bluuebunny/crossref_metadata_2025_split huggingface dataset:
Weil Representations as Globally Irreducible Representations
Authors: Tiep Pham Huu 
Published: May 2007

AbstractThe notion of globally irreducible representations of finite groups was introduced by B.H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell–Weil lattices of elliptic curves. It has been observed by R. Gow and Gross that irreducible Weil representations of certain finite classical groups lead to globally irreducible representations. In this paper we classify all globally irreducible representations coming from Weil representations of finite classical groups.
On the Limit‐Point /Limit‐Circle Problem for Nonlinear Third Order Differential Equations
Authors: Bartušek Miroslav , Došlá Zuzana 
Published: May 2007

AbstractWe introduce the limit‐point/limit‐circle classification for the nonlinear differential equations of higher order. We give limit‐point as well as limit‐circle criteria for nonlinear differential equations of the third order.
A New Proof of the Existence of Homoclinic Orbits for a Class of Autonomous Second Order Hamiltonian Systems in IR.N
Authors: Caldiroli Paolo 
Published: May 2007

AbstractWe consider the Hamiltonian system in IRN given by

where V : IRN rarr; IR is a smooth potential having a non degenerate local maximum at 0 and we assume that there is an open bounded neighborhood ft of 0 such that V(x) < V(0) for x δ Ω / {0}, V(x) = V(0) and V′(x) ≠ 0 for x ∈ ∂Ω. Using a refined version of the mountain pass lemma [4], we give a further proof of the existence of a solution of ü + V′(u) = 0, homoclinic to 0.
The Hausdorff Moment Problem with Complex Exponents and a Müntz‐Szasz Theorem for Distributions
Authors: Duran Antonio J. 
Published: May 2007

AbstractThis paper deals with a Hausdorff moment problem with complex exponents, that is, given a sequence of complex numbers (zn)n and a fixed space X of functions denned on [0, 1], we ask under which conditions on a sequence (an)n the moment problem an = ∫ tZn f(t) dt for n ∈ IN has a solution in the space X. Mainly, we study the solution belonging to the space D[0, 1] The results which we will obtain will lead us to prove a Müntz‐Szasz Theorem for distributions.
Representations for the Three‐Body T‐Matrix, Scattering Matrices and Resolvent in Unphysical Energy Sheets
Authors: Motovilov Alexander K. 
Published: May 2007

AbstractExplicit representations for the Faddeev components of the three‐body T‐matrix continued analytically into unphysical sheets of the energy Riemann surface are formulated. According to the representations, the T‐matrix in unphysical sheets is explicitly expressed in terms of its components taken in the physical sheet only. The representations for the T‐matrix are then used to construct similar representations for the analytic continuation of the three‐body scattering matrices and the resolvent. Domains on unphysical sheets are described where the representations obtained can be applied. A method for finding three‐body resonances based on the Faddeev differential equations is proposed.
Some Weighted Weak Type Estimates for Rough Operators
Authors: Sato Shuichi 
Published: May 2007

AbstractWe prove weighted vector‐valued weak type (1,1) inequalities for some rough operators. Here we consider A1 weights. As application, we prove weighted weak type estimates for square functions of Littlewood‐Paley type arising from Bochner‐Riesz means of the critical order on the weighted Hardy spaces H (w ∈ A1) and weighted weak type (1,1) estimates for some singular integral operators and convolution operators with oscillating kernels.
Spherical Maximal Operators on Radial Functions
Authors: Seeger Andreas , Wainger Stephen , Wright James 
Published: May 2007

AbstractLet Atf(x) denote the mean of f over a sphere of radius t and center x. We prove sharp estimates for the maximal function ME f(X) = supt∈E |Atf(x)| where E is a fixed set in IR+ and f is a radial function ∈ Lp(IRd). Let Pd = d/(d−1) (the critical exponent for Stein's maximal function). For the cases (i) p < pd, d ⩾ 2, and (ii) p = pd, d ⩽ 3, and for p ⩽ q ⩽ ∞ we prove necessary and sufficient conditions on E for ME to map radial functions in Lp to the Lorentz space LP,q.
On the Chow Ring of a Flag
Authors: Wenzel Christian 
Published: May 2007

