an object X of C, let C(X) be the complex associated with an injective resolution of X. Grothendieck gets a first quadrant spectral sequence by taking an injective resolution of the complex F(C(X)) and applying G to the associated double complex.
Polynomial rings and their projective modules
Authors: Popescu Dorin
Published: July 2016

Let R be a regular noetherian ring. A central question concerning projective modules over polynomial R-algebras is the following.

(1.1) BASS-QUILLEN CONJECTURE ([2] Problem IX, [10]). Every finitely generated projective module P over a polynomial R-algebra R[T], T = (T1,…, Tn) is extended from R, i.e.

P≊R[T]⊗R P/(T)P.
Algebraic singularities have maximal reductive automorphism groups
Authors: Hauser Herwig , Müller Gerd
Published: July 2016

LetX = On/ibe an analytic singularity where ṫ is an ideal of theC-algebraOnof germs of analytic functions on (Cn, 0). Letdenote the maximal ideal ofXandA= AutXits group of automorphisms. An abstract subgroupequipped with the structure of an algebraic group is calledalgebraic subgroupofAif the natural representations ofGon all “higher cotangent spaces”are rational. Letπbe the representation ofAon the first cotangent spaceandA1=π(A).
A convergence theorem for Riemannian manifolds and some applications
Authors: Kasue Atsushi
Published: July 2016

The purpose of the present paper is first to reformulate a Lipschitz convergence theorem for Riemannian manifolds originally introduced by Gromov [17] and secondly to give some applications of the theorem to a class of open Riemannian manifolds.
Notes on projective structures on complex manifolds
Authors: Gustafsson Björn , Peetre Jaak
Published: July 2016

Consider a Riemann surface X equipped with a projective structure, that is, a covering of X with coordinate neighborhoods U and corresponding (holomorphic) local coordinates {t} such that in the intersection U ∩ U′ of any two such coordinate neighborhoods U and U′ change of local coordinates is mediated by a fractional linear transformation
The volumes of small geodesic balls and generalized Chern numbers of Kaehler manifolds
Authors: Blazic Novica
Published: July 2016

In this paper we study a connection between global and local properties of Kaehler manifolds, more specifically we study a connection between the volumes of small geodesic balls of a manifold M and some generalized Chern numbers. We use the standard power series expansion for Vm(r).

In Theorem 3.1 we give characterizations of a flat compact Kaehler manifold in terms of the volumes of small geodesic balls and generalized Chern numbers ωn-1c1(M) and ωn-2c12(M). In Theorem 4.1 similar questions for complex space forms are considered. So we prove one particular case of the Conjecture (IV) stated by Gray and Vanhecke [6].
Second proof of the irreducibility of the first differential equation of painlevé
Authors: Umemura Hiroshi
Published: July 2016

In our paper [U2], we proved the irreducibility of the first differential equation y″ = 6y2 + x of Painlevé. In that paper we explained the origin of the problem and the importance of giving a rigorous proof. We can say that our method in [U2] is algebraic and finite dimensional in contrast to a prediction of Painlevé who expected a proof depending on the infinite dimensional differential Galois theory. Even nowadays the latter remains to be established. It seems that Painlevé needed an armament with the general theory (the infinite dimensional differential Galois theory) in the controversy with R. Liouville on the mathematical foundation of the proof of the irreducibility of the first differential equation (1902-03).
On the Dimension of Modules and Algebras, V. Dimension of Residue Rings
Authors: Eilenberg Samuel , Nakayama Tadasi
Published: July 2016

We shall consider a semi-primary ring ۸ with radical N (i.e. N is nilpotent and ۸/N is semi-simple (with minimum condition)). All modules considered are left ۸-modules. We refer to [1] for all notions relevant to homological algebra.

The objective of this paper is to establish the following two theorems:

Theorem I. Let a be a two-sided ideal in A such that
Sur la Structure du Groupe d’Homéomorphismes Analytiques d’une Certaine Variété Kaehlérinne
Authors: Matsushima Yozô
Published: July 2016

Soit V une variété complexe et soit I le champ de tenseurs de type (1,1) de V définissant la structure complexe de V. Un champ de vecteurs ξ sur V sera dit conforme si I [ξ, η]= [ξ, Iη] pour tout champ de vecteurs η sur V. On désignera par α l’ensemble de tous les champs de vecteurs comformes sur V. α est une sous-algèbre de Lie de l’algèbre de Lie de tous les champs de vecteurs sur V. Si V est compacte, α est de dimension finie et s’identifie avec l’algèbre de Lie du groupe de Lie A(V) d’homéomorphismes analytiques de V [2] De plus, si ξ, η ∈ α, on a On peut donc définir une structure d’algèbre de Lie complexe de α en posant pour tout ξ ∈ α.
A Foundation of Torsion Theory for Modules Over General Rings
Authors: Hattori Akira
Published: July 2016

