bluuebunny/crossref_metadata_2025 huggingface dataset:
Half‐Linear Eigenvalue Problems
Authors: Eberhard Walter , Elbert Árpad
Published: May 2007

We consider the eigenvalue problem
magnified image
for t ϵ [0, b], where an = |a|n sgna, a ϵ ℝ, λ ϵ ℝ, the constants μ, v are real such that 0 ≤ μ < n and derive asymptotic estimates for solutions of the differential equation in the definite case q(t)> 0 which corresponds to the well‐known WKB‐approximation in the linear case n = 1, μ = 0. In the second part we investigate the asymptotic distribution of the eigenvalues in the general case of two ‐point boundary conditions and refine these results for the so called separated boundary conditions.
Nonlinear Riemann ‐ Hilbert Problems without Transversality
Authors: Efendiev M. A. , Wendland W. L.
Published: May 2007

Nonlinear Riemann ‐ Hilbert problems (RHP) generalize two fundamental classical problems for complex analytic functions, namely: 1. the conformal mapping problem, and 2. the linear Riemann ‐ Hilbert problem. This paper presents new results on global existence for the nonlinear (RHP) in doubly connected domains with nonclosed restriction curves for the boundary data. More precisely, our nonlinear (RHP) is required to become „at infinity”︁, i.e., for solutions having large moduli, a linear (RHP) with variable coefficients. Global existence for q‐connected domains was already obtained in [9] for the special case that the restriction curves for the boundary data „at infinity”︁ coincide with straight lines corresponding to linear (RHP)‐s with special so‐called constant ‐ coefficient transversality boundary conditions. In this paper, the boundary conditions are much more general including highly nonlinear conditions for bounded solutions in the context of nontransversality. In order to prove global existence, we reduce the problem to nonlinear singular integral equations which can be treated by a degree theory of Fredholm ‐ quasiruled mappings specifically constructed for mappings defined by nonlinar pseudodifferential operators.
Cusp Forms on GL(2n) with GL(n) × GL (n) Periods, and Simple Algebras
Authors: Flicker Yuval Z.
Published: May 2007

The notion of a period of a cusp form on GL(2,D(𝔸)), with respect to the diagonal subgroup D(𝔸)X × D(𝔸)X, is defined. Here D is a simple algebra over a global field F with a ring 𝔸 of adeles. For Dx = GL(1), the period is the value at 1/2 of the L‐function of the cusp form on GL(2, 𝔸). A cuspidal representation is called cyclic if it contains a cusp form with a non zero period. It is investigated whether the notion of cyclicity is preserved under the Deligne ‐ Kazhdan correspondence, relating cuspidal representations on the group and its split form, where D is a matrix algebra. A local analogue is studied too, using the global technique. The method is based on a new bi‐period summation formula. Local multiplicity one statements for spherical distributions, and non ‐ vanishing properties of bi ‐ characters, known only in a few cases, play a key role.
The Quantization of the Cantor Distribution
Authors: Graf S. , Luschgy H.
Published: May 2007

For a real‐valued random variable whose distribution is the classical Cantor probability, the n ‐ quantization error and the n ‐ optimal quantization rules are calculated for every natural number n. Moreover, the connection between the rate of convergence of the logarithms of the quantization errors for n going to infinity and the Hausdorff dimension of the Cantor set is indicated.
On Hardy ‐ Littlewood Maximal Functions in Orlicz Spaces
Authors: Kita H.
Published: May 2007

Let Φ(t) and Ψ(t) be the functions having the following representations Φ(t) = ∫a(s)ds and Ψ(t) = ∫b(s) ds, where a(s) is a positive continuous function such that ∫a(s)/s ds = + ∞ and b(s) is an increasing function such that lims→ ∞ b(s) = + ∞. Then the following statements for the Hardy ‐ Littlewood maximal function M f (x) are equivalent:

(i) there exist positive constants c1 and s0 such that magnified image

(ii) there exist positive constant c2 and c3 such thatmagnified image

.
Powerful Necessary Conditions for Class Number Problems
Authors: Louboutin Stéphane
Published: May 2007

