bluuebunny/crossref_metadata_2025_split huggingface dataset:
A global theory of flexes of periodic functions
Authors: Thorbergsson Gudlaugur , Umehara Masaaki 
Published: July 2016

AbstractFor a real valued periodic smooth function u on R, n ≥ 0, one defines the osculating polynomial φs (of order 2n + 1) at a point s ∈ R to be the unique trigonometric polynomial of degree n, whose value and first 2n derivatives at s coincide with those of u at s. We will say that a point s is a clean maximal flex (resp. clean minimal flex) of the function u on S1 if and only if φs ≥ u (resp. φs ≤ u) and the preimage (φ - u)-1(0) is connected. We prove that any smooth periodic function u has at least n + 1 clean maximal flexes of order 2n + 1 and at least n + 1 clean minimal flexes of order 2n + 1. The assertion is clearly reminiscent of Morse theory and generalizes the classical four vertex theorem for convex plane curves.
Modular forms arising from zeta functions in two variables attached to prehomogeneous vector spaces related to quadratic forms
Authors: Ueno Takahiko 
Published: July 2016

AbstractIn this paper, we prove the functional equations for the zeta functions in two variables associated with prehomogeneous vector spaces acted on by maximal parabolic subgroups of orthogonal groups. Moreover, applying the converse theorem of Weil type, we show that elliptic modular forms of integral or half integral weight can be obtained from the zeta functions.
Topological triviality of families of functions on analytic varieties
Authors: Ruas Maria Aparecida Soares , Tomazella João Nivaldo 
Published: July 2016

AbstractWe present in this paper sufficient conditions for the topological triviality of families of germs of functions defined on an analytic variety V. The main result is an infinitesimal criterion based on a convenient weighted inequality, similar to that introduced by T. Fukui and L. Paunescu in [8]. When V is a weighted homogeneous variety, we obtain as a corollary, the topological triviality of deformations by terms of non negative weights of a weighted homogeneous germ consistent with V. Application of the results to deformations of Newton non-degenerate germs with respect to a given variety is also given.
Types of complete Infinitely sheeted Planes
Authors: Nakai Mitsuru 
Published: July 2016

AbstractWe will answer negatively to the question whether the completeness of infinitely sheeted covering surfaces of the extended complex plane have anything to do with their types being parabolic or hyperbolic. This will be accomplished by giving a one parameter family {W[α]: α ∈ A} of complete infinitely sheeted planes W[α] depending on the parameter set A of sequences α = (an)n>1 of real numbers 0 < an ≤ 1/2 (n ≥ 1) such that W[α] is parabolic for ‘small’ α’s and hyperbolic for ‘large’ α’s.
L2Extension for jets of holomorphic sections of a Hermitian line Bundle
Authors: Popovici Dan 
Published: July 2016

AbstractLet (X, ω) be a weakly pseudoconvex Kähler manifold,Y ⊂ Xa closed submanifold defined by some holomorphic section of a vector bundle overX, andLa Hermitian line bundle satisfying certain positivity conditions. We prove that for any integerk> 0, any section of the jet sheafwhich satisfies a certain L2condition, can be extended into a global holomorphic section ofLoverXwhose L2growth on an arbitrary compact subset ofXis under control. In particular, ifYis merely a point, this gives the existence of a global holomorphic function with an L2norm under control and with prescribed values for all its derivatives up to orderkat that point. This result generalizes the L2extension theorems of Ohsawa-Takegoshi and of Manivel to the case of jets of sections of a line bundle. A technical difficulty is to achieve uniformity in the constant appearing in the final estimate. To this end, we make use of the exponential map and of a Rauch-type comparison theorem for complete Riemannian manifolds.
A Mirror Construction for the Totally Nonnegative Part of the Peterson Variety
Authors: Rietsch Konstanze 
Published: July 2016

AbstractWe explain how A. Givental’s mirror symmetric family [14] to the typeAag variety and its proposed generalization [3] to partial ag varieties by Batyrev, Ciocan-Fontanine, Kim and van Straten relate to the Peterson varietyY ⊂ SLn/B. We then use this theory to describe the totally nonnegative part ofY, extending a result from [30].
Infinitesimal Invariant and vector bundles
Authors: Pirola Gian Pietro , Rizzi Cecilia 
Published: July 2016

