bluuebunny/crossref_metadata_2025 huggingface dataset:
Method of Construction of Partial Tetra‐Allel Crosses and Its Analysis
Authors: Ponnuswamy K. N. , Natarajan S. , Anbupalam T.
Published: May 2007

The present paper deals with a method of construction of Partial Tetra‐allel Crosses (PTAC) through Doubly Balanced Incomplete Block Designs (DBIBD) and its analysis by explicit expressions of symmetric sums approach. We have also established an inequality for the estimability of individual design components of variance in the Hinkelmann's double crosses model. A simulation study has been carried out to compare the precision of the estimates of genetic components of variance based on the two different PTAC with same experimental size. A list of DBIBD's will be useful in the construction of PTAC has given in the appendix.
Computation of Some Exact Properties of Wald's Sprt when Sampling from a Class of Discrete Distributions
Authors: Young L. J.
Published: May 2007

An algorithm is developed for determining exact values of the Operating Characteristic and Average Sample Number functions for Wald's Sequential Probability Ratio Test (SPRT) when observations are drawn from a discrete, Koopman‐Darmois density with positive probability on the nonnegative integers. The sample size distribution and percentiles of sample size are also considered. An example is given for the negative binomial distribution.
Testing Equivalence Simultaneously for Location and Dispersion of two Normally Distributed Populations
Authors: Bauer Peter , Bauer Michael M.
Published: May 2007

In clinical trials with an active control usually therapeutical equivalence of a new treatment is investigated by looking at a location parameter of the distributions of the primary efficacy variable. But even if the location parameters are close to each other existing differences in variability may be connected with different risks for under or over treatment in an individual patient.

Assuming normally distributed responses a multiple test procedure applying two shifted one‐sided t‐tests for the mean and accordingly two one‐sided F‐tests for the variances is proposed. Equivalence in location and variability is established if all four tests lead to a rejection at the (one‐sided) level α. A conservative procedure “correcting” the t‐tests for heteroscedasticity is derived. The choice of a design in terms of the global level α, the global power, the relevant deviations in the population means and variances, as well as the sample size is outlined. Numerical calculations of the actual level and power for the proposed designs show, that for balanced sample sizes the classical uncorrected one‐sided t‐tests can be used safely without exaggerating the global type I error probability.

Finally an example is given.
The Estimation of Skewness and Kurtosis of Random Effects in the Linear Model
Authors: Teuscher F. , Herrendörfer G. , Guiard V.
Published: May 2007

Generalising the ANOVA method of estimating variance components in mixed linear models a simple procedure is presented to estimate skewness and kurtosis of the distributions of the random effects of the model. For the model II of a one‐way classification this procedure is demonstrated explicitly.
Pivotal Quantities for the Substitution Values of Various Entries, Each in Place of its Best Contender, Given the Standard Analysis of Variance Model
Authors: van Aarde I. M. R.
Published: May 2007

Consider a yield trial involving entries such as the apple cultivars named “Cox's Pippin”, “Granny Smith”, “Rome Beauty”, etc., where interest is in mean performance, the higher the better. For any of the entries, say Granny Smith, an unknown “X” names the best of the other entries. The substitution value of Granny Smith in place of its best contender, is given in terms of expectations by E (yield of Granny Smith) — E (yield of X). This parameter takes on any real value. A system of interval estimates of the parameter is shown to arise in the standard analysis of variance case. In fact, there arises such a system for each of the entries involved. These systems supersede procedures recently discussed in this journal by VAN DER LAAN (1992).
A Comparison of Robust Estimators in the Presence of Arbitrarily Right Censored Data
Authors: Khan‐Malek R. C. , Magel Rhonda C.
Published: May 2007

Robust estimation of a location parameter is considered when the data from an unknown symmetric population are subject to arbitrary right‐censorship. Comparisons are made between various M‐estimators, several L‐estimators (trimmed means), and the Kaplan‐Meier median. Ten sampling distributions, two uniform censoring distributions, and three sample sizes are examined. A Cauchy censoring distribution is also considered when the sample size is equal to twenty for each of the ten sampling distributions. Performance is based on the estimated mean square error.
On Choosing Among Several Experimental Treatments and a Control
Authors: Chen Pinyuen
Published: May 2007