When we consider modules A over a ring R which is not a commutative integral domain, the usual torsion theory becomes somewhat inadequate, since zero-divisors of R are disregarded and since the torsion elements of A do not in general form a submodule. In this paper we shall try to remedy such defects by modifying the fundamental notions such as torsion modules, divisible modules, etc.
On Multiple Transitivity of Permutation Groups
Authors: Tsuzuku Tosiro
Published: July 2016

It is well known that a doubly transitive group has an irreducible character χ1 such that χ1(R) = α(R) − 1 for any element R of and a quadruply transitive group has irreducible characters χ3 and χ3 such that χ2(R) = where α(R) and β(R) are respectively the numbers of one cycles and two cycles contained in R. G. Frobenius was led to this fact in the connection with characters of the symmetric groups and he proved the following interesting theorem: if a permutation group of degree n is t-ply transitive, then any irreducible character of the symmetric group of degree n with dimension at most equal to is an irreducible character of .
Minimal linkage and the Gorenstein locus of an ideal
Authors: Huneke Craig , Ulrich Bernd
Published: July 2016

Let I be a Cohen-Macaulay ideal of grade g > 0 in a local Gorenstein ring (R, m) with residue class field k. An R-ideal J is said to be linked to I with respect to the regular sequence α = α1 …, αg ⊂ I ∩ J if J = (α): I and I = (α): J ([6]). In this paper we are concerned with the following question: how big is dimk ((α, mJ)/mJ)? Obviously this dimension is at most g, but it could be as small as 0. If it is g then the link from J to I is called a minimal link, which is in most respects the desired type of link. The only general result known in this direction is that if I is Gorenstein, then dimk {(α, mJ)/mJ) = g unless both I and J are complete intersections (see [1], Proposition 5.2). We are able to generalize this fact to the case where (R/I)p is Gorenstein for all prime ideals p in R/I with dim (R/J)p ≤ 4; however we have to assume that I is generically a complete intersection ideal, and that R is a complete intersection (Theorem 2.3). Without the assumption on R we prove that if I is generically a complete intersection, and if for a fixed integer r the type of (R/I)p is at most r for all prime ideals p in R/I with dim (R/I)P ≤ (r + 1)2, then dimk ((α, mJ/mJ)) ≥ g — r (Proposition 2.1). If r = 1, i.e. if R/I is Gorenstein in codimension 4, then this estimate shows the dimension is at least g — 1. Theorem 2.3 can also be interpreted to yield a strong upper bound for the codimension of the non-Gorenstein-locus of certain perfect ideals: Let R be a regular local ring. Let I be an R-ideal which is generically a complete intersection, and assume that I is in the even linkage class of a Gorenstein ideal (i.e., there exists a sequence of links I ~ I1 ~ I2 ~ … ~ I2n with I2n a Gorenstein ideal); then I is a Gorenstein ideal provided that {R/I)p is Gorenstein for all prime ideals p of R/I with dim (R/I)p ≤ 4 (Corollary 3.1).
A decomposition theorem of 2-type immersions
Authors: Kotani Motoko
Published: July 2016

One branch of the research of submanifolds was introduced by Chen in terms of type in [2]. Type of a submanifold makes clear how the eigenspace decomposition of the Laplacian (of the ambient space) preserve after restricted to the submanifold.
The law of the iterated logarithm on subsequences-characterizations
Authors: Weber Michel
Published: July 2016

Let be any increasing sequence of integers and M> 1; we connect to them in a very simply way, an increasing unbounded function φ: → R+. Let also X1, X2, · · · be a sequence of i.i.d. random vectors with value in euclidian space Rm. We prove that the cluster set of the sequence almost surely coincides with the unit ball of Rm, if, and only if, the covariance matrix of X1 is the identity matrix of Rm and EX1 is the zero vector of Rm. We define a functional A on the set of increasing sequences of integers as follows:

.
Joint reductions of complete ideals
Authors: Verma J. K.
Published: July 2016

The aim of this paper is to extend and unify several results concerning complete ideals in 2-dimensional regular local rings by using the theory of joint reductions and mixed multiplicities. The theory of complete ideals in a 2-dimensional regular local ring was developed by Zariski in his 1938 paper [Z]. This theory is presented in a simpler and general form in [ZS, Appendix 5] and [H2].
Super congruence for the Apéry numbers
Authors: Ishikawa Tsuneo
Published: July 2016

Let, for any n ≥ 0,

.

