In this paper we present some general properties concerning area functionals, both continuous and discrete, used in the variational approach of numerical grid generation. In particular we introduce a new proof of a theorem concerning the classical area functional which has served us as a guide in the design of new area functionals yielding better performance than the currently used. In particul...

Cameron and Storvick introduced the concept of a sequential Fourier-Feynman transform and established the existence of this transform for functionals in a Banach algebra Ŝ of bounded functionals on classical Wiener space. In this paper we investigate various relationships between the sequential Fourier-Feynman transform and the convolution product for functionals which need not be bounded or co...

Three different reformulations of a free surface problem as shape optimization problems are considered. These give rise to three different cost functionals which apparently have not been exploited in literature. The shape derivatives of the cost functionals are explicitly determined. The gradient information is combined with the boundary variation method in a steepest descent algorithm to solve...

The 14 Minnesota density functionals published between the years 2005 and early 2016 are benchmarked on a comprehensive database of 4986 data points (84 data sets) involving molecules composed of main-group elements. The database includes noncovalent interactions, isomerization energies, thermochemistry, and barrier heights, as well as equilibrium bond lengths and equilibrium binding energies o...

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as fully lower semicontinuous closed convex-valued mappings that arise in variational analysis and optimization of integral functionals. The characterization allo...

We study the tail behavior of the distribution of certain subadditive functionals acting on the sample paths of L evy processes. The functionals we consider have, roughly speaking, the following property: only the points of the process that lie above a certain curve contribute to the value of the functional. Our assumptions will make sure that the process ends up eventually below the curve. Our...

We present an improvement over the Wang-Teter, Perrot, and Smargiassi-Madden kinetic-energy functionals without going beyond linear-response theory and without introducing a density-dependent kernel. The improved functionals were tested on bulk aluminum, and excellent results were obtained. Accurate densityfunctional calculations using the new functionals on systems larger than one can study by...

The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice. Two different types of aggregation functionals are introduced and investigated. We consider a target-based approach that has been studied in Decision Theory and we focus on the equivalence between a utility-based approach and target-based approach. Moreover we study a c...

Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. We prove general Donsker–Varadhan large deviation principles (LDP) for such functionals and show that the general result can be applied to prove LDPs for various particular functionals, including those concerned with random packing, nearest neighbor graphs, and lattice versions of the ...

In [10], Perelman discovered two important functionals, the F -functional and the W functional. The corresponding entropy functionals λ and ν are monotone along the Ricci flow ∂gij ∂t = −2Rij and constant precisely on steady and shrinking solitons. In [2], H.-D. Cao, R. Hamilton and T. Ilmanen presented the second variations of both entropy functionals and studied the linear stabilities of cert...