bluuebunny/crossref_metadata_2025 huggingface dataset:
Algebraic threefolds with two extremal morphisms
Authors: Iliev Atanas
Published: July 2016

In [3] Mori gives a description of all extremal rays (extremal morphisms) arising on a smooth projective threefold with a numerically non-effective canonical bundle. Generally speaking, every smooth projective threefold V with a numerically non-effective canonical class Kv admits an extremal morphism π: V— → Y. The assumption that V admits a non-trivial pair of extremal morph-isms

imposes strong conditions on V. This is the essence of the Theorem 1.5 of the present work. In particular, we obtain a description of the threefolds which admit two biregular structures of conic bundles over non-singular surfaces S1 = Y1 and S2 = Y2. By the results of §3 the surfaces Sl and S2 must be either ruled surfaces with isomorphic basic curves, or S1 ≈ S2 ≈ P2.
Existence of Dirichlet finite harmonic measures on Euclidean balls
Authors: Nakai Mitsuru
Published: July 2016

Divide the ideal boundary of a noncompact Riemannian manifold M into two parts δ0 and δ1 Viewing that M is surrounded by two conducting electrodes δ0 and δ1 we ask whether (M; δ0, δ1) functions as a condenser in the sense that the unit electrostatic potential difference between two electrodes is produced by putting a charge of finite energy on one electrode when the other is grounded. The generalized condenser problem asks whether there exists a subdivision δ0 ∪ δ1 of the ideal boundary of M such that (M; δ0, δ1 functions as a condenser.
The theory of KM2O-Langevin equations and applications to data analysis (II): Causal analysis (1)
Authors: Okabe Yasunori , Inoue Akihiko
Published: July 2016

It is not too much to say that the problem of finding a cause-and-effect relationship is a fascinating and eternal theme in both natural and social sciences. It is often difficult to decide whether one is the cause of another in two related phenomena, but it is an important problem. It is related to the internal structure of phenomena which generate deterministic or random changes as time passes. We note that the phenomena to be considered are often not deterministic but random. For example, in physical systems such as quantum mechanics or chaotic classical mechanics, it is well known that certain probabilistic reasonings are indispensable.
Automorphism groups of a class of expanding attractors
Authors: Tezer Cem
Published: July 2016

In the following, for any group G and any g ∈ G, Ad[g] stands for the inner automorphism defined by Ad[g] (x) = gxg−1 for any x ∈ G.
6-vertex theorem for closed planar curve which bounds an immersed surface with non-zero genus
Authors: Umehara Masaaki
Published: July 2016

A vertex of a planar curve γ of class is a point which attains a local maximum or minimum of its curvature function. By the definition, the number of vertices are even whenever it is finite. As a generalization of famous four vertex theorem, Pinkall [P] showed that a closed curve γ has at least 4 vertices if it bounds an immersed surface, and he conjectured that γ has at least 4g + 2 vertices when the surface has genus g.
Criteria for recurrence and transience of semistable processes
Authors: Choi Gyeong Suck
Published: July 2016

The definition of semistable laws was originally given by Lévy in [11]. Two books, Kagan, Linnik and Rao [6] and Ramachandran and Lau [13], call a probability measure on R “semistable” when it is nondegenerate and its characteristic function (ch.f.) f(z) does not vanish on R and satisfies a functional equation of the form

for some real numbers b (0 < | b | <1) and c > 1.
Affine hypersurfaces with parallel cubic form
Authors: Dillen Franki , Vrancken Luc , Yaprak Sahnur
Published: July 2016

As is well known, there exists a canonical transversal vector field on a non-degenerate affine hypersurface M. This vector field is called the affine normal. The second fundamental form associated to this affine normal is called the affine metric. If M is locally strongly convex, then this affine metric is a Riemannian metric. And also, using the affine normal and the Gauss formula one can introduce an affine connection ∇ on M which is called the induced affine connection. Thus there are in general two different connections on M: one is the induced connection ∇ and the other is the Levi Civita connection of the affine metric h. The difference tensor K is defined by K(X, Y) = KXY — ∇XY — XY. The cubic form C is defined by C = ∇h and is related to the difference tensor by

.
Existence of Dirichlet infinite harmonic measures on the unit disc
Authors: Nakai Mitsuru
Published: July 2016

The primary purpose of this paper is to give an affirmative answer to a problem posed by Ohtsuka [13] whether there exists a p-harmonic measure on the unit disc in the 2-dimensional Euclidean space R2 with an infinite p-Dirichlet integral for the exponent 1 < p < 2.
Derivations on white noise functionals
Authors: Obata Nobuaki
Published: July 2016

The Gaussian space (E*, μ) is a natural infinite dimensional analogue of Euclidean space with Lebesgue measure and a special choice of a Gelfand triple gives a fundamental framework of white noise calculus [2] as distribution theory on Gaussian space. It is proved in Kubo-Takenaka [7] that (E) is a topological algebra under pointwise multiplication. The main purpose of this paper is to answer the fundamental question: what are the derivations on the algebra (E)?
Logarithmic forms on affine arrangements
Authors: Terao Hiroaki , Yuzvinsky Sergey
Published: July 2016

Let V be an affine of dimension l over some field K. An arrangement A is a finite collection of affine hyperplanes in V. We call A an l-arrangement when we want to emphasize the dimension of V. We use [6] as a general reference. Choose an arbitrary point of V and fix it throughout this paper. We will use it as the origin.
Spherical functions on orthogonal groups
Authors: Kajima Yasuhiro
Published: July 2016

