bluuebunny/crossref_metadata_2025 huggingface dataset:
Belemnite-based strontium, carbon and oxygen isotope stratigraphy of the type area of the Maastrichtian Stage
Authors: Vonhof H.B. , Jagt J.W.M. , Immenhauser A. , Smit J. , van den Berg Y.W. , Saher M. , Keutgen N. , Reijmer J.J.G.
Published: July 2016

Belemnitellid cephalopods from the Maastrichtian stratotype area (southeast Netherlands) are shown to be comparatively well preserved. Although partial diagenetic alteration has been observed, micromilling techniques have permitted the extraction of pristine belemnite calcite, suitable for the reconstruction of strontium (Sr), oxygen (O) and carbon (C) isotope variation of Maastrichtian seawater. A distinct Sr isotope pattern in the Maastricht record can be matched stratigraphically with records from Hemmoor (northern Germany), El Kef (Tunisia) and ODP site 690 (Maud Rise, Antarctica), leading to a new chemostratigraphical age model for the Maastrichtian stratotype section. Our data improve currently applied strontium isotope stratigraphical reference curves by revealing an Sr isotope inflection pattern near the lower/upper Maastrichtian boundary that is a potentially diagnostic feature for intra-Maastrichtian stratigraphical correlation between distant sections. Belemnites further show significant stratigraphical oxygen isotope variation through the Maastrichtian. We interpret this variation to have resulted from palaeoceanographic reorganisations in the Atlantic Ocean during this time interval.
Unravelling the depositional environment of the Archaean Rajkharsawan conglomerate (Jharkhand, eastern India)
Authors: van Loon A.J. , Mazumder R. , De S.
Published: July 2016

Large conglomerate lenses occur in a fine-grained siliciclastic succession of the Singhbhum craton, eastern India. They overlie an Archaean orthogneiss, from which they are separated by a palaeosol. Neither the conglomerates nor the directly overlying rocks have been dated, but the conglomerate unit is assumed to have also an Archaean age. The conglomerate lenses occur within a succession of pelitic and mafic schists, and the depositional environment of this conglomerate/schist unit had not been clarified thus far. On the basis of a combination of the vertical and horizontal distribution of the conglomerates, their stratigraphic position and analysis of their sedimentological characteristics and the sedimentological context, it is concluded that the succession must have developed in a fluvial lowland environment where volcanic input contributed significantly to the sediment accumulation.
Multi-proxy analysis: a reflection on essence and potential pitfalls
Authors: Vandenberghe J.
Published: July 2016

Multi-disciplinarity and multi-proxy approaches are necessary to understand the processes in complex earth systems. However, unlimited and uncontrolled multi-proxy-correlations may be risky. A number of case studies illustrate the potential pitfalls when the processes that drive the individual proxies have no common causal significance or dating is not precise enough. Crossing thresholds at different levels and delay times may also be factors that hamper direct correlations of proxies. Multi-proxy analysis of the intrinsic relationships between proxies in a system is the primary task before any correlation should be made.
Why Splinter? Parties that Split from the FSLN, FMLN and URNG
Authors: ALLISON MICHAEL E.
Published: July 2016

Following the ends to the civil wars in Nicaragua, El Salvador and Guatemala, the revolutionary coalitions that had led the fight against authoritarian regimes began to fracture. However, none of the splinter parties that broke from the Sandinista National Liberation Front, Farabundo Martí National Liberation Front, and Guatemalan National Revolutionary Unit has succeeded on their own as political parties. In this article, I argue that there is no single reason to explain the poor performances of the Democratic Party (PD), the Renovating Movement (MR), and the Democratic Front Party (FDR) in El Salvador, the Sandinista Renovation Movement (Renovate-MRS) and the Movement to Rescue Sandinismo (Rescue-MRS) in Nicaragua, and the New Nation Alliance (ANN) in Guatemala. However, their limited financial resources, alliances with non-revolutionary centrist and centre-right parties, and voter tendency to overlook internal ideological and personal debates within the original political parties, especially the FSLN and FMLN, have not helped.
On Montel’s Theorem
Authors: Kawakami Yoshiro
Published: July 2016

In this note we shall prove a theorem which is related to Montel’s theorem [1] on bounded regular functions. Let E be a measurable set on the positive y-axis in the z( = x + iy)-plane, E(a, b) be its part contained in 0 ≦ a ≦ y ≦ b, and ∣E(a, b)∣ be its measure. We define the lower density of E at y = 0 by

LEMMA, Let E be a set of positive lower density λ at y = 0. Then E contains a subset E1 of the same lower density at y = 0 such that E1 ∪ {0} is a closed set.
Quadratic variation and energy
Authors: Graversen S. E. , Rao M.
Published: July 2016

It is well known that the concept of energy has played a fruitful role in potential theory and Markov processes. Cartan’s work [6] led to kernel-free potential theories of Beurling-Deny [2]. Since then many authors have worked on this, M. Fukushima [8], M. Silverstein [16], J. Bliedner [3], Berg-Forst [1], to name some. In these works, however, the main thrust is Hubert space theoretic.
Le principe semi-complet du maximum pour les noyaux de convolution réels
Authors: Itô Masayuki
Published: July 2016

Soit X un groupe abélien localement compact, non-compact, séparé et dénombrable à l’infini. On désignera par ξ une mesure de Haar fixée sur X. Pour les noyaux de convolution réels sur X, le principe semi-complet du maximum est fondamental dans la théorie du potentiel. Soit N un noyau de convolution réel sur X vérifiant le principe semi-complet du maximum (désigné par Nє(PSM)). Pour déterminer l’allure de N à l’infini, la N-réduite ηN, δ de N à l’infini δ joue un rôle essentiel. Pour une exhaustion de compacts de est décroissante et est une mesure de Radon réelle sur X ou bien, pour une fonction finie et continue dans X à support compact quelconque, est la iV-réduite de N sur CKn. Dans ce cas, est indépendant du choix de Posons
On the calculation of the units of algebraic number fields
Authors: Azuhata Takashi
Published: July 2016