R. Apéry’s proof of the irrationality of ζ(2) and ζ(3) made use of these numbers (see [10]). As a result, many properties of the Apéry numbers were found (see [l]-[9]). In particular, Beukers and Stienstra showed the interesting congruence (see [11, Theorem 13.1]).
The fundamental unit and class number one problem of real quadratic fields with prime discriminant
Authors: Yokoi Hideo
Published: July 2016

Class number one problem for imaginary quadratic fields was solved in 1966 by A. Baker and H.M. Stark independently. However, the problem for real quadratic fields is still unsolved. It seems to us that one of the most essential difficulties of the problem for real quadratic fields comes from deep connection of the class number with the fundamental unit.
On Fano manifolds, which are PK-bundles over P2
Authors: Szurek Michał , Wiśniewski Jarosław A.
Published: July 2016

In our earlier paper [8] we discussed Fano manifolds X that are of the form X = ℙ() with a rank-2 vector bundle on a surface S. Here we study a more general situation of Fano manifolds, ruled over the complex projective plane P2 as Pr-1-bundles, i.e., being of the form ℙ() with -a bundle of rank r ≥ 3 on P2.
Siegel modular forms and theta series attached to quaternion algebras
Authors: Böcherer Siegfried , Schulze-Pillot Rainer
Published: July 2016

The two main problems in the theory of the theta correspondence or lifting (between automorphic forms on some adelic orthogonal group and on some adelic symplectic or metaplectic group) are the characterization of kernel and image of this correspondence. Both problems tend to be particularly difficult if the two groups are approximately the same size.
Fibrations with moving cuspidal singularities
Authors: Takeda Yoshifumi
Published: July 2016

Let f: V → C be a fibration from a smooth projective surface onto a smooth projective curve over an algebraically closed field k. In the case of characteristic zero, almost all fibres of f are nonsingular. In the case of positive characteristic, it is, however, known that there exist fibrations whose general fibres have singularities. Moreover, it seems that such fibrations often have pathological phenomena of algebraic geometry in positive characteristic (see M. Raynaud [7], W. Lang [4]).
On a class of insoluble binary quadratic diophantine equations
Authors: Halter-Koch Franz
Published: July 2016

The binary quadratic diophantine equation

is of interest in the class number problem for real quadratic number fields and was studied in recent years by several authors (see [4], [5], [2] and the literature cited there).
Modified defect relations for the gauss map of minimal surfaces, III
Authors: Fujimoto Hirotaka
Published: July 2016

In [5], the author proved that the Gauss map of a nonflat complete minimal surface immersed in R3 can omit at most four points of the sphere, and in [7] he revealed some relations between this result and the defect relation in Nevanlinna theory on value distribution of meromorphic functions. Afterwards, Mo and Osserman obtained an improvement of these results in their paper [11], which asserts that if the Gauss map of a nonflat complete minimal surface M immersed in R3 takes on five distinct values only a finite number of times, then M has finite total curvature. The author also gave modified defect relations for holomorphic maps of a Riemann surface with a complete conformai metric into the n-dimensional complex projective space Pn(C) and, as its application, he showed that, if the (generalized) Gauss map G of a complete minimal surface M immersed in Rm is nondegenerate, namely, the image G(M) is not contained in any hyperplane in Pm − 1(C), then it can omit at most m(m + 1)/2 hyperplanes in general position ([8]). Here, the number m(m + 1)/2 is best-possible for arbitrary odd numbers and some small even numbers m (see [6]). Recently, Ru showed that the “nondegenerate” assumption of the above result can be dropped ([13]). In this paper, we shall introduce a new definition of modified defect and prove a refined Modified defect relation. As its application, we shall give some improvements of the above-mentioned results in [5], [7], [8], [11] and [13].
On determining certain real quadratic fields with class number one and relating this property to continued fractions and primality properties
Authors: Dubois Eugène , Levesque Claude
Published: July 2016

Thanks to K. Heegner [He], A. Baker [Ba] and H. Stark [S], we know that there are nine imaginary quadratic fields of class number one. Gauss conjectured that there are infinitely many real quadratic fields of class number one, but the conjecture is still open.
Hypertranscendental elements of a formal power-series ring of positive characteristic
Authors: Shikishima-Tsuji Kayoko , Katsura Masashi
Published: July 2016

Throughout this paper, we denote by N, Q and R the set of all natural numbers containing 0, the set of all rational numbers, and the set of all real numbers, respectively.
On the least degree of polynomials bounding above the differences between lengths and multiplicities of certain systems of parameters in local rings
Authors: Cuong Nguyen Tu
Published: July 2016

Let A be a commutative local Noetherian ring with the maximal ideal m and M a finitely generated A-module, d = dim M. It is well-known that the difference between the length and the multiplicity of a parameter ideal q of M

gives a lot of informations on the structure of the module M. For instance, M is a Cohen-Macaulay (CM for short) module if and only if IM(q) = 0 for some parameter ideal q or M is Buchsbaum module (see [S-V]) if and only if IM(q) is a constant for all parameter ideals q of M.
The low density limit in finite temperature case
Authors: Accardi L. , Lu Y. G.
Published: July 2016

The low density limit in the Boson Fock case has been investigated in [1] where also the physical meaning and their motivations have been explained (cf. also [0]). From these papers one knows how the number processes can be obtained from a quantum Hamiltonian model via a certain limit procedure.
Remarks on extremal Kähler metrics on ruled manifolds
Authors: Fujiki Akira
Published: July 2016