Let G be a p-adic connected reductive algebraic group and K a maximal compact subgroup of G. In [4], Casselman obtained the explicit formula of zonal spherical functions on G with respect to K on the assumption that K is special. It is known (Bruhat and Tits [3]) that the affine root system of algebraic group which has good but not special maximal compact subgroup is A1 C2, or Bn (n > 3), and all Bn-types can be realized by orthogonal groups. Here the assumption “good” is necessary for the Satake’s theory of spherical functions.
Fibrés Holomorphes Sur un Tore Complexe
Authors: Matsushima Yozô
Published: July 2016

Le problème de classifier les fibrés vectoriels holomorphes sur une variété complexe M a été résolu récemment dans les deux cas suivants : 1) M est la sphère de Riemann (Grothendieck [4]), 2) M est une courbe elliptique (Atiyah [2]). Mais si la dimension complexe de M est > 1, nous ne connaissons presque rien de ce problème, sauf le cas où la dimension complexe de fibre est égale à 1.
A Generalization of the Almost Zero Theory
Authors: Sridharan R.
Published: July 2016

In this note we shall give a modified definition of cohomology groups for algebras. For a class of (infinite rank) algebras (which includes Frobenius algebras, group rings of infinite groups and division algebras of countable rank over fields), these groups can be characterized in a manner similar to the cohomology groups in the * Almost Zero theory’ of B. Eckmann [2]. Actually, in the case of group rings, these coincide with the cohomology groups in the almost zero theory.
An Investigation on the Logical Structure of Mathematics (VIII):: Consistency of the Natural-Number Theory T1(N)
Authors: Kuroda Sigekatu
Published: July 2016

The consistency of the natural number theory was proved, as is well known, by G. Gentzen in 1935 for the first time in such generality that the mathematical induction can be consistently used for any arbitrary predicate of natural numbers, which is well-formed in his system so that every quantifier ranges over all natural numbers.
Holomorphic Functions with Spiral asymptotic Paths
Authors: Seidel W.
Published: July 2016

Let f(z)be a holomorphic and unbounded function in| z |< 1, with the property that it remains bounded on some spiral S in| z |< 1 which approaches| z |= 1 asymptotically. The existence of such functions was first established by G. Valiron. Accordingly, we shall refer to such functions asfunctions of class (V) relative to S. More recently, F. Bagemihl and W. Seidel obtained examples of functions holomorphic and unbounded in| z |< 1 which approach prescribed finite or infinite values as| z |→ 1 on any given enumerable set of disjunct spirals which approach| z |=1 asymptotically, as well as on certain sets of such spirals having the power of the continuum.
The convergency of some routing protocols
Authors: Kawamoto Takuji
Published: July 2016

In every network, many nodes with brains are connected by many links each other. Some nodes are, for example, computers, terminals, or routers. The both ends of a link can communicate directly each other. For example, local area network, in which every nodes are directly connected each other, looks like Figure 1, then every nodes can communicate directly to others.
On an optimal control problem for a parabolic inclusion
Authors: an Ton Bui
Published: July 2016

Let H, U be two real Hilbert spaces and let g be a proper lower semi-continuous convex function from L2 (0, T;H) into R+. For each t in [0, T], let φ(t,.) be a proper l.s.c. convex function from H into R with effective domain Dφ(t,.)) and let h be a l.s.c. convex function from a closed convex subset u of U into L2(0, T;H) with

for all u in U. The constants γ and C are positive.
A note on characteristic equation of Toeplitz operators on the spaces Ak
Authors: Cao Guangfu
Published: July 2016

Let k be any integer, k > 0. The k-th Bergman measure on unit ball B of Cn, μk, is given by
Discrete spectrum of many body Schrödinger operators with non-constant magnetic fields II
Authors: Hattori Tetsuya
Published: July 2016

This paper is continuation from [10], in which we studied the discrete spectrum of atomic Hamiltonians with non-constant magnetic fields and, more precisely, we showed that any atomic system has only finitely many bound states, corresponding to the discrete energy levels, in a suitable magnetic field. In this paper we show another phenomenon in non-constant magnetic fields that any atomic system has infinitely many bound states in a suitable magnetic field.
Integration of local actions on holomorphic fiber spaces
Authors: Heinzner Peter , Iannuzzi Andrea
Published: July 2016

It is proved that every holomorphically convex complex space endowed with an action of a compact Lie group K can be realized as an open K-stable subspace of a holomorphically convex space endowed with a holomorphic action of the complexified group KC. Similar results are obtained for holomorphic if-bundles over such spaces.
On twisted de Rham cohomology
Authors: Adolphson Alan , Sperber Steven
Published: July 2016

Consider the complex of differential forms on an open affine subvarietyUofANwith differentialwheredis the usual exterior derivative and ø is a fixed 1-form onU. For certainUand ø, we compute the cohomology of this complex.
The mixed Hodge structure on the fundamental group of the fiber type 2-arrangement
Authors: Kawahara Yukihito
Published: July 2016

The complement of an arrangement of hyperplanes is a good example of the mixed Hodge structure on the fundamental group of an algebraic variety. We compute its isomorphic class using iterated integrals in the fiber type case and then get the combinatorial and projective invariant.
On plain lattice points whose coordinates are reciprocals modulo a prime
Authors: Fujii Akio , Kitaoka Yoshiyuki
Published: July 2016

We consider, for a given large prime p, the problem of covering a square [0, p] × [0, p] with discs center at the lattice point (x, y), x and y subject to condition xy ≡ 1 (mod p) and with radius r. We are concerned with the size of r.
A sufficient condition for Nevanlinna parametrization and an extension of Heins theorem
Authors: Takahashi Sechiko
Published: July 2016