AbstractLet G be a reductive linear algebraic group over an algebraically closed field K, let P̃ be a parabolic subgroup scheme of G containing a Borel subgroup B, and let P = P̃red ⊂ P̃ be its reduced part. Then P is reduced, a variety, one of the well known classical parabolic subgroups. For char(K) = p > 3, a classification of the P̃'s has been given in [W1].The Chow ring of G/P only depends on the root system of G. Corresponding to the natural projection from G/P to G/P̃ there is a map of Chow rings from A(G/P̃) to A(G/P). This map will be explicitly described here. Let P = B, and let p > 3. A formula for the multiplication of elements in A(G/P̃) will be derived. We will prove that A(G/P̃) ≃ A(G/P) (abstractly as rings) if and only if G/P ≃ G/P̃ as varieties, i. e., the Chow ring is sensitive to the thickening. Furthermore, in certain cases A(G/P̃) is not any more generated by the elements corresponding to codimension one Schubert cells.
Stability of the Poincaré Bundle
Authors: Balaji V. , Brambila‐Paz L. , Newstead P. E. 
Published: May 2007

AbstractLet C be a nonsingular projective curve of genus g ≥2 defined over the complex numbers, and let Mξ denote the moduli space of stable bundles of rank n and determinant ξ on C, where ξ is a line bundle of degree don C and n and d are coprime. It is shown that a universal bundle Uξ on C × Mξ is stable with respect to any polarisation on C × Mξ. Similar results are obtained for the case where the determinant is not fixed and for the bundles associated to the universal bundles by irreducible representations of GL(n, C). It is shown further that the connected component of the moduli space of bundles with the same Hilbert polynomial as Uξ on C × Mξ containing Uξ is isomorphic to the Jacobian of C.
Representing Groups by Colourings of Graphs
Authors: Baumann Ulrike 
Published: May 2007

AbstractThe topic of this paper is representing groups by edge‐coloured graphs. Every edge‐coloured graph determines a group of graph automorphisms which preserve the colours of the edges. An edge colouring of a graph G is called a perfect one iff every colour class is a perfect matching in G.We prove that every group H and all of its subgroups can be represented (up to isomorphism) by a group of colour preserving automorphisms related to some perfect colouring of the same graph.
Some Boundary — Contact Problems of the Elasticity Theory with Mixed Boundary Conditions Outside the Contact Surface
Authors: Chkadua O. 
Published: May 2007

Abstractn — Dimensional (n ≥ 2) boundary‐contact problems of statics of the elasticity theory for homogeneous anisotropic media are investigated when the contact of two bounded domains occurs from the outside on some part of boundaries with mixed boundary conditions. Theorems on the existence and uniqueness of solutions of boundary‐contact problems in Besov and Bessel potential spaces are obtained. The smoothness of solutions is studied in closed domains occupied by elastic media.
The Jump of the Laplacian on a Submanifold
Authors: Dudek Ewa , Holly Konstanty 
Published: May 2007

AbstractAssume that a submanifold M ⊂ ℝn of an arbitrary codimension k ϵ {1, …, n} is closed in some open set O→ℝn. With a given function u ϵ C2(O\M) we may associate its trivial extension u: O→ℝ such that u|O\M=u and u|m ≡ 0. The jump of the Laplacian of the function u on the submanifold M is defined by the distribution Δu — Δu. By applying some general version of the Fubini theorem to the nonlinear projection onto M we obtain the formula for the jump of the Laplacian (Theorem 2.2).
Interprétation et Calcul du Groupe de Défaut d'un Principe de Hasse
Authors: Gras Georges , Cortella Anne 
Published: May 2007

AbstractNous reprenons, dans le cadre de la théorie normique explicite du corps de classes, l'étude du groupe de défaut du principe de Hasse pour les similitudes de formes bilinéaires, effectuée par Anne Cortella dans sa thèse; nous en donnons une interprétation galoisienne concrète puis nous obtenons de nouveaux cas de validité de ce principe ainsi qu'une famille infinie de contre ‐ exemples pour la structure ℤ/4ℤ × ℤ/2ℤ.
Discrete and Cantor Spectrum for Neumann Laplacians of Combs
Authors: Hempel Rainer , Kriecherbauer Thomas , Plankensteiner Peter 
Published: May 2007

AbstractExtending results of [HSS] on the construction of Neumann Laplacians of combs with given essential spectrum S = S [0,∞], we show that, in addition to the essential spectrum, a bounded sequence of discrete eigenvalues can be prescribed. More generally, we find that certain types of spectra can be constructed precisely, in a bounded interval [0, s].
Dependence of Eigenvalues on the Problem
Authors: Kong Q. , Wu H. , Zettl A. 
Published: May 2007

