bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Kottwitz-Shelstad normalization of transfer factors for automorphic induction for GLn
Authors: Hiraga Kaoru , Ichino Atsushi 
Published: July 2016

AbstractAutomorphic induction for GLnis a case of endoscopic transfer, and its character identity was established by Henniart and Herb, up to a constant of proportionality. We determine this constant in terms of the Kottwitz-Shelstad normalization of transfer factors, which involves certainε-factors.
On zeta functions associated to symmetric matrices, II: Functional equations and special values
Authors: Ibukiyama Tomoyoshi , Saito Hiroshi 
Published: July 2016

AbstractNew simple functional equations of zeta functions of the prehomogeneous vector spaces consisting of symmetric matrices are obtained, using explicit forms of zeta functions in the previous paper, Part I, and real analytic Eisenstein series of half-integral weight. When the matrix size is 2, our functional equations are identical with the ones by Shintani, but we give here an alternative proof. The special values of the zeta functions at nonpositive integers and the residues are also explicitly obtained. These special values, written by products of Bernoulli numbers, are used to give the contribution of “central” unipotent elements in the dimension formula of Siegel cusp forms of any degree. These results lead us to a conjecture on explicit values of dimensions of Siegel cusp forms of any torsion-free principal congruence subgroups of the symplectic groups of general degree.
Deformations of elliptic fiber bundles in positive characteristic
Authors: Partsch Holger 
Published: July 2016

AbstractWe study the deformation theory of elliptic fiber bundles over curves in positive characteristics. As applications, we give examples of nonliftable elliptic surfaces in characteristics 2 and 3, which answer a question of Katsura and Ueno. Also, we construct a class of elliptic fibrations, whose liftability is equivalent to a conjecture of Oort concerning the liftability of automorphisms of curves. Finally, we classify deformations of bielliptic surfaces.
A Proof of Brauer’s Theorem on Generalized Decomposition Numbers
Authors: Nagao Hirosi 
Published: July 2016

In [3] R. Brauer gave a proof of his theorem on generalized decomposition numbers which was first announced in [1], and a simplification of it has been made by K. Iizuka [5]. In this note we shall show that the theorem may be proved from another point of view by using some results obtained by J. A. Green in [4].After stating some results by Green and Osima in the first and second sections we first prove a theorem on characters (Theorem 1) and by using the theorem we prove Brauer’s theorem in the fourth section.
Analytic Functions on Some Riemann Surfaces
Authors: Toda Nobushige , Matsumoto Kikuji 
Published: July 2016

Some years ago, Kuramochi gave in his paper [5] a very interesting theorem, which can be stated as follows.THEOREM OF KURAMOCHI. Let R be a hyperbolic Riemann surface of the class Of OHR(OHD,resp.). Then, for any compact subset K of R such that R—K is connected, R—K as an open Riemann surface belongs to the class 0AB(OAD resp.).
Crossed Products and Maximal Orders
Authors: Williamson Susan 
Published: July 2016

Let I’ be a maximal order over a complete discrete rank one valuation ring R in a central simple algebra over the quotient field of R. The purpose of this paper is to determine necessary and sufficient conditions for I’ to be equivalent to a crossed product over a tamely ramified extension of R.It is a classical result that every central simple algebra over a field k is equivalent to a crossed product over a Galois extension of k. Furthermore, it has been proved by Auslander and Goldman in [2] that every central separable algebra over a local ring is equivalent to a crossed product over an unramified extension.
On Some Infinite Dimensional Representations of Semi-Simple Lie Algebras
Authors: Kimura Hiroshi 
Published: July 2016

Let g be a semi-simple Lie algebra over an algebraically closed field K of characteristic 0. For finite dimensional representations of g, the following important results are known;
1) H1(g, V) = 0 for any finite dimensional g space V. This is equivalent to the complete reducibility of all the finite dimensional representations,2) Determination of all irreducible representations in connection with their highest weights.3) Weyl’s formula for the character of irreducible representations [9].4) Kostant’s formula for the multiplicity of weights of irreducible representations [6],5) The law of the decomposition of the tensor product of two irreducible representations [1].
A Characterization of the Simple Group U3(5)
Authors: Harada Koichiro 
Published: July 2016

