bluuebunny/crossref_metadata_2025_split huggingface dataset:
Chisquare Tests From Clusters of Observations
Authors: Helland Inge S. 
Published: May 2007

AbstractA simple model for categorical observations that are correlated in clusters is developed. The implied correlation coefficient is used to define an effective number of observations, and a natural estimation procedure for the correlation coefficient is proposed. By grouping the clusters of observations, and by relating them to models of the probabilities for the implied categories, common chisquare tests are formulated and motivated asymptotically. As an example of applications we look at forage registrations for radio‐collared moose.
Classification of Trends Via the Linear State Space Model
Authors: Gantert C. 
Published: May 2007

AbstractA method is presented for classification of trend curves based on the linear state space model. In this approach information about the smoothness of the trend curves is incorporated into the classification model by a nonstationary stochastic trend model and can thereby be used to obtain a better classification. In the case of small data sets the performance of the classification is significantly improved in comparison with the usual cluster analysis. Maximum likelihood estimation can be used to calculate the parameters of this model and to determine the classification. The classification algorithm is described in detail and the results are compared to those of the usual cluster analysis by simulation studies and by an application to tree ring data.
On the Automorphism Group of a Free Pro‐l Meta‐abelian Group and an Application to Galois Representations
Authors: Tsunogai Hiroshi 
Published: May 2007

AbstractIn § l of this article, we study group‐theoretical properties of some automorphism group Ψ* of the meta‐abelian quotient § of a free pro‐l group § of rank two, and show that the conjugacy class of some element of order two of Ψ* is not determined by the action induced on the abelian quotient § of § in the case of § = 2. In § 2 we apply the results to the outer Galois representation § attached to the curve C deleted one point from an elliptic curve E, and give an example that §c does not factor through the l‐adic representation attached to E.
Tangential Convergence of Temperatures and Harmonic Functions in Besov and in Triebel‐Lizorkin Spaces
Authors: Colzani Leonardo , Laeng Enrico 
Published: May 2007

AbstractWe study the maximal function Mf(x) = sup |f(x + y, t)| when Ω is a region in the (y,t) Ω upper half space R and f(x, t) is the harmonic extension to R+N+1 of a distribution in the Besov space Bαp,q(RN) or in the Triebel‐Lizorkin space Fαp,q(RN). In particular, we prove that when Ω= {|y|N/ (N‐αp) < t < 1} the operator M is bounded from F (RN) into Lp (RN). The admissible regions for the spaces B (RN) with p < q are more complicated.
Left‐Definite Regular Hamiltonian Systems
Authors: Krall Allan M. 
Published: May 2007

AbstractLinear Hamiltonian systems allow us to generalize, as well as consider, self‐adjoint problems of any even order. Such left‐definite problems are interesting, not only because of the generalization, but also because of the new intricacies they expose, some of which have made it possible to go beyond fourth order scale problems.We explore the left definite Sobolev settings for such problems, which are in general subspaces determined by boundary conditions. We show that the Hamiltonian operator remains self‐adjoint, and inherits the same resolvent and spectral resolution from its original L2 space when set in the left‐definite Sobolev space.
About the Regularity of Solutions of the Nonstationary Navier‐Stokes System
Authors: Chelkak S. , Koshelev A. 
Published: May 2007

AbstractThe problem of existence of regular (continuous, Holder continuous) solutions of the nonstationary Navier‐Stokes system is an important one in modern mathematical physics. It is closely connected with two main issues: the uniqueness of the solution and the possibility to apply approximate methods in numerical analysis and practical computations. Pointwise estimates of the velocity fields are essential for different numerical applications. We consider here mainly the multidimensional nonstationarity problem for finite (not necessarily small) times. In this paper we show that for small Reynold's numbers the boundedness of the velocity can be obtained and therefore the existence of unique strong solution can be proved for a certain class of external forces.
On the Cavities and Rigid Inclusions Correspondence and the Cosserat Spectrum
Authors: Markenscoff X. , Paukshto M. 
Published: May 2007

