Rigidity of subfamilies of hypersurfaces in P~n with maximal length of Griffiths-Yukawa coupling

Let f:X→U be a family of smooth hypersurfaces in P nof degree dn+1 over a smooth curve U.Assume that the Griffiths-Yukawa coupling of f is non-vanishing.Then f is rigid.Moreover,we generalize it to the case when the Griffiths-Yukawa coupling of f is degenerated.     

SUPERCONVERGENCE OF GRADIENT RECOVERY SCHEMES ON GRADED MESHES FOR CORNER SINGULARITIES

For the linear finite element solution to the Poisson equation, we show that supercon- vergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^2-projection from the piecewise constant field △↓UN to the continuous and piecewise linear finite element space gives a better approximation of △↓U in the Hi-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.     

Weighted Hardy and potential operators in the generalized Morrey spaces

We study the weighted p→q-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces Lp,φ(Rn,w) defined by an almost increasing function φ(r) and radial type weight w(|x|). We obtain sufficient conditions, in terms of some integral inequalities imposed on φ and w, for such a p→q-boundedness. In some cases the obtained conditions are also necessary. These results are applied to derive a similar weighted p→q-boundedness of the Riesz potential operator.     

ON COMPACTNESS FOR ITERATED COMMUTATORS

The authors study the iterated commutators on the weighted Bergman spaces A 2 (φ), and prove that C n h is compact on A 2 (φ) if and only if h ∈ B0 .     

Reliability and covariance estimation of weighted k-out-of-n multi-state systems

In the literature of reliability engineering, reliability of the weighted k-out-of-n system can be calculated using component reliability based on the structure function. The calculation usually assumes that the true component reliability is completely known. However, this is not the case in practical applications. Instead, component reliability has to be estimated using empirical sample data. Uncertainty arises during this estimation process and propagates to the system level. This paper studies the propagation mechanism of estimation uncertainty through the universal generating function method. Equations of the complete solution including the unbiased system reliability estimator and the corresponding unbiased covariance estimator are derived. This is a unified approach. It can be applied to weighted k-out-of-n systems with multi-state components, to weighted k-out-of-n systems with binary components, and to simple series and parallel systems. It may also serve as building blocks to derive estimators of system reliability and uncertainty measures for more complicated systems.     

Schofield Induction for Sheaves on Weighted Projective Lines

We show that each exceptional vector bundle on a weighted projective line in the sense of Geigle and Lenzing can be obtained by Schofield induction from exceptional sheaves of rank one and zero. This relates to results of Ringel concerning modules over finite dimensional k-algebras over an arbitrary field.     

Maxwell-Lorentz Dynamics of Rigid Charges

We establish global existence and uniqueness of the dynamics of classical electromagnetism with extended, rigid charges and fields which need not to be square integrable. We also consider a modified theory of electromagnetism where no self-interaction occurs. That theory and our results are crucial for approaching the as yet unsolved problem of the general existence of dynamics of Wheeler-Feynman electromagnetism, which we shall address in the follow up paper. We conclude by discussing the energy conservation without self-interaction.     

Density Estimation under Constraints

Abstract

We suggest a general method for tackling problems of density estimation under constraints. It is, in effect, a particular form of the weighted bootstrap, in which resampling weights are chosen so as to minimize distance from the empirical or uniform bootstrap distribution subject to the constraints being satisfied. A number of constraints are treated as examples. They include conditions on moments, quantiles, and entropy, the latter as a device for imposing qualitative conditions such as those of unimodality or “interestingness.” For example, without altering the data or the amount of smoothing, we may construct a density estimator that enjoys the same mean, median, and quartiles as the data. Different measures of distance·give rise to slightly different results.     

On the existence and the uniqueness of the solution of a fluid–structure interaction scattering problem

The existence and uniqueness of the solution of a fluid–structure interaction problem is investigated. The proposed analysis distinguishes itself from previous studies by employing a weighted Sobolev space framework, the DtN operator properties, and the Fredholm theory. The proposed approach allows to extend the range of validity of the standard existence and uniqueness results to the case where the elastic scatterer is assumed to be only Lipschitz continuous, which is of more practical interest.     

The mean transform of bounded linear operators

In this paper we introduce the mean transform of bounded linear operators acting on a complex Hilbert space and then explore how the mean transform of weighted shifts behaves, in comparison with the Aluthge transform.