Let X be a compact Kähler manifold and γ Kähler class. For a Kàhler metric g on X we denote by Rg the scalar curvature on X According to Calabi [3][4], consider the functional defined on the set of all the Kähler metrics g whose Kähler forms belong to γ, where dvg is the volume form associated to g. Such a Kähler metric is called extremal if it gives a critical point of Ф. In particular, if Rg is constant, g is extremal. The converse is also true if dim L(X) = 0, where L(X) is the maximal connected linear algebraic subgroup of AutoX (cf. [5]). Note also that any Kähler-Einstein metric is of constant scalar curvature.
Holomorphic families of geodesic discs in infinite dimensional Teichmüller spaces
Authors: Tanigawa Harumi
Published: July 2016

The theory of quasiconformal mappings plays an important role in Teichmüller theory. The Teichmüller spaces of Riemann surfaces are defined as quotient spaces of the spaces of Beltrami differentials, and the Teichmüller distances are defined to measure quasiconformal deformations between the Riemann surfaces representing points in the Teichmüller spaces. The Teichmüller spaces are complex Banach manifolds equipped with natural complex structures such that the canonical projections are holomorphic. It is known (see Gardinar [4]) that the Teichmüller distance, defined independently of the complex structures, coincides with the Kobayashi distance.

In spite of the naturality of the definition of a Teichmüller space as a quotient of Beltrami differentials, for given two Beltrami differentials it is hard to determine whether they are equivalent or not. For this reason, it is not trivial to describe geodesic lines with respect to the Teichmüller-Kobayashi metric.
On subclasses of infinitely divisible distributions on R related to hitting time distributions of 1-dimensional generalized diffusion processes
Authors: Yamazato Makoto
Published: July 2016

A distribution μ on R+ = [0, ∞) is said to be a distribution if there are an increasing (in the strict sense) sequence of positive real numbers such that, for each j = 0, …, m, there is at least one ak satisfying bj < ak < b+1 and the

Laplace transform of μ is represented as
On a Bingham fluid whose viscosity and yield limit depend on the temperature
Authors: Kato Yoshio
Published: July 2016

Duvaut and Lions [2] studied the field of velocities and of temperatures in a moving incompressible Bingham fluid endowed with viscosity μ(θ) depending on the temperature θ and established the existence of a weak solution in the case of a two dimensional fluid. However, the problem of uniqueness remained unsolved. The purpose of the present paper is to give an affirmative answer to the problem, that is, to show the local existence (resp. the global existence) in the time and the uniqueness of (strong) solutions in three dimensions under the conditions that (i) the time (resp. the initial velocity and the external force) and (ii) the rate of variation of the viscosity and the yield limit with respect to the temperature are both sufficiently small. It will be easily seen that the global existence and the uniqueness also hold in the two dimensional case whenever the rate (ii) is sufficiently small.
Newton polygons and gevrey indices for linear partial differential operators
Authors: Miyake Masatake , Hashimoto Yoshiaki
Published: July 2016

This paper is a continuation of Miyake [7] by the first named author. We shall study the unique solvability of an integro-differential equation in the category of formal or convergent power series with Gevrey estimate for the coefficients, and our results give some analogue in partial differential equations to Ramis [10, 11] in ordinary differential equations.

In the study of analytic ordinary differential equations, the notion of irregularity was first introduced by Malgrange [3] as a difference of indices of a differential operator in the categories of formal power series and convergent power series. After that, Ramis extended his theory to the category of formal or convergent power series with Gevrey estimate for the coefficients. In these studies, Ramis revealed a significant meaning of a Newton polygon associated with a differential operator.
Martin boundaries of cartesian products of markov chains
Authors: Picardello Massimo A. , Woess Wolfgang
Published: July 2016

Let P and Q be the stochastic transition operators of two time-homogeneous, irreducible Markov chains with countable, discrete state spaces X and Y, respectively. On the Cartesian product Z = X x Y, define a transition operator of the form Ra = a·P + (1 — a) · Q, 0 < a < 1, where P is considered to act on the first variable and Q on the second. The principal purpose of this paper is to describe the minimal Martin boundary of Ra (consisting of the minimal positive eigenfunctions of Ra with respect to some eigenvalue t, also called t-harmonic functions) in terms of the minimal Martin boundaries of P and Q.
Estimates for fourier coefficients of siegel cusp forms of degree two, II
Authors: Kohnen Winfried
Published: July 2016

Let F be a Siegel cusp form of integral weight k on Γ2: = Sp2(Z) and denote by a(T) (T a positive definite symmetric half-integral (2,2)-matrix) its Fourier coefficients. In [2] Kitaoka proved that

(1)

(the result is actually stated only under the assumption that k is even). In our previous paper [3] it was shown that one can attain

(2)
Even canonical surfaces with small K2, I
Authors: Konno Kazuhiro
Published: July 2016

Let S be a minimal algebraic surface of general type defined over the complex number field C, and let K denote the canonical bundle. According to [10], we call S a canonical surface if the rational map ФK associated with | K | induces a birational map of S onto the image X. We denote by Q (X) the intersection of all hyperquadrics through X.
Minorations d’unités fondamentales—applications
Authors: Louboutin Stéphane
Published: July 2016