AbstractThe correspondence in two‐dimensional elasticity between the stress fields of cavities and rigid inclusions has been obtained by Dundurs [1] and Markenscoff [3]. It was shown that if the limit of the stress of the inclusion boundary‐value problem, which depends on the elastic constants, exists when the Poisson's ratio v tends to 1, then this solves the traction boundary‐value problem for the cavity problem since it satisfies equilibrium and boundary conditions, and, by the uniqueness theorem, exists and is unique.In three dimensions the solution of the traction boundary‐value problem of elasticity does depend on Poisson's ratio since the Beltrami‐Mitchell compatability conditions for the stress depend on Poisson's ratio. So the similar argument for the correspondence between cavities and rigid inclusions cannot in principle be made. However, the Beltrami‐Mitchell compatability conditions are independent of v if the dilatation is a constant or a linear function of the position. In this case we can show that the same result goes through for the correspondence.In order to investigate the behavior of the solutions in the vicinity of v = 1, we use some results obtained for the Cosserat spectrum by Mikhlin [4], Maz'ya and Mikhlin [3], see also [6]. The existence of the limit for 2D and 3D when v tends to 1 is proved on the basis of the fact that the eigenvalue ω = — 1 of the Cosserat spectrum is isolated.
Elastodynamical Scattering by N Parallel Half‐Planes in IR3
Authors: Meister E. , Rottbrand K. 
Published: May 2007

AbstractLinear boundary value problems of elasticity describe the propagation of time‐ harmonic waves outside of N parallel half‐plane shaped cracks in the Euclidian 3‐space.Equivalent systems involving 6N Wiener‐Hopf equations are obtained for first, second and third kind conditions simultaneously. To find explicit solutions, complex‐valued matrix functions with nonrational entries, are to be factorized in a generalized manner. This is done for two double‐knife screen crack problems in Part II.Problems for waves in acoustics, hydro‐and electrodynamics with an analogous geometry for rigid walls, or perfectly conducting metallic sheets, are contained in the problems formulated above: In Part II, for pure Dirichlet‐, or Neumann conditions, the corresponding (reduced) Wiener‐Hopf operator is seen to be invertible by an operator Neumann series for all distances (≠ 0) between the N half‐planes Σm.
Difference Potentials Method and its Applications
Authors: Ryaben'kii V. S. 
Published: May 2007

AbstractThe purpose of this article is to acquaint the reader with the general concepts and capabilities of the Difference Potentials Method (DPM).DPM is used for the numerical solution of boundary‐value and some other problems in difference and differential formulations.Difference potentials and DPM play the same role in the theory of solutions of linear systems of difference equations on multi‐dimensional non‐regular meshes as the classical Cauchy integral and the method of singular integral equations do in the theory of analytical functions (solutions Cauchy‐Riemann system).The application of DPM to the solution of problems in difference formulation forms the first aspect of the method. The second aspect of the DPM implementation is the discretization and numerical solution of the Calderon‐Seeley boundary pseudo‐differential equations. The latter are equivalent to elliptical differential equations with variable coefficients in the domain; they are written making no use of fundamental solutions and integrals. Because of this fact ordinary methods for discretization of integral equations cannot be applied in this case. Calderon‐Seeley equations have probably not been used for computations before the theory of DPM appeared. This second aspect for the implementation of DPM is that it does not require difference approximation on the boundary conditions of the original problem. The latter circumstance is just the main advantage of the second aspect in comparison with the first one.To begin with, we put forward and justify the main constructions and applications of DPM for problems connected with the Laplace equation. Further, we also outline the general theory and applications: both those already realized and anticipated.
Two‐Grid Solution of Symm's Integral Equation
Authors: Saranen J. , Vainikko G. 
Published: May 2007

AbstractWe propose two‐grid iteration methods for Symm's integral equation discretized by quadrature‐collocation or quadrature methods. Asymptotically the optimal order of error estimate is achieved already on the first iteration, for some modifications on the second iteration. This enables us to introduce some solvers which are of the optimal convergence order and cheap in a practical implementation; the cost varies between O(N2) and O(N log N) arithmetic operations. Numerical experiments confirm the approximation properties of the schemes.
Extension of Functions in Sobolev Spaces on Parameter Dependent Domains
Authors: Maz'ya Vladimir G. , Poborchi Sergey V. 
Published: May 2007

AbstractTwo‐sided ϵ‐dependent estimates for norms of extension operators acting in Sobolev spaces on the exterior or interior of an ϵ‐ thin cylindrical layer are obtained. Applications to some particular domains depending on small parameters are given.
Spectral Components of Selfadjoint Block Operator Matrices with Unbounded Entries
Authors: Adamyan Vadim , Langer Heinz , Mennicken Reinhard , Saurer Josef 
Published: May 2007