AbstractWe study the Saito-Ikeda infinitesimal invariant of the cycle defined by curves in their Jacobians using rank k + 1 vector bundles. We give a criterion for which the higher cycle class map is not trivial. When k = 2, this turns out to be strictly linked to the Petri map for vector bundles. In this case we can improve a result of Ikeda: an explicit construction on a curve of genus g ≥ 10 shows the existence of a non trivial element in the higher Griffiths group.
Estimates for the Products of the Green Function and the Martin Kernel
Authors: Hirata Kentaro 
Published: July 2016

AbstractLet Ω be a proper subdomain of ℝn, n ≥ 2, and let x0∈ Ω be fixed. By GΩ and KΩ we denote the Green function and the Martin kernel for Ω, respectively. Under a certain assumption on Ω near a boundary point ξ, we show that the product GΩ(x, x0)KΩ(x, ξ) is comparable to |x - ξ|2-n for x in a nontangential cone with vertex at ξ. We also give an estimate for the product KΩ(x, ξ)KΩ(x,η) in a uniform domain, where η is another boundary point.
Symmetry on Linear Relations for Multiple Zeta Values
Authors: Ihara Kentaro , Ochiai Hiroyuki 
Published: July 2016

AbstractWe find a symmetry for the reflection groups in the double shuffle space of depth three. The space was introduced by Ihara, Kaneko and Zagier and consists of polynomials in three variables satisfying certain identities which are connected with the double shuffle relations for multiple zeta values. Goncharov has defined a space essentially equivalent to the double shuffle space and has calculated the dimension. In this paper we relate the structure among multiple zeta values of depth three with the invariant theory for the reflection groups and discuss the dimension of the double shuffle space in this view point.
Analytic Jet Parametrization for CR Automorphisms of Some Essentially Finite CR Manifolds
Authors: Kim Sung-Yeon 
Published: July 2016

AbstractIn this paper we construct analytic jet parametrizations for the germs of real analytic CR automorphisms of some essentially finite CR manifolds on their finite jet at a point. As an application we show that the stability groups of such CR manifolds have Lie group structure under composition with the topology induced by uniform convergence on compacta.
Nonrational Weighted Hypersurfaces
Authors: Okada Takuzo 
Published: July 2016

AbstractThe aim of this paper is to construct (i) infinitely many families of nonrational ℚ-Fano varieties of arbitrary dimension ≥ 4 with at most quotient singularities, and (ii) twelve families of nonrational ℚ-Fano threefolds with at most terminal singularities among which two are new and the remaining ten give an alternate proof of nonrationality to known examples. These are constructed as weighted hypersurfaces with the reduction mod p method introduced by Kollár [10].
C∞-Convergence of Circle Patterns to Minimal Surfaces
Authors: Lan Shi-Yi , Dai Dao-Qing 
Published: July 2016

AbstractGiven a smooth minimal surface F: Ω → ℝ3 defined on a simply connected region Ω in the complex plane ℂ, there is a regular SG circle pattern . By the Weierstrass representation of F and the existence theorem of SG circle patterns, there exists an associated SG circle pattern in ℂ with the combinatoric of . Based on the relationship between the circle pattern and the corresponding discrete minimal surface F∊: → ℝ3 defined on the vertex set of the graph of , we show that there exists a family of discrete minimal surface Γ∊: → ℝ3, which converges in C∞(Ω) to the minimal surface F: Ω → ℝ3 as ∊ → 0.
Logarithmic Vector Fields and Hyperbolicity
Authors: Rousseau Erwan 
Published: July 2016

AbstractUsing vector fields on logarithmic jet spaces we obtain some new positive results for the logarithmic Kobayashi conjecture about the hyperbolicity of complements of curves in the complex projective plane. We are interested here in the cases where logarithmic irregularity is strictly smaller than the dimension. In this setting, we study the case of a very generic curve with two components of degrees d1 ≤ d2 and prove the hyperbolicity of the complement if the degrees satisfy either d1 ≥ 4, or d1 = 3 and d2 ≥ 5, or d1 = 2 and d2 ≥ 8, or d1 = 1 and d2 ≥ 11. We also prove that the complement of a very generic curve of degree d at least equal to 14 in the complex projective plane is hyperbolic, improving slightly, with a new proof, the former bound obtained by El Goul.
Truncated Euler Systems over Imaginary Quadratic Fields
Authors: Seo Soogil 
Published: July 2016

AbstractLet K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group ClF of F is equal to the order of the quotient UF/ElF of the group of global units UF by the group of elliptic units ElF of F. We introduce a filtration on UF/ElF made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We provide evidence for the conjecture using Iwasawa theory.
Lefschetz operator and local Langlands modℓ: The regular case
Authors: Dat Jean-François 
Published: July 2016