The two classical selection approaches in comparing experimental treatments with a control are combined to form an integrated approach. In this integrated approach, there is a preference zone (PZ) and an indifference zone (IZ), and the concept of a correct decision (CD) is defined differently in each of these zones. In the PZ, we are required to select the best treatment for a correct decision (CD1) but in the IZ, we define any selected subset to be correct (CD2) if it contains the best treatment among all the experimental treatments and the controlled treatment. We propose a single‐stage procedure R to achieve the selection goals CD1 and CD2 simultaneously with certain probability requirements. It is shown that both the probability of a correct decision under PZ, P(CD1 | PZ), and the probability of a correct decision under IZ, P(CD2 | IZ), satisfy some monotonicity properties and the least favorable configuration in PZ and the worst configuration in IZ are derived by these properties. We also derive formulas for the probabilities of correct decision and provide a brief table to illustrate the magnitude of the procedure parameters and the common sample sizes needed for various probability requirements and configurations.
Relationships Between Kendall's Coefficient of Concordance and a Nonparametric Measure of Phenotypic Stability with Implications for the Consistency in Rankings as Affected by Variance Components
Authors: Hühn M. , Piepho H. P.
Published: May 2007

For a two‐way classification with rows (= genotypes) and columns (= environments) relationships between Kendall's coefficient of concordance W and a nonparametric measure of phenotypic stability S (= variance among the ranks over the environments) are presented.

This provides an analogy between Wricke's ecovalence and the sum of squares of genotype‐environment interactions on the parametric side and S and Kendall's W on the nonparametric side: S is a genotype's contribution to the discordance (1 — W) in the data set, while Wricke's ecovalence is a genotype's contribution to the genotype‐environment interaction sum of squares.

Genotype x environment interactions may lead, but must not necessarily lead to non‐identical rank orders of the genotypes in different environments (crossover versus noncrossover interactions). When does interaction become rank interaction?

The similarity of the rank orders (measured by W) can be approximately expressed by the ratio of the genotypic variance and sum of genotypic variance plus residual variance. For the consistency of rankings this relation leads to an approximate test of significance which is based on variance components.

Finally, a numerical example is given using grain yield data of 20 genotypes (varieties) of winter wheat in 10 environments (locations) from German registration trials.
An Exact Unconditional test for the Hardy‐Weinberg Equilibrium
Authors: Haber Michael
Published: May 2007

An exact test based on the unconditional distribution of a test statistic for the Hardy‐Weinberg equilibrium is introduced. This test is usually more powerful and requires less extensive tabulations compared with the (ordinary) exact conditional test. Tables of critical values are given for N = 5(1)100 and α =·10, ·05, ·01. Sample sizes required to attain a given power with the unconditional and conditional exact tests are provided.
Body Proportions of the Infant
Authors: Gerver W. J. M. , de Bruin R. , Blanco C. E.
Published: May 2007

Growth is usually evaluated by single measurements which reflect only that direction of growth. At birth the relationship between measurements is often considered as Rohrer's Ponderal Index which describes weight in relation to length but can be misleading especially when considering premature infants. We propose that it is more appropriate to study the relationship of different anthropometric measurements to define normality and thereby create limits from which abnormalities in growth may be diagnosed.

Weight, crown heel length, crown rump length and head circumference were measured in 305 healthy infants, at 26–42 gestational weeks to obtain reference values. Subischial leg length was calculated. A multivariate model was made which could be useful to distinguish the form and shape of an infant and to identify abnormalities in growth.
A Mixed Model for Binary Data: The Modified X2‐test
Authors: Hecker Hartmut , Wiese Birgitt
Published: May 2007

In this paper, a statistical model for clinical trials is presented for the special situation that a varying and unstructered number of binary responses is obtained from each subject. The assumptions of the model are the following: 1.) For each subject there is a (constant) individual Bernoulli parameter determining the distribution of the binary responses of this subject. 2.) The Bernoulli parameters associated with the subjects are realizations of independent random variables with distributions Pg in treatment group g(g = 1, 2, …, G).

3.) Given the value of the Bernoulli parameter, the observations are stochastically independent within each subject.

Under these assumptions, a test statistic is derived to test the hypothesis H0:E(P1) = E(P2) = … = E(PG). It is proven and demonstrated by simulations, that the test statistic asymptotically (i.e. for a large number of subjects) follows the X2‐distribution.
Unbalanced Repeated Measures with Random Coefficients
Authors: Wu Yuan , McGilchrist Clyde A.
Published: May 2007

In a random coefficient repeated measures model, the regression coefficients relating the observations to some underlying variable, such as time, are themselves taken to be random distributed over experimental units. In this paper, a general approach to repeated measures analysis is extended to this wider model. In the model three specific error structures for the random regression coefficients have been studied,viz, the random coefficients variance matrix is considered to be (i) diagonal, (ii) proportional to the identity matrix and (iii) completely general. An example will be analyzed to illustrate the procedure.
Chisquare Tests From Clusters of Observations
Authors: Helland Inge S.
Published: May 2007