In this note we consider a finite group G which satisfies the following conditions:
(0. 1) G is a doubly transitive permutation group on a set Ω of m + 1 letters, where m is an odd integer ≥ 3,(0. 2) if H is a subgroup of G and contains all the elements of G which fix two different letters α, β, then H contains unique permutation h0 ≠ 1 which fixes at least three letters,(0. 3) every involution of G fixes at least three letters,(0. 4) G is not isomorphic to one of the groups of Ree type.
On a Propositional Calculus Whose Decision Problem is Recursively Unsolvable
Authors: Nakamura Akira 
Published: July 2016

The purpose of this paper is to present a propositional calculus whose decision problem is recursively unsolvable. The paper is based on the following ideas:
(1) Using Löwenheim-Skolem’s Theorem and Surányi’s Reduction Theorem, we will construct an infinitely many-valued propositional calculus corresponding to the first-order predicate calculus.(2) It is well known that the decision problem of the first-order predicate calculus is recursively unsolvable.(3) Thus it will be shown that the decision problem of the infinitely many-valued propositional calculus is recursively unsolvable.
Stable Vector Bundles on Algebraic Surfaces
Authors: Takemoto Fumio 
Published: July 2016

AbstractLet k be an algebraically closed field, and X a nonsingular irreducible protective algebraic variety over k. These assumptions will remain fixed throughout this paper. We will consider a family of vector bundles on X of fixed rank r and fixed Chern classes (modulo numerical equivalence). Under what condition is this family a bounded family? When X is a curve, Atiyah [1] showed that it is so if all elements of this family are indecomposable. But when I is a surface, he showed also that this condition is not sufficient. We give the definition of an H-stable vector bundle on a variety X. This definition is a generalization of Mumford’s definition on a curve. Under the condition that all elements of a family are H-stable of rank two on a surface X, we prove that the family is bounded. And we study H-stable bundles, when X is an abelian surface, the protective plane or a geometrically ruled surface.
Long Exact Sequences and the Transgression Relation
Authors: Berkson A. , McConnell Alan 
Published: July 2016

Throughout what follows, let H be a normal subgroup of the group G, be G/H, M a left G module, and HomH(G,M) = a left G module via (τϕ(σ) = (ϕ(στ)In [1] the present authors compared the 5-term Hochschild Serre sequence to the long exact sequence arising from the short exactsequence of modules
On stochastic optimal control laws
Authors: Nisio Makiko 
Published: July 2016

Let us begin by recalling the existence of optimal controls for a class of stochastic differential equationswith given initial condition X(0) = x, where B is an n-dimensional Brownian motion and the control U is a stochastic process. As admissible controls, let us allow all non-anticipative process U(t) = (U1(t),…Um(t)) ∈ Γ where Γ is a compact subset of Rm. We call Γ a control region. Assume that the matrix valued functional β and the n-vector valued α satisfy a Lipscitz condition in X and some growth condition. Then we have a unique solution Xu for an admissible control U.
On some degenerate parabolic equations II
Authors: Matsuzawa Tadato 
Published: July 2016

In the article I: [8], we have proved the hypoellipticity of a degenerate parabolic equation of the form:where the coefficients a(x, t), b(x,t) and c(x, t) are complex valued smooth functions. The fundamental assumption on the coefficients is that Re a(x, t) satisfies the condition of Nirenberg and Treves ([8], (1.5)). To prove the hypoellipticity we have constructed recurcively the parametrices as pseudodifferential operators with parameter. This method may be viewed as an improvement of that of [9] and [7]. We have analyzed the properties of these parametrices by estimating the symbols with parameter associated with the given operator. We shall summerize these results in §3.
On the conductor of an elliptic curve with a rational point of order 2
Authors: Hadano Toshihiro 
Published: July 2016

Let C be an elliptic curve (an abelian variety of dimension one) defined over the field Q of rational numbers. A minimal Weierstrass model for C at all primes p in the sense of Néron [3] is given by a plane cubic equation of the formwhere aj belongs to the ring Z of integers of Q, the zero of C being the point of infinity.
Large increments of Brownian motion
Authors: Kaufman R. 
Published: July 2016

Let X(t) denote Brownian motion on the line 0 ≤ t < ∞, let and let 0 < α < 1. Orey and Taylor [5] have investigated the random set defined by the inequalitiesand proved that P{dim Eα = 1 – α2} = 1. Here we prove two theorems on Eα that reflect more subtle properties of Eα than its Hausdorff dimension alone.
Hida-Cramér Multiplicity Theory for Multiple Markov Processes and Goursat Representations
Authors: Pitt Loren D. 
Published: July 2016