AbstractLetpandℓbe two distinct primes. The aim of this paper is to show how, under a certain congruence hypothesis, the modℓcohomology complex of the Lubin-Tate tower, together with a natural Lefschetz operator, provides a geometric interpretation of Vignéras’s local Langlands correspondence moduloℓfor unipotent representations.
Some conjectures on endoscopic representations in odd orthogonal groups
Authors: Ginzburg David , Jiang Dihua 
Published: July 2016

AbstractIn this paper, we introduce two conjectures on characterizations of endoscopy structures of irreducible generic cuspidal automorphic representations of odd special orthogonal groups in terms of nonvanishing of certain period of automorphic forms. We discuss a relation between the two conjectures and prove that a special case of Conjecture 1 (and hence Conjecture 2) is true.
Matrix coefficients of the large discrete series representations of Sp(2; R) as hypergeometric series of two variables
Authors: Oda Takayuki 
Published: July 2016

AbstractWe investigate the radial part of the matrix coefficients with minimal K-types of the large discrete series representations of Sp(2; R). They satisfy certain difference-differential equations derived from Schmid operators. This system is reduced to a holonomic system of rank 4, which is finally found to be equivalent to higher-order hypergeometric series in the sense of Appell and Kampé de Fériet.
The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces
Authors: Tanaka Minoru , Kondo Kei 
Published: July 2016

AbstractWe construct distinctive surfaces of revolution with finite total curvature whose Gauss curvatures are not bounded. Such a surface of revolution is employed as a reference surface of comparison theorems in radial curvature geometry. Moreover, we prove that a complete noncompact Riemannian manifold M is homeomorphic to the interior of a compact manifold with boundary if the manifold M is not less curved than a noncompact model surface of revolution and if the total curvature of the model surface is finite and less than 2π. By the first result mentioned above, the second result covers a much wider class of manifolds than that of complete noncompact Riemannian manifolds whose sectional curvatures are bounded from below by a constant.
Nonarchimedean geometry of Witt vectors
Authors: Kedlaya Kiran S. 
Published: July 2016

AbstractLetRbe a perfect 𝔽-algebra equipped with the trivial norm. LetW(R) be the ring ofp-typical Witt vectors overRequipped with thep-adic norm. At the level of nonarchimedean analytic spaces (in the sense of Berkovich), we demonstrate a close analogy betweenW(R) and the polynomial ringR[T] equipped with the Gauss norm, in which the role of the structure morphism fromRtoR[T] is played by the Teichmüller map. For instance, we show that the analytic space associated toRis a strong deformation retract of the space associated toW(R). We also show that each fiber forms a tree under the relation of pointwise comparison, and we classify the points of fibers in the manner of Berkovich’s classification of points of a nonarchimedean disk. Some results pertain to the study ofp-adic representations of étale fundamental groups of nonarchimedean analytic spaces (i.e., relativep-adic Hodge theory).
A Localization Principle for a Class of Analytic Functions
Authors: Storvick D. A. 
Published: July 2016

It has been shown by Kiyoshi Noshiro [8; p. 35] that a bounded analytic function w = f(z) in |z| < 1 having radial limit values of modulus one almost everywhere satisfies a localization principle of the following type. Let (c) be any circular disk: | w − α | < ρ lying inside |w| < 1 whose periphery may be tangent to the circumference |w| = 1. Denote by Δ any component of the inverse image of (c) under w = f(z) and by z = z(ξ) a function which maps |ξ| < 1 onto the simply connected domain Δ in a one-to-one conformal manner. Then, the functionis also a bounded analytic function in | ξ | < 1 with radial limits of modulus one almost everywhere.
On Feller’s Kernel and the Drichlet Norm
Authors: Fukushima Masatoshi 
Published: July 2016

Recently J. L. Doob [2] evaluated the Dirichlet integral of the BLD harmonic funtion on a Green space in terms of its fine boundary values and θ-kernel of L. Naïm.On the other hand, the general theory of additive functionals of Markov processes enables us to define the concept of the Dirichlet norm of functions with respect to Markov processes.
A Remark on Finitely Generated Modules
Authors: Nakayama Tadasi 
Published: July 2016

Theorem 5 of Azumaya’s recent article can be formulated in the following generalized form:Let R be a ring. Let m be a finitely generated right-module of R such that mR = m. Assume that m = u1r + ubr + … + umr for every generating system of u1, u2, …, um of m and for every maximal right-ideal r of R. Then m = 0.
On Boundary Value Problems for Elliptic Equations in a Singular Domain
Authors: Hayashida Kazunari 
Published: July 2016

