Geometric and transformational properties of Lipschitz domains,Semmes-Kenig-Toro domains,and other classes of finite perimeter domains

In the first part of this article we give intrinsic characterizations of the classes of Lipschitz and C¹ domains. Under some mild, necessary, background hypotheses (of topological and geometric measure theoretic nature), we show that a domain is Lipschitz if and only if it has a continuous transversal vector field. We also show that if the geometric measure theoretic unit normal of the domain is continuous, then the domain in question is of class C¹. In the second part of the article, we study the invariance of various classes of domains of locally finite perimeter under bi-Lipschitz and C¹ diffeomorphisms of the Euclidean space. In particular, we prove that the class of bounded regular SKT domains (previously called chord-arc domains with vanishing constant, in the literature) is stable under C¹ diffeomorphisms. A number of other applications are also presented. Acknowledgements and Notes. The work of the authors was supported in part by NSF grants DMS-0245401, DMS-0653180, DMS-FRG0456306, and DMS-0456861.     

On regularization and discretization control for the numerical solution of inverse problems in parabolic equations

In this paper, the influence of modelling, a priori information, discretization and measurement error to the numerical solution of inverse problems is investigated. Given an a priori approximation of the unknown parameter function in a parabolic problem, we propose a strategy for the regularized determination of a skeleton solution to the inverse problem. This strategy is based on a discretization control of the forward problem in order to find a trade-off between accuracy and computational efficiency. Numerical results with regard to a nonlinear inverse heat conduction problem illustrate the study.     

The Green function estimates for strongly elliptic systems of second order

We establish existence and pointwise estimates of fundamental solutions and Green’s matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq {\mathbb{R}}^n, n \geq 3We establish existence and pointwise estimates of fundamental solutions and Green’s matrices for divergence form, second order strongly elliptic systems in a domain , under the assumption that solutions of the system satisfy De Giorgi-Nash type local H?lder continuity estimates. In particular, our results apply to perturbations of diagonal systems, and thus especially to complex perturbations of a single real equation.     

A molecular simulation study on β-cyclodextrins included in PEEK membrane

Molecular dynamics simulations have been performed on β-cyclodextrins octyl- derivative (β-CD) encapsulated into a polymer matrix of glassy poly(ether ether-ketone) material. Results considering the internal motion and dynamical features of the cyclodextrins in this environment are given and discussed.     

Modifying operator product expansions by non-perturbative non-locality

Local quark–hadron duality violations in conventional applications of the operator product expansion are proposed to have their origin in the fact that the QCD vacuum or a hadronic state is not only characterized by nonvanishing expectation values of local, gauge invariant operators but also by finite correlation lengths of the corresponding gauge invariant n-point functions. Utilizing high-resolution lattice information on these correlators a non-perturbative component of OPE coarse graining is proposed which, in principle, allows for a determination of the critical dimension where the break-down of the expansion sets in.     

Progress in multi-ion counting spark-source mass spectrometry (MIC-SSMS) for the analysis of geological samples

Spark source mass spectrometry (SSMS) has experienced important and significant improvements in nearly all analytical features by the use of a multiple ion counting (MIC) system. Two procedures have recently been developed to further increase the analytical capabilities of MIC-SSMS in geochemistry. These are a mathematical correction of interferences, which is often necessary for the ultra trace element analysis of Nb, Ta, Zr, Hf and Y, and the development of an autospark system to hold the total ion beam constant. New analytical data for geological samples, especially international reference materials, are presented using the improved MIC-SSMS technique. The data set consists of high precision and low abundance data for Zr, Nb and Y in depleted reference materials. The MIC-SSMS results are compared with those of conventional SSMS using photoplates for ion detection. The precision of the MIC-SSMS isotope ratio measurements (about 1%) is more than a factor of 3 better than that of conventional SSMS, as demonstrated by analyses of Hawaiian samples. Total uncertainties of MIC-SSMS concentration data including all sources of error are generally between 2 and 5% for concentrations higher than about 0.3 μg/g and about 10% for trace element abundances in the ng/g range.