The method to find a system of fundamental units were given by G. F. Voronoi in the case of purely cubic fields (see B. N. Delone and D. K. Faddeev [1]), and by K. K. Biilebic [2] in general case of algebraic number fields except for quadratic fields. But they are rather complicated for direct calculation. On the other hand, in some special cases, units can be calculated by the Jacobi-Perron algorithm which is a generalization of the continued fractional expansion (see, for example, L. Bernstein [3]). In this paper, we will show the new method to calculate a system of independent units by multiplying several numbers. We will give some examples for purely cubic fields in Section 3.
Toward a theory of generalized Cohen-Macaulay modules
Authors: Trung Ngô Viêt
Published: July 2016

Throughout this paper, A denotes a noetherian local ring with maximal ideal m and M a finitely generated A-module with d: = dim M≥1.
Tensor products and localizations of algebras
Authors: Bowman S. R. , O’Carroll L.
Published: July 2016

In a recent paper [5], it was shown that the tensor product of a finite number of fields over a common subfield satisfies the property that each localization at a prime ideal is a primary ring (in the sense that a zero-divisor is in fact a nilpotent element).

In the first section of this paper, we exploit the properties of associated primes and of flat extensions so as to generalize the above result to zero-dimensional algebras; a simple example shows that this is the best one can hope for. The converse situation is also investigated.
Remarks on the paper “Transient Markov convolution semi-groups and the associated negative definite functions”
Authors: Itô Masayuki
Published: July 2016

Let X be a locally compact and σ-compact abelian group and let denote the dual group of X. We denote by ξ a fixed Haar measure on X and by the Haar measure associated with ξ. In [2], we show the following

Theorem. Let (αt)t≧0 be a sub-Markov convolution semi-group on X and let ψ be the negative definite function associated with (αt)t≧0. Then (αt)t≧0 is transient if and only if Re (1/ψ) is locally -summable.
Local densities of quadratic forms and Fourier coefficients of Eisenstein series
Authors: Kitaoka Yoshiyuki
Published: July 2016

Local densities of quadratic forms are important invariants in the theory of quadratic forms and they appear in Fourier coefficients of Eisenstein series. But it is not easy to evaluate them. To study their properties, it is desirable to look for relations among them, and it is known that there are many relations [3], but they are not concise. We consider a different kind of relations here and improve a result of Zharkovskaja [8, 9] in the case of Eisenstein series as an application.
Nonstandard Arithmetic of Polynomial Rings
Authors: Yasumoto Masahiro
Published: July 2016

Let f(X, T1,…, Tm) be a polynomial over an algebraic number field k of finite degree. In his paper [2], T. Kojima proved

THEOREM. Let K = Q. if for every m integers t1, …, tm, there exists an r ∈ K such that f(r, t1, …, tm) =), then there exists a rational function g(T1,…,Tm) over Q such that

F(g(T1,…,Tm), T1,…,T)= 0.
Generalized Radon Transform and Lévy’s Brownian Motion, II
Authors: Noda Akio
Published: July 2016

As a continuation of the author’s paper, we shall investigate the null spaces of a dual Radon transform R*, in connection with a Lévy’s Brownian motion X with parameter space (Rn, d). We shall follow the notation used in (I).
Problèmes d’Interpolation dans des Espaces d’Ultradistributions de Type Roumieu
Authors: Meril Alex
Published: July 2016

Nous avons étudié en [12] des problèmes d’interpolation dans des espaces de fonctions holomorphes sur un cône ouvert convexe de sommet l’origine dans Cn, la croissance de ces fonctions étant contrôlée à l’infini. Nous nous intéressons maintenant à un espace plus petit en imposant en outre un contrôle de croissance à l’origine dans le cas où le cône est strict.
For Which Finite Groups G is the Lattice ℒ(G) of Subgroups Gorenstein?
Authors: Hibi Takayuki
Published: July 2016

Let G be a finite group and ℒ(G) the lattice consisting of all subgroups of G. It is well known that ℒ(G) is distributive if and only if G is cyclic (cf. [2, p. 173]). Moreover, the classical result of Iwasawa [8] says that ℒ(G) is pure if and only if G is supersolvable. Here, a finite lattice is called pure if all of maximal chains in it have same length and a finite group G is called supersolvable if ℒ(G) has a maximal chain which consists of normal subgroups of G.
On Some Dimension Formula for Automorphic Forms of Weight One, II
Authors: Hiramatsu Toyokazu
Published: July 2016

Let Γ be a fuchsian group of the first kind and assume that Γ contains the element and let x be a unitary representation of Γ of degree 1 such that X(—I) = — 1. Let S1(Γ,X) be the linear space of cusp forms of weight one on the group Γ with character X. We shall denote by d1 the dimension of the linear space S1(Γ, X). It is not effective to compute the number dl by means of the Riemann-Roch theorem. Because of this reason, it is an interesting problem in its own right to determine the number d1 by some other method (for example,).
Distributive and related ideals in generic extensions
Authors: Johnson C. A.
Published: July 2016

Let κ: be a regular uncountable cardinal and I a κ-complete ideal on te. In [11] Kanai proved that the μ-distributivity of the quotient algebra P(κ)I is preserved under κ-C.C. μ-closed forcing. In this paper we extend Kanai’s result and also prove similar preservation results for other naturally occurring forms of distributivity. We also consider the preservation of two game theoretic properties of I and in particular, using a game theoretic equivalent of precipitousness we give a new proof of Kakuda’s theorem ([10]) that the precipitousness of I is preserved under κ-C.C. forcing.
Equivalent conditions for the tightness of a sequence of continuous Hilbert valued martingales
Authors: Métivier Michel , Nakao Shintaro
Published: July 2016

