Variational principles have become quite popular in the design of free form surfaces. Among others they are used for fairing purposes. The choice of the ‘right’ fairness functional is a crucial step. There is always a tradeoff between high quality and computational effort. I n this paper we present fairness functionals that allow fairing efficiently, i.e., produce high quality surfaces in a rea...

Different extensions of an isomorphism theorem of Dynkin are developed and are used to study two distinct but related families of functionals of Lévy processes; n-fold “near-intersections” of a single Lévy process and continuous additive functionals of several independent Lévy processes. Intersection local times for n independent Lévy processes are also studied. They are related to both of the ...

The performance of conjugate gradient schemes for minimizing unconstrained energy functionals in the context of condensed matter electronic structure calculations is studied. The unconstrained functionals allow a straightforward application of conjugate gradients by removing the explicit orthonormality constraints on the quantum-mechanical wave functions. However, the removal of the constraints...

We show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition, are strictly convex in the sense of displacement convexity under a natural change of variables. We use this to show that in certain cases, the only critical points of these functionals are minimizers. This approach based on displacement convexity permits us ...

‎In this paper‎, ‎by using four functionals fixed point theorem‎, ‎we obtain sufficient conditions for the existence of‎ ‎at least one positive solution of an $n$th-order $m$-point boundary value problem‎. ‎As an application‎, ‎we give an example to demonstrate our main result.

‎We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces‎. ‎Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), ge...

The system of Gegenbauer polynomials fC n (x); n = 0; 1; : : :g is a classical family of polynomials orthogonal with respect to the weight function ! (x) = (1?x 2) ? 1 2 on the support interval ?1; +1]. Integral functionals of Gegenbauer polynomials with kernel f(x))C n (x)] 2 ! (x), where f(x) is an arbitrary function which does not depend on n or , are considered in this paper. Firstly, a gen...