A 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

A 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 Approximate and Exact Sample Sizes of Equivalence Tests for Binomial Proportions
Authors: Frick H.
Published: May 2007

There exist several formulae for sample sizes for testing the equivalence of binomial proportions which are based on approximations by the normal distribution. Quite often these formulae produce drastically different results. In this paper the validity of the approximate sample sizes is investigated with respect to the exact distributions.
Strong Solutions of the Navier–Stokes System in Lipschitz Bounded Domains
Authors: Deuring Paul , Wahl Wolf Von
Published: May 2007

Let Ω be a bounded domain in ℝ3 with a connected Lipschitz boundary ∂Ω. Consider the Navier‐Stokes system.
On the Automorphism Group of a Free Pro‐l Meta‐abelian Group and an Application to Galois Representations
Authors: Tsunogai Hiroshi
Published: May 2007

In § 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

We 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

Linear 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

The 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

The 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

Linear 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

The 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

We 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.
Asymptotics of Stable Viscoelastic Fluid Motion (Oldroyd's Mathematical Model)
Authors: Sobolevskii P. E.
Published: May 2007

An asymptotic series of the solution is constructed.
Extension of Functions in Sobolev Spaces on Parameter Dependent Domains
Authors: Maz'ya Vladimir G. , Poborchi Sergey V.
Published: May 2007

Two‐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

This 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

Stein 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

Let 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

A 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.
Self‐affine Lattice Reptiles with Two Pieces in IRn
Authors: Gelbrich Götz
Published: May 2007

We prove that for every number n ≥ 1, there is a finite number of affine types of self‐affine lattice tilings in ℝn, such that the expansion carries each tile onto the union of two tiles.
Spectral Properties of a Multiplication Operator
Authors: Hardt Volker , Wagenführer Ekkehard
Published: May 2007

In 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

A 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

In 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

Let 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

This 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

In 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

The 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

A 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

The 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.
k—Very Ample Line Bundles on Del Pezzo Surfaces
Authors: di Rocco Sandra
Published: May 2007

A k‐very ample line bundle L on a Del Pezzo Surface is numerically characterized, improving the results of Biancofiore— Ceresa in [7].
Representations of Blocks Associated to Induced Modules of Restricted Lie Algebras
Authors: Farnsteiner Rolf
Published: May 2007

Let (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

Higher 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

Let 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

For 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.
Non ‐ Classical Mixed Interface Problems for Anisotropic Bodies
Authors: Jentsch Lothar , Natroshvili David
Published: May 2007

The paper deals with the three‐dimensional mathematical problems of the elasticity theory of anisotropic piece‐wise homogeneous bodies. Non ‐ classical mixed type boundary value problems are studied when on one part (S1) of the interface the rigid contact conditions (jumps of displacement and stress vectors) are given, while conditions of the non ‐ classical interface Problem H or Problem G are imposed on the remaining part (S2) of the interface, i. e., in both cases jumps of the normal components of displacement and stress vectors are known on S2 and, in addition, in the first one (Problem H) the tangent components of the displacement vector and in the second one (Problem G) the tangent components of the stress vector are given from the both sides on S2.

The investigation is carried out by the potential method and the theory of pseudodifferential equations on manifolds with boundary.
Algebras of Singular Integral Operators with Piecewise Continuous Coefficients on Reflexive Orlicz Spaces
Authors: Karlovich Aleksey Yu.
Published: May 2007

We consider singular integral operators with piecewise continuous coefficients on reflexive Orlicz spacesLm(σ) which are generalizations of the Lebesgue spacesLP(σ), 1 < p < ∞. We suppose that σ belongs to a large class of Carleson curves, including curves with corners and cusps as well as curves that look locally like two logarithmic spirals scrolling up at the same point. For the singular integral operator associated with the Riemann boundary value problem with a piecewise continuous coefficientG, we establish a Fredholm criterion and an index formula in terms of the essential range ofGcomplemented by spiralic horns depending on the Boyd indices ofLM(σ) and contour properties. Our main result is a symbol calculus for the closed algebra of singular integral operators with piecewise continuous matrix ‐ valued coefficients onLMn(σ).
Trace Theorems for Sobolev Spaces of Variable Order of Differentiation
Authors: Leopold Hans ‐ Gerd , Schrohe Elmar
Published: May 2007

We prove a trace theorem and an extension theorem for Sobolev spaces of variable order of differentiation which are defined by pseudodifferential operators.
On the Size of the Exceptional Set in Nevanlinna's Second Fundamental Theorem for Certain Classes of Meromorphic Functions
Authors: Rodríguez Francisco
Published: May 2007