AbstractThe eigenvalues of linear, regular, two point boundary value problems depend continuously on the problem. In the important self‐adjoint case studied by Naimark and Weidmann this dependence is differentiable and the derivatives of the eigenvalues with respect to a given parameter: an endpoint, a boundary condition, a coefficient, or the weight function, are found. Monotone properties of the eigenvalues with respect to the coefficients and the weight function are established without using the variational (min‐max) characterization.
Potential Bounds in Nonpotential Two‐Point Boundary ‐ Value Problems
Authors: Krasnosel'skii Mark , Mennicken Reinhard , Rachinskii Dmitrii 
Published: May 2007

AbstractNew conditions are suggested for the existence of solutions of two‐point boundary ‐value problems. The situation is studied when monotone bounds of nonlinear terms do not guarantee the solvability of the problems. The approach developed is a combination of variational methods, simple fixed point principles, and methods of partially ordered spaces.
On the Convolution of the Generalized Finite Legendre Transform
Authors: Méndez‐Pérez J. M. R. , Morales G. Miquel 
Published: May 2007

AbstractThe translation operator and the convolution for the finite Legendre transformation are investigated in the space ℒ︁(−1,1) of testing‐functions and its dual through an approach that emphasizes the close similarity existing between this transform and the infinite Mehler ‐ Fock transformation. The theory developed is used in solving some distributional boundary‐value problems.
On the Solution Structure of Nonlinear Hill's Equation I, Global Results
Authors: Mrziglod Thomas 
Published: May 2007

AbstractThe solution structure in W2,p(ℝ) × ℝ of nonlinear Hill's equation is discussed in full detail. In a recent article, the existence of unbounded solution components was shown for values of the branching parameter in the gaps of the continuous spectrum of the linearized problem. This result is the starting point of further investigations concerning the existence region of the corresponding solution components. In particular, new phenomena such as asymptotic bifurcation from infinity at a specific parameter value inside of each gap of the spectrum can be shown, if the nonlinearity satisfies a growth condition. The main assumption is the concentration of the nonlinearity to a compact interval which allows the reduction to an equivalent nonlinear Sturm ‐ Liouville problem with parameter dependent boundary conditions, if the parameter does not belong to the continuous spectrum. Extending this problem to all real parameter values makes it possible to get information about the existence region of the solution components with the help of a priori bounds for solutions of the Sturm‐Liouville problem.
On Characteristic Polynomials of Formal Groups over Finite Fields
Authors: Nakamura Tetsuo 
Published: May 2007

AbstractGeneralizing the results of Serre, Hill and Koch, we give some classification theorems of higher dimensional simple formal groups over finite fields. A relation between endomorphism rings of formal groups over ℤp and characteristic polynomials of their reductions mod p is studied. A condition of existence of formal groups over ℤp with complex multiplication is given. Some formal groups over ℤp are also constructed.
Moduli of Polarised Abelian Surfaces
Authors: Sankaran G. K. 
Published: May 2007

AbstractThe moduli variety parametrising abelian surfaces over ℂ with a polarisation of type (1, p) may be compactified by toroidal methods. We show that if p is a prime and p ≥ 173 then the compactified moduli variety is of general type.
Asymptotics of Damped Periodic Motions with Random Initial Speed
Authors: Baryshnikov Yuliy , Stadje Wolfgang 
Published: May 2007

AbstractWe consider motion on the circle, possibly with friction and external forces, the initial velocity being a large random variable. We prove that under various assumptions the probability law of the stopping position of the motion converges to a distribution depending only on the motion equation. Here the time of stopping is either a constant or the first time instant at which the velocity vanishes, and the initial velocity is of the form αU + β, where U is a fixed random variable and α and/or β tend to infinity.
A Fixed Point Theorem of Krasnoselskii—Schaefer Type
Authors: Burton T. A. , Kirk Colleen 
Published: May 2007

AbstractIn this paper we focus on three fixed point theorems and an integral equation. Schaefer's fixed point theorem will yield a T‐periodic solution of(0.1) x(t)= a(t) + tt‐h D(t,s)g(s,x(s))dsif D and g satisfy certain sign conditions independent of their magnitude. A combination of the contraction mapping theorem and Schauder's theorem (known as Krasnoselskii's theorem) will yield a T‐periodic solution of(0.2) x(t) = f(t,x(t)) + tt‐h D(t,s)g(s,x(s))dsif f defines a contraction and if D and g are small enough.We prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T‐periodic solution of (0.2) when / defines a contraction mapping, while D and g satisfy the aforementioned sign conditions.
Characterizations of the Optimal Descartes' Rules of Signs
Authors: Carnicer J. M. , Peña J. M. 
Published: May 2007