AbstractThis paper is devoted to the study of the spectral components of selfadjoint operator matrices which are generated by symmetric operator matrices of the form

in the product Hilbert space H1 × H2 where the entries A, B and C are not necessarily bounded operators in the Hilbert spaces H1, H2 or between them, respectively. Under suitable assumptions a selfadjoint operator L is associated with Lo and the spectral properties of L are studied. The main result concerns the case in which the spectra of the selfadjoint operators A and C are weakly separated. If a is a real number such that max σ(C) ≤ α ≤ min σ(A), descriptions of the spectral subspaces of L corresponding to the intervals [— ∞, α] and ]α,∞[ and of the restrictions of L to these subspaces are given. From this main result half range completeness and basis properties for certain parts of the spectrum of L are deduced. The paper closes with two applications to systems of differential operators from magnetohydrodynamics.
Lipschitz — Orlicz Spaces and the Laplace Equation
Authors: Aksoy A. G. , Maligranda L. 
Published: May 2007

AbstractStein and Taibleson gave a characterization for f ϵ Lp(ℝn) to be in the spaces Lip (α, Lp) and Zyg(α, Lp) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz‐Orlicz spaces Lip (α, Lm) and Zygmund‐Orlicz spaces Zyg (φ, Lm) and to the general function φ ϵ P instead of the power function φ(t)= tα. Such results describe the behavior of the Laplace equation in terms of the smoothness property of differences of f in Orlicz spaces Lm (IRn). More general spaces δk(φ,X, q) are also considered.
On Certain Densely Invariant Quantities of Linear Operators
Authors: Cross R. W. 
Published: May 2007

AbstractLet L(X,Y) denote the class of linear transformations T:D(T) ⊂ X → Y where X and Y are normed spaces. A quantity f is called densely invariant if for every system L(X, Y) and every operator T ϵ L(X,Y) we have f(T/E)= f(T) whenever E is a core of T. The density invariance of certain well known quantities is established. In case Y is complete and T is closable, a stronger property is shown to hold for some of these quantitites, namely invariance under restriction to dense subspaces.
Inequalities for Stationary Poisson Cuboid Processes
Authors: Favis Wassilis 
Published: May 2007

AbstractA cuboid is a rectangular parallelepipedon. By the notion “stationary Poisson cuboid process” we understand a stationary Poisson hyperplane process which divides the Euclidean space ℝdinto cuboids. It is equivalent to speak of a stationary Poisson cuboid tessellation. The distributions of volume and total edge length of the typical cuboid and the origin‐cuboid of a stationary Poisson cuboid process are considered. It is shown that these distributions become minimal, in the sense of a specific order relation, in the case of quasi‐isotropy. A possible connection to a more general problem, treated in [6], is also discussed.
Spectral Properties of a Multiplication Operator
Authors: Hardt Volker , Wagenführer Ekkehard 
Published: May 2007

AbstractIn this note we study the spectral properties of a multiplication operator in the space Lp(X)m which is given by an m by m matrix of measurable functions. Our particular interest is directed to the eigenvalues and the isolated spectral points which turn out to be eigenvalues. We apply these results in order to investigate the spectrum of an ordinary differential operator with so called “floating singularities”.
A Global Theory of Some Nonlinear Cauchy‐Riemann System in Several Complex Variables
Authors: Hayashi Yasuo 
Published: May 2007

AbstractA system of nonlinear differential equations of the type magnified image on a domain of ℂn is studied. Functional relations between the fj's, j = 1, …, n, and other necessary conditions are deduced when at each point of the domain the system has a manifold of local solutions. A structure theorem, that makes possible to reduce the problems of the system, e.g. the global solvability of it, to the corresponding questions for a connection of the type ∂z̄w = g(z, w)in a fibre bundle over a Riemann surface is proved, and through this reduction we obtain theorems of identity, extension, global factorization, and so on, for the solutions of the system. As an example, a system of nonlinear differential equations of the type magnified image is studied and its global solutions are constructed.
The Essential Spectrum of a Non‐Elliptic Boundary Value Problem
Authors: Langer Heinz , Möller Manfred 
Published: May 2007

AbstractIn this note a matrix partial differential operator is considered. It is shown that under certain conditions it defines a closed operator with nonempty resolvent set, and its essential spectrum is determined. In the symmetric case G.D. Raikov obtained earlier corresponding results (under slightly different assumptions) for the Friedrichs extension of the operator.
Generalized Poincaré Classes and Cubic Equivalences
Authors: Lewis James D. 
Published: May 2007