This work grew out of an attempt to prove the false result that ann-ple Markov process in the sense of Hida (1960) or Lévy (1956a) has multiplicity one. Instead we proved the representation theorem (Theorem III. 1.) that a centered Gaussian processx(t)isn-ple Markov iff it can be written in the form(I.1)whereis a Gaussian martingale with(I.2) sp {x(s):s≤t} ≡sp{ai(s):s≤tand 1 ≤i≤n}andA(t) and {ei(t)} satisfy some non-degeneracy condition. We also show (Corollary IV. 13.) that for any Gaussian martingaleA(t) with simple left innovation spectrum, continuousei(t) may be found so that the processx(t) given in (I.1) will satisfy (I.2).
Correction to My Paper “On Titchmarsh-kodaira’s Formula Concerning Weyl-Stone’s Eigenfunction Expansion” in Nagoya Mathematical Journal, Vol. 1 (1950), 49–58
Authors: Yosida Kôsaku 
Published: July 2016

Recently Mr. Seizô Itô kindly called the author’s attention to the fact that the derivation of (4.15) in the above referred paper is insufficient since the paper does not contain the proof of the compactness condition:(1) uniformaly in a and b
A classification of irreducible prehomogeneous vector spaces and their relative invariants
Authors: Sato M. , Kimura T. 
Published: July 2016

LetGbe a connected linear algebraic group, andpa rational representation ofGon a finite-dimensional vector spaceV, all defined over the complex number fieldC.We call such a triplet (G, p, V) aprehomogeneous vector spaceifVhas a Zariski-denseG-orbit. The main purpose of this paper is to classify all prehomogeneous vector spaces whenpis irreducible, and to investigate their relative invariants and the regularity.
An application of Ritt’s low power theorem
Authors: Matsuda Michihiko 
Published: July 2016

AbstractConsider an algebraic differential equation F = 0 of the first order. A rigorous definition will be given to the classical concept of “particular solutions” of F = 0. By Ritt’s low power theorem we shall prove that a singular solution of F = 0 belongs to the general solution of F if and only if it is a particular solution of F = 0.
Stochastic stability of Anosov diffeomorphisms
Authors: Kato Kazuhisa 
Published: July 2016

R. Bowen [1] introduced the notion of pseudo-orbit for a homeomorphism f of a metric space X as follows: A (double) sequence {xi}i∈Z of points Xi in X is called a δ-pseudo-orbit of f iffd(fxi, xi+1) ≤ δfor every i ∈ Z, where d denotes the metric in X. We say f is stochastically stable if for every ε > 0 there exists δ > 0 such that every δ pseudo-orbit {Xi}i∈Z of f is ε-traced by some x ∈ X, i.e.,d(fix, xi) ≤ εfor every i ∈ Z. He proved in [1] that if a compact hyperbolic set Λ for a diffeomorphism f of a compact manifold M has local product structure then the restriction f | Λ of f to Λ is stochastically stable, using stable and unstable manifolds.
On the decay of solutions for some nonlinear evolution equations of second order
Authors: Yamada Yoshio 
Published: July 2016

In this paper we consider nonlinear evolution equations of the form(E) u″(t) + Au(t) + B(t)u′(t) = f(t), 0 ≦ t < ∞,(u′(t) = d2u(t)/dt2, u′(t) = du(t)/dt), where A and B(t) are (possibly) nonlinear operators. Various examples of equations of type (E) arise in physics; for instance, if Au = –Δu and B(t)u′ = | u′ | u′, the equation represents a classical vibrating membrane with the resistance proportional to the velocity.
A numerical criterion of quasi-abelian surfaces
Authors: Iitaka Shigeru 
Published: July 2016

At first, we fix the notation. Letk=Cand we shall work in the category of schemes overk. For an algebraic varietyVof dimensionn, we have the following numerical invariants:Pm(V) = them-genus ofV,q(V) = the irregularity ofV,k(V) = the Kodaira dimension ofV;= the logarithmicm-genus ofV,= the logarithmic irregularity ofV,= the logarithmic Kodaira dimension ofV.
The group of automorphisms of a differential algebraic function field
Authors: Matsuda Michihiko 
Published: July 2016

AbstractConsider a one-dimensional differential algebraic function field K over an algebraically closed ordinary differential field k of characteristic 0. We shall prove the following theorem:Suppose that the group of all automorphisms of K over k is infinite. Then, K is either a differential elliptic function field over k or K = k(ν) with ν′ = ξ or ν′ = ην, where ξ, η ϵ k.
Invariant subrings which are complete intersections, I: (Invariant subrings of finite Abelian groups)
Authors: Watanabe Keiichi 
Published: July 2016