We give a necessary condition for the ideal class group of a CM‐field to be of exponent at most two. This condition enables us to drastically reduce the amount of relative class number computation for determination of the CM ‐ fields of some types (e. g. the imaginary cyclic non ‐quadratic number fields of 2 ‐ power degrees) whose ideal class groups are of exponents at most two. We also give a necessary condition for some quartic non ‐ CM ‐ fields to have class number one.
On the Embedded Eigenvalues and Dense Point Spectrum of the Stark‐Like Hamiltonians
Authors: Naboko Sergei N. , Pushnitski Alexander B.
Published: May 2007

The point spectrum lying on the essential spectrum is investigated for the one‐dimensional Schrödinger operator \documentclass{article}\pagestyle{empty}\begin{document}$ \- \frac{{d^2 }}{{dx^2 }} + q(x) $\end{document} with decaying potential q, and weakly perturbed Stark‐like operator \documentclass{article}\pagestyle{empty}\begin{document}$ - \frac{{d^2 }}{{dx^2 }} - \left| x \right|^\alpha {\rm sign }x + q(x). $\end{document} An elementary constructive technique is developed to obtain various results concerning embedded eigenvalues of Schrödinger operators. In Section 3 a constructive example of the Stark ‐ like operator with the potential q decaying slightly slowlier than o(1/|x|1‐α/2)and dense point spectrum on the whole real axis is presented.
Estimates of Weyl Sums over Subsequences of Natural Number
Authors: Schmeling Joerg
Published: May 2007

In this paper we introduce the notion of pseudo ‐ergodicity to generalize Pustyl'nikov's estimates of Weyl sums to Weyl sums over subsequence of the natural numbers.
Some Remarks on the Boundedness of Pseudodifferential Operators
Authors: Shargorodsky Eugene
Published: May 2007

Some methods are described for reducing the problem of the boundedness of pseudodifferential operators (ΨDOs) to the theory of Fourier multipliers. Special attention is given to the boundedness of ΨDOs in Besov ‐ Triebel ‐ Lizorkin spaces.
Spectral Theory for Slowly Oscillating Potentials II. Schrödinger Operators
Authors: Stolz G.
Published: May 2007

The absolutely continuous and singular spectrum of one‐dimensional Schrödinger operators with slowly oscillating potentials and perturbed periodic potentials is studied, continuing similar investigations for Jacobi matrices from [14]. Trace class methods are used to locate the singular spectrum. The absolutely continuous spectrum is determined by iterated diagonalization of transfer matrices to prove boundedness of eigensolutions.
Gevrey Asymptotic Representation of the Solutions of Equations with One Turning Point
Authors: Yagdjian Karen
Published: May 2007

An ordinary differential equation of the type
magnified image
with parameterξ ϵ IRn and smooth coefficients aj,a ϵ C∞([‐T,T]) is studied. It is assumed that all the characteristic roots of the equation vanish at t = 0 while for t ≠ 0 they are real and distinct. The constructions of real‐valued phase functions ϕpHkl (k,l = 1., m) and of amplitude functions Ajkl such that for a given s ϵ [‐T, T] every solution u(t, ξ) of the equation can be represented as magnified image
where Ψj(s, ξ)= Djtu(s,ξ), j = 0,m‐1 are given.
ℋ︁ — Cohomologies Versus Algebraic Cycles
Authors: Viale Luca Barbieri
Published: May 2007

Global intersection theories for smooth algebraic varieties via products in appropriate Poincaré duality theories are obtained. We assume given a (twisted) cohomology theory H* having a cup product structure and we consider the ℋ︁‐ cohomology functor X ↝ H#Zar(X, ℋ︁*) whereℋ︁* is the Zariski sheaf associated to H*. We show that the ℋ︁‐ cohomology rings generalize the classical “intersection rings” obtained via rational or algebraic equivalences. Several basic properties e. g. Gysin maps, projection formula and projective bundle decomposition, of ℋ︁‐ cohomology are obtained. We therefore obtain, for X smooth, Chern classes cP, i :Ki(X)→ Hp‐i(X,ℋ︁ p) from the Quillen K‐theory to ℋ︁‐ cohomologies according to Gillet and Grothendieck. We finally obtain the “blow‐up formula” magnified image where X′ is the blow–up of X smooth, along a closed smooth subset Z of pure codimension c. Singular cohomology of associated analityc space, étale cohomology, de Rham and Deligne–Beilinson cohomologies are examples for this setting.
Bounds for the Genus of Space Curves
Authors: Beorchia Valentina
Published: May 2007