In D. Aldous gave a sufficient condition for the tightness of a sequence (Xn)n≥0 of right continuous (with left limits) processes taking their values in a separable complete metric space S. As already noted by Aldous this condition is far from being necessary when the processes Xn are not continuous. More precisely the Aldous-condition implies the left-quasi-continuity of all the weak limits of the sequence (Xn)n≥0.
Certain unitary representations of the infinite symmetric group, II
Authors: Obata Nobuaki
Published: July 2016

The infinite symmetric group is the discrete group of all finite permutations of the set X of all natural numbers. Among discrete groups, it has distinctive features from the viewpoint of representation theory and harmonic analysis. First, it is one of the most typical ICC-groups as well as free groups and known to be a group of non-type I. Secondly, it is a locally finite group, namely, the inductive limit of usual symmetric groups . Furthermore it is contained in infinite dimensional classical groups GL(ξ), O(ξ) and U(ξ) and their representation theories are related each other.
On Meyer’s equivalence
Authors: Potthoff Jürgen
Published: July 2016

In the recent years there has been a considerable effort to construct and analyze spaces of test and generalized functionals in infinite dimensional situations, cf. [3, 5, 12, 14] and literature quoted there. In particular Meyer [4, 5] has introduced a certain space of “smooth” functionals on the Wiener space, which was used by Watanabe [14] for an elegant formulation of “Malliavin’s calculus” (i.e. he proved a criterion for the existence and regularity of densities of Wiener functionals). This functional space is countably normed and one of its important properties is its algebraic structure. The proof of this property follows from an equivalence of the norms defining the space with a system of norms of Sobolev type [4, 5] (cf. also (1.5), (1.6)).
On the isomorphism class of the ring of all integers of a cyclic wildly ramified extension of degree p II
Authors: Miyata Yoshimasa
Published: July 2016

Let k be an algebraic number field with the ring of integers ok = o and let G be a cyclic group of order p, an odd prime.
Ultrapotentials and positive eigenfunctions for an absolutely continuous resolvent of kernels
Authors: Beznea Lucian
Published: July 2016

Let (X, ) be a measurable space and be a submarkovian resolvent of kernels (with the initial kernel V proper) on X which is absolutely continuous and has a dual resolvent (with the same properties) with respect to a σ-finite measure.
Note on the class-number of the maximal real subfield of a cyclotomic field, II
Authors: Osada Hiroyuki
Published: July 2016

For an integer m > 2, we denote by C(m) and H(m) the ideal class group and the class-number of the field

K = Q(ζm + ζm−1)

respectively, where ζm is a primitive m-th root of unity. Let q be a prime and /Q be a real cyclic extension of degree q. Let C() and h() be the ideal class group and the class-number of . In this paper, we give a relation between C() (resp. h()) and C(m) (resp. H(m)) in the case that m is the conductor of (Main Theorem). As applications of this main theorem, we give the following three propositions. In the previous paper [4], we showed that there exist infinitely many square-free integers m satisfying n|H(m) for any given natural number n. Using the result of Nakahara [2], we give first an effective sufficient condition for an integer m to satisfy n|H(m) for any given natural number n (Proposition 1). Using the result of Nakano [3], we show next that there exist infinitely many positive square-free integers m such that the ideal class group C(m) has a subgroup which is isomorphic to (Z/nZ)2 for any given natural number n (Proposition 2). In paper [4], we gave some sufficient conditions for an integer m to satisfy 3|H(m) and m≡l (mod 4). In this paper, using the result of Uchida [5], we give moreover a sufficient condition for an integer m to satisfy 4|H(m) and m ≡ 3 (mod 4) (Proposition 3). Finally, we give numerical examples of some square-free integers m satisfying 4|H(m) and m ≡ 3 (mod 4).
On ζn-Weyl algebra Wr(ζn, Z)
Authors: Morikawa Hisasi
Published: July 2016

Weyl algebra is an associative algebra generated by two elements â and a over R such that the generating relation is given by

âa — aâ = 1,

which is isomorphic to the algebra of differential operators
On polylogarithms
Authors: Dupont Johan L.
Published: July 2016

Some functions related to the complex dilogarithmic function

(in the notation of Lewin [9]) are known to occur in connection with algebraic K-theory and characteristic classes (see e.g. Bloch [1], Gelfand-MacPherson [7], Dupont [5], and the references given there). Recently MacPherson and Hain (see [10]) has announced results of a similar kind for some higher polylogarithmic functions. Also Ramakrishnan [11] and [12] has recently studied the classical polylogarithms, which for |z| < 1 are given by
Ergodic properties of the stepping stone model
Authors: Itatsu Seiichi
Published: July 2016

The purpose of this paper is to discuss some ergodic properties of the stepping stone model proposed by Kimura, M. [4] and developed by Weiss, G.H. and Kimura, M. [12]. Our model to be discussed in this paper involves selection in addition to mutation and migration which are dealt with in [4], [12]. Because of the additional factor selection, the stochastic process describing our model becomes complicated and presents particularly interesting profound structure of the random phenomena in question.
A note on Lévy’s Brownian motion II
Authors: Si Si
Published: July 2016

The purpose of this paper is to discuss some particular random fields derived from Lévy’s Brownian motion to find its characteristic properties of the joint probability distributions. In [9], special attention was paid to the behaviour of the Brownian motion when the parameter runs along a curve in the parameter space, and with this property the conditional expectation has been obtained when the values are known on the curve.