1. Let Ω be a bounded domain in the plane and denotes its closure and boundary by Ω̅ and ∂Ω, respectively. We shall say that the domain Ω is regular, if every point P ∈ ∂û has an 2-dimensional neighborhood U such that dΩ ∩ U can be mapped in a one-to-one way onto a portion of the tangent line through P by a mapping T which together with its inverse is infinitely differentiable. Let L be an elliptic operator of order 2m defined in Ω̅ and let be a normal set of boundary operators of orders mf <2m. If f is a given function in Ω, the boundary value problem II(L,f,Bj) will be to find a solution u ofsatisfyingBju = 0 on ∂Ω, j = 1, …, m.
Note on the Behavior of Solutions of Parabolic Equations with Unbounded Coefficients
Authors: Chen Lu-San 
Published: July 2016

Letbe a parabolic differential operator defined in Ω = Rn + (0, ∞), where Rn is the n-dimensional Euclidean space, the point x ∈ Rn is represented by its coordinates (x1,...,xn) and aij(=aji), bi and c are functions in (x,t)∈Ω.
Units and Class Numbers of Real Quadratic Fields
Authors: Yokoi Hideo 
Published: July 2016

The aim of this paper is to prove the following main theorem:
THEOREM. For the discriminant d>0 of a real quadratic field let (x,y) = (t,u) be the least positive integral solution of Pell’s equation x2 — dy2 = 4 and put and denote by hd the ideal class number.
Hypoelliptic Overdetermined Systems with Variable Coefficients
Authors: Hashimoto Yoshiaki 
Published: July 2016

Let(1) p(x,D)u = fbe a system of partial difierential equations. We shall say that p (x,D) is hypoelliptic if the distribution solution u is in C∞ wherever f∈C∞ (cf. section 2, Definition 5.)Here we shall give a sufficient condition for the hypoellipticity of overdetermined systems with variable coefficients.
Some Groups Whose S3-Subgroups Have Maximal Class
Authors: Cline Ed 
Published: July 2016

In this paper, we investigate several classes of groups, among which the most general is defined as follows:Definition 1.1. A finite group G is a SR-group if it contains a subgroup P1 of order 3 satisfying:
(a)A/S3-subgroup P2 of NGP1 is elementary of order 9;(b)NG(P2)/P2 acts semi-regularly by conjugation on the conjugates of P1 contained in P2.
On Asymptotic Values of Slowly Growing Algebroid Functions
Authors: Suzuki Junji 
Published: July 2016

Let f(z) be a k-valued algebroid function in |z| <. ∞ and(1) F(z, f) ≡ A0(z)fk + A1(z)fk-1 + · · · Ak(z) = 0be its defining equation such that the coefficients Ai(z) (i = 0, 1, · · ·, k) are entire functions without any common zero and the left hand side is irreducible.
Comparison Theorems on Regular Points for Multidimensional Markov Processes of Transient Type
Authors: Kanda Mamoru 
Published: July 2016

The study of regular points for the Dirichlet problem has a long history. The probabilistic approach to regular points is originated by Doob [2] and [3] for Brownian motion and the heat process. The extension to general Markov processes is discussed in Dynkin [4] and [5]. They also clarified the relation between the fine topology and regular points.Regular points are by definition reflected in the behaviour of sample paths of Markov processes. Further the inclusion relation of collections of regular points for open sets determines the strength and the weakness of fine topologies between two processes. Hence it is meaningful to compare the collections of regular points for compact or open sets between two Markov processes apart from the Dirichlet problem.
Note on the Harmonic Measure of the Accessible Boundary of a Covering Riemann Surface
Authors: Ohtsuka Makoto 
Published: July 2016

The following relation was set up in [5] for an open covering Riemann surface ℜ with positive boundary over an abstract Riemann surface (1) when the universal covering surface of the projection is not of hyperbolic type when is of hyperbolic type this relation is reduced to(2)
On some degenerate parabolic equations
Authors: Matsuzawa Tadato 
Published: July 2016

Let Ω, I be open intervals in Rx = (— ∞ < x < ∞), Rt = (— ∞ < t < ∞) respectively. For a function a(x, t) ∈ C∞(Ω × I), consider the partial differential operator(1.1) .
On the theorem of Kishi for a continuous function-kernel
Authors: Higuchi Isao , Itô Masayuki 
Published: July 2016