An extended interpolation problem on a Riemann surface is formulated in terms of local rings and ideals. A sufficient condition for Nevanlinna parametrization is obtained. By means of this, Heins theorem on Pick-Nevanlinna interpolation in doubly connected domains is generalized to extended interpolation.
The eigenforms of the complex Laplacian for a Hermitian submersion
Authors: Gilkey Peter B. , Leahy John V. , Park JeongHyeong
Published: July 2016

Let π : Z → Y be a Hermitian submersion. We study when the pull-back of an eigenform of the complex Laplacian on Y is an eigenform of the complex Laplacian on Z.
Integers free of small prime factors in arithmetic progressions
Authors: Xuan Ti Zuo
Published: July 2016

For real x ≥ y ≥ 2 and positive integers a, q, let Φ(x, y; a, q) denote the number of positive integers ≤ x, free of prime factors ≤ y and satisfying n ≡ a (mod q). By the fundamental lemma of sieve, it follows that for (a,q) = 1, Φ(x,y;a,q) = φ(q)-1, Φ(x, y){1 + O(exp(-u(log u- log2 3u- 2))) + (u = log x log y) holds uniformly in a wider ranges of x, y and q.

Let χ be any character to the modulus q, and L(s, χ) be the corresponding L-function. Let be a (‘exceptional’) real character to the modulus q for which L(s, ) have a (‘exceptional’) real zero satisfying > 1 - c0/log q. In the paper, we prove that in a slightly short range of q the above first error term can be replaced by where ρ(u) is Dickman function, and ρ′(u) = dρ(u)/du.

The result is an analogue of the prime number theorem for arithmetic progressions. From the result can deduce that the above first error term can be omitted, if suppose that 1 < q < (log q)A.
The determination of caloric morphisms on Euclidean domains
Authors: Shimomura Katsunori
Published: July 2016

LetDbe a domain in ℝm+1andEbe a domain in ℝn+1. A pair of a smooth mappingf:D → Eand a smooth positive function ϕ onDis called a caloric morphism if ϕ˙uofis a solution of the heat equation inDwheneveruis a solution of the heat equation inE. We give the characterization of caloric morphisms, and then give the determination of caloric morphisms. In the case ofm < n, there are no caloric morphisms. In the case ofm = n, caloric morphisms are generated by the dilation, the rotation, the translation and the Appell transformation. In the case ofm > n, under some assumption onf, every caloric morphism is obtained by composing a projection with a direct sum of caloric morphisms of ℝn+1.
Remarks on the Yablonskii-Vorob’ev polynomials
Authors: Taneda Makoto
Published: July 2016

We study the Yablonskii-Vorob’ev polynomial associated with the second Painlevé equation. To study other special polynomials (Okamoto polynomials, Umemura polynomials) associated with the Painlevé equations, our purely algebraic approach is useful.
A unitary representation of the basical central extension of a loop group
Authors: Léandre Rémi
Published: July 2016

We construct a measure over the string bundle associated to the loop space of a Riemannian manifold. We deduce a representation of a finite energy Kac-Moody group analoguous to the energy representation.
On Unit Groups of Absolute Abelian Number Fields of Degree pq
Authors: Yokoi Hideo
Published: July 2016

In this note, we denote by Q the rational number field, by EΩ the whole unit group of an arbitrary number field Ω of finite degree, and by rΩ the rank of where generally G* for an arbitrary abelian group G means a maximal torsion-free subgroup of G. (NK/ΩEK)* is shortly denoted by and (G1 : G2) is, as usual, the index of a subgroup G2 in G1.
On the Continuity of Brownian Motion with a Multidimensional Parameter
Authors: Sirao Tunekiti
Published: July 2016

A stochastic process X(A, ω) is called Brownian motion with an N-dimensional parameter when it satisfies the following conditions:

1) For any positive integer n and any set of points A1, A2, …, An in an N-dimensional Euclidian space EN, the joint variable is subject to an n-dimensional Gaussian distribution having the vector 0 as its mean vector.
Twistor theory of manifolds with Grassmannian structures
Authors: Machida Yoshinori , Sato Hajime
Published: July 2016

As a generalization of the conformal structure of type (2, 2), we study Grassmannian structures of type (n, m) forn, m≥ 2. We develop their twistor theory by considering the complete integrability of the associated null distributions. The integrability corresponds to global solutions of the geometric structures.

A Grassmannian structure of type (n, m) on a manifoldMis, by definition, an isomorphism from the tangent bundleTMofMto the tensor productV ⊗ Wof two vector bundlesVandWwith ranknandmoverMrespectively. Because of the tensor product structure, we have two null plane bundles with fibresPm-1(ℝ) andPn-1(ℝ) overM. The tautological distribution is defined on each two bundles by a connection. We relate the integrability condition to the half flatness of the Grassmannian structures. Tanaka’s normal Cartan connections are fully used and the Spencer cohomology groups of graded Lie algebras play a fundamental role.