The present paper deals with the variation of the Brownian motion in the normal direction to a given curve, in contrast to the case in [9], where we discussed the properties along the curve. Actually we shall find, in this paper, formulae of the variation with the help of the normal derivative of Brownian motion and observe its singularity. We then discuss partial derivatives of Rd-parameter Lévy’s Brownian motion and make attempt to restrict the parameter to a hypersurface so that we obtain new random fields on that hypersurface. By comparing such derivatives with those of other Gaussian random fields, we can see that the singularity of the new random fields seems to be an interesting characteristic of Lévy’s Brownian motion. Further, we hope that our approach may be thought of as a first step to the variational calculus for Gaussian random fields.
Two-number of symmetric R-spaces
Authors: Takeuchi Masaru
Published: July 2016

Chen-Nagano [2] introduced a Riemannian geometric invariant v(M), called the 2-number, for a compact (connected) symmetric space M: Points p, q ∊ M are said to be antipodal to each other, if p = q or there is a closed geodesic of M on which p and q are antipodal to each other. A subset A of M is called an antipodal subset if every pair of points of A are antipodal to each other. Now the 2-number v(M) is defined as the maximum possible cardinality |A| of an antipodal subset A of M. The 2-number is finite.
Integration with respect to the product of a measure and a closable set function
Authors: Jefferies Brian
Published: July 2016

The notion of a set function being closable with respect to a family of measures was introduced in [1] and applied there to the integration of Feynman-Kac functionals. In [2], it is shown how the interchange of integrals for the product of an operator valued measure and a scalar measure can be used to solve operator equations associated with the perturbation of semigroups. The purpose of this article is to develop the analogous machinery for closable set functions with the view of applying it to Schrödinger’s equation.
On the unramified extensions of the prime cyclotomic number field and its quadratic extensions
Authors: Nakagoshi Norikata
Published: July 2016

It is interesting to know what kinds of primes are the factors of the class number of an algebraic number field, and especially to find ones being prime to the degree. About this matter it is desirable to construct the unramified Abelian extensions plainly. In this paper we shall show some of them for the prime cyclotomic number field and its quadratic extensions using the units of subfields.
On a problem of Ono and quadratic non-residues
Authors: Leu Ming-Guang
Published: July 2016

Let k be a quadratic field, Δk the discriminant and Mk the Minkowski constant:

Consider the finite set of prime numbers

There are exactly 8 fields for which Πk = ∅. They make up an exceptional family:
On some generalizations of theorems of Toda and Weissenborn to differential polynomials
Authors: Ishizaki Katsuya
Published: July 2016

We assume that the readers are familiar with the notations in Nevanlinna theory, see [2], [9].
A probabilistic study on the value-distribution of Dirichlet series attached to certain cusp forms
Authors: Matsumoto Kohji
Published: July 2016

The existence of the asymptotic probability measure of the Riemann zeta-function was proved in Bohr-Jessen’s classical paper [3] [4].

Lets = σ + itbe a complex variable, ζ(s) the Riemann zeta-function, andRan arbitrary rectangle with the edges parallel to the axes. Then, for any σ0> ½ andT> 0, the set

is Jordan measurable, and we denote the Jordan measure of this set by V(T, R; ξ). Then, Bohr-Jessen’s main result asserts the existence of the limit
Connection problem in holonomicq-difference system associated with a Jackson integral of Jordan-Pochhammer type
Authors: Mimachi Katsuhisa
Published: July 2016

Fix a complex numberqwith|q|< 1. LetT1…,Tnbe n-commutingq-difference operators defined by

for a functionf(x), x=(x1,…,xn)ε (C*)n. Consider a system of linearq-difference equations in several variables for a matrix valued functionon(C*)nas follows:
Equilibrium fluctuations for one-dimensional Ginzburg-Landau lattice model
Authors: Zhu Ming
Published: July 2016

We shall investigate a system of spin configurations S = {S(t, x); t ≥ 0, x ∊ ℤ} on a one-dimensional lattice ℤ changing randomly in time. The evolution law is described by an infinite-dimensional stochastic differential equation (SDE):

where {β(t, x); t > 0, x ∊ Z} is a family of independent standard Wiener processes and U′ is the derivative of a self-potential U: R → R.
The Selberg trace formula for modular correspondences
Authors: Akiyama Shigeki , Tanigawa Yoshio
Published: July 2016

In Selberg [11], he introduced the trace formula and applied it to computations of traces of Hecke operators acting on the space of cusp forms of weight greater than or equal to two. But for the case of weight one, the similar method is not effective. It only gives us a certain expression of the dimension of the space of cusp forms by the residue of the Selberg type zeta function. Here the Selberg type zeta function appears in the contribution from the hyperbolic conjugacy classes when we write the trace formula with a certain kernel function ([3J, [4], [7], [8], [9], [12]).
On the Dimension of Modules and Algebras, VI. Comparison of Global and Algebra Dimension
Authors: Auslander Maurice
Published: July 2016

Throughout this paper all rings are assumed to have unit elements. A ring Λ is said to be semi-primary if its Jacobson radical N is nilpotent and Г = Λ/N satisfies the minimum condition. The main objective of this paper is

THEOREM I. Let A be a semi-primary algebra over a field K. Let N be the radical of Λ and Г = Λ/N. If

Then

dim Λ = gl.dim Λ.
Sur les Ensembles d’Accumulation Relatifs à des Transformations Localement Pseudo-Analytiques au Sens de Pfluger-Ahlfors
Authors: Ohtsuka Makoto
Published: July 2016