Let G be a finite subgroup of GL(n, C) (C is the field of complex numbers). Then G acts naturally on the polynomial ring S = C[X1, …, Xn]. We consider the followingProblem. When is the invariant subring SG a complete intersection?In this paper, we treat the case where G is a finite Abelian group. We can solve the problem completely. The result is stated in Theorem 2.1.
Corrigenda On a classification of the function fields of algebraic tori: (Nagoya Math. J. 56 (1975), 85–104)
Authors: Endo Shizuo , Miyata Takehiko 
Published: July 2016

There are some errors in Theorems 3.3 and 4.2 in [2]. In this note we would like to correct them.1) In Theorem 3.3 (and [IV]), the condition (1) must be replaced by the following one;(1) П is (i) a cyclic group, (ii) a dihedral group of order 2m, m odd, (iii) a direct product of a cyclic group of order qf, q an odd prime, f ≧ 1, and a dihedral group of order 2m, m odd, where each prime divisor of m is a primitive qf-1(q — 1)-th root of unity modulo qf, or (iv) a generalized quaternion group of order 4m, m odd, where each prime divisor of m is congruent to 3 modulo 4.
Completely superharmonic measures for the infinitesimal generator A of a diffusion semi-group and positive eigen elements of A
Authors: Itô Masayuki , Suzuki Noriaki 
Published: July 2016

Let X be a locally compact Hausdorff space with countable basis. We denote byM(X) the topological vector space of all real Radon measures in X with the vague topology,MK(X) the topological vector space of all real Radon measures in X whose supports are compact with the usual inductive limit topology.
On a generalization of the abstract Morse complex and its applications
Authors: Hong Suk Ho 
Published: July 2016

Klingenberg refers in [4] the fact that the homology group of the spaceΛof closedH1curves on a manifold is isomorphic to that of the Morse complex. In this paper, we generalize the fact above and at the same time give a proof to it through cell decomposition method under a strong non degeneracy condition.We first introduce so-called generalized Morse complex on a spaceXwith an action of Lie groupGand an invariant energy functionEonX. The case of the spaceΛof closed curves is obviously obtained throughG=S1.
Remark on Smith’s result on a divisor problem in arithmetic progressions
Authors: Matsumoto Kohji 
Published: July 2016

Let dk(n) be the number of the factorizations of n into k positive numbers. It is known that the following asymptotic formula holds:
where r and q are co-prime integers with 0 < r < q, Pk is a polynomial of degree k − 1, φ(q) is the Euler function, and Δk(q; r) is the error term. (See Lavrik [3]).
Remarks to the uniqueness problem of meromorphic maps into PN(C), II
Authors: Fujimoto Hirotaka 
Published: July 2016

In [7], R. Nevanlinna gave the following uniqueness theorem of meromorphic functions as an improvement of a result of G. Pólya ([8]).Theorem A. Let f, g be non-constant meromorphic functions on C. If there are five mutually distinct values a1, …, a5 such that f−1(ai = g−1(ai) (1 ≦ i ≦ 5), then f ≡ g.
Galois Group of the Maximal Abelian Extension over an Algebraic Number Field
Authors: Kubota Tomio 
Published: July 2016

The aim of the present work is to determine the Galois group of the maximal abelian extensionΩAover an algebraic number fieldΩof finite degree, which we fix once for all.Let Z be a continuous character of the Galois group ofΩA/Ω. Then, by class field theory, the character Z is also regarded as a character of the idele group of Ω. We call such Zcharacter of Ω. For our purpose, it suffices to determine the groupXlof the characters ofΩwhose orders are powers of a prime numberl.
Capacities of Borelian Sets and the Continuity of Potentials
Authors: Kishi Masanori 
Published: July 2016

One of the most important problems in the potential theory is the one of capacitability, that is, whether the inner capacity of an arbitrary borelian subset B is equal to the outer capacity of B. As for the capacities induced by the Newtonian potentials and other classical potentials, Choquet [5] has shown that every borelian and, more generally, every analytic set are capacitable. He goes on as follows : first he shows that, for the Newtonian capacity f, the inequality of strong subadditivity holds, that is,and then, using this inequality, he shows that the outer capacity f* has the analogous property to one of the outer measure, more precisely, if an increasing sequence {An} of arbitrary subsets converges to A, then f*(A) = limf*(An)- This property plays an important role in his proof.
On the second Gaussian map for curves on a K3 surface
Authors: Colombo Elisabetta , Frediani Paola 
Published: July 2016

