bluuebunny/crossref_metadata_2025_split huggingface dataset:
Class-number problems for cubic number fields
Authors: Louboutin Stéphane 
Published: July 2016

Let M be any number field. We let DM, dM, hu, , AM and RegM be the discriminant, the absolute value of the discriminant, the class-number, the Dedekind zeta-function, the ring of algebraic integers and the regulator of M, respectively.we set
If q is any odd prime we let (⋅/q) denote the Legendre’s symbol.
On compactness of isospectral conformal, metrics of 4-manifolds
Authors: Xu Xingwang 
Published: July 2016

In this paper, we are interested in the compactness of isospectral conformal metrics in dimension 4.Let us recall the definition of the isospectral metrics. Two Riemannian metricsg, g′on a compact manifold are said to be isospectral if their associated Laplace operators on functions have identical spectrum. There are now numeruos examples of compact Riemannian manifolds which admit more than two metrics such that they are isospectral but not isometric. That is to say that the eigenvalues of the Laplace operatorΔon the functions do not necessarily determine the isometry class of (M, g). If we further require the metrics stay in the same conformal class, the spectrum of Laplace operator still does not determine the metric uniquely ([BG], [BPY]).
The minimum and the primitive representation of positive definite quadratic forms II
Authors: Kitaoka Yoshiyuki 
Published: July 2016

We are concerned with representation of positive definite quadratic forms by a positive definite quadratic form. Let us consider the following assertion
Am, n : Let M, N be positive definite quadratic lattices over Z with rank(M) = m and rank(N) = n respectively. We assume that the localization Mp is represented by Np for every prime p, that is there is an isometry from Mp to Np. Then there exists a constant c(N) dependent only on N so that M is represented by N if min(M) > c(N), where min(M) denotes the least positive number represented by M.
Conformal immersions of compact Riemann surfaces into the 2n-sphere (n ≥ 2)
Authors: Hano Jun-Ichi 
Published: July 2016

The purpose of this article is to prove the following theorem:Let n be a positive integer larger than or equal to 2, and let S be the unit sphere in the 2n + 1 dimensional Euclidean space. Given a compact Riemann surface, we can always find a conformal and minimal immersion of the surface into S whose image is not lying in any 2n — 1 dimensional hyperplane.This is a partial generalization of the result by R. L. Bryant. In this papers, he demonstrates the existence of a conformal and minimal immersion of a compact Riemann surface into S2n, which is generically 1:1, when n = 2 ([2]) and n = 3 ([1]).
Exponential asymptotics in the small parameter exit problem
Authors: Sugiura Makoto 
Published: July 2016

Let M be a d-dimensional Riemannian manifold of class C∞ with Riemannian metric and let D be a connected domain in M having a non-empty smooth boundary and a compact closure . Suppose that are given and that converges uniformly to on D′ as for some neighborhood D′ of D. Consider the diffusion process on D′ with a small parameter generated by(1.1)
Finite arithmetic subgroups of GLn, V
Authors: Kitaoka Yoshiyuki 
Published: July 2016

Abstract.Let K be a finite Galois extension of the rational number field Q and G a Gal(K/Q)-stable finite subgroup of GLn(OK). We have shown that G is of A-type in several cases under some restrictions on K. In this paper, we show that it is true for n = 2 without any restrictions on K.
Sobolev and Lipschitz estimates for weighted Bergman projections
Authors: Chang Der-Chen , Li Bao Qin 
Published: July 2016

AbstractLet Ω be a bounded, decoupled pseudo-convex domain of finite type in ℂn with smooth boundary. In this paper, we generalize results of Bonami-Grellier [BG] and Bonami-Chang-Grellier [BCG] to study weighted Bergman projections for weights which are a power of the distance to the boundary. We define a class of operators of Bergman type for which we develop a functional calculus. Then we may obtain Sobolev and Lipschitz estimates, both of isotropic and anisotropic type, for these projections.
The genus of curves on the three dimensional quadric
Authors: De Cataldo Mark Andrea A. 
Published: July 2016

AbstractBy means of an ad hoc modification of the so-called “Castelnuovo-Harris analysis” we derive an upper bound for the genus of integral curves on the three dimensional nonsingular quadric which lie on an integral surface of degree 2/c, as a function of k and the degree d of the curve. In order to obtain this we revisit the Uniform Position Principle to make its use computation-free. The curves which achieve this bound can be conveniently characterized.
On differential polynomials I
Authors: Morikawa Hisasi 
Published: July 2016