La question posée par Noshiro dans [5] pour les ensembles d’accumulation relatifs à des fonctions pseudo-analytiques classiques a été résolue par (T.) Yosida [12] premièrement et ensuite, le présent auteur [8] a étendu son résultat (théorème 1 de [12]) au cas où un nombre fini ou dénombrable de surfaces de Riemann, qui sont des surfaces de recouvrement, sont transformées dans une autre surface de Riemann par une application continue à dérivées partielles continues sauf en un ensemble fermé de mesure linéaire nulle, ayant pour image un ensemble de mesure linéaire également nulle; le quotient de dilatation n’y est pas nécessairement borné mais subit certaine condition, et les ensembles d’accumulation y sont définis pour les éléments frontières de Kerékjartô-Stoïlow. Une généralisation d’un théorème étoilé de Gross obtenue dans [7] a été utilisée dans sa démonstration. L’auteur a continué son étude sur ce théorème étoilé et un de ses résultats établis dans [9] lui permettra d’améliorer les résultats de [8] dans le présent mémoire. L’idée fondamentale est la même que dans [8] mais nous la récrirons, en nous reportant à [8] le moins possible.
Über Das Verhalten Der Analytischen Abbildungen Riemannscher Flächen Auf Dem Idealen Rand Von Martin
Authors: Constantinescu C. , Cornea A.
Published: July 2016

Es sei f eine meromorphe nichtkonstante Funktion im Kreise |z|, < 1. Die Theorie des Verhaltens von f auf dem Rande des Kreises wird von zwei bekannten Sätzen beherrscht: der Satz von Riesz-Lusin-Priwaloff-Frostman-Nevanlinna, auf Grund dessen eine Menge aus |z| = 1, für die die Winkelgrenzwerte von f in einer Menge der Kapazität Null liegen, vom Lebesgueschen Masse Null ist und der Satz von Fatou-Nevanlinna, welcher besagt, dass, falls die Funktion f beschränktartig ist, dann hat sie fast überall auf |z| = 1 Winkelgrenzwerte. In vorliegender Arbeit werden diese zwei Sätze auf folgende Weise verallgemeinert. An Stelle des Kreises |z| < 1 betrachten wir eine beliebige Riemannsche Fläche R mit Greenscher Funktion, und an Stelle der meromorphen Funktion f nehmen wir eine nichtkonstante analytische Abbildung von R in einer Riemannschen Fläche R′(R′ offen oder kompakt, mit oder ohne Greenscher Funktion). Es sei Δ, bzw. Δ′, der ideale Rand von R, bzw. R′, im Sinne von Martin [11]; wir werden im Abschnitt IV eine Teilmenge der Menge Δ und eine Abbildung von (f) in R′ ∪ Δ′ definieren. Die Verallgemeinerung des Satzes von Fatou-Nevanlinna besteht in der Behauptung, dass, falls f eine Lindelöfsche Abbildung ist [6], so ist Δ-(f) von harmonischen Masse Null und die des Satzes von Riesz-Lusin-Priwaloff-Frostman-Nevanlinna darin, dass, wenn (A) eine polare Menge auf R′∪Δ′ ist, so ist die Menge A ⊂(f) vom harmonischen Masse Null.
Note on Non-Commutative Semi-Local Rings
Authors: Hinohara Yukitoshi
Published: July 2016

Our aim in this note is to generalize some topological results of commutative noetherian rings to non-commutative rings. As a supplemental remark of [2] we prove in § 1 that any right ideal of a complete right semi-local ring is closed, and that

for any finitely generated right module M over a complete right semi-local ring Λ where J is the Jacobson radical of Λ.
On the Weakness of Some Boundary Component
Authors: Akaza Tohru
Published: July 2016

Let D be a domain in the complex z-plane and γ be a boundary component of D consisting of a single point. The component γ is said to be weak if its image under any conformal mapping of D consists of a single point. If γ is not weak, then we say that γ is unstable (Sario [3], [4]).
Espaces Homogènes de Stein des Groupes de Lie Complexes, II
Authors: Matsushima Yozô
Published: July 2016

Ce travail est une suite du mémoire [8] paru dans ce journal. Dans [8], on a étudié la structure du groupe connexe d’isotropie d’un espace homogène de Stein G/H d’un groupe de Lie semi-simple complexe et connexe G et on a montré que le groupe H est égal au complexifié d’un sous-groupe compact maximal de H ([8], Théorème 3). Le but essentiel de ce travail est d’étendre ce résultat au cas d’un espace homogène de Stein d’un groupe de Lie complexe et connexe quelconque.
On Exceptional Values of Meromorphic Functions with the Set of Singularities of Capacity Zero
Authors: Matsumoto Kikuji
Published: July 2016

LetEbe a compact set in thez-plane and letΩbe its complement with respect to the extendedz-plane. Suppose thatEis of capacity zero. ThenΩis a domain and we shall consider a single-valued meromorphic functionw=f(z) onΩwhich has an essential singularity at each point ofE. We shall say that a valuewis exceptional forf(z)at a point ζ ∈Eif there exists a neighborhood of C where the functionf(z)does not take this valuew.
An Axiomatic Theory of Ordinal Numbers
Authors: Umezawa Toshio
Published: July 2016

In this paper, a formal theory of ordinal numbers is developed on an axiomatic basis whose details are described in § 1. Our primitive notions are set, class, collection, a binary relation ∈, and collection formation {!}. Sets and classes in our theory play similar roles as sets and classes respectively in Gödel [1] except the difference that an element of a class is a class but not necessarily a set. A new notion, introduced into our theory is that of collections. A collection relates to a class, just as a class relates to a set in von Neumann’s theory. That is; a set is a class and a class is a collection but the converses are not generally the case. For example, all the natural numbers, all the real numbers etc. constitute sets, the ordinal numbers which are sets constitute a proper class, and the totality of ordinal numbers as well as that of all classes are proper collections. These relations are described by axiom group (A).
On the Local Theory of Continuous Infinite Pseudo Groups II
Authors: Kuranishi Masatake
Published: July 2016