We compute the following upper bounds for the maximal arithmetic genus Pa(d,t) over all locally Cohen ‐ Macaulay space curves of degree d, which are not contained in a surface of degree magnified image These bounds are sharp for t ≤ 4 abd any d ≥ t.
Anisotropic Edge Pseudo — Differential Operators with Discrete Asymptotics
Authors: Buchholz Thilo
Published: May 2007

An anisotropic pseudo — differential calculus aimed at solving parabolic differential and pseudo — differential equations in terms of Volterra pseudo–differential operators was studied by Piriou for spatial variables on a closedC∞– manifold. Such a program also makes sense when the spatial variables run over a manifold with edges. Our approach deals with this case. It covers, in particular, manifolds with conical singularities. The main point of the present paper is the anisotropic edge pseudo — differential calculus, obtained as a substructure of our corresponding abstract anisotropic edge calculus with operator — valued symbols.
Zur Zerlegung von Primelementen quadratischer Zahlkörper in relativ–quadratischen Oberkörpern
Authors: Burde Klaus
Published: May 2007

Für gewisse quadratische Erweiterungen wird ein geometrisch interpretierbares Kriterium dafür angegeben, ob ein ungerades Primelement von verzweigt, zerfällt oder träge ist.
On Indefinite Moment Problems and Resolvent Matrices of Hermitian Operators in Kreîn Spaces
Authors: Derkach Vladimir
Published: May 2007

Let (sj)∞j=0 be a sequence of real numbers such that the Hankel matrices (si+j)∞0, (Si+j+i)∞0 have finite numbers of negative eigenvalues. The indefinite moment problem with the moments Sj (j = 0,1,2, …) and the corresponding Stieltjes string are investigated. We use the approach via the Kreîn — Langer extension theory of symmetric operators in spaces with indefinite metric. In the framework of this approach a description of L– resolvents of a class of symmetric operators in Kreîn space and a simple formula for the calculation of the L– resolvent matrix in terms of boundary operators are given.
The Distribution of Reciprocal Pairs Modulo Polynomials over a Finite Field
Authors: Hensley Doug
Published: May 2007

Given a finite field Fq of order q, a fixed polynomial g in –Fq[X] of positive degree, and two elements u and v in the ring of polynomials in R = Fq [X]/gFq[X], the question arises: How many pairs (a, 6) are there in R × R so that ab  1 mod g and so that a is close to u while b is close to v ? The answer is, about as many as one would expect. That is, there are no favored regions in R × R where inverse pairs cluster. The error term is quite sharp in most cases, being comparable to what would happen with random distribution of pairs. The proof uses Kloosterman sums and counting arguments. The exceptional cases involve fields of characteristic 2 and composite values of g. Even then the error term obtained is nontrivial. There is no computational evidence that inverses are in fact less evenly distributed in this case, however.
Resolvent Estimates for Singularly Perturbed Elliptic Operators in Hölder Spaces
Authors: Najman Branko
Published: May 2007

The norm of the inverse operator of ϵA + B ‐ λI between the Besov spaces B, ∞ (Ω) and Bt∞,∞(Ω) is estimated, where A and B are uniformly elliptic operators with smooth coefficients and Dirichlet boundary conditions, A is of order 2m, B of order 2m, m > m'. The estimate holds for negative t. The Besov space B, ∞ (Ω) reduces to the space of Hölder continuous functions Cs (Ω) if s < 0 is non – integer.

In particular, it is shown that Aϵ generates an analytic semigroup in B, ∞ (Ω), s ϵ (‐1,0), if Ω = ℝn or ℝ and A, B are constant coefficient operators without lower order terms.
On Picard Modular Forms
Authors: Runge Bernhard
Published: May 2007

We study moduli spaces of principally polarized abelian varieties with an automorphism of finite order. After some examples (e. g. hermitian modular forms) we compute the ring of Picard modular forms in the case considered by Picard.
Singularities in Quasi–Banach Spaces with Applications to Semilinear Elliptic Equations II
Authors: Runst Thomas
Published: May 2007