AbstractA system of functions satisfies Descartes' rule of signs if the number of zeros (with multiplicities) of a linear combination of these functions is less than or equal to the number of variations of strict sign in the sequence of the coefficients. In this paper we characterize the systems of functions satisfying a stronger property than the above mentioned Descartes' rule: The difference between the number of zeros and the changes of sign in the sequence of coefficients must be always a nonnegative even number. We show that the approximation to the number of zeros given by these systems of functions is better than the approximation provided by any other systems of functions satisfying a Descartes' rule of signs. This last result improves, in the particular case of polynomials, the main theorem of [14].
Irreducible Components of Fixed Point Subvarieties of Flag Varieties
Authors: Douglass J. Matthew 
Published: May 2007

AbstractSuppose G is a connected reductive algebraic group, P is a parabolic subgroup of G, L is a Levi factor of P, and e is a regular nilpotent element in Lie L. We assume that the characteristic of the underlying field is good for G. Choose a maximal torus, T, and a Borel subgroup, B, of G, so that T⊆B∩L, B ⊆ P and e ∈ Lie B. Let β be the variety of Borel subgroups of G and let 𝔙e be the subset of 𝔙 consisting of Borel subgroups whose Lie algebras contain e. Finally, let W be the Weyl group of G with respect to T. For ω ∈ W let 𝔒ω be the B‐orbit in 𝔙 containing ωB. We consider the intersections 𝔒ω ∩ 𝔙e. The main result is that if dim 𝔒ω ∩ 𝔙e = dim 𝔙e, then 𝔒ω ∩ 𝔙e is an affine space. Thus, the irreducible components of 𝔙e are indexed by Weyl group elements. It is also shown that if G is of type A, then this set of Weyl group elements is a right cell in W.
Perturbative Oscillation Criteria and Hardy‐Type Ineqalities
Authors: Gesztesy F. , Ünal M. 
Published: May 2007

AbstractWe prove a natural generalization of Kneser's oscillation and Hardy's inequality for Sturm‐Liouville differential expressions. In Particular, assuming − d/dxp0(x)+q0(x), x ∈ a, b), −∞≦a<b≦∞, to be nonoscillatory near a (or b), we determine condition on q(x) such that − d/dxp0(x)+q0(x)+q(x) is nonoscillatory, respectively, oscillatory near a (or b)
Globalization of Holomorphic Actions on Principal Bundles
Authors: Gilligan Bruce , Heinzner Peter 
Published: May 2007

AbstractSuppose G is a Lie group acting as a group of holomorphic automorphisms on a holomorphic principal bundle P → X. We show that if there is a holomorphic action of the complexification GC of G on. X, this lifts to a holomorphic action of GC on the bundle P → X. Two applications are presented. We prove that given any connected homogeneous complex manifold G/H with more than one end, the complexification GC of G acts holomorphically and transitively on G/H. We also show that the ends of a homogeneous complex manifold G/H with more than two ends essentially come from a space of the form S/Γ, where Γ is a Zariski dense discrete subgroup of a semisimple complex Lie group S with S and Γ being explicitly constructed in terms of G and H.
A Note on the Embedding of Subspaces of Lp into ℓNr, 0 < r < 1, r ≦ p < 2
Authors: Peña Ana 
Published: May 2007

AbstractIn this paper we extend a result by Bourgain‐Lindenstrauss‐Milman (see [1]). We prove: Let 0 < ϵ < 1/2, 0< r < 1, r< p < 2. There exists a constant C = C(r,p,ϵ) such that if X is any n‐dimensional subspace of Lp(0, l), then there exists Y ⊂ ℓNr with d(X, Y) ≦ 1 + ϵ, whenever N > Cn.As an application, we obtain the following partial result: Let 0 < r < 1. There exist constants C = C(r) and C' = C' (r) such that if X is any n‐dimensional subspace of Lr(0,1), then there exists Y ⊂ Nr with d(X, Y) ≦ C (logn)l/r, whenever N ≧ C'n.
On Marcinkiewicz‐Zygmund Type Inequalities for Irregular Knots in Lp‐Spaces, 0 < p ≦ +∞
Authors: Runovskii K. V. , Schmeisser H. J. 
Published: May 2007

AbstractAn equivalence of a discrete norm and a continuous norm of a trigonometric polynomial is proved for the case of irregular knots in Lp‐spaces, where 0 < p ≦ +∞.
On the Approximation of Irrationals by Rationals
Authors: Carstenelsner  
Published: May 2007

AbstractLet ξ be a real irrational number, anda≧ 0,b≧ 0,s> 1 be integers. A theorem of S. UCHIYAMA states that there are infinitely many pairs of integersuand v ≠ 0 such that OVBARξ−u/vOVBAR ≤s2/4v2andua,vbmods, provided that it is not a  6  0 mod s. It is shown that this result is best‐possible for all integerss> 1.
Generalized Toeplitz Forms and Interpolation Colligations
Authors: Albgría Pedro , Cotlar Mischa 
Published: May 2007