In this chapter, we shall formulate, without proof, the theorys of exterior differential systems and of their prolongations using the language in the theory of jets developed by C. Ehresman, because such formulation seems to be most convenient in order to apply the theory to the theory of continuous infinite pseudo-groups, which we shall discuss in the next chapter. Since important theorems in our theory hold only in the real analytic case, we shall exclusively consider the real analytic case. So, we shall omit the adjective “analytic”, unless explicitly stated otherwise. As for the fundamental notions in the theory of jets and of differential systems, we refer to [5] and [6], respectively. Detailed proof of the contents of this Chapter will be published in [7].
The inner product of an automorphic wave form with the pullback of an Eisenstein series
Authors: Niwa Shinji
Published: July 2016

In this paper we shall show a relation between a special value of an automorphic wave form and the inner product of the automorphic wave form with the pullback of an Eisenstein series on the upper half space. The main theorem is Theorem 3 in the end of this paper. As is shown in P. B. Garrett [13], pullbacks of Eisenstein series on Siegel upper half spaces have interesting properties as a kernel function of an integral operator. It is natural to try to investigate pullbacks of Eisenstein series of Hilbert type. We can say that Theorem 3 clarifies a property of such pullbacks in a special case. The idea of the proof is a lifting of automorphic forms by theta functions. We discuss a lifting of automorphic wave forms in 1, 2 and 3, and obtain Theorem 2 in the end of 3 as a result. We can prove Theorem 3 without much difficulty by using Theorem 2.
La balayabilité au sens fort des noyau-fonctions continues du potentiel
Authors: Higuchi Isao
Published: July 2016

Soient X un espace localement compact et non-compact à base dénombrable, G une noyau-fonction continue sur X et M (resp. MK) l’ensemble des toutes mesures de Radon positives sur X (resp. des toutes mesures de Radon positives sur X à support compact).
Littlewood-Paley theory on Gaussian spaces
Authors: Potthoff Jürgen
Published: July 2016

In this article we prove a number of inequalities of Littlewood-Paley-Stein (LPS) type for functions on general Gaussian spaces (s. below).

In finite dimensional Euclidean spaces (with Lebesgue measure) the power of such inequalities has been demonstrated in Stein’s book [12]. In his second book [13], Stein treats other spaces too: also the situation of a general measure space (X, μ). However the latter case is too general to allow for a rich class of inequalities (cf. Theorem 10 in [13]).
Minimal rational threefolds II
Authors: Umemura Hiroshi
Published: July 2016

The Enriques-Fano classification ([E.F], [F]) of the maximal connected algebraic subgroups of the three variable Cremona group, despite of its group theoretic feature, seems to be the most significant result on the rational threefolds so far known. In this paper as in [MU] we interpret the Enriques-Fano classification from a geometric view point, namely the geometry of minimal rational threefolds. We explained in [MU] the link between the two objects; the maximal algebraic subgroups and the minimal rational threefolds. Let (G, X) be a maximal algebraic subgroup of three variable Cremona group. We denote by ℓ(G, X) the set of all the algebraic operations (G, Y) such that Y is non-singular and projective and such that (G, Y) is isomorphic to (G, X) as law chunks of algebraic operation: namely (G, Y) is birationally equivalent to (G, X). Then we define an order in ℓ(G, X): for (G, Z), (G, W) ∊ ℓ(G, X), (G, Z)>(G, W) if there exists an G-equivariant birational morphism of Z onto W.
On the divisor class groups of a two-dimensional local ring and its form ring
Authors: Portelli Dario , Spangher Walter
Published: July 2016

LetAbe a noetherian ring and letIbe an ideal ofAcontained in the Jacobson radical ofA: Rad (A). We assume that the form ring ofAwith respect to the idealI: G= Gr (A, I), is a normal integral domain. HenceAis a normal integral domain and one can ask for the links between Cl(A) and Cl(G).
The Feynman integral of quadratic potentials depending on n time variables
Authors: Park Chull , Skoug David
Published: July 2016

Let C1[0, T] denote (one-parameter) Wiener space; that is the space of continuous functions x on [0, T] such that x(0) = 0. In a recent expository essay [21], Nelson calls attention to some functions on Wiener space which were discussed in the book of Feynman and Hibbs [13, section 3-10] and in Feynman’s original paper [12, section 13]. These functions have the form
White noise approach to Gaussian random fields
Authors: Lee Ke-Seung
Published: July 2016

The purpose of this paper is to investigate way of dependency of Gaussian random fields X(D) indexed by a domain D in d-dimensional Euclidean space Rd. Our main tool is variational calculus, where the boundary of a domain varies and deforms and we appeal to the white noise analysis. We therefore assume that X(D) is expressed white noise integral of the form

(0.1) X(D) = X(D, W)=∫D F(D, u)W(u)du,

where W is the Rd-parameter white noise and the kernel F(D, u) is a square integrable function over Rd, and where D is a bounded domain with smooth boundary.
Injective modules over twisted polynomial rings
Authors: Osofsky Barbara L.
Published: July 2016

Differential polynomial rings over a universal field and localized twisted polynomial rings over a separably closed field of non-zero characteristic twisted by the Frobenius endomorphism were the first domains not divisions rings that were shown to have every simple module injective (see [C] and [C-J]). By modifying the separably closed condition for the polynomial rings twisted by the Frobenius, the conditions of every simple being injective and only a single isomorphism class of simple modules were shown to be independent (see [O]). In this paper we continue the investigation of injective cyclic modules over twisted polynomial rings with coefficients in a commutative field.
The Kubota symbol for Sp(4, Q(i))
Authors: Bump Daniel , Friedberg Solomon , Hoffstein Jeffrey
Published: July 2016