This paper continues the investigation about the singularity theory in dual rich quasi–Banach spaces given in T. Runst [Ru 2]. The abstract results are applied to the study of the solution structure of semilinear elliptic boundary value problems in spaces of Besov – Triebel – Lizorkin type.
Weil Representations as Globally Irreducible Representations
Authors: Tiep Pham Huu
Published: May 2007

The 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

We 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

We 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.
Towards a Mori Theory on Compact Kähler Threefolds, I
Authors: Campana Frédéric , Peternell Thomas
Published: May 2007

In this paper we construct from non‐splitting families of rational curves special contractions on compact Kähler threefolds, i.e., morphisms which are analogous to those in the Mori theory in algebraic geometry.
Uniform Boundedness of Lagrange Operator in Some Weighted Sobolev‐Type Space
Authors: Capobianco Maria Rosaria , Mastroianni Giuseppe
Published: May 2007

The authors show the uniform boundedness of the Lagrange operator in some weighted Sobolev‐type space.
The Hausdorff Moment Problem with Complex Exponents and a Müntz‐Szasz Theorem for Distributions
Authors: Duran Antonio J.
Published: May 2007

This 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

Explicit 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

We 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

Let 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 Holomorphic Perturbations of Infinite Order Differential Equations
Authors: Vidras Alekos
Published: May 2007

It is proven in the present article that the solutions of infinite order differential equation with holomorphic parameter w ∈ U ⊂ ℂ depend holomorphically on w in the neighborhood of characteristic points of certain directions.
On the Chow Ring of a Flag
Authors: Wenzel Christian
Published: May 2007

Let 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

Let 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

The 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

n — 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

Assume 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).
Degree Ten Manifolds of Dimension n Greater than or Equal to 3
Authors: Fania Maria Lucia , Livorni Elvira Laura
Published: May 2007

Manifolds of dimension n ≥ 3 and degree 10 in ℙN are studied.
Interprétation et Calcul du Groupe de Défaut d'un Principe de Hasse
Authors: Gras Georges , Cortella Anne
Published: May 2007

Nous 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

Extending 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].
On a Universality of the Heat Equation
Authors: Herzog Gerd
Published: May 2007

We prove that there are solutions u(t,x) of the heat equation ut = uxx such that every continuous function f : [a, b] → ℝ can be uniformly approximated by a subsequence of u (n, ·), nϵ ℕ.
Dependence of Eigenvalues on the Problem
Authors: Kong Q. , Wu H. , Zettl A.
Published: May 2007

The 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

New 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

The 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

The 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

Generalizing 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

The 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

We 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

In 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))ds

if 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))ds

if 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

A 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

Suppose 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

We 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

Suppose 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

In 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

An 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

Let 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

In 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

Let q ∈ Q, ∣q∣> 1 and
equation image

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

Let 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

In 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

We study the Abel‐summability of the eigenfunction expansions associated with the differential operator L generated by
equation image
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

We 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

The 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

We 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.
On the Solution Structure of Nonlinear Hill's Equation II, Local Results
Authors: Mrziglod Thomas
Published: May 2007

The behavior of solution components in W2,P(ℝ) × ℝ of nonlinear Hill's equation near boundary points of the continuous spectrum is discussed in full detail. The starting point of several articles concerned with the study of this solution structure is the existence result of unbounded solution components in a recent paper. The main assumption there 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. In particular, this approach makes it possible to analyse the solution structure of the Sturm‐Liouville and the original problem. It turns out in the present article that each solution component consists of a. branch near the bifurcation point. For the behavior of the solution branches of the original problem, the bifurcation direction and order of bifurcation play an important role. Using the corresponding local results, a class of nonlinearities can be constructed such that at each boundary point of the spectrum infinitely many branches bifurcate asymptotically from infinity.
The Triebel ‐ Lizorkin Scale of Function Spaces for the Fourier ‐ Helgason Transform
Authors: Skrzypczak Leszek
Published: May 2007

We define and investigate the Triebel ‐ Lizorkin scale of function spaces F, with 1< p < ∞, 1< q ≤ ∞ for the Fourier‐Helgason transform on symmetric Riemannian manifolds of the noncompact type.
Mixed Crack Type Problem in Anisotropic Elasticity
Authors: Duduchava R. , Natroshvili D.
Published: May 2007