AbstractThe content of Part I is nothing else than, the theory of binomial polynomial sequences in infinite variables (u(1), u(2), u(3), …) with weight u(1) = l. However, sometimes we are concerned with specialization therefore, we call the elements in K[u(1), u(2), u(3), …] differential polynomials. As analogies of special polynomials with binomial property, we may construct special differential polynomials with binomial property.
On differential polynomials, II
Authors: Morikawa Hisasi 
Published: July 2016

AbstractIn Part II, we shall be concerned with applications of classical invariant theory, to statistic physics and to theta functions. Main theorem in Chapter 2 is stated as follows:For a partition functionsatisfying γl ≥ 0 (l ≥ 1) and α > 0, the 2n-apolar of ξ(s)has the expansionsuch that βn,1 ≥ 0 (l ≥ 2). This means, for a given partition function ξ(s) with nonnegative relative probabilities, we construct a sequence of partition functions A2n (ξ(s), ξ(s))n≥1 with the same properties, which may be considered a sequence of symbolical higher derivative of ξ(s). The main theorem in Chapter 3 is stated as follows: For given theta functions φ1(z) and φ2(z) of level n1 and n2 respectively, in g variables z = (z1, z2,…, zg), then r = (r1, r2,…, rg-apolaris a theta function of level n1 + n2, and
On the centralizer algebra of the unitary reflection group G(m,p,n)
Authors: Tanabe Kenichiro 
Published: July 2016

AbstractThe imprimitive unitary reflection group G(m, p, n) acts on the vector space V =Cn naturally. The symmetric group Sk acts on ⊗kV by permuting the tensor product factors. We show that the algebra of all matrices on ⊗kV commuting with G(m, p, n) is generated by Sk and three other elements. This is a generalization of Jones’s results for the symmetric group case [J].
Bounded p.s.h. functions and pseudoconvexity in Kähler manifold
Authors: Ohsawa Takeo , Sibony Nessim 
Published: July 2016

Abstract.It is proved that the C2-smoothly bounded pseudoconvex domains in Pn admit bounded plurisubharmonic exhaustion functions. Further arguments are given concerning the question of existence of strictly plurisubharmonic functions on neighbourhoods of real hypersurfaces in Pn.
Optimalities for random functions Lee-Wiener’s network and non-canonical representation of stationary Gaussian processes
Authors: Htay Win Win 
Published: July 2016

Abstract.Representation of a Gaussian process in terms of a Brownian motion is a powerful tool in the investigation of its structure. Among various representations is the canonical representation which is viewed as the best one from the viewpoint of the prediction theory. We have discovered some significance of non-canonical representations and discuss their optimality in an information theoretical approach.
On standard L-functions attached to automorphic forms on definite orthogonal groups
Authors: Murase Atsushi , Sugano Takashi 
Published: July 2016

Abstract.We show an explicit functional equation of the standard L-function associated with an automorphic form on a definite orthogonal group over a totally real algebraic number field. This is a completion and a generalization of our previous paper, in which we constructed standard L-functions by using Rankin-Selberg convolution and the theory of Shintani functions under certain technical conditions. In this article we remove these conditions. Furthermore we show that the L-function of f has a pole at s = m/2 if and only if f is a constant function.
Degree bounds for generators of cohomology modules and Castelnuovo-Mumford regularity
Authors: Nagel Uwe , Schenzel Peter 
Published: July 2016

Abstract.By extending Mumford’s result on the generating by global sections there are estimates on the degree for generators of local cohomology modules. These arguments provide bounds on the Castelnuovo-Mumford regularity, in particular for Cohen-Macaulay varieties. As an application they imply a few more cases of varieties that satisfy a conjecture posed by Eisenbud and Gôto.
Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations
Authors: Chae Dongho , Kim Sung-Ki , Nam Hee-Seok 
Published: July 2016