Following eariler work of Kubota and Mennicke, the major work of Bass, Milnor and Serre [1] constructed characters of congruence subgroups of the modular subgroups of SL(n) and Sp(2n) over a totally complex number field, which are related to the power residue symbol. They do not obtain the lowest possible level of these Kubota characters, nor does it appear possible to modify their arguments to extend the characters to the lowest possible level.
Quantization of a Poisson algebra and polynomials associated to links
Authors: Ozawa Tetsuya
Published: July 2016

A formal quantization of Poisson algebras was discussed by several authors (see for instance Drinfel’d [D]). A formal Lie algebra generated by homotopy classes of loops on a Riemann surface ∑ was obtained by W. Goldman in [G], and its Poisson algebra was quantized, in the sense of Drinfel’d, by Turaev in [T].
The ideal boundaries and global geometric properties of complete open surfaces
Authors: Shioya Takashi
Published: July 2016

In this paper we study the ideal boundaries of surfaces admitting total curvature as a continuation of [Sy2] and [Sy3]. The ideal boundary of an Hadamard manifold is defined to be the equivalence classes of rays. This equivalence relation is the asymptotic relation of rays, defined by Busemann [Bu]. The asymptotic relation is not symmetric in general. However in Hadamard manifolds this becomes symmetric. Here it is essential that the manifolds are focal point free.
On the Strong Unimodality of Lévy Processes
Authors: Watanabe Toshiro
Published: July 2016

A measure μ(dx) on R is said to be unimodal with mode a if μ(dx) = cδa(dx) + f(x) dx, where c ≧ 0, δa(dx) is the delta measure at a and f(x) is non-decreasing for x < a and non-increasing for x > a. A measure is said to be unimodal with mode a if pn is non-decreasing for n ≦ a and non-increasing for n ≧ a. A probability measure μ(dx) on R (resp. on Z) is said to be strongly unimodal on R (resp. on Z) if, for every unimodal probability measure η(dx) on R (resp. on Z), the convolution μ*η(dx) is unimodal on R (resp. on Z).
White noise analysis and Tanaka formula for intersections of planar Brownian motion
Authors: Shieh Narn-Rueih
Published: July 2016

In this paper, we shall use Hida’s [5, 7, 9] theory of generalized Brownian functionals (or named white noise analysis) to establish a stochastic integral formula concerning the multiple intersection local times of planar Brownian motion B(t).
Lattice path proof of the ribbon determinant formula for Schur functions
Authors: Ueno Kazuo
Published: July 2016

In this note we give a lattice path proof of the ribbon determinant formula for Schur functions ((1) below) which was originally formulated and proved in [2].
Symmetric forms, idempotents and involutary antiisomorphisms
Authors: Landrock Peter , Manz Olaf
Published: July 2016

Let G be a finite group, F a field and M an irreducible F[G]-module. By ^ we denote the F-linear involutary antiautomorphism of F[G], induced by inversion on group elements. Suppose that char (F) ≠. 2. We then show that M carries a non-singular G-invariant symmetric bilinear form with values in F if and only if there exists a ^-invariant idempotent e ∈ F [G] which generates the projective cover of M. This extends earlier results of W. Willems [Wi]. The assertion is not true if char(F) = 2.
The jacobian of a cyclic quotient of a fermat curve
Authors: Lim Chong Hai
Published: July 2016

Fix a positive integer m. Let Fm denote the Fermat curve over Q of degree m, given by the projective equation
Diffeomorphisms with pseudo orbit tracing property
Authors: Sakai Kazuhiro
Published: July 2016

We shall discuss a differentiable invariant that arises when we consider a class of diffeomorphisms having the pseudo orbit tracing property (abbrev. POTP).
Residual automorphic representations of Sp4
Authors: Watanabe Takao
Published: July 2016

Let G = Sp4 be the symplectic group of degree two defined over an algebraic number field F and K the standard maximal compact subgroup of the adele group G (A). By the general theory of Eisenstein series ([14]), one knows that the Hilbert space L2(G(F)\G(A)) has an orthogonal decomposition of the form

L2(G(F)\G(A)) = L2(G) ⊕ L2(B) ⊕ L2(P1) ⊕ L2(P1),

where B is a Borel subgroup and Pi are standard maximal parabolic subgroups in G for i = 1,2. The purpose of this paper is to study the space L2d(B) associated to discrete spectrurns in L2(B).
Automorphic forms and infinite matrices
Authors: Kubota Tomio
Published: July 2016

In the present paper, we show that an infinite dimensional vector whose components are Fourier coefficients of an automorphic form is characterized as an infinite dimensional vector which is annihilated by an infinite matrix constructed by the values of a Bessel function. Results and methods are all simple and concrete.

Although the idea in the present paper is applicable to more general cases, our investigation will be restricted to the case of automorphic forms of weight 0, i.e., automorphic functions, with respect to SL(2, Z) on the upper half plane, in order to explain the main idea distinctly.
On the Cohen-Macaulay property of A[pt, p(2)t2] for space monomial curves
Authors: Nakamura Yukio
Published: July 2016

Let A = k[X, Y, Z] and k[U] be polynomial rings over a field k and let l, m and n be positive integers with gcd(l, m, n) = 1. We denote by p the defining ideal of the space monomial curve x = ul, y = um, and z = un.
On the invariant differential metrics near pseudoconvex boundary points where the Levi form has corank one
Authors: Herbort Gregor
Published: July 2016