Un idéal entierId’un corps quadratique réelkest ditprimitiflorsquen∈ N* et (n) diviseIimpliquentn =1. Un idéal entier est primitif si et seulement si il vérifie les trois conditions suivantes:

(i) il n’est divisible par aucun idéal premier inerte,

(ii) il n’est divisible par le carré d’aucun idéal premier ramifié,

(iii) si il est divisible par un idéal premier totalement décomposé, alors il n’est pas divisible par son idéal premier conjugué.
The efimov effect of three-body schrödinger operators: Asymptotics for the number of negative eigenvalues
Authors: Tamura Hideo
Published: July 2016

The Efimov effect is one of the most remarkable results in the spectral theory for three-body Schrödinger operators. Roughly speaking, the effect will be explained as follows: If all three two-body subsystems have no negative eigenvalues and if at least two of these two-body subsystems have resonance states at zero energy, then the three-body system under consideration has an infinite number of negative eigenvalues accumulating at zero. This remarkable spectral property was first discovered by Efimov [1] and the problem has been discussed in several physical journals. For related references, see, for example, the book [3]. The mathematically rigorous proof of the result has been given by the works [4, 8, 9]. The aim of the present work is to study the asymptotic distribution of these negative eigenvalues below zero (bottom of essential spectrum). Denote by N(E), E > 0, the number of negative eigenvalues less than – E. Then the main result obtained here is, somewhat loosely stating, that N(E) behaves like | log E | as E → 0. We first formulate precisely the main theorem and then make a brief comment on the recent related result obtained by Sobolev [7].
The deligne complex of a real arrangement of hyperplanes
Authors: Paris Luis
Published: July 2016

Let V be a real vector space. An arrangement of hyperplanes in V is a finite family of hyperplanes of V through the origin. We say that is essential if ∩H ∊H = {0}
A note on the Følner condition for amenability
Authors: Adachi Toshiaki
Published: July 2016

Let G be a countably generated discrete group. A right-invariant mean μ on G is a bounded linear functional of the space L∞(G) of bounded functions on G having the property:

We say that G is amenable if it is equipped with a right-invariant mean. Finite groups, abelian groups, in fact, groups of subexponential growth are amenable. Solvable group are also amenable. Subgroups and quotients of amenable groups are amenable. On the other hand, free groups having two generators and over are non-amenable.
On twisting operators and newforms of half-integral weight
Authors: Ueda Masaru
Published: July 2016

The theory of newforms is very important and useful for arithmetical study of modular forms of integral weight. It is natural to try to extend this theory into the case of modular forms of half-integral weight Until now, several authors have attempted to find a theory of newforms of half-integral weight (cf. [She], [N], [K], [M-R-V], [She-W]). But complete results have not been obtained yet.
Lifts of some tensor fields and connections to product preserving functors
Authors: Gancarzewicz Jacek , Mikulski Włodzimierz , Pogoda Zdzisław
Published: July 2016

In this paper we define some lifts of tensor fields of types (1,k)and (0,k)as well as connections to a product preserving functor. We study algebraic properties of introduced lifts and we apply these lifts to prolongation of geometric structures from a manifoldMto(M).In particular cases of the tangent bundle ofpr-velocities and the tangent bundle of infinitesimal near points our constructions contain all constructions due to Morimoto (see [20]-[23]). In the cases of the tangent bundle our definitions coincide with the definitions of Yano and Kobayashi (see [31]). To construct our lifts and to study its properties we use only general properties of product preserving functors. All lifts verify so-calledthe naturality condition.It means that for a smooth mappingφ:M → Nand for two φ-related geometric objects defined onMandNits lifts to(M)and(N)respectively are(φ)-related. We explain later the termφ-relatedfor considered geometric objects.
Tight closure in F-rational rings
Authors: Aberbach Ian M.
Published: July 2016

All rings are commutative with unit and modules are unital. With one exception all rings are Noetherian. We consider only rings of positive characteristic p. Section 0 contains background, definitions and terminology.
Classical solutions of the third Painlevé equation
Authors: Murata Yoshihiro
Published: July 2016

The big problem “Do Painlevé equations define new functions?”, what is called the problem of irreducibilities of Painlevé equations, was essentially solved by H. Umemura [16], [17] and K. Nishioka [9].
Positive definite hyperfunctions
Authors: Chung Jaeyoung , Chung Soon-Yeong , Kim Dohan
Published: July 2016

S. Bochner proved the following theorem in [B].
A note on a formula of the Lévy-Khinchin type in quantum probability
Authors: Barchielli A. , Paganoni A. M.
Published: July 2016

In the past few years there has been an increasing interest in a certain class of stochastic differential equations (SDE’s) in Hilbert spaces for applications in quantum mechanics (measurements continuous in time [1-5]) and in quantum optics (photon-detection theory and numerical simulations of master equations [6-10]). Part of the mathematical theory of these equations has been developed in [11], where also “structural properties” of this class of equations have been studied. In the paper [11] it has been shown that such equations are connected with certain semigroups of linear operators and the form of the generator of semigroups related to such SDE’s has been established.
Functional equations of iterated integrals with regular singularities
Authors: Wojtkowiak Zdzisław
Published: July 2016

Polylogarithmic functions satisfy functional equations. The most famous equation is of course the functional equation of the logarithm

log x + log y = log(x · y).