AbstractIn a recent paper, V. KATSNELSON related the Cotlar‐Sadosky theory of Generalized Toeplitz Forms in the space P of trigonometric polynomials to the Katsnelson‐Kheifets‐Yuditskii interpolation theory. In this paper it is pointed out that the Generalized Toeplitz Forms in P give rise to almost commuting pairs of operators which in turn induce Potapov colligations in the same space P and that this leads to a new setting for the Generalized Toeplitz Forms.
Sur les Propriétés Arithmétiques d'une Fonction Entière
Authors: Bézivin Par Jean‐Paul 
Published: May 2007

AbstractLet q ∈ Q, ∣q∣> 1 and
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In this paper, we study the arithmetical nature of the values of f at algebraic points. We prove that if α belongs to a quadratic extension 𝕂 of ℚ, then f(α) ∉ 𝕂.
Verdier Duality for Systems of Coefficients over Simplicial Sets
Authors: Fimmel Torsten 
Published: May 2007

AbstractLet X. be a simplicial set. A cohomological system of coefficients F. on X. with values in an abelian category A is given by an object F σ ∈ A for every σ ∈ X. and by a compatible set of morphisms Fα*σ → Fσ for every map of ordered sets α : m → n, m, n = 0, … and σ ∈ Xn. We denote by SH(X.) the category of cohomological systems F. of coefficients on X, such that the maps Fα * σ → Fσ, are isomorphisms if α is surjective. This category is equivalent to a certain subcategory of the category of sheaves SH(X) on the geometric realization X = ∣X.∣ of the simplicial set X.The present paper gives a construction of a duality theory for SH(X.) which is analogue to the topological Verdier duality for SH(X). It consists of a construction of a right adjoint to the cohomology with compact support functor and a resulting duality theory given by a dualizing complex. These constructions are much more explicit than in the topological case. We compare the simplicial and topological constructions via the embedding SH(X.) → SH(X). In particular, we get an explicit description of the dualizing sheaf complex for topological spaces X = ∣X∣.
A Counterexample to Completeness Properties for Indefinite St urm—Liouville Problems
Authors: Fleige Andreas 
Published: May 2007

AbstractIn this note we construct an odd weight function ω on (—1, 1) with ω(x)> 0 for x> 0 such that the eigenfunctions of the indefinite Sturm‐Liouville problem‐f″ = λωf with boundary conditions f(—1) = f(1) = 0 do not form a Riesz basis of L2∣ω∣(—1, 1).
Abel‐Summability of Eigenfunction Expansions of Three—Point Boundary Value Problems
Authors: Freiling Gerhard , Trooshin Igor Yu. 
Published: May 2007

AbstractWe study the Abel‐summability of the eigenfunction expansions associated with the differential operator L generated by
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and splitting three‐point boundary conditions. It is shown that there is no straightforward analogy between multipoint and twopoint boundary value problems. Counterexamples show that our main results are best possible. Classification. 34L10, 34B10.
Global Smooth Solutions of the Equations of a Viscous, Heat ‐ Conducting, One ‐ Dimensional Gas with Density ‐ Dependent Viscosity
Authors: Jiang Song 
Published: May 2007

AbstractWe consider initial boundary value problems for the equations of the one‐dimensional motion of a viscous, heat‐conducting gas with density‐dependent viscosity that decreases (to zero) with decreasing density. We prove that if the viscosity does not decrease to zero too rapidly, then smooth solutions exist globally in time.
Regularity ‐ Properties of the Solution of the Homogeneous Wave Equation
Authors: Malarski Mircea 
Published: May 2007

AbstractThe aim of this paper is to prove regularity‐properties for solutions of the wave equation in B with p < 1. Up to now no such result is known. For p ≥ 1 a large amount of work has been done, cf. for instance [9], [7], [8], [10]. The results in this paper for p> 1 are not optimal, which can be seen comparing them with [9]. Whether or not our results are optimal for p ≤ 1 is open.
A Remark on the Sobolev Regularity of Classical Solutions of Strongly Elliptic Equations
Authors: Milani Albert 
Published: May 2007

AbstractWe prove that C2,α(Ω) solutions of problem (1.2) below are in Hm+2(Ω) for all m ∈ ℕ, if f and the coefficients are in Hm (Ω) n C0,α (Ω) Previously, this result was explicitly known only if m> n/2 (or if m = 0). A similar result holds for the quasi‐linear equation (1.11) below.