Besides the integrability conditions corrsponding to the twistor theory, the lifting theorems and the reduction theorems are derived. We also study twistor diagrams under Weyl connections.
On a regularity property and a priori estimates for solutions of nonlinear parabolic variational inequalities
Authors: Nagase Haruo
Published: July 2016

In this paper we consider the following nonlinear parabolic variational inequality; u(t) ∈ D(Φ) for all where Δp is the so-called p-Laplace operator and Φ is a proper, lower semicontinuous functional. We have obtained two results concerning to solutions of this problem. Firstly, we prove a few regularity properties of solutions. Secondly, we show the continuous dependence of solutions on given data u0 and f.
A note on the congruent distribution of the number of prime factors of natural numbers
Authors: Kubota Tomio , Yoshida Mariko
Published: July 2016

Let n = p1p2 … pr be a product of r prime numbers which are not necessarily different. We define then an arithmetic function µm(n) by

where m is a natural number. We further define the function L(s, µm) by the Dirichlet series

and will show that L(s, µm), (m ≥ 3), has an infinitely many valued analytic continuation into the half plane Re s > ½.
Peterson-type dimension formulas for graded Lie superalgebras
Authors: Kang Seok-Jin , Kwon Jae-Hoon , Oh Young-Tak
Published: July 2016

Let be a free abelian group of finite rank, let Γ be a sub-semigroup of satisfying certain finiteness conditions, and let be a (Γ × Z2)-graded Lie superalgebra. In this paper, by applying formal differential operators and the Laplacian to the denominator identity of , we derive a new recursive formula for the dimensions of homogeneous subspaces of . When applied to generalized Kac-Moody superalgebras, our formula yields a generalization of Peterson’s root multiplicity formula. We also obtain a Freudenthal-type weight multiplicity formula for highest weight modules over generalized Kac-Moody superalgebras.
Uniformly perfect sets and distortion of holomorphic functions
Authors: Zheng Jian-Hua
Published: July 2016

We investigate the uniform perfectness on a boundary point of a hyperbolic open set and distortion of a holomorphic function from the unit disk Δ into a hyperbolic domain with a uniformly perfect boundary point, especially of a universal covering map of such a domain from Δ, and we obtain similar results to celebrated Koebe’s Theorems on univalent functions.
Lp-curvature and the Cauchy-Riemann equation near an isolated singular point
Authors: Harris Adam , Tonegawa Yoshihiro
Published: July 2016

Let X be a complex n-dimensional reduced analytic space with isolated singular point x0, and with a strongly plurisubharmonic function ρ : X → [0, ∞) such that ρ(x0) = 0. A smooth Kähler form on X \ {x0} is then defined by i∂∂ρ. The associated metric is assumed to have -curvature, to admit the Sobolev inequality and to have suitable volume growth near x0. Let E → X \ {x0} be a Hermitian-holomorphic vector bundle, and ξ a smooth (0, 1)-form with coefficients in E. The main result of this article states that if ξ and the curvature of E are both then the equation has a smooth solution on a punctured neighbourhood of x0. Applications of this theorem to problems of holomorphic extension, and in particular a result of Kohn-Rossi type for sections over a CR-hypersurface, are discussed in the final section.
On the slope of fibred surfaces
Authors: Barja Miguel Ángel , Zucconi Francesco
Published: July 2016

We give an asymptotically sharp lower bound for the slope λ(f) of a fibration f : S → B, where S is a surface and B is a curve, if there exists an involution on the general fibre F of f. We also construct a new lower bound of λ(f) depending increasingly on the irregularity of S; as an application of this new bound we have a criteria to control the existence of other fibrations on S.
Nonlinear potentials in function spaces
Authors: Rao Murali , Vondraćek Zoran
Published: July 2016

We introduce a framework for a nonlinear potential theory without a kernel on a reflexive, strictly convex and smooth Banach space of functions. Nonlinear potentials are defined as images of nonnegative continuous linear functionals on that space under the duality mapping. We study potentials and reduced functions by using a variant of the Gauss-Frostman quadratic functional. The framework allows a development of other main concepts of nonlinear potential theory such as capacities, equilibrium potentials and measures of finite energy.
Birth and death processes in randomly fluctuating environments
Authors: Ichihara Kanji
Published: July 2016

A birth and death process in a time-dependent random environment is introduced. We will discuss the recurrence and transience properties for the process.
On purely periodic beta-expansions of Pisot numbers
Authors: Sano Yuki
Published: July 2016

We characterize numbers having purely periodic β-expansions where β is a Pisot number satisfying a certain irreducible polynomial. The main tool of the proof is to construct a natural extension on a d-dimensional domain with a fractal boundary.
Shellability of semigroup rings
Authors: Aramova Annetta , Herzog Jürgen , Hibi Takayuki
Published: July 2016

The concepts of Λ-shellability of locally finite posets as well as of extendable sequentially Koszul algebras will be introduced. It will be proved that the divisor poset of a homogeneous semigroup ring is Λ-shellable if and only if the semigroup ring is extendable sequentially Koszul. Examples of extendable sequentially Koszul semigroup rings contain all monomial ASL’s (algebras with straightening laws) and all second squarefree Veronese subrings.
Hardy spaces estimates for multilinear operators with homogeneous kernels
Authors: Ding Yong , Lu Shanzhen
Published: July 2016

In this paper the authors prove that a class of multilinear operators formed by the singular integral or fractional integral operators with homogeneous kernels are bounded operators from the product spacesLp1× Lp2× · · · × LpK(ℝn) to the Hardy spacesHq(ℝn) and the weak Hardy spaceHq,∞(ℝn), where the kernel functions Ωijsatisfy only theLs-Dini conditions. As an application of this result, we obtain the (Lp, Lq) boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.
A canonical bundle formula for certain algebraic fiber spaces and its applications
Authors: Fujino Osamu
Published: July 2016

We investigate period maps of polarized variations of Hodge structures of weight one or two. We treat the case when the period domains are bounded symmetric domains. We deal with a relationship between canonical extensions of some Hodge bundles and automorphic forms. As applications, we obtain a canonical bundle formula for certain algebraic fiber spaces, such as Abelian fibrations, K3 fibrations, and solve Iitaka’s famous conjecture Cn,m for some algebraic fiber spaces.
Classification of the periodic monodromies of hyperelliptic families
Authors: Ishizaka Mizuho
Published: July 2016