The other well known equation is the Abel equation of the dilogarithm
On Real Irreducible Representations of Lie Algebras
Authors: Iwahori Nagayoshi
Published: July 2016

Let us consider the following two problems:

Problem A. Let g be a given Lie algebra over the real number field R. Then find all real, irreducible representations of g.

Problem B. Let n be a given positive integer. Then find all irreducible subalgebras of the Lie algebra ôí(w, R) of all real matrices of degree n.
An Investigation on the Logical Structure of Mathematics (VI): Consistent V-System T(V) (With Corrections to Part (XII))
Authors: Kuroda Sigekatu
Published: July 2016

The V-system T(V) is defined in §2 by using §1, and its consistency is proved in §3. The definition of T(V) is given in such a way that the consistency proof of T(V) in §3 shows a typical way to prove the consistency of some subsystems of UL. Otherwise we could define T(V) more simply by using truth values. After T(V)-sets are treated in §4, it is proved in §5 as a T(V)-theorem that T(V)-sets are all equal to V.
On Meta Abelian Fields of a Certain Type
Authors: Furuta Yoshiomi
Published: July 2016

Let k be an algebraic number field of finite degree, and l a rational prime (including 2); k and l being fixed throughout this paper. For any power ln of l, denote by ζn an arbitrarily fixed primitive ln-th root of unity, and put kn = k(ζn). Let r be the maximal rational integer such that ζr∈k i.e. kr = k and kr+1≠k.
Discrete spectrum of many body Schrödinger operators with non-constant magnetic fields I
Authors: Hattori Tetsuya
Published: July 2016

In this paper we discuss the discrete spectrum of the Schrödinger operatorHNZ(b), defined as below, for an atomic system in a magnetic field. Letwherexjis a point inR3(1≥ j ≥ N), and∇jbe the gradient inR3with respect toxj(1 ≥ j ≥ N). Then we consider the following operator:

(1.1)

defined on, where3 being real-valued and

(1.2)
On Barth’s conjecture concerining
Authors: Coltoiu Mihnea
Published: July 2016

A classical, still unsolved problem, is the following: is every connected curve A ⊂ P3 a set-theoretic complete intersection? It is clear that if A is a set-theoretic complete intersection then:

a) The algebraic cohomology groups vanish for every coherent algebraic sheaf on P3.

b) The analytic cohomology groups vanish for every coherent analytic sheaf on P3\A.
A Construction of asymptotic solutions and the existence of smooth null-solutions for a class of non-Fuchsian partial differential operators
Authors: Mandai Takeshi
Published: July 2016

Consider a partial differential operator

(1.1)

where K is a non-negative integer and aj,a are real-analytic in a neighborhood of (0, 0)
On first-passage-time and transition densities for strongly symmetric diffusion processes
Authors: Crescenzo A. Di , Giorno V. , Nobile A. G. , Ricciardi L. M.
Published: July 2016

One dimensional diffusion processes have been increasingly invoked to model a variety of biological, physical and engineering systems subject to random fluctuations (cf., for instance, Blake, I. F. and Lindsey, W. C. [2], Abrahams, J. [1], Giorno, V.et al[10] and references therein). However, usually the knowledge of the ‘free’ transition probability density function (pdf) is not sufficient; one is thus led to the more complicated task of determining transition functions in the presence of preassigned absorbing boundaries, or first-passage-time densities for time-dependent boundaries (see, for instance, Daniels, H. E. [6], [7], Giorno, V.et al. [10]). Such densities are known analytically only in some special instances so that numerical methods have to be implemented in general (cf., for instance, Buono-core, A.et al[3], [4], Giorno, V.et al[11]). The analytical approach becomes particularly effective when the diffusion process exhibits some special features, such as the symmetry of its transition pdf. For instance, in [10] special symmetry conditions on the transition pdf of one-dimensional time-homogeneous diffusion process with natural boundaries are investigated to derive closed form results concerning the transition pdf’s and the first-passage-time pdf for particular time-dependent boundaries. On the other hand, by using the method of images, in [6] Daniels has obtained a closed form expression for the transition pdf of the standard Wiener process in the presence of a particular time-dependent absorbing boundary. It is interesting to remark that such density cannot be obtained via the methods described in [10], even though the considered process exhibits the kind of symmetry discussed therein.
A criterion for the parity of the class number of an Abelian field with prime power conductor
Authors: Yoshino Ken-Ichi
Published: July 2016