Some conditions on the size of the exceptional set that arise in Nevanlinna's Second Fundamental Theorem are established, showing that previous sharp results can be improved by restricting the class of functions considered and suggesting a close relationship between the size of the exceptional set and the lower growth of the characteristic function. Examples of functions of rapid growth possessing exceptional sets are built, showing that these conditions are sharp for the class of functions considered.
Spectral Decomposition of Symmetric Operator Matrices
Authors: Mennicken Reinhard , Shkalikov Andrey A.
Published: May 2007

The authors study symmetric operator matricesmagnified imagein the product of Hilbert spaces H = H1×H2, where the entries are not necessarily bounded operators. Under suitable assumptions the closure Lo exists and is a selfadjoint operator in H. With Lo, the closure of the transfer functionmagnified imageis considered. Under the assumption that there exists a real number β < inf p(A) such that M(β)<< 0, it follows that β ε p(Lo). Applying a factorization result of A.I. Virozub and V.I. Matsaev [VM] to the holomorphic operator function M(λ, the_spectral subspaces of Lo corresponding to the intervals ] — ∞, β] and [β, ∞[ and the restrictions of Lo to these subspaces are characterized. Similar results are proved for operator matricesmagnified imagewhich are symmetric in a Krein space.
Spectral Analysis for Linear Pencils N — λP of Ordinary Differential Operators
Authors: Shkalikov Andrey A. , Tretter Christiane
Published: May 2007

Boundary eigenvalue problems for linear pencils N — λ of two ordinary differential operators are studied where P is of lower order than N. In a suitable scale of subspaces of Sobolev spaces and spaces of continuously differentiable functions results on minimality and basis properties of the eigenfunctions and associated functions are proved, including explicit formulas for the Fourier coefficients. As an application the Orr ‐ Sommerfeld equation is considered.
Instability Phenomena for the Fourier Coefficients
Authors: Aizenberg Lev , Tarkhanov Nikolai
Published: May 2007

Let P be an elliptic differential operator on a non‐compact connected manifold X; suppose that both X and the coefficients of P are real analytic. Given a pair of open sets D and σ in X with σ⊂⊂ D ⊂⊂ X, we fix a sequence {ev} of solutions of Pu = 0 in D which are pairwise orthogonal under integration over both D and σ. By orthogonality is meant the orthogonality in the corresponding Sobolev spaces; we also assume a completeness of the system on σ. For a fixed y ε X/⊂, denote by kv(y) the Fourier coefficients of a fundamental solution ϕ(·, y) of P with respect to the restriction of {ev} to σ. Suppose K is a compact set in D/σ, and let f be a distribution with support on K. In this paper we show, under appropriate conditions on K, that if the moments (f, kv) decrease sufficiently rapidly in a certain precise sense, then these moments vanish identically. In the most favorable cases, it is then possible to conclude that f = 0. This phenomenon was previously noticed by the first author and L. Zalcman for analytic and harmonic moments of f.
The Trace Formula for Schrödinger Operators from Infinite Dimensional Oscillatory Integrals
Authors: Albeverio Sergio , De Monvel‐Berthier Anne Boutet , Brzeźniak Zdzislaw
Published: May 2007

The theory of infinite dimensional oscillatory integrals by finite dimensional approximations is shown to provide new information on the trace formula for Schrödinger operators. In particular, the explicit computation of contributions given by constant and non constant periodic orbits, for potentials which are quadratic plus a bounded nonlinear part, is provided. The heat semigroup as well as the Schrödinger group are discussed and it is shown in particular that their singular supports are contained in an explicit countable set independent of the bounded part of the potential.
An Oscillation Theorem for a Sturm ‐Liouville Eigenvalue Problem
Authors: Bohner Martin
Published: May 2007

We consider a certain Sturm ‐ Liouville eigenvalue problem with self‐ adjoint and non ‐separated boundary conditions. We derive an explicit formula for the oscillation number of any given eigenfunction.
Regular Sturm ‐ Liouville Problems Whose Coefficients Depend Rationally on the Eigenvalue Parameter
Authors: De Snoo Henk
Published: May 2007

In this note we consider regular Sturm‐Liouville equations with a floating singularity of a special type: the coefficient of the second order derivative contains the eigenvalue parameter. We determine the form of the boundary conditions which make the problem selfadjoint after linearizing. In general the boundary conditions for the linearized system give rise to boundary conditions which involve the eigenvalue parameter in the original, non‐linearized, problem. The boundary conditions give rise to a 2 × 2 matrix function, the so‐called Titchmarsh‐Weyl coefficient. The characteristic properties of this function are studied. The formal aspects of the theory of this class of equations turn out to be quite parallel to those for the usual situation when there is no floating singularity.
Eigenvalue Asymptotics for an Oblique Derivative Problem Involving an Indefinite Weight
Authors: Faierman M.
Published: May 2007