We classify the periodic monodromies which are realized as the monodromies of hyperelliptic families.
On a generalization of test ideals
Authors: Hara Nobuo , Takagi Shunsuke
Published: July 2016

The test ideal τ(R) of a ring R of prime characteristic is an important object in the theory of tight closure. In this paper, we study a generalization of the test ideal, which is the ideal τ(at) associated to a given ideal a with rational exponent t ≥ 0. We first prove a key lemma of this paper (Lemma 2.1), which gives a characterization of the ideal τ(at). As applications of this key lemma, we generalize the preceding results on the behavior of the test ideal τ(R). Moreover, we prove an analogue of so-called Skoda’s theorem, which is formulated algebraically via adjoint ideals by Lipman in his proof of the “modified Briançon-Skoda theorem.”
On Hyperbolicity of balanced domains
Authors: Park Sung-Hee
Published: July 2016

We compare the hyperbolicity with respect to the Lempert function with the other hyperbolicities in the class of pseudoconvex balanced domains.
Onl-Adic Iterated Integrals, III Galois Actions on Fundamental Groups
Authors: Wojtkowiak Zdzisław
Published: July 2016

We continue to studyl-adic iterated integrals introduced in the first part. We shall calculate explicitlyl-adic logarithm andl-adic polylogarithms. Next we shall use these results to study Galois representations on the fundamental group of.
A Remark on Partial Resolutions of 3-Dimensional Terminal Singularities
Authors: Hayakawa Takayuki
Published: July 2016

Let X be a 3-dimensional terminal singularity of index ≥ 2. We study projective birational morphisms ϕ: Y → X such that the exceptional divisor of ϕ consists of all prime divisors with discrepancies < 1 (resp. ≤ 1) over X.
Renormalization Of The Local Time For The d-Dimensional Fractional Brownian Motion With N Parameters
Authors: Eddahbi M. , Lacayo R. , Solé J. L. , Vives J. , Tudor C. A.
Published: July 2016

We study the asymptotic behavior in Sobolev norm of the local time of the d-dimensional fractional Brownian motion with N-parameters when the space variable tends to zero, both for the fixed time case and when simultaneously time tends to infinity and space variable to zero.
Nakajima Monomials and Crystals for Special Linear Lie Algebras
Authors: Lee Hyeonmi
Published: July 2016

Nakajima introduced a certain set of monomials realizing the irreducible highest weight crystalsB(λ). The monomial set can be extended so that it contains crystalB(∞) in addition toB(λ). We present explicit descriptions of the crystalsB(∞) andB(λ) over special linear Lie algebras in the language of extended Nakajima monomials. There is a natural correspondence between the monomial description and Young tableau realization, which is another realization of crystalsB(∞) andB(λ).
Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, II
Authors: Shoji Toshiaki
Published: July 2016

This paper is concerned with the problem of the determination of unknown scalars involved in the algorithm of computing the generalized Green functions of reductive groups G over a finite field. In the previous paper, we have treated the case where G = SLn. In this paper, we determine the scalars in the case where G is a classical group Sp2n or SON for arbitrary characteristic.
On L-Functions of Twisted 3-Dimensional Quaternionic Shimura Varieties
Authors: Virdol Cristian
Published: July 2016

In this paper we compute and continue meromorphically to the entire complex plane the zeta functions of twisted quaternionic Shimura varieties of dimension 3. The twist of the quaternionic Shimura varieties is done by a mod ℘ representation of the absolute Galois group.
Normality, Quasinormality and Periodic Points
Authors: Chang Jianming
Published: July 2016

Let M > 1 be a positive number. Let be a family of holomorphic functions f in some domain D ⊂ ℂ for which there exists an integer k = k(f) > 2 such that |(fk)′(ζ)| ≤ Mk for every periodic point ζ of period k of f in D. We show first that is quasinormal of order at most one in D. This strengthens a result of W. Bergweiler. Secondly, for the case M = 1, we prove that is normal in D if there exists a positive number K < 3 such that | f(η)| ≤ K for each f ∈ and every fixed point η of f in D. This improves a result of M. Esséen and S. J. Wu. We also construct an example which shows that the condition |f’(η)| ≤ K < 3 can not be replaced by | f′(η) | < 3.
Enriques Surfaces Covered by Jacobian Kummer Surfaces
Authors: Ohashi Hisanori
Published: July 2016

This paper classifies Enriques surfaces whose K3-cover is a fixed Picard-general Jacobian Kummer surface. There are exactly 31 such surfaces. We describe the free involutions which give these Enriques surfaces explicitly. As a biproduct, we show that Aut(X) is generated by elements of order 2, which is an improvement of the theorem of S. Kondo.
Some Studies on Group Characters
Authors: Itô Noboru
Published: July 2016

The theory of group characters was originated by G. Frobenius and has been studied by many authors including, above all, I. Schur and W. Burnside. As to the modular theory we owe it to recent works by R. Brauer and his collaborators, including T. Nakayama and C. Nesbitt, which clarified also the connections between the structure theory and the representation theory.
Crossed Products and Hereditary Orders
Authors: Williamson Susan
Published: July 2016

Let S be the integral closure of a discrete rank one valuation ring R in a finite Galois extension of the quotient field of R, and denote the Galois group of the quotient field extension by G. It has been proved by Auslander and Rim in [4] that the trivial crossed product Δ(l, S, G) is an hereditary order for tamely ramified extensions S of R and that Δ(l, S, G) is a maximal order if and only if S is an unramified extension of R. The purpose of this paper is to study the crossed product Δ(f, S, G) where [f] is any element of H2(G, U(S)) and S is a tamely ramified extension of R with multiplicative group of units U(S).
Maximum Principles in the Potential Theory
Authors: Kishi Masanori
Published: July 2016