AbstractIn this paper we prove the local existence and uniqueness of C1+γ solutions of the Boussinesq equations with initial data υ0, θ0 ∈ C1+γ, ω0, ∇θ0 ∈ Lq for 0 < γ < 1 and 1 < q < 2. We also obtain a blow-up criterion for this local solutions. More precisely we show that the gradient of the passive scalar θ controls the breakdown of C1+γ solutions of the Boussinesq equations.
On the rank of the first radical layer of ap-class group of an algebraic number field
Authors: Yamashita Hiroshi 
Published: July 2016

Letpbe a prime number. LetMbe a finite Galois extension of a finite algebraic number fieldk. Suppose thatMcontains a primitive pth root of unity and that thep-Sylow subgroup of the Galois groupG= Gal(M/k) is normal. LetKbe the intermediate field corresponding to thep-Sylow subgroup. Let= Gal(K/k). Thep-class groupCofMis a module over the group ringZpG, whereZpis the ring ofp-adic integers. LetJbe the Jacobson radical ofZpG. C/JCis a module over a semisimple artinian ringFp. We study multiplicity of an irreducible representation Φ apperaring inC/JCand prove a formula giving this multiplicity partially. As application to this formula, we study a cyclotomic fieldMsuch that the minus part ofCis cyclic as aZpG-module and a CM-fieldMsuch that the plus part ofCvanishes for oddp.To show the formula, we apply theory of central extensions of algebraic number field and study global and local Kummer duality between the genus group and the Kummer radical for the genus field with respect toM/K.
Conformally flat hypersurfaces in Euclidean 4-space
Authors: Suyama Yoshihiko 
Published: July 2016

AbstractWe study generic and conformally flat hypersurfaces in Euclidean four-space. What kind of conformally flat three manifolds are really immersed generically and conformally in Euclidean space as hypersurfaces? According to the theorem due to Cartan [1], there exists an orthogonal curvature-line coordinate system at each point of such hypersurfaces. This fact is the first step of our study. We classify such hypersurfaces in terms of the first fundamental form. In this paper, we consider hypersurfaces with the first fundamental forms of certain specific types. Then, we give a precise representation of the first and the second fundamental forms of such hypersurfaces, and give exact shapes in Euclidean space of them.
Tangent loci and certain linear sections of adjoint varieties
Authors: Kaji Hajime , Yasukura Osami 
Published: July 2016

AbstractAn adjoint variety X(g)associated to a complex simple Lie algebra is by definition a projective variety in ℙ*(g) obtained as the projectivization of the (unique) non-zero, minimal nilpotent orbit in g. We first describe the tangent loci of X(g) in terms of triples. Secondly for a graded decomposition of contact type we show that the intersection of X(g) and the linear subspace ℙ*(g1) in ℙ*(g) coincides with the cubic Veronese variety associated to g.
Fixed point theorems of discontinuous increasing operators and applications to nonlinear integro-differential equations
Authors: Zhang Jinqing 
Published: July 2016

AbstractIn this paper, we obtain some new existence theorems of the maximal and minimal fixed points for discontinuous increasing operators in C[I,E], where E is a Banach space. As applications, we consider the maximal and minimal solutions of nonlinear integro-differential equations with discontinuous terms in Banach spaces.
Two-weighted inequalities for the derivatives of holomorphic functions and Carleson measures on the unit ball
Authors: Kang Hyeonbae , Koo Hyungwoon 
Published: July 2016

AbstractWe characterize those positive measure µ’s on the higher dimensional unit ball such that “two-weighted inequalities” hold for holomorphic functions and their derivatives. Characterizations are given in terms of the Carleson measure conditions. The results of this paper also distinguish between the fractional and the tangential derivatives.
Distribution of units of real quadratic number fields
Authors: Chen Yen-Mei J. , Kitaoka Yoshiyuki , Yu Jing 
Published: July 2016

AbstractLet k be a real quadratic field and k, E the ring of integers and the group of units in k. Denoting by E() the subgroup represented by E of (k/)× for a prime ideal , we show that prime ideals for which the order of E() is theoretically maximal have a positive density under the Generalized Riemann Hypothesis.
Values of zeta functions and class number 1 criterion for the simplest cubic fields
Authors: Kim Hyun Kwang , Hwang Hyung Ju 
Published: July 2016

AbstractLet K be the simplest cubic field defined by the irreducible polynomial
where m is a nonnegative rational integer such that m2 + 3m + 9 is square-free. We estimate the value of the Dedekind zeta function ζK(s) at s = −1 and get class number 1 criterion for the simplest cubic fields.
Numerical criteria for certain fiber spaces to be birationally trivial
Authors: Cai Jin-Xing 
Published: July 2016