The paper deals with three‐dimensional mixed boundary value problem of the anisotropic elasticity theory when the elastic body under consideration has a cut in the form of an arbitrary non‐closed, two‐dimensional, smooth surface with a smooth boundary: on one side of the cut surface the Dirichlet type condition (i.e., the displacement vector) is given, while on the other side the Neumann type condition (i.e., the stress vector) is prescribed. Applying the potential method and invoking the theory of ΨDEs uniqueness, existence and regularity results are proved in various function spaces. The asymptotic expansion of the solution of the corresponding system of boundary ΨDEs is written.
Some Estimates for Radial Fourier Multiplier Operators with Slowly Decaying Kernels
Authors: Epperson Jay
Published: May 2007

We consider the restriction to radial functions of a class of radial Fourier multiplier operators containing the Bochner‐Riesz multiplier operator. The convolution kernel K(x) of an operator in this class decays too slowly at infinity to be integrable, but has enough oscillation to achieve Lp ‐boundedness for p inside a suitable interval (a, b). We prove boundedness results for the maximal operator Kf(x) = supr>0 rn∣K(r) * f(x)∣ associated with such a kernel. The maximal operator is shown to be weak type bounded at the lower critical index a, restricted weak type bounded at the upper critical index b, and strong type bounded between. This together with our assumptions on K(x) leads to the pointwise convergence result limγ→ γn K(γ·) * f(x) = cf(x) a. e. for radial f ϵ LP(ℝn), a ≥ p > b.
Boundary Integral Operators in Countably Normed Spaces
Authors: Heubr Norbert , Stephan Ernst P.
Published: May 2007

We show the mapping properties of several integral operators acting on polygons within countably normed spaces. The integral operators are the weakly singular single layer potential operator for the Laplacian, the corresponding double layer potential operator and the normal derivatives of these operators. Our analysis of the boundary integral equations in the countably normed spaces is based on Mellin techniques and uses the Mellin symbols of the integral operators. Functions of these countably normed spaces can be approximated very efficiently by splines through the use of well adapted mesh‐refinement and polynomial degree distribution. Therefore the hp‐version of the boundary element method with geometric mesh can be proved to converge exponentially fast for the solutions to those integral equations.
Poisson Lie Groups and Non‐Linear Convexity Theorems
Authors: Hilgert Joachim , Neeb Karl‐Hermann
Published: May 2007

In this paper we describe how one can derive nonlinear convexity theorems which are similar to Kostant's nonlinear convexity theorem for the Iwasawa decomposition from Hamiltonian actions on Poisson Lie groups. Our results generalize those of LU and Ratiu ([24]) and aim at a unified symplectic framework for the convexity theorem in [32] and the linear convexity theorems for coadjoint orbits of convex type in [15].
Homogeneous Vector Bundles and Koszul Algebras
Authors: Hille Lutz
Published: May 2007

Let G be a reductive algebraic group defined over an algebraically closed field of characteristic zero and let P be a parabolic subgroup of G. We consider the category of homogeneous vector bundles over the flag variety G/P. This category is equivalent to a category of representations of a certain infinite quiver with relations by a generalisation of a result in [BK]. We prove that both categories are Koszul precisely when the unipotent radical Pu of P is abelian.
Growth Estimates for the Solutions of the Vlasov‐Poisson System in the Plasma Physics Case
Authors: Rein Gerhard
Published: May 2007

In [3] new a—priori—estimates for solutions of the Vlasov‐Poisson system in the plasma physics case were obtained. We show that these lead to improved estimates on the possible growth of the solutions.
Algebras of Pseudodifferential Operators in L2 Given by Smooth Measures on Hilbert Spaces
Authors: Albeverio Sergio , Daletskh Alexei
Published: May 2007

Pseudodifferential operators with symbols on a Hilbert phase space are defined as symmetric operators in L2 given by a smooth measure. The main formulae of symbolic calculus are proved in this context.
The Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients
Authors: Alefeld Götz , Kreinovich Vladik , Mayer Günter
Published: May 2007

A standard system of interval linear equations is defined by Ax = b, where A is an m × n coefficient matrix with (compact) intervals as entries, and b is an m‐dimensional vector whose components are compact intervals. It is known that for systems of interval linear equations the solution set, i. e., the set of all vectors x for which Ax = b for some A ϵ A and b ϵ b, is a polyhedron.