In this paper we derive asymptotic formulae for the distribution functions of the real parts of the eigenvalues of an oblique derivative problem involving an indefinite weight function.
Global Bifurcation from the First Eigenvalue for a System of p ‐ Laplacians
Authors: Fleckinger Jacqueline , Manásevich Raäl , De Thélin Franqois
Published: May 2007

We prove here bifurcation and existence results for a nonlinear elliptic system involving the p‐ Laplacian.
On Some Properties of the Solutions of Quasilinear Degenerate Elliptic Equations
Authors: Kondratiev Wladimir , Nicolosi Francesco
Published: May 2007

We prove the existence of bounded solutions of some boundary value problems for degenerate elliptic equations of second order in divergence form. Our results cover also the unbounded domain case. We discuss also the uniqueness problem and asymptotic behaviour of the solutions of our equation.
Asymptotics of the Spectrum of Douglis ‐ Nirenberg Elliptic Operators on a Compact Manifold
Authors: Kozhevnikov Alexander
Published: May 2007

Pseudo‐ differential systems on closed manifolds, elliptic in the sense of DOUGLIS and Nirenberg. are considered. It is proved that the system is similar to an diagonal operator up to an operator of order ‐ ∞, and the similarity transformation preserves ellipticity and parameter ‐ellipticity. The similarity transformation may be chosen so that it preserves even self adjointness up to an operator of order less than the lowest order of the diagonal entry. These results are applied to prove the eigenvalue asymptotics with the sharp estimate of the remainder in the self adjoint case as well as a rough asymptotics in the non‐self‐adjoint case. Another application is the eigenvalue asymptotics with the sharp estimate of the remainder for general self‐ adjoint elliptic boundary value problems with the spectral parameter appearing linearly in boundary conditions.
On the Nonoscillatory Behavior of Solutions of a Second Order Linear Differential Equation
Authors: Li Horng‐Jaan , Yeh Cheh‐Chih
Published: May 2007

In this paper, wo improve the Sturm comparison theorem and two nonoscillation criteria of Leighton and Wintner, and establish two variants of a Wintner' s nonoscillatory criterion of the second order linear differential equation magnified image where r, c : t0,∞) →, R > 0 a. e. on t0,∞) and 1/r, c ε Ll(t0,b) for each b ∞ (t0,>) for some t0 > 0. Using these two criteria, we improve some nonoscillation criteria of Hartman. Hille. Moore. Potter. WintnEr, and Willett. These proofs are more elegant and concise than those of theirs.
A Generalization of the Theorem of Hardy: A Most General Version of the Uncertainty Principle for Fourier Integrals
Authors: Pfannschmidt Christian
Published: May 2007

N. Wiener remarked that a non ‐ identically vanishing real function and its Fourier transform cannot both decay “very fast”. It was Hardy who specified and proved this assertion in 1933. In the present paper Hardy's theorem will be generalized. Moreover, it will be shown that further weakening of these assumptions does not make sense.
On Cauchy Homomorphisms of Nearness Frames
Authors: Banaschewski B. , Pultr A.
Published: May 2007

To include the pointfree case, the notion of a Cauchy map easily extends as the condition that the preimage of any regular Cauchy filter contains a regular Cauchy filter. This extension, however, can be unsatisfactory if the regular Cauchy filters are scarce or non‐existent, making the condition too weak, indeed sometimes even void. In this paper a variant of the notion, independent on the existence of any kind of filters, is studied: a homomorphism is called fully Cauchy if it lifts to the completions. This is generally stronger than, and in the spatial and metric cases it coincides with the previously mentioned property. Moreover, it is stable under localization.
Subelliptic Estimates for a Class of Degenerate Elliptic Integro‐Differential Operators
Authors: Cancelier Claudy , Franchi Bruno
Published: May 2007

In this paper we prove subelliptic estimates for operators of the form Δx + λ2 (x)S in ℝN = ℝ × ℝ, where the operator S is an elliptic integro ‐ differential operator in ℝN and λ is a nonnegative Lipschitz continuous function.
On the Boundedness of Pseudo ‐ Differential Operators on Weighted Besov ‐ Triebel Spaces
Authors: Dintelmann Peter
Published: May 2007

An elementary straightforward proof for the boundedness of pseudo ‐ differential operators of the Hörmander class ΨμI,δ on weighted Besov ‐ Triebel spaces is given using a discrete characterization of function spaces.