Ninomiya, in his thesis [13] on the potential theory with respect to a positive symmetric continuous kernel G on a locally compact Hausdorff space Ω, proves that G satisfies the balayage (resp. equilibrium) principle if and only if G satisfies the domination (resp. maximum) principle. He starts from the Gauss-Ninomiya variation and shows that for any given compact set K in Ω and any positive upper semi-continuous function u on K, there exists a positive measure μ on K such that its potential Gμ is ≥ u on the support of μ and Gμ≥u on K almost everywhere with respect to any positive measure with finite energy.
Green Potential of Evans Type on Royden’s Compactification of a Riemann Surface
Authors: Nakai Mitsuru
Published: July 2016

Let R be a hyperbolic Riemann surface and gw(z) be the Green function on R with its pole w in R. We denote by (R) the totality of sequences of points in R not accumulating in R and
Unique Continuation Property of Non-Positive Weak Subsolutions for Parabolic Equations of Higher Order
Authors: Hayashida Kazunari
Published: July 2016

When L is a parabolic differential operator of second order, Nirenberg [6] proved the maximum principle for the function u which has second order continuous derivatives and satisfies Lu≧0. Recently Friedman [2] has proved the maximum principle for the measurable function satisfying Lu≧O in the wide sense. This function is named a weakly L-subparabolic function. On the other hand, Littman [5] earlier than Friedman, has defined a weakly A- subharmonic function for an elliptic differential operator A of second order and has showed the maximum principle for it.
On Certain Mappings of Riemannian Manifolds
Authors: Kurita Minoru
Published: July 2016

In this paper we consider certain tensors associated with differentiable mappings of Riemannian manifolds and apply the results to a p-mapping, which is a special case of a subprojective one in affinely connected manifolds (cf. [1], [7]). The p-mapping in Riemannian manifolds is a generalization of a conformal mapping and a projective one. From a point of view of differential geometry an analogy between these mappings is well known. On the other hand it is interesting that a stereographic projection of a sphere onto a plane is conformal, while a central projection is projectve, namely geodesic-preserving. This situation was clarified partly in [6]. A p-mapping defined in this paper gives a precise explanation of this and also affords a certain mapping in the euclidean space which includes a similar mapping and an inversion as special cases.
The Order of Certain Classes of Functions Defined in the Unit Disk
Authors: Rung D. C.
Published: July 2016

Let D denote the open unit disk in the complex plane and let C be the boundary of D. If, for a given complex-valued function f(z) defined in D, the existence of a subset M of C is known, with the linear measure of M equal to 2 π, as well as an estimate on the growth of |f/(z)| I on sequences in D which tends to a point of M, then such a result will be called a “statistical” result on order. This terminology is due to Lelong-Ferrand [3].
Homology of Non-Commutative Polynomial Rings
Authors: Sridharan R.
Published: July 2016

LetΓbe a ring with unit element and letΛbe the Ore extension ofΓwith respect to a derivationdofΓ[4, 3]. It is shown in [3] that l.gl. dimΛ≦ 1 + l.gl. dimΓ. It is not in general possible to replace this inequality by equality.
On α-Harmonic Functions
Authors: Itô Masayuki
Published: July 2016

M. Riesz [8] introduced the notion of α-superharmonic functions in n(≥1)-dimensional Euclidean space Rn in connection with the potential of order α. In this paper, we shall first define the α-superharmonic and α-harmonic functions in a domain D. In case α = 2, they coincide with ones in the usual sense.
Radon-Nikodym Densities between Harmonic Measures on the Ideal Boundary of an Open Riemann Surface
Authors: Nakai Mitsuru
Published: July 2016

Resolutive compactification and harmonic measures. Let R be an open Riemann surface. A compact Hausdorff space R* containing R as its dense subspace is called a compactification of R and the compact set Δ = R* -R is called an ideal boundary of R. Hereafter we always assume that R does not belong to the class OG. Given a real-valued function f on Δ, we denote by the totality of lower bounded superharmonic (resp. upper bounded subharmonic) functions sonis satisfying
Über eine Diophantische Gleichung von Ramanujan-Nagell und ihre Verallgemeinerung
Authors: Hasse Helmut
Published: July 2016

Einleitung: Die Ramanujan-Nagellshe Gleichung (Basis 2, Diskriminante—7).

Verallgemeinerung auf beliebige negative Diskriminanten D ≡ 1 mod. 23: Systematischer Ansatz zur Behandlung und erste notwendige Bedingungen für Lösbarkeit und Lösungen.

Endlichkeit der Lösungsanzahl.

Notwendige Bedingung für die Lösungen durch Kongruenzbetrachtung nach Potenzen von 2.

