bluuebunny/crossref_metadata_2025_split huggingface dataset:
Enriques Surfaces Covered by Jacobian Kummer Surfaces
Authors: Ohashi Hisanori 
Published: July 2016

AbstractThis 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.
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.
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). Setand
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 numberis 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’équationP(x,D)u=fest 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).
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.
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)
Cohomological dimension of group schemes
Authors: Umemura Hiroshi 
Published: July 2016

In Umemura [9], we calculated the invariants algcd (G), p(G), q(G) for a commutative algebraic group G. We remark that all the results hold for a group scheme which is not necessarily commutative.To determine p(G), I cannot succeed in dropping the hypothesis “quasi-projective” but this assumption is satisfied in the characteristic 0 case.
On symmetric Siegel domains
Authors: Takeuchi Masaru 
Published: July 2016

Let V be a convex cone in a real vector space X, F: Y × Y → Xc a V-positive hermitian map on a complex vector space Y, andthe Siegel domain associated to V and F. D(V,F) is said to be symmetric, if for each point p ∈ D(V, F) there exists an involutive holomorphic automorphism σp of D(V,F) such that the fixed point set of σp consists of only the point p. Satake [6] showed that the symmetric Siegel domain D(V, F) is characterized by the following three conditions (i), (ii) and (iii).
Some Remarks on Local Rings
Authors: Nagata Masayoshi 
Published: July 2016

Previously C. Chevalley [1] proved the followings:1.	Let x1,…, Xn be algebraically independent elements over a field t which has infinitely many elements. Then :a)	If y is an element of [x1,…, xn] and if y is not in , then there exist elements y2…, yn of [x1,…, xn] such that [x1,…, xn] is integral over [y1, y2,…, yn]
A characterization of the Veronese varieties
Authors: Nomizu Katsumi 
Published: July 2016

Let Pm(C) be the complex projective space of dimension m. In a previous paper [2] we have provedTHEOREM A. Let f be a Kaehlerian immersion of a connected, complete Kaehler manifold Mn of dimension n into Pm(C). If the image f(τ) of each geodesic τ in Mn lies in a complex projective line P1(C) of Pm(C), then f(Mn) is a complex projective subspace of Pm(C), and f is totally geodesic.
On a conjecture of M. P. Murthy
Authors: Boratyński M. 
Published: July 2016

In [M] Murthy asked if every subvariety V of kn (k-any field) with a trivial conormal bundle is a (scheme theoretic) complete intersection.In [B] we were able to prove that all such subvarieties of kn are at least set theoretic complete intersections. Mohan Kumar has shown in [MK] that if one assumes moreover that n ≥ 2 dim V + 2 then V is a complete intersection. The aim of this paper is to prove the following result which extends the Mohan Kumar Theorem in the nonsingular (and connected) case and moreover sheds some light on his bound for n.
Continuous valuation and logic
Authors: Yasugi Mariko 
Published: July 2016

We consider the continuous valuation of logic, where the certainty of a statement is measured with a number in the closed unit interval I =[0, 1].The idea originates in continuous logics, which have been investigated from various standpoints, in [1] ~ [4] and [8] ~ [10], for example. More comprehensive information can be seen in [4] and others.
A connection between blowing-up and gluings in one-dimensional rings
Authors: Tamone Grazia 
Published: July 2016

Let C be an affine curve, contained on a non-singular surface X as a closed 1-dimensional subscheme. If P is a closed point on C, the blowing-up C′ of C with center P (induced by the blowing-up of X with center P) is an affine curve. It is known that there is a sequence:where C is the normalization of C, and each Ci + 1 is the blowing-up of Ci with center a singular point Pt on Ci (i = 0, …, k – 1).
Normal holomorphic mappings and classical theorems of function theory
Authors: Funahashi Ken-Ichi 
Published: July 2016