In the potential theory with respect to a non-symmetric function-kernel, the following theorem is obtained by M. Kishi ([3]).Let X be a locally compact Hausdorff space and G be a lower semi-continuous function-kernel on X. Assume that G(x, x)>0 for any x in X and that G and the adjoint kernel Ğ of G satisfy “the continuity principle”.
On the existence of various bounded harmonic functions with given periods, II
Authors: Hara Masaru 
Published: July 2016

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.
On the Hopf fibration S7 → S4 Over Z
Authors: Ono Takashi 
Published: July 2016

Let K be the classical quaternion field over the field Q of rational numbers with the quaternion units 1, i, j, k, with relations i2 = j2 = − 1, k = ij = −ji. For a quaternion x ∈ K, we write its conjugate, trace and norm by and Nx, respectively. Putand consider the map h: A → B defined by
Potential theoretic properties of the gradient of a convex function on a functional space
Authors: Kenmochi Nobuyuki , Mizuta Yoshihiro 
Published: July 2016

In the previous paper [11], introducing the notions of potentials and of capacity associated with a convex function Φ given on a regular functional space we discussed potential theoretic properties of the gradient ∇Φ which were originally introduced and studied by Calvert [5] for a class of nonlinear monotone operators in Sobolev spaces. For example:
(i)The modulus contraction operates.(ii)The principle of lower envelope holds.(iii)The domination principle holds.(iv)The contraction Tk onto the real interval [0, k] (k > 0) operates.(v)The strong principle of lower envelope holds.(vi)The complete maximum principle holds.
Holomorphic mappings into a compact quotient of symmetric bounded domain
Authors: Sunada Toshikazu 
Published: July 2016

In this paper, we shall be concerned with the finiteness property of certain holomorphic mappings into a compact quotient of symmetric bounded domain.Let be a symmetric bounded domain in n-dimensional complex Euclidean space Cn and Γ\ be a compact quotient of S by a torsion free discrete subgroup Γ of automorphism group of . Further, we denote by l() the maximum value of dimension of proper boundary component of , which is less than n (=dim).
Sur l’unicité du cône convexe divisible relatif au noyau de convolution de Hunt défini par l’opérateur différentiel
Authors: Itô Masayuki 
Published: July 2016

Dans toute la suite Rn désignera l’espace euclidien à dimension n(≧ 1). Pour un point x = x1, x2, … xn) de Rn, on note |x| = et la coordonnée sphérique dans Rn désignera (r, α).Rappelons qu’un noyau de convolution N sur Rn est une mesure (de Radon) positive dans Rn dans la théorie du potentiel. Pour une mesure réelle μ dans Rn, N * μ s’appelle le N-potentiel de μ dès que cette convolution est définie au sens des mesures. On connaît bien que, dans la théorie du potentiel, les noyaux de convolution de Hunt possédent les propriétés définitives.
Construction of a solution of a certain evolution equation
Authors: Shimizu Akinobu 
Published: July 2016

Let us consider the stochastic differential equation,with initial condition,where Bt, t ≧ 0,is a one-dimensional Brownian motion, and Lxis a second order uniformly elliptic partial differential operator satisfying some additional conditions that will be described in §2. The existence and the uniqueness of solutions of the Cauchy problem have been established by B. L. Rozovskii [8].
Algebras and differential equations
Authors: Röhrl Helmut 
Published: July 2016

One purpose of this paper is a purely algebraic study of (systems of) ordinary differential equations of the typewhere the coefficients are taken from a fixed associative, commutative, unital ring R, such as the field R of real or C of complex numbers or a commutative, unital Banach algebra. The right hand sides of D are considered to be elements in the polynomial ring R[X1, …, Xn] of associating but non-commuting variables X1, …, Xn. An algebraic study calls for maps between such differential equations and, in fact, morphisms are defined between differential equations having the same arity m but not necessarily the same dimension n. These morphisms are rectangular matrices with entries in R which satisfy certain relations. This leads to a category RDiffm whose objects are precisely the differential equations of arity m and in which the composition of the morphisms is the usual matrix multiplication.
Representations of quadratic forms
Authors: Kitaoka Yoshiyuki 
Published: July 2016

We have shown in [1]Theorem A. Let L be a lattice in a regular quadratic space U over Q; then L has a submodule M satisfying the following conditions 1),2):
1)dM ≠ 0, rank M = rank L — 1, and M is a direct summand of L as a module.2)Let L′ be a lattice in some regular quadratic space U′ over Q satisfying dL′ = dL, rank L′ — rank L, tp(L′) ≥ tp(L) for any prime p. If there is an isometry α from M into L′ such that α(M) is a direct summand of L′ as a module, then L′ is isometric to L.