Symmetric Boundary Value Methods for Second Order Initial and Boundary Value Problems

We introduce symmetric Boundary Value Methods for the solution of second order initial and boundary value problems (in particular Hamiltonian problems). We study the conditioning of the methods and link it to the boundary loci of the roots of the associated characteristic polynomial. Some numerical tests are provided to assess their reliability. Dedicated to the memory of Professor Aldo Cossu     

The problem of Dirichlet for anisotropic quasilinear degenerate elliptic equations

We consider the Dirichlet problem for a class of anisotropic degenerate elliptic equations. New a priori estimates for solutions and for the gradient of solutions are established. Based on these estimates sufficient conditions guaranteeing the solvability of the problem are formulated. The results are new even in the semilinear case when the principal part is the Laplace operator.     

A complete global solution to the pressure gradient equation

We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes.     

The time recovery of the spectroscopic properties of heavily irradiated CdZnTe and CdTe detectors

The time recovery of the spectroscopic capabilities of CdZnTe and CdTe detectors, irradiated with increasing doses of high- and low-energy neutrons, as well as electrons, has been investigated by studying their spectroscopic behavior at different photon energies using leakage current measurements and PICTS (photo-induced current transient spectroscopy) analysis. The detectors were stored at room temperature for up to one year to study the time evolution of their spectroscopic performance and to correlate it with the presence of defective states in the material. We have observed a clear improvement in the material’s detection properties with time, though only in those detectors which have not been severely degraded by the irradiation. The recovery can be associated with a decrease in the concentration of some defective states, thus allowing the assessment of the crucial role these play in determining the charge collection processes in the material and its spectroscopic capabilities. Received: 1 August 2001 / Accepted: 3 August 2001 / Published online: 20 December 2001     

Analysis of X（1576） as a Tetraquark State with the QCD Sum Rules

We take the viewpoint that X（1576） is the tetraquark state which consists of a scalar diquark and an antiscalar-diquark in relative P-wave, and calculate its mass in the framework of the QCD sum rule approach. The numerical value of the mass mx= （1.66 =k 0.14） GeV is consistent with the experimental data. There might be some tetraquark components in the vector meson X（1576）.     

A nondifferentiable extension of a theorem of Pucci and Serrin and applications

We study the multiplicity of critical points for functionals which are only differentiable along some directions. We extend to this class of functionals the three critical point theorem of Pucci and Serrin and we apply it to a one-parameter family of functionals Jλ, λ∈I⊂R. Under suitable assumptions, we locate an open subinterval of values λ in I for which Jλ possesses at least three critical points. Applications to quasilinear boundary value problems are also given.     

Almost sure estimates for the concentration neighborhood of Sinai’s walk

We consider Sinai’s random walk in random environment. We prove that infinitely often (i.o.) the size of the concentration neighborhood of this random walk is bounded almost surely. We also get that i.o. the maximal distance between two favorite sites is bounded almost surely.     

Bias of the structural quasi-score estimator of a measurement error model under misspecification of the regressor distribution

In a structural measurement error model the structural quasi-score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified, the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification, the true model consists of a mixture of normal distributions which cluster around a single normal distribution, in the second type, the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification, the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero in a flat way so that small deviations from the true model lead to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model.     

Completeness and compactness for varieties over a local field

This paper shows that for a local field K, a subfield k ⊂ K and a variety X over k, X is complete if and only if for every finite field extension Kʹ | K, the set X(Kʹ) is compact in its strong topology. The author likes to thank Florian Pop, Jakob Stix, Stefan Wewers, Gunther Cornelissen and his own parents for their support. Received: 13 April 2006     

Prospective and retrospective analyses under logistic regression models

In logistic case-control studies, Prentice and Pyke (Biometrika 66 (1979) 403-411) showed that valid point estimators of the odds-ratio parameters and their standard errors may be obtained by fitting the prospective logistic regression model to case-control data. Wang and Carroll (Biometrika 80 (1993) 237-241; J. Statist. Plann. Inference 43 (1995) 331-340) generalized Prentice and Pyke's (Biometrika 66 (1979) 403-411) results to robust logistic case-control studies. In this paper, we extend the results of Prentice and Pyke (Biometrika 66 (1979) 403-411) and Wang and Carroll (Biometrika 80 (1993) 237-241; J. Statist. Plann. Inference 43 (1995) 331-340) to a class of statistics and a class of unbiased estimating equations. We present some results on simulation and on the analysis of two real datasets.