In [7], O. Lehto and K. I. Virtanen introduced the concept of normal meromorphic functions in connection with the study of boundary behaviour of meromorphic functions of one complex variable.In this paper, we generalize the theory of normal meromorphic functions to the case of holomorphic mappings into higher dimensional complex spaces in connection with the theory of hyperbolic manifolds and Nevanlinna theory.The main concern of this paper is the generalizations of the big Picard theorem and Lindelöf’s theorem which appear in the classical function theory.
Lévy’s Brownian motion; Total positivity structure of M(t)-process and deterministic character
Authors: Noda Akio 
Published: July 2016

Let X = {X(A); A ∈ Q} be a Lévy’s Brownian motion with the basic time parameter space Q, where Q is taken to be the n-dimensional metric space Qn,k of constant curvature (2 ≤ n ≤ ∞, — ∞ < k: < ∞), i.e., Q is one of(a) Euclidean space for k = 0, (b) sphere for k > 0 and(c) real hyperbolic space for K < 0.The increment X(A) — X(B) is, by definition, Gaussian in distribution and has mean 0 and variance d(A, B), the distance between A and B. The existence of such a Gaussian random field is well known ([3], [4], [16] and [23]).
Smoothness of Noetherian rings
Authors: Tanimoto Hiroshi 
Published: July 2016

In [16] we studied the following problems which had been asked by H. Matsumura (cf. [11]):
(I)What is the difference between smoothness and J-smoothness? In particular, concerning the characterization of smoothness,(II)When is a ring A[X1 …, Xn]/a smooth over A?In this paper, according to these problems, we will study J-smoothness further when rings are noetherian as in [16].
Sur les variétés canoniques de dimension 3 d’indice positif
Authors: Benveniste X. 
Published: July 2016

Dans tout ce qui suit, les varietés qui interviendront seront définies sur le corps des nombres complexes C. L’objet de cet article est de préciser le résultat suivant obtenu dans [B-2] et [K-1]:Théorème 0. Soit X une variété protective normale de dimension 3, dont les singularités sont canoniques au sens de [R-1]. Soient e le p.p.c.m. des indices des points singuliers de X. Soit R un diviseur de Cartier sur X, tel que le bidual de soit isomorphe à Supposons que R soit numériquement positif et que R3 > 0. Alors il existe un entier n0 > 0 tel que pour tout le système linéaire |nR| soit sans point base; en particulier l’anneau est de type fini sur C.
On the Behaviour of Analytic Functions in the Neighbourhood of the Boundary of a Riemann Surface
Authors: Cornea A. 
Published: July 2016

Mr. Z. Kuramochi has recently obtained the following very interesting result concerning the classification of Riemann surfaces [1]:If we delete from a Riemann surface belonging to the class an arbitrary compact set, the resulting surface remains in the class .In the present paper we indicate a new method of proving this theorem, simultaneously for the cases B and D.
Differentiable Structures on the 15-Sphere and Pontrjagin Classes of Certain Manifolds
Authors: Shimada Nobuo 
Published: July 2016

No manifold had been known which can carry two distinct differentiable structures until the recent important contribution due to J. Milnor [7] concerning the 7-sphere appeared.In connection with his work, there are several problems, for example, about the existence of any other manifold with such property, about the topological invariance of the Pontrjagin classes of manifolds, etc.; some of them will be discussed in the present note.
An Investigation on the Logical Structure of Mathematics (III): Fundamental Deductions
Authors: Kuroda Sigekatu 
Published: July 2016

In this Part (III) the proofs in UL are given for fundamental formulas concerning the following dependent variables:
Elementary set {a1, … , an};Ordered pair ‹a, b›;Image by σ of aσ‘a;Image by σ of elements of aσ“a;Domain of operator Dσ;Range of operator Wσ;Uniqueness Un;Bi-uniqueness Un2;Inverse operator σ-1;One-to-one mapping Map2a, b;Composition of operators σ o τ;Restriction of operator Identical mapping ℓ
On the Existence of Unramified Separable Infinite Solvable Extensions of Function Fields over Finite Fields
Authors: Morikawa Hisasi 
Published: July 2016