Notwendige Bedingung für die Lösungen durch Kongruenzbetrachtung nach Potenzen eines Primteilers von D.
On a Homotopy Classification of Mappings of an (n+1) Dimensional Complex Into an Arcwise Connected Topological Space Which is Aspherical in Dimensions Less Thann (n >2)
Authors: Shimada Nobuo , Uehara Hiroshi
Published: July 2016

Pontrjagin classified mappings of a three dimensional sphere into anndimensional complex, where he made use of a new type of product of cocycles. By the aid of the generalized Pontrjagin’s product of cocycles Steenrod enumerated effectively all the homotopy classes of mappings of an (n+1) dimensional complex into annsphere. According to the recent issue of the Mathematical Reviews it is reported that M. M. Postnikov extended Steenrod’s case to the case where an arcwise connected topological space which is aspherical in dimensions less thann, takes place of annsphere. (Postnikov M. M., Classification of continuous mappings of an(n+1)dimensional complex into a connected topological space which is aspherical in dimensions less thann. Doklady Akad. Nauk SSSR (N.S.) 71., 1027-1028, 1950 (Russian. No. proof is given.)) But here in Japan no details are yet to hand. We intend to give a solution to this problem in case wheren>2, and also to give an application concerning the(n+ 3)-extension cocycle.
Characterization of Certain Riemann Spaces by Development
Authors: Kurita Minoru
Published: July 2016

The purpose of this paper is to characterize the Riemann space whose line element is given by

Through the whole description we use the indices i, j, α, β, γ, λ, μ, ν when they run as follows
Circular Slit Disk with Infinite Radius
Authors: Oikawa Kótaro , Suita Nobuyuki
Published: July 2016

Let W be a plane domain such that ∞∉W. Given a point a∉W and a boundary component C of W, consider the family consisting of all the functions f satisfying the following conditions: f is regular and univalent in W, f(a) = 0, f′(a) = l, and the image f(C) of C under f is the outer boundary component of the image domain f(W). Set

and
On a Conjecture of J.S. Frame
Authors: Ito Noboru
Published: July 2016

Let be a transitive group of degree n, and let be the stabilizer of a symbol in ®. Then we owe to J.S. Frame the following remarkable relations between the lengths ni of the orbits of and the degrees fi of the absolutely irreducible components of the permutation matrix representation * of :

(A) If the irreducible constituents of * are all different, then the rational number

is an integer, where k is the number of the orbits of
Une Remarque sur Hypoellipticité
Authors: Kato Yoshio
Published: July 2016

Un opérateur différentiel P(x,D) à coefficients C∞ est dit hypoelliptique si toute solution de l’équation

P(x,D)u=f

est indéfiniment derivable quand f∈C∞. II est bien connu qu’un opérateur formellement hypoelliptique est hypoelliptique (dont la démonstration a été donnée par plusieurs auteurs). D’autre part, Trèves [2] a introduit une condition suffisante sous laquelle un opérateur est hypoelliptique et qui englobe le cas formellement hypoelliptique (voir Définition 1).
On Total Masses of Balayaged Measures
Authors: Itô Masayuki
Published: July 2016

Beurling and Deny [1], [2] introduced the notion of Dirichlet spaces. They [2] showed the existence of balayaged measures and equilibrium measures in the theory of Dirichlet spaces. In this paper, we shall show that the following equivalence is valid for a Dirichlet space on a locally compact Hausdorff spaceX.
The Centers of Semi-Simple Algebras over a Commutative Ring
Authors: Endo Shizuo , Watanabe Yutaka
Published: July 2016

Recently A. Hattori introduced in [7], [8], [9] the notion of simple algebras over a commutative ring. Especially, in [9], he examined, as a fundamental problem on simple algebras, whether a directly indecomposable semi-simple algebra is simple or not and gave affirmative answers to this in some particular cases. In this note we shall first prove, as a complete answer to this, that any directly indecomposable semi-simple algebra over a Noetherian ring is simple.
A Study on Formal Deductions in the Primitive Logic
Authors: Ono Katuzi
Published: July 2016

Main purpose of the present paper is to study formal deductions described along the line of my former work [1]. In the present paper, I restrict myself to the primitive logic. To extend this method to other logics such as the lower classical predicate logic or the intuitionistic predicaste logic, my way of practical discription has to undergo a certain extent of modification.
Existence of Non-Trivial Deformations of Some Inseparable Extension Fields
Authors: Kimura Hiroshi
Published: July 2016

A deformation theory for rings and algebras was introduced recently by M. Gerstenhaber [1]. Let K be an extension of a field k, and p denotes the characteristic. One of his results is that, if K is separable over k, then it is rigid. It was conjectured in [1] that, if K is not separable over k, then it is not rigid, and if it is further finitely generated, then an integrable element of (see [2]) will be found in the image of Sqp. In this note we shall study the above conjecture in certain special case.
Higher Extensions of Abelian Varieties
Authors: Oort Frans , Oda Tadao
Published: July 2016

In this paper we prove:

THEOREM: Let k be an algebraically closed field of characteristic p > 0, and let X and Y be abelian varieties over k. Then the group Ext2(X, Y) = 0.
A Note on Homotopy Invariance of Tangent Bundles
Authors: Ishimoto Hiroyasu
Published: July 2016

Although tangent bundles of manifolds are not always homotopically invariant, but in some categories of the manifolds they can be homotopically invariant.

In this note, I show that tangent bundles of π-manifolds and almost parallelizable manifolds depend only on their homotopy types.
The Continuation of sections of Torsion-Free Coherent Analytic Sheaves
Authors: Fujimoto Hirotaka
Published: July 2016

The purpose of this paper is to extend the continuation theorem of holomorphic functions, especially the generalized Hartogs-Osgood’s theorem given in the previous papers [6] and [8], to the case of sections of torsion-free coherent analytic sheaves over a reduced complex space. In the following, we restrict ourselves only to reduced complex spaces.
A Correction to “The Schur Multipliers of the Mathieu Groups”
Authors: Burgoyne N. , Fong P.
Published: July 2016