AbstractBy a theorem of Wahl, for canonically embedded curves which are hyperplane sections of K3 surfaces, the first Gaussian map is not surjective. In this paper we prove that ifCis a general hyperplane section of high genus (&gt; 280) of a general polarized K3 surface, then the second Gaussian map ofCis surjective. The resulting bound for the genusgof a general curve with surjective second Gaussian map is decreased tog&gt; 152.
The structure of sally modules and Buchsbaumness of associated graded rings
Authors: Ozeki Kazuho 
Published: July 2016

AbstractLetAbe a Noetherian local ring with the maximal ideal m, and letIbe an m-primary ideal inA. This paper examines the equality on Hilbert coefficients ofIfirst presented by Elias and Valla, but without assuming thatAis a Cohen–Macaulay local ring. That equality is related to the Buchsbaumness of the associated graded ring ofI.
Minimal Models and Abundance for Positive Characteristic Log Surfaces
Authors: Tanaka Hiromu 
Published: July 2016

AbstractWe discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for ℚ-factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.
Some applications of Synge’s formula to the theory of several complex variables
Authors: Sasaki Takeshi , Suzuki Osamu 
Published: July 2016

In [10] and [11], the second author proved the following theorem by using Synge’s formula:THEOREM I. Let M be a kähler manifold with positive holomorphic bi-sectional curvature. Then every pseudoconvex domain in M is a Stein manifold.
Remarks on the Elliptic Case of the Mapping Theorem for Simply-Connected Riemann Surfaces
Authors: Heins Maurice 
Published: July 2016

It is well-known that the conformal equivalence of a compact simply-connected Riemann surface to the extended plane is readily established once it is shown that given a local uniformizer t(p) which carries a given point p0 of the surface into 0, there exists a function u harmonic on the surface save at p0 which admits near p0 a representation of the form(α complex 0; h harmonic at p0). For the monodromy theorem then implies the existence of a meromorphic function on the surface whose real part is u. Such a meromorphic function has a simple pole at p0 and elsewhere is analytic. It defines a univalent conformal map of the surface onto the extended plane.
Note on Complete Cohomology of a Quasi-Frobenius Algebra
Authors: Nakayama Tadasi 
Published: July 2016

Let A be a quasi-Frobenius algebra over a field K. A has a complete (co)homology theory which may be established upon an augmented acyclic projective complex, i.e. a commutative diagram
of A-double-modules with exact horizontal row, projective Xp, and with epimorphic resp. monomorphic ε and t. Negative-dimensional cohomology groups, over an A-double-module, are expected to be in close relationship with (ordinary positive-dimensional) homology groups.
A Lemma which Distinguishes Minimal Logics from Other Logics
Authors: Ono Katuzi 
Published: July 2016

In my joint work with J. Ito [7], we have pointed out that the following property (called ASSUMPTION REMOVABILITY) is characteristic of positive logics LO, LP, and LQ:ASSUMPTION REMOVABILITY. If → is provable for any pair of propositions andhaving no primitive notions (proposition-, predicate-, and relation-symbols) in common, thenis also provable.
Symplectic structures and symmetries of solutions of the complex Monge-Ampére equation
Authors: Einstein-Matthews Stanley M. 
Published: July 2016

Abstract.The graphs that arise from the gradients of solutionsuof the homogeneous complex Monge-Ampère equation are characterized in terms of the natural symplectic structure on the cotangent bundle. This characterization is invariant under symplectic biholomorphisms. Using the symplectic structures we construct symmetries (to be called Lempert transformations) for real valued functionsuwhich are absolutely continuous on lines. We then use these symmetries to generate interesting solutions to the homogeneous complex Monge-Ampère equation and to transform the Poincaré-Lelong equation and the ∂-equation. An example of Lempert transform is given and the main theorem is applied to prove regularity results for exterior nonlinear Dirichlet problem for the homogeneous complex Monge-Ampère equation.
Moduli spaces of stable vector bundles on Enriques surfaces
Authors: Kim Hoil 
Published: July 2016

Abstract.We show that the image of the moduli space of stable bundles on an Enriques surface by the pull back map is a Lagrangian subvariety in the moduli space of stable bundles, which is a symplectic variety, on the covering K3 surface. We also describe singularities and some other features of it.