In the present note, using the results in the previous paper, we shall prove the following existence theorem:THEOREM. Let k be a finite field with q elements and K/k be a regular extension of dimension one over k. Then, if q ≧ 11 and the genus gK of K/k is greater than one, there exists an unramified separable infinite solvable extension of K ivhich is regular over k.
On a Practical Way of Describing Formal Deductions
Authors: Ono Katuzi 
Published: July 2016

IntroductionEven though the logical structure of any formal deduction can be nicely expressed in a tree-form diagram, it is more practical to write it down in a series of propositions. In each step of inference, we usually deduce a proposition on basis of some foregoing propositions. However, global aspects of mathematical theories show us that this is not always the case. For, in mathematical theories, theorems are usually stated before their proofs. In fact, also in proofs of theorems, it is often practical that we prove propositions after stating them. Accordingly, in our real way of thinking, we arrange propositions going back and forth in the logical order.
Perfect Picard Set of Positive Capacity
Authors: Matsumoto Kikuji 
Published: July 2016

In our previous paper [1], we proved that any Cantor set E with successive ratios ξn satisfying the condition
is a Picard set, that is, each single-valued meromorphic function with E as the set of essential singularities takes on every value infinitely often in any neighborhood of each singularity with the possible exception of two values.
The Theorem of Identity for Coherent Analytic Modules
Authors: Fujimoto Hirotaka 
Published: July 2016

The theorem of identity for analytic subsets of a reduced complex space is stated as follows;
Let V and V′ be two analytic subsets of a reduced complex space. If V is irreducible and there exists a point x ∊ V such that the germ Vx of V at x is included in V′x, then V is included in V′.
On a class of non-elliptic boundary problems
Authors: Kato Yoshio 
Published: July 2016

Let Ω be a bounded domain in Rl (l ≥ 2) with, C∞ boundary Γ of dimension l — 1 and let there be given a second order elliptic differential equation(1)	in Ω,where ∂j = ∂/∂xi and all coefficients are assumed, for the sake of simplicity, to be real-valued and C∞ on .
Reducing towers of principal fibrations
Authors: McClendon J. F. 
Published: July 2016

Consider a tower of principal fibrationsThat is, Ei+1 is the pullback of Ei→Ri and the path fibration PRi → Ri. The question arises as to whether or not the tower can be shortened, that is, whether or not En+1→ B is fiber homotopically equivalent to a nice fibration E → B. If “nice” is taken to mean “principal” then sufficient conditions are known. They involve connectivity assumptions on the Ei. In this paper “nice” is taken to mean “D-relatively principal” for some space D.
Les pseudo-groupes intransitifs et le probleme d’equivalence
Authors: Higa Tatsuo 
Published: July 2016

Dans les travaux célèbres [1], [2], [3], E. Cartan a fait des recherches sur les pseudo-groupes, sans distinguer entre les deux cas, transitif ou intransitif. Tout d’abord, Cartan a abouti au théorème qu’il a considéré comme la base de la théorie des pseudo-groupes continus, c’est-à-dire le premier théorème fondamental: Tout pseudo-groupe de Lie admet un prolongement holoédrique opérant sur un certain nombre r de variables xi et défini comme l’ensemble des transformations qui laissent invariants1° un certain nombre de fonctions des xi;2° r formes de Pfaff wi(x, y, dx) linéairement indépendantes par rapport aux différentielles dxi et dont les coefficients peuvent dépendre d’autres variables auxiliaires yj; enfin le prolongement considéré a ses équations de définition du premier ordre (voir [5]). Puis, il a introduit l’équation structurale de manière à caractériser le pseudo-groupe.
Complexes of Cousin type and modules of generalized fractions
Authors: Chung Sang-Cho 
Published: July 2016