In the paper [1] mentioned in the title, the authors attempted to determine the Schur multipliers of the five simple Mathieu groups. In rechecking the calculations, we find that an error was made, leading to incorrect results for M12 and M22. Our purpose here is to compute again the multipliers of M12 and M22, which turn out to be cyclic groups of orders 2 and 6 respectively. The multipliers of M11M23, M24 were originally (and correctly) determined to be trivial.
A Remark on Peirce’s Law
Authors: Tugué Tosiyuki , Nagata Shûrô
Published: July 2016

Before stating the purpose, we explain some propositional logics treated in this paper. The logical symbols we use are: implication →, conjunction ∧, disjunction ∨, and the propositional constant ⋏ denoting contradiction.
On The Holomorphic Automorphism Groups of Complex Spaces
Authors: Fujimoto Hirotaka
Published: July 2016

For a complex space X we consider the group Aut (X) of all automorphisms of X, where an automorphism means a holomorphic automorphism, i.e. an injective holomorphic mapping of X onto X itself with the holomorphic inverse. In 1935, H. Cartan showed that Aut (X) has a structure of a real Lie group if X is a bounded domain in CN([7]) and, in 1946, S. Bochner and D. Montgomery got the analogous result for a compact complex manifold X ([2] and [3]). Afterwards, the latter was generalized by R.C. Gunning ([11]) and H. Kerner ([16]), and the former by W. Kaup ([14]), to complex spaces. The purpose of this paper is to generalize these results to the case of complex spaces with weaker conditions. For brevity, we restrict ourselves to the study of σ-compact irreducible complex spaces only.
Some types of Separable Extensions of Rings
Authors: Hirata Kazuhiko
Published: July 2016

In [5] we defined the notion of separable extensions of a ring as a generalization of that of separable algebras. In this paper we try to introduce the notion of ‘central’ separable algebras to separable extensions. Such extensions are viewed in §2. But we do not know that it is suitable or not to call them central separable extensions. As the Morita theorem for projective generators is fundamental to examine the central separable algebras we generalize it in §1. Let R be a ring and let A and B be left R-modules. We assume that R-module B is isomorphic to a direct summand of a finite direct sum of copies isomorphic to A.
On Commutative Compositions Determined by Their Origins
Authors: Morikawa Hisasi
Published: July 2016

Let K be the universal domain. Let G be a finite additive group of odd order |G| and Xa(a ∈ G) be indeterminates indexed by the elements in G. We mean by PG the projective space Projk(K[(Xa)a ∈ G]).
On Some Properties of Normal Meromorphic Functions in the Unit Disc
Authors: Zinno Toshiko
Published: July 2016

We denote by D the unit disc {z; |z| < 1} and by the totality of one to one conformal mappings z′ = s(z) of D onto itself. A meromorphic function f(z) in D is normal if and only if the family is a normal family in D in the sense of Montel. We denote by the totality of the normal meromorphic functions in D.
On the Formal Theta Functions of Countably Many Variables
Authors: Tahara Kenichi
Published: July 2016

In the previous paper [6] we have shown the examples of hyperelliptic Riemann surfaces of infinite genus such that the Riemann’s theta functions associated with them are absolutely convergent.
Separable Extensions and Centralizers of Rings
Authors: Hirata Kazuhiko
Published: July 2016

We have introduced in [9] a type of separable extensions of a ring as a generalization of the notion of central separable algebras. Unfortunately it was unsuitable to call such extensions ‘central5 as Sugano pointed out in [15] (Example below Theorem 1.1). Some additional properties of such extensions were given in [15]. Especially Propositions 1. 3 and 1. 4 in [15] are interesting and suggested us to consider the commutor theory of separable extensions.
On the Upper and Lower Class For Gaussian Processes with Several Parameters
Authors: Kawada Takayuki
Published: July 2016

1.In the study on Hölder-continuity of Brownian motion, A.N.Kol-mogorov introduced the concept of upper and lower classes and presented a criterion with the integral form to test whether some function belongs to upper or lower class; the so-called Kolmogorov’s test (I.Petrovesky [10]). P.Lévy considered the upper and lower class with regard to the uniform continuity of Brownian motion. We shall recall the definition of the upper and lower classes. We shall call <p(t) a function belonging to the upper class with regard to the uniform continuity of Brownian motion x(t) if there exists a positive number s{w) such that, for almost all w,

implies

(1.1)
On a Uniqueness Theorem
Authors: Gavrilov V. I.
Published: July 2016

1. Let D be the open unit disk and r be the unit circle in the complex plane, and denote by Q the extended complex plane or the Rie-mann sphere.
On Reducibility of Provability in the Primitive Logic [LO]
Authors: Ito Jiro
Published: July 2016

In the present paper, we would like to show a theorem concerning with reducibility of provability in the primitive logic. This theorem seems to suggest a procedure to find the proof-note of a given proposition which is provable in the primitive logic.
On Some Results on Theta Constants (I)
Authors: Morikawa Hisasi
Published: July 2016

D. Mumford has shown an excelent algebralization of theory of theta constants and theta functions in his papers: On the equations defining abelian varieties I, II, III (Invent. Math. 1. 237-354 (1966), 3. 75-135 (1967), 3. 215-244) (1967). Our starting point and idea, however, are something different from those of Mumford; we begin our study at characterizing abelian addition formulae among all the possible addition formulae, and we want to give expressions to everything in words of matric notations.
On a Classical Theta-Function
Authors: Kubota Tomio
Published: July 2016

The purpose of this paper is to get a certain explicit expression of automorphic factors, formulated rather differently than usual, of the classically well known theta function

(1)
On the Boundary Condition of Transport Semigroup
Authors: Watanabe Toitsu
Published: July 2016

Let S be the product space of finite interval [—r, r] and two points Θ = {θ±1}.