AbstractLet f: X → B be a fiber space over a curve B whose general fiber F belongs to one of the following type: 1) F is of general type and satisfying some mild conditions, 2) F is with trivial canonical sheaf. In this note, a numerical characterization for f: X → B to be birationally trivial is given.
On the cohomological completeness of q-complete domains with corners
Authors: Matsumoto Kazuko 
Published: July 2016

AbstractWe prove the vanishing and non-vanishing theorems for an intersection of a finite number of q-complete domains in a complex manifold of dimension n. When q does not divide n, it is stronger than the result naturally obtained by combining the approximation theorem of Diederich-Fornaess for q-convex functions with corners and the vanishing theorem of Andreotti-Grauert for q-complete domains. We also give an example which implies our result is best possible.
Modification of balayage spaces by transitions with application to coupling of PDE’s
Authors: Hansen Wolfhard 
Published: July 2016

AbstractModifications of balayage spaces are studied which, in probabilistic terms, correspond to killing and transitions (creation of mass combined with jumps). This is achieved by a modification of harmonic kernels for sufficiently small open sets. Applications to coupling of elliptic and parabolic partial differential equations of second order are discussed.
Algebraic dependence of meromorphic mappings in value distribution theory
Authors: Aihara Yoshihiro 
Published: July 2016

AbstractIn this paper we first prove some criteria for the propagation of algebraic dependence of dominant meromorphic mappings from an analytic finite covering space X over the complex m-space into a projective algebraic manifold. We study this problem under a condition on the existence of meromorphic mappings separating the generic fibers of X. We next give applications of these criteria to the uniqueness problem of meromorphic mappings. We deduce unicity theorems for meromorphic mappings and also give some other applications. In particular, we study holomorphic mappings into a smooth elliptic curve E and give conditions under which two holomorphic mappings from X into E are algebraically related.
Invariant Kähler structures on the cotangent bundles of compact symmetric spaces
Authors: Mykytyuk Ihor V. 
Published: July 2016

AbstractFor rank-one symmetric spacesMof the compact type all Kähler structuresFλ, defined on their punctured tangent bundlesT0Mand invariant with respect to the normalized geodesic flow onT0M, are constructed. It is shown that this class {Fλ} of Kähler structures is stable under the reduction procedure.
Character sheaves and generalized Springer correspondence
Authors: Aubert Anne-Marie 
Published: July 2016

AbstractLetGbe a connected reductive algebraic group over an algebraic closure of a finite field of characteristicp. Under the assumption thatpis good forG, we prove that for each character sheafAonGwhich has nonzero restriction to the unipotent variety ofG, there exists a unipotent classCAcanonically attached toA, such thatAhas non-zero restriction onCA, and any unipotent classCinGon whichAhas non-zero restriction has dimension strictly smaller than that ofCA.
The transcendence degree of an integral domain over a subfield and the dimension of the domain
Authors: Tanimoto Hiroshi 
Published: July 2016

AbstractFor a domain A containing a field k with tr.degkA < ∞, we define a new transcendence degree of A with respect to k, which is denoted by tdkA. By using this, we generalize the theorem that for every affine domain A over a field k it holds that dim A = tr.degkA. For example, we show that if A is a quasi-local domain containing a field k with dim A = tdkA < ∞, then for every Noetherian local k-subalgebra R of A it holds that dim R = tdkR. Moreover we also generalize the theorem due to Gilmer, Nashier and Nichols.
Lp extension of holomorphic functions from submanifolds to strictly pseudoconvex domains with non-smooth boundary
Authors: Adachi Kenzō 
Published: July 2016

AbstractLet D be a bounded strictly pseudoconvex domain in ℂn (with not necessarily smooth boundary) and let X be a submanifold in a neighborhood of . Then any Lp (1 ≥ p < ∞) holomorphic function in X ∩ D can be extended to an Lp holomorphic function in D.
Harder–Narasimhan reduction of a principal bundle
Authors: Biswas Indranil , Holla Yogish I. 
Published: July 2016