Letfbe a positive integer such thatf≢ 2 (mod 4). Leth0be the class number of the maximal real subfield offth cyclotomic fieldQ(ζf)- It is interesting to determine whenh0is even. Kummer [11] investigated this problem whenfis a prime and showed that ifh0is even, then the relative class numberhof the cyclotomic field is even (Satz III). Moreover he gave another necessary condition forh0to be even (Satz IV). In [7] Hasse gave a necessary and sufficient condition forhto be even (Satz 45).
On zeta functions associated to symmetric matrices III – An explicit form of L-Functions
Authors: Ibukiyama Tomoyoshi , Saito Hiroshi
Published: July 2016

In [I-S2], we gave an explicit form of zeta functions associated to the space of symmetric matrices. In this paper, the case of L-functions is treated. In the case of definite symmetric matrices, we show the ratinality of special values of these L-functions.
Criterion of (Lp, Lr) boundedness for a class of multilinear oscillatory singular integrals
Authors: Chen Wengu , Hu Guoen , Lu Shanzhen
Published: July 2016

In this paper, we consider a kind of multilinear operators related to oscillatory singular integrals with rough kernels and give a criterion of certain boundedness for this kind of operators.
Injective Modules Over Prufer Rings
Authors: Matlis Eben
Published: July 2016

The purpose of this paper is to find out what can be learned about valuation rings, and more generally Prufer rings, from a study of their injective modules. The concept of an almost maximal valuation ring can be reformulated as a valuation ring such that the images of its quotient field are injective. The integral domains with this latter property are found to be the Prufer rings with a (possibly) weakened form of linear precompactness for their quotient fields.
Irregular Canonical Double Surfaces
Authors: Mendes Lopes Margarida , Pardini Rita
Published: July 2016

We classify minimal irregular surfaces of general type X with Kx ample and such that the canonical map is 2-to-l onto a canonically embedded surface.
Symmetries in the fourth Painlevé equation and Okamoto polynomials
Authors: Noumi Masatoshi , Yamada Yasuhiko
Published: July 2016

The fourth Painlevé equation PIV is known to have symmetry of the affine Weyl group of type with respect to the Bäcklund transformations. We introduce a new representation of PIV, called the symmetric form, by taking the three fundamental invariant divisors as the dependent variables. A complete description of the symmetry of PIV is given in terms of this representation. Through the symmetric form, it turns out that PIV is obtained as a similarity reduction of the 3-reduced modified KP hierarchy. It is proved in particular that the special polynomials for rational solutions PIV, called Okamoto polynomials, are expressible in terms of the 3-reduced Schur functions.
On the behavior of the solutions of degenerate parabolic equations
Authors: Ishige Kazuhiro
Published: July 2016

In this paper we consider degenerate parabolic equations, and obtain an interior and a boundary Harnack inequalities for nonnegative solutions to the degenerate parabolic equations. Furthermore we obtain boundedness and continuity of the solutions.
Magnetic scattering at low energy in two dimensions
Authors: Tamura Hideo
Published: July 2016

We study the asymptotic behavior at low energy of scattering amplitudes in two dimensional magnetic fields with compact support. The obtained result depends on the total flux of magnetic fields. It should be noted that magnetic potentials do not necessarily fall off rapidly at infinity. The main body of argument is occupied by the resolvent analysis at low energy for magnetic Schrödinger operators with perturbations of lang-range class. We can show that the dimension of resonance spaces at zero energy does not exceed two. As a simple application, we also discuss the scattering by magnetic field with small support and the convergence to the scattering amplitude by δ-like magnetic field.
Determinant formulas for theτ-functions of the Painlevé equations of typeA
Authors: Yamada Yasuhiko
Published: July 2016

Explicit determinant formulas are presented for theτ-functions of the generalized Painlevé equations of typeA. This result allows an interpretation of theτ-functions as the Plücker coordinates of the universal Grassmann manifold.
A remark on algebraic surfaces with polyhedral Mori cone
Authors: Nikulin Viacheslav V.
Published: July 2016

We denote by FPMC the class of all non-singular projective algebraic surfaces X over ℂ with finite polyhedral Mori cone NE(X) ⊂ NS(X) ⊗ ℝ. If ρ(X) = rk NS(X) ≥ 3, then the set Exc(X) of all exceptional curves on X ∈ FPMC is finite and generates NE(X). Let δE(X) be the maximum of (-C2) and pE(X) the maximum of pa(C) respectively for all C ∈ Exc(X). For fixed ρ ≥ 3, δE and pE we denote by FPMCρ,δE,pE the class of all algebraic surfaces X ∈ FPMC such that ρ(X) = ρ, δE(X) = δE and pE(X) = pE. We prove that the class FPMCρ,δE,pE is bounded in the following sense: for any X ∈ FPMCρ,δE,pE there exist an ample effective divisor h and a very ample divisor h′ such that h2 ≤ N(ρ, δE) and h′2 ≤ N′(ρ, δE, pE) where the constants N(ρ, δE) and N′(ρ, δE, pE) depend only on ρ, δE and ρ, δE, pE respectively.