Let R be a commutative (Noetherian) ring, M an R-module and let ℱ = (Fi)i≥0 be a filtration of Spec(R) which admits M.A complex of R-modules is said to be of Cousin type if it satisfies the four conditions of ([GO], 3.2) which are reproduced below (Definition (1.5)). In ([RSZ], 3.4), Riley, Sharp and Zakeri proved that the complex, which is constructed from a chain of special triangular subsets defined in terms of ℱ (Example (1.3)(3)), is of Cousin type for M with respect to ℱ (Corollary (3.5)(2)). Gibson and O’carroll ([GO], 3.6) showed that the complex, which is obtained by means of a chain = (Ui)i≥1 of saturated triangular subsets and the filtration = (Gi)i≥0 induced by and M, is of Cousin type for M with respect to (Corollary (3.5)(3)).
Defining ideals of Buchsbaum semigroup rings
Authors: Kamoi Yuuji 
Published: July 2016

Let H be a simplicial semigroup. We consider the semigroup ring k[H] and its defining ideal IH. For definition see the first paragraph of Section 1.When dim(k[H]) = 1, the defining ideal IH of k[H] has been studied by many authors (e.g. [1], [2], [8], [11], [3]). In this paper, we study the ideal IH using the notion of Gröbner bases for arbitrary dimension.
Sur l’incomplétude de la série linéaire caractéristique d’une famille de courbes planes à nœuds et à cusps
Authors: Guffroy Sébastien 
Published: July 2016

AbstractSince J.Wahl ([27]), it is known that degreedplane curves having some fixed numbers of nodes and cusps as its only singularities can be represented by a scheme, let sayH, which can be singular. In Wahl’s example,His singular along a subschemeFbut the induced reduced schemeHredis smooth alongF. In this work, we construct explicitly a family of plane curves with nodes and cusps which are represented by singular points ofHred.To this end, we begin to show that the Hilbert scheme of smooth and connected space curves of degree 12 and genus 15 is irreducible and generically smooth. It follows that it is singular along a hypersurface (3.10). This example is minimal in the sense that the Hilbert scheme of smooth and connected space curves is regular in codimension 1 ford< 12 (B.2). Finally we construct our plane curves from the space curves represented by points of this hypersurface (4.7).
Invariant theory for linear differential systems modeled after the grassmannian Gr(n, 2n)
Authors: Sasaki Takeshi , Yoshida Masaaki 
Published: July 2016

AbstractWe find invariants for the differential systems of rank 2n in n2 variables with n unknowns under the linear changes of the unknowns with variable coefficients. We look for a set of coefficients that determines the other coefficients, and give transformation rules under the linear changes above and coordinate changes. These can be considered as a generalization of the Schwarzian derivative, which is the invariant for second order ordinary differential equations under the change of the unknown by multiplying a non-zero function. Special treatment is done when n = 2: the conformal structure obtained through the Plücker embedding is studied, and a relation with line congruences is discussed.
Convolution Dirichlet Series and a Kronecker Limit Formula for Second-Order Eisenstein Series
Authors: Jorgenson Jay , O’Sullivan Cormac 
Published: July 2016

AbstractIn this article we derive analytic and Fourier aspects of a Kronecker limit formula for second-order Eisenstein series. Let Γ be any Fuchsian group of the first kind which acts on the hyperbolic upper half-space H such that the quotient Γ\H has finite volume yet is non-compact. Associated to each cusp of Γ\H, there is a classically studiedfirst-ordernon-holomorphic Eisenstein seriesE(s, z) which is defined by a generalized Dirichlet series that converges for Re(s) > 1. The Eisenstein seriesE(s, z) admits a meromorphic continuation with a simple pole ats= 1. Classically, Kronecker’s limit formula is the study of the constant term1(z) in the Laurent expansion ofE(s, z) ats= 1. A number of authors recently have studied what is known as thesecond-orderEisenstein seriesE*(s, z), which is formed by twisting the Dirichlet series that defines the seriesE(s, z) by periods of a given cusp formf. In the work we present here, we study an analogue of Kronecker’s limit formula in the setting of the second-order Eisenstein seriesE* (s, z), meaning we determine the constant term2(z) in the Laurent expansion ofE*(s, z) at its first pole, which is also ats= 1. To begin our investigation, we prove a bound for the Fourier coefficients associated to the first-order Kronecker limit function1. We then define two families of convolution Dirichlet series, denoted byandwithm∈ ℕ, which are formed by using the Fourier coefficients of1and the weight two cusp formf. We prove that for allm,andadmit a meromorphic continuation and are holomorphic ats= 1. Turning our attention to the second-order Kronecker limit function2, we first express2as a solution to various differential equations. Then we obtain its complete Fourier expansion in terms of the cusp formf, the Fourier coefficients of the first-order Kronecker limit function1, and special values(1) and(1) of the convolution Dirichlet series. Finally, we prove a bound for the special values(1) and(1) which then implies a bound for the Fourier coefficients of2. Our analysis leads to certain natural questions concerning the holomorphic projection operator, and we conclude this paper by examining certain numerical examples and posing questions for future study.
Classification of Möbius Isoparametric Hypersurfaces in 4
Authors: Hu Zejun , Li Haizhong 
Published: July 2016