AbstractLet E be a principal G–bundle over a smooth projective curve over an algebraically closed field k, where G is a reductive linear algebraic group over k. We construct a canonical reduction of E. The uniqueness of canonical reduction is proved under the assumption that the characteristic of k is zero. Under a mild assumption on the characteristic, the uniqueness is also proved when the characteristic of k is positive.
Homology and residues of adiabatic pseudodifferential operators
Authors: Moroianu Sergiu 
Published: July 2016

AbstractWe compute the Hochschild homology groups of the adiabatic algebra Ψa(X), a deformation of the algebra of pseudodifferential operators Ψ(X) when X is the total space of a fibration of closed manifolds. We deduce the existence and uniqueness of traces on Ψa(X) and some of its ideals and quotients, in the spirit of the noncommutative residue of Wodzicki and Guillemin. We introduce certain higher homological versions of the residue trace. When the base of the fibration is S1, these functionals are related to the η function of Atiyah-Patodi-Singer.
Geometric Quantities of Manifolds with grassmann structure
Authors: Bokan N. , Matzeu P. , Rakić Z. 
Published: July 2016

AbstractWe study geometry of manifolds endowed with a Grassmann structure which depends on symmetries of their curvature. Due to this reason a complete decomposition of the space of curvature tensors over tensor product vector spaces into simple modules under the action of the group G = GL(p, ℝ) ⊗ GL(q, ℝ) is given. The dimensions of the simple submodules, the highest weights and some projections are determined. New torsion-free connections on Grassmann manifolds apart from previously known examples are given. We use algebraic results to reveal obstructions to the existence of corresponding connections compatible with some type of normalizations and to enlighten previously known results from another point of view.
Equivalence Classes of Ideals in the Nilradical of a Borel Subalgebra
Authors: Sommers Eric N. 
Published: July 2016

AbstractAn equivalence relation is defined and studied on the set of B-stable ideals in the nilradical of the Lie algebra of a Borel subgroup B. Techniques are developed to compute the equivalence relation and these are carried out in the exceptional groups. There is a natural partial order on equivalence classes coming from inclusion of one ideal in another. A main theorem is that this partial order is a refinement of the closure ordering on nilpotent orbits.
Direct Summands of Syzygy Modules of the Residue Class Field
Authors: Takahashi Ryo 
Published: July 2016

AbstractLetRbe a commutative Noetherian local ring. This paper deals with the problem asking whetherRis Gorenstein if thenth syzygy module of the residue class field ofRhas a non-trivial direct summand of finite G-dimension for somen. It is proved that ifnis at most two then it is true, and moreover, the structure of the ringRis determined essentially uniquely.
Logarithmic Abelian Varieties
Authors: Kajiwara Takeshi , Kato Kazuya , Nakayama Chikara 
Published: July 2016

AbstractWe develop the algebraic theory of log abelian varieties. This is Part II of our series of papers on log abelian varieties, and is an algebraic counterpart of the previous Part I ([6]), where we developed the analytic theory of log abelian varieties.
The Centralizer of a Nilpotent Section
Authors: McNinch George J. 
Published: July 2016

Let F be an algebraically closed field and let G be a semisimple F-algebraic group for which the characteristic of F is very good. If X ∈ Lie(G) = Lie(G)(F) is a nilpotent element in the Lie algebra of G, and if C is the centralizer in G of X, we show that (i) the root datum of a Levi factor of C, and (ii) the component group C/C° both depend only on the Bala-Carter label of X; i.e. both are independent of very good characteristic. The result in case (ii) depends on the known case when G is (simple and) of adjoint type.The proofs are achieved by studying the centralizer of a nilpotent section X in the Lie algebra of a suitable semisimple group scheme over a Noetherian, normal, local ring . When the centralizer of X is equidimensional on Spec(), a crucial result is that locally in the étale topology there is a smooth -subgroup scheme L of such that Lt is a Levi factor of for each t ∈ Spec ().
Vector Semi-Fredholm Toeplitz Operators and Mean Winding Numbers
Authors: Yakubovich Dmitry 
Published: July 2016

AbstractFor a continuous nonvanishing complex-valued function g on the real line, several notions of a mean winding number are introduced. We give necessary conditions for a Toeplitz operator with matrix-valued symbol G to be semi-Fredholm in terms of mean winding numbers of det G. The matrix function G is assumed to be continuous on the real line, and no other apriori assumptions on it are made.