AbstractLet Y be a smooth projective algebraic surface over ℂ, and T(Y) the kernel of the Albanese map CH0(Y)deg0 → Alb(Y). It was first proven by D. Mumford that if the genus Pg(Y) > 0, then T(Y) is 'infinite dimensional'. One would like to have a better idea about the structure of T(Y). For example, if Y is dominated by a product of curves E1 × E2, such as an abelian or a Kummer surface, then one can easily construct an abelian variety B and a surjective 'regular' homomorphism B⊗z2 → T(Y). A similar story holds for the case where Y is the Fano surface of lines on a smooth cubic hypersurface in P4. This implies a sort of boundedness result for T(Y). It is natural to ask if this is the case for any smooth projective algebraic surface Y ? Partial results have been attained in this direction by the author [Illinois. J. Math. 35 (2), 1991]. In this paper, we show that the answer to this question is in general no. Furthermore, we generalize this question to the case of the Chow group of k—cycles on any projective algebraic manifold X, and arrive at, from a conjectural standpoint, necessary and sufficient cohomological conditions on X for which the question can be answered affirmatively.
The Poisson Voronoi Tessellation II. Edge Length Distribution Functions
Authors: Muche Lutz 
Published: May 2007

AbstractThis paper presents a method for the determination of the distribution function of the length of the 'typical' edge of the Poisson Voronoi tessellation. The method is based on distributional properties of the configuration of the centres in the neighbourhood of the 'typical' vertex. The distribution and density functions of the edge lengths are given in double integral form for various dimensions. Analogous characteristics are considered for two‐dimensional sections through higher‐dimensional Poisson Voronoi tessellations.
Levi Conditions and Global Gevrey Regularity for the Solutions of Quasilinear Weakly Hyperbolic Equations
Authors: Reissig Michael , Yagdjian Karen 
Published: May 2007

AbstractIn the present paper the authors prove a global Gevrey regularity result for the solutions of the Cauchy problem for the quasilinear weakly hyperbolic equation with spatial degeneracy utt−(a(x, t)ux)x = f(x, t, u, ux). The basic tool is a well ‐ posedness result (local existence and cone of dependence) in Gevrey spaces. Such a result can be proved only under the assumption of Levi conditions. Suitable energy estimates lead to the regularity of solutions. This result generalizes results from the strictly hyperbolic case.
On the Law of The Iterated Logarithm for Rapidly Increasing Subsequences
Authors: Schwabe Rainer , Gut Allan 
Published: May 2007

AbstractThe usual law of the iterated logarithm states that the partial sums Sn of independent and identically distributed random variables can be normalized by the sequence an = √nlog log n, such that limsupn→∞ Sn/an = √2 a.s. As has been pointed out by Gut (1986) the law fails if one considers the limsup along subsequences which increase faster than exponentially. In particular, for very rapidly increasing subsequences {nk≥1} one has limsupk→∞ Snk/ank = 0 a.s. In these cases the normalizing constants ank have to be replaced by √nk log k to obtain a non‐trivial limiting behaviour: limsupk→∞ Snk/ √nk log k = √2 a.s. We will present an intelligible argument for this structural change and apply it to related results.
Instability of Spatially — Periodic States for a Family of Semilinear PDE's on an Infinite Strip
Authors: Bridges Thomas J. , Mielke Alexander 
Published: May 2007

AbstractA family of time‐evolution equations, for which the time‐independent part is a semilinear elliptic equation on an infinite strip, is considered with attention to the instability of spatially‐periodic states. The analysis uses a sequence of center ‐ manifold reductions; first, every local, small norm, bounded solution is contained in a center manifold. Second, it is proved that every local, small norm, solution of the linear stability problem is also contained in a related non‐autonomous center manifold. For the case where the center manifold is foliated by periodic states, with wavelength L(s), parametrized by s, the level sets of a suitably defined spatial Hamiltonian functional, we prove a geometric criterion for instability: a spatially periodic state is linearly unstable in the time—dependent problem if L'(s) > 0. Properties of the manifold of periodic states and their linear stability are explicitly constructed for a family of potentials.
The Evolution of the Weyl and Maxwell Fields in Curved Space—Times
Authors: de Vries Andreas 
Published: May 2007