AbstractLet Mn be an immersed umbilic-free hypersurface in the (n + 1)-dimensional unit sphere n+1, then Mn is associated with a so-called Möbius metric g, a Möbius second fundamental form B and a Möbius form Φ which are invariants of Mn under the Möbius transformation group of n+1. A classical theorem of Möbius geometry states that Mn (n ≥ 3) is in fact characterized by g and B up to Möbius equivalence. A Möbius isoparametric hypersurface is defined by satisfying two conditions: (1) Φ ≡ 0; (2) All the eigenvalues of B with respect to g are constants. Note that Euclidean isoparametric hyper-surfaces are automatically Möbius isoparametric, whereas the latter are Dupin hypersurfaces.In this paper, we prove that a Möbius isoparametric hypersurface in 4 is either of parallel Möbius second fundamental form or Möbius equivalent to a tube of constant radius over a standard Veronese embedding of ℝP2 into 4. The classification of hypersurfaces in n+1 (n ≥ 2) with parallel Möbius second fundamental form has been accomplished in our previous paper [6]. The present result is a counterpart of Pinkall’s classification for Dupin hypersurfaces in 4 up to Lie equivalence.
Positive Toeplitz Operators of Schatten–Herz Type
Authors: Choe Boorim , Koo Hyungwoon , Na Kyunguk 
Published: July 2016

AbstractMotivated by a recent work of Loaiza et al. for the holomorphic case on the disk, we introduce and study the notion of Schatten-Herz type Toeplitz operators acting on the harmonic Bergman space of the ball. We obtain characterizations of positive Toeplitz operators of Schatten-Herz type in terms of averaging functions and Berezin transforms of symbol functions. Our characterization in terms of Berezin transforms settles a question posed by Loaiza et al.
Truncated Microsupport and Hyperbolic Inequalities
Authors: Martins Ana Rita , Fernandes Teresa Monteiro 
Published: July 2016

AbstractWe prove that the k-truncated microsupport of the specialization of a complex of sheaves F along a submanifold is contained in the normal cone to the conormal bundle along the k-truncated microsupport of F. In the complex case, applying our estimates to , where is a coherent -module, we obtain new estimates for the truncated microsupport of real analytic and hyperfunction solutions. When is regular along Y we also obtain estimates for the truncated microsupport of the holomorphic solutions of the induced system along Y as well as for the nearby-cycle sheaf of when Y is a hypersurface.
Note on Schiffer’s Variation in the Class of Univalent Functions in the Unit Disc
Authors: Matsumoto Kikuji 
Published: July 2016

Let S denote the class of univalent functions f(z) in the unit disc D: | z | < 1 with the following expansion:
(1)	f(z) = z + a2z2 + a3z3 + · · · · anzn + · ··.We denote by fn(z) the extremal function in S which gives the maximum value of the real part of an and by Dn the image of D under w = fn(z).
Note sur L’ensemble D’Adhérence Fine des Fonctions Algébroïdes
Authors: Toda Nobushige 
Published: July 2016

Soit f(z) une fonction algébroïde dans | z | < ∞ définie par
où cette équation est irréducible dans | z | < ∞. Rf est la surface de Riemann définie par f(z) comme surface de recouvrement de | z | < ∞.