One can consider Theory of surfaces X ∈ FPMC as Algebraic Geometry analog of the Theory of arithmetic reflection groups in hyperbolic spaces.
On the domain and range of the maximal operator
Authors: Fiorenza Alberto , Krbec Miroslav
Published: July 2016

We give a detailed survey, known and new results on the domain and the range of the maximal operator. In particular we employ the grand Lpspaces and logarithmic Lebesgue spaces.
Affine structure on Weil bundles
Authors: Kolář Ivan
Published: July 2016

For every r-th order Weil functor TA, we introduce the underlying k-th order Weil functors We deduce that is an affine bundle for every manifold M. Generalizing the classical concept of contact element by C. Ehresmann, we define the bundle of contact elements of type A on M and we describe some affine properties of this bundle.
A note on weighted Bergman spaces and the Cesaro Operator
Authors: Benke George , Chang Der-Chen
Published: July 2016

Let B denote the unit ball in ℂn, and dV(z) normalized Lebesgue measure on B. For α > -1, define dVα(z) = (1 - \z\2)αdV(z). Let (B) denote the space of holomorhic functions on B, and for 0 < p < ∞, let p(dVα) denote Lp(dVα) ∩ (B). In this note we characterize p(dVα) as those functions in (B) whose images under the action of a certain set of differential operators lie in Lp(dVα). This is valid for 1 < p < oo. We also show that the Cesàro operator is bounded on p(dVα) for 0 < p < oo. Analogous results are given for the polydisc.
Algebraic Criterion on Quasiconformal Equivalence of Riemann Surfaces
Authors: Nakai Mitsuru
Published: July 2016

1. Various strides have been done to characterize the conformal structure of Riemann surfaces by the algebraic structure of some appropriate function algebras on them (cf. Bers [2], Rudin [29], Royden [26], [28], Heins [7], Kakutani [12], Wermer [33] etc.). In this paper we discuss, corresponding to the above, the problem to determine the quasiconformal structure of Riemann surfaces by the algebraic structure of some function algebras on them.
An Investigation on the Logical Structure of Mathematics (XIII): A Method of Programming of Proofs in Mathematics for Electronic Computing Machines
Authors: Kuroda Sigekatu
Published: July 2016

In spite of invaluable importance of the fundamental circuit logic of performing the basic logical operators AND, OR, and NOT in achieving complicated computations for electronic computing machines, the research of planning and programming of proving a given mathematical or logical assertion for electronic computing machines is incomparatively far behind. This is of course partly because of little practical demand for solving such a theoretical problem, but there is also the essential reason for it that the proving procedures are much more difficult than the computing ones.
On the Steinitz module and capitulation of ideals
Authors: Khare Chandrashekhar , Prasad Dipendra
Published: July 2016

Let L be a finite extension of a number field K with ring of integers and respectively. One can consider as a projective module over . The highest exterior power of as an module gives an element of the class group of , called the Steinitz module. These considerations work also for algebraic curves where we prove that for a finite unramified cover Y of an algebraic curve X, the Steinitz module as an element of the Picard group of X is the sum of the line bundles on X which become trivial when pulled back to Y. We give some examples to show that this kind of result is not true for number fields. We also make some remarks on the capitulation problem for both number field and function fields. (An ideal in is said to capitulate in L if its extension to is a principal ideal.)
On the deduction of the class field theory from the general reciprocity of power residues
Authors: Kubota Tomio , Oka Satomi
Published: July 2016

We denote by (A) Artin’s reciprocity law for a general abelian extension of a finite degree over an algebraic number field of a finite degree, and denote two special cases of (A) as follows: by (AC) the assertion (A) where K/F is a cyclotomic extension; by (AK) the assertion (A) where K/F is a Kummer extension. We will show that (A) is derived from (AC) and (AK) only by routine, elementarily algebraic arguments provided that n = (K : F) is odd. If n is even, then some more advanced tools like Proposition 2 are necessary. This proposition is a consequence of Hasse’s norm theorem for a quadratic extension of an algebraic number field, but weaker than the latter.
Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings
Authors: Watanabe Kei-Ichi , Yoshida Ken-Ichi
Published: July 2016

We study the behavior of Hilbert-Kunz multiplicity for powers of an ideal, especially the case of stable ideals and ideals in local rings of dimension 2. We can characterize regular local rings by certain equality between Hilbert-Kunz multiplicity and usual multiplicity.

We show that rings with “minimal” Hilbert-Kunz multiplicity relative to usual multiplicity are “Veronese subrings” in dimension 2.
Hypothesis Testing for Signal Detection Problem and Large Deviations
Authors: Chiyonobu Taizo
Published: July 2016

We consider a signal detection problem for the continuous-time stationary diffusion processes. The optimal decision region is given by Neyman-Pearson’s lemma. We establish certain large deviation estimates, and with the help of it we show that the error probability of the second kind of the signal detection tends to zero or one exponentially fast, depending on the fixed exponent of the decay of the error probability of the first kind, as the observation time goes to infinity.