Let D be a bounded domain in Cn; in the space L2(D) of functions on D which are square-integrable with respect to the Lebesgue measure d2nz the holomorphic functions form a closed subspace H2(D). Therefore there exists a well-defined orthogonal projection PD: L2(D) → H2(D) with an integral kernel KD:D × D → C, the Bergman kernel function of D. An explicit computation of this function directly from the definition is possible only in very few cases, as for instance the unit ball, the complex “ellipsoids” , or the annulus in the plane. Also, there is no hope of getting information about the function KD in the interior of a general domain. Therefore the question for an asymptotic formula for the Bergman kernel near the boundary of D arises.
A characterization of complete Riemannian manifolds minimally immersed in the unit sphere
Authors: Cheng Qing-Ming
Published: July 2016

Let Mn be an n-dimensional Riemannian manifold minimally immersed in the unit sphere Sn+p (1) of dimension n + p. When Mn is compact, Chern, do Carmo and Kobayashi [1] proved that if the square ‖h‖2 of length of the second fundamental form h in Mn is not more than , then either Mn is totally

geodesic, or Mn is the Veronese surface in S4 (1) or Mn is the Clifford torus .

In this paper, we generalize the results due to Chern, do Carmo and Kobayashi [1] to complete Riemannian manifolds.
Oscillation of modes of some semi-stable Lévy processes
Authors: Watanabe Toshiro
Published: July 2016

In this paper it is shown that there is a unimodal Levy process with oscillating mode. After the author first constructed an example of such a self-decomposable process, Sato pointed out that it belongs to the class of semi-stable processes with β < 0. We prove that all non-symmetric semi-stable self-decomposable processes with β < 0 have oscillating modes.
Complete conformal metrics with prescribed scalar curvature on subdomains of a compact manifold
Authors: Kato Shin , Nayatani Shin
Published: July 2016

Let (M, g) be a Riemannian manifold of dimension n≥ 3 and ĝanother metric on M which is pointwise conformai to g. It can be written where u is a positive smooth function on M. Then the curvature of g is computable in terms of that of g and the derivatives of u up to second order. In particular, if S and S denote the scalar curvature of g and g respectively, they are related by the equation

where ▽u denotes the Laplacian of u, defined with respect to the metric g.
On a class of numbers generated by differencial equations related with algebraic groups
Authors: Umemura Hiroshi
Published: July 2016

In this paper we propose a new category Qcl of complex numbers which contains π, e and the set of algebraic numbers. In fact this category contains most of the numbers studied so far in number theory. An element of the category is here called a classical number. The category of the classical numbers forms an algebraically closed field and consists of countably many numbers. The definition depends on algebraic differential equations related with algebraic groups. Throughout the paper unless otherwise stated, we deal with functions of one variable and a differential equation is an ordinary differential equation. We are inspired of the Leçons de Stockholm of Painlevé [P].
On the projective varieties associated with some subrings of the ring of Thetanullwerte
Authors: Manni Riccardo Salvati
Published: July 2016

Let (X, L) be a principally polarized abelian variety (ppav) of dimension g such that L is a symmetric line bundle, i.e. i*L ≃ L where i is the inversion map i(x) = — x. We shall denote by X[2] the two torsion points of X which are fixed by i. For any x in X[2] we have an isomorphism

(1) .
Generalized independent increments processes
Authors: Thu Nguyen Van
Published: July 2016

We study a class of Markov processes which arise in the theory of generalized convolutions and stand for a generalization of processes with independent increments.
Solvability of the diophantine equation x2 − Dy2 = ± 2 and new invariants for real quadratic fields
Authors: Yokoi Hideo
Published: July 2016

In our recent papers [3, 4, 5], we defined some new D-invariants for any square-free positive integer D and considered their properties and interrelations among them. Especially, as an application of it, we discussed in [5] the characterization of real quadratic field Q() of so-called Richaud-Degert type in terms of these new D-invariants.
The mean values of Dirichlet L-functions at integer points and class numbers of cyclotomic fields
Authors: Katsurada Masanori , Matsumoto Kohji
Published: July 2016

Let q be a positive integer, and L(s, χ) the Dirichlet L-function corresponding to a Dirichlet character χ mod q. We put

where χ runs over all Dirichlet characters mod q except for the principal character χ0.
Des derivees de residus et une identite remarquable
Authors: Gomez Francisco , Lehmann Daniel
Published: July 2016

Soit φ un polynome symétrique de q variables (q ≥ 1), homogène de degré p (p entier ≥ 2), à coefficients complexes. Soient (α1, α2, . . . , p) et (β1, β2, . . . , βp) deux familles de p nombres complexes, tous non nuls, et telles que toutes les différences soient également non nulles pour i ≠ j. Soient enfin (λ1, λ2, . . . , λq) et (μ1, μ2, . . . , μq) deux familles de q nombres complexes. On a alors:

THÉORÈME 1.

.
Integral geometry under cut loci in compact symmetric spaces
Authors: Tasaki Hiroyuki
Published: July 2016

The theory of integral geometry has mainly treated identities between integral invariants of submanifolds in Riemannian homogeneous spaces like as dμg(g) where M and N are submanifolds in a Riemannian homogeneous spaces of a Lie group G and I(M ∩ gN) is an integral invariant of M ∩ gN. For example Poincaré’s formula is one of typical identities in integral geometry, which is as follows. We denote by M(R2) the identity component of the group of isometries of the plane R2 with a suitable invariant measure μM(R2).
The continuity principle in exponential type Orlicz spaces
Authors: Graversen S. E. , Peškir G. , Weber M.
Published: July 2016

In this section we shall present some facts in the background of the problem under our next consideration. Let (X, A, μ) be a finite measure space, and let B be a Banach space with a norm ‖ • ‖. Let M(μ) denote the linear space of all μ-measurable functions from X into R, and let T be a linear operator from B into M (μ).