In some cases, it makes sense to consider not all possible A ϵ A and b ϵ b, but only those A and b that satisfy certain linear conditions describing dependencies between the coefficients. For example, if we allow only symmetric matrices A (aij = aji), then the corresponding solution set becomes (in general) piecewise‐quadratic.

In this paper, we show that for general dependencies, we can have arbitrary (semi)algebraic sets as projections of solution sets.
Non‐Autonomous Evolution Equations on Nonsmooth Domair
Authors: Mehmeti Felix Ali , Nicaise Serge
Published: May 2007

The solution of a stationary boundary value problem on a domain with conical points has singularities near these points. Here we first consider existence results in appropriate weighted Sobolev spaces in order to incorporate the singularities. We secondly use these results to prove existence, uniqueness and regularity of solutions of non‐autonomous second order evolution equations on such domains.
On Schur σ—Groups
Authors: Arrigoni Maurice
Published: May 2007

In this paper, we consider some conditions of finiteness related to the p‐class field tower problem over an imaginary quadratic field, where p is an odd prime.
Use of the Domain Derivative to Prove Symmetry Results in Partial Differential Equations
Authors: Choulli Mourad , Henrot Antoine
Published: May 2007

In this paper we present a different method for proving symmetry results in partial differential equations. The principal idea is to use the classical tool of shape optimization, namely, the differentiation with respect to the domain. The aim is to derive, from an optimality condition, information on the boundary of the domain.
Finite and Infinite Systems of Interacting Diffusions: Cluster Formation and Universality Properties
Authors: Cox John Ted , Greven Andreas , Shiga Tokuzo
Published: May 2007

We study some aspects of the relationship between the long time behaviour of systems with a finite but large number of components and their idealizations with countably many components. The following class of models is considered in detail, which contains examples occuring in population growth and population genetic models.
Some Remarks on Almost and Stable Almost Complex Manifolds
Authors: Dessai Anand
Published: May 2007

In the first part we give necessary and sufficient conditions for the existence of a stable almost complex structure on a 10‐manifold M with H1(M;ℤ) = 0 and no 2‐torsion in H1(M;ℤ) for i = 2,3. Using the Classification Theorem of Donaldson we give a reformulation of the conditions for a 4‐manifold to be almost complex in terms of Betti numbers and the dimension of the ±‐eigenspaces of the intersection form. In the second part we give general conditions for an almost complex manifold to admit infinitely many almost complex structures and apply these to symplectic manifolds, to homogeneous spaces and to complete intersections.
When Do Some Geodesics of the Induced and the Metrical Connection Coincide?
Authors: Dillen Franki , Vrancken Luc
Published: May 2007

In affine differential geometry, three natural connections can be considered, namely the induced connection, the Levi Civita connection of the affine metric and the conjugate connection. Quadrics are characterized by the conditions that all the pre‐geodesies with respect to one of these connections are also pre‐geodesies with respect to the other two connections. In the present paper we describe 3‐dimensional affine hypersurfaces for which some of the geodesies or pre‐geodesies for the different connections coincide.
On Principal Eigenvalues for Indefinite Problems in Euclidean Space
Authors: Rozenblum Grigori , Solomyak Michael
Published: May 2007

For the eigenvalue problem—λΔu = q(x)u in IRd, with the weight function q changing sign, conditions are discussed for existence of eigenvalues with positive decaying eigenfunctions.
Multiplicity Results for Second Order Nonlinear Problems with Maximum and Minimum
Authors: Stanêk Svatoslav
Published: May 2007

A functional differential equation of the type where F: C1(J) → L1(J) is a unbounded operator, is considered. Sufficient conditions for the existence of at least two different solutions satisfying boundary conditions min{x(t): t ϵ J} = α, max{x(t): t ϵ J} = β are given.
On the Growth of Convergence Radii for the Eigenvalues of the Mathieu Equation
Authors: Volkmer Hans
Published: May 2007

It is proved that the convergence radii ρn of the eigenvalues of the Mathieu equation satisfy lim inf ρn/n2 > kk′K2 = 2.0418., where the modulus k of the complete elliptic integrals is determined by 2E = K.