AbstractThe covariant Weyl (spin s = 1/2) and Maxwell (s = 1) equations in certain local charts (u, φ) of a space‐time (M, g) are considered. It is shown that the condition g00(x) > 0 for all x ε u is necessary and sufficient to rewrite them in a unified manner as evolution equations δtφ = L(s)φ. Here L(s) is a linear first order differential operator on the pre—Hilbert space (C (Ut, 2s+1). (…)), where Ut ⊂ IR3 is the image of the coordinate map of the spacelike hyper‐surface t = const, and (φ, C) = ƒUt ϕ *Q d(3)x with a suitable Hermitian n × n‐ matrix Q = Q(t,x). The total energy of the spinor field ϕ with respect to Ut is then simply given by E = 〈ϕ,ϕ〉. In this way inequalities for the energy change rate with respect to time, δt|ϕ|2 = 2Re (ϕ, L(s)ϕ) are obtained. As an application, the Kerr—Newman black hole is studied, yielding quantitative estimates for the energy change rate. These estimates especially confirm the energy conservation of the Weyl field and the well—known superradiance of electromagnetic waves.
Representations of Blocks Associated to Induced Modules of Restricted Lie Algebras
Authors: Farnsteiner Rolf 
Published: May 2007

AbstractLet (L, [p]) be a finite dimensional restricted Lie algebra over an algebraically closed field F of characteristic p ≧ 3, and x ε L* be a linear form. In this article we investigate the structure and representation theory of those blocks of the reduced enveloping algebra u(L,x) that are associated to irreducible modules of the form u(L, x) ⊗ u(K,x|k)Fλ.
Positivity for Perturbations of Polyharmonic Operators with Dirichlet Boundary Conditions in Two Dimensions
Authors: Grunau Hans — Christoph , Sweers Guido 
Published: May 2007

AbstractHigher order elliptic partial differential equations with Dirichlet boundary conditions in general do not satisfy a maximum principle. Polyharmonic operators on balls are an exception. Here it is shown that in IR2 small perturbations of polyharmonic operators and of the domain preserve the maximum principle. Hence the Green function for the clamped plate equation on an ellipse with small eccentricity is positive.
Note on a Paper by G. J. Rieger
Authors: Hensley Doug 
Published: May 2007

AbstractLet c ε IN. For d ε ℤ with gcd (d, c) = 1 let δ(d, c) be defined by d · δ(d, c)  1 mod c, 1 ⩽ δ(d, c) ⩽ c. Let s, t ε IN with 1 ⩽ s ⩽ c, 1 ⩽ t ⩽ c. The main result is that for arbitrary fixed ε > 0, but uniformly over c, s and tmagnified imageEquivalently, the points (d, δ(c,d)) are approximately uniformly distributed in [0, c] × [0, c]: The two‐dimensional discrepancy of {(d,δ (c, d)): 1 ⩽ d ⩽ c and (c, d)= 1} in [0,c] × [0,c] is Oε(cε‐1/2).
Weyl Groups are Finite — and Other Finiteness Properties of Cartan Subalgebras
Authors: Hofmann Karl H. , Lawson Jimmie D. , Ruppert Wolfgang A. F. 
Published: May 2007

AbstractFor each pair (𝔤,𝔞) consisting of a real Lie algebra 𝔤 and a subalgebra a of some Cartan subalgebra 𝔥 of 𝔤 such that [𝔞, 𝔥]∪ [𝔞, 𝔞] we define a Weyl group W(𝔤, 𝔞) and show that it is finite. In particular, W(𝔤, 𝔥,) is finite for any Cartan subalgebra h. The proof involves the embedding of 0 into the Lie algebra of a complex algebraic linear Lie group to which the structure theory of Lie algebras and algebraic groups is applied. If G is a real connected Lie group with Lie algebra 𝔤, the normalizer N(𝔥, G) acts on the finite set Λ of roots of the complexification 𝔤c with respect to hc, giving a representation π : N(𝔥, G)→ S(Λ) into the symmetric group on the set Λ. We call the kernel of this map the Cartan subgroup C(𝔥) of G with respect to h; the image is isomorphic to W(𝔤, 𝔥), and C(𝔥)= {g G : Ad(g)(h)— h ε [h,h] for all h ε h }. All concepts introduced and discussed reduce in special situations to the familiar ones.The information on the finiteness of the Weyl groups is applied to show that under very general circumstance, for b ∪ 𝔥 the set 𝔥⊂ ϕ(b) remains finite as ϕ ranges through the full group of inner automorphisms of 𝔤.