Steiner and Schwarz symmetrizations, their most important relatives, the Minkowski, Minkowski-Blaschke, fiber, inner rotational, outer rotational are investigated. The focus is on convergence of successive symmetrals with respect to a sequence $i$-dimensional subspaces $\mathbb{R}^n$. Such called universal for family sets if any set in converge ball center at origin. New sequences main all vali...

Abstract We study the weak convergence order of two Euler-type discretizations log-Heston model where we use symmetrization and absorption, respectively, to prevent discretization underlying CIR process from becoming negative. If Feller index $\nu $ satisfies $\nu>1$, establish 1 $, while for \leq 1$, obtain -\epsilon $\epsilon>0$ arbitrarily small. illustrate our theoretical find...

c = c = c . (2) 1 We use the notation of Schouten [9]. Symmetrization over two indices is denoted by parentheses, A(ij) := (Aij + Aji)/2!, antisymmetrization by brackets, B[ij] := (Bij − Bji)/2!. The analogous is valid for more indices, as, e.g., in (13): c i[jk]l = (c − c)/2!. If one or more indices are exempt from (anti)symmetrization, they are enclosed by vertical bars, as, e.g., in (12), c ...

We re-investigate the image charge model of Iori and Corni (Iori and Corni, J. Comput. Chem. 2008, 29, 1656). We find that a simple symmetrization of their model allows to obtain quantitatively correct results for the electrostatic interaction of a water molecule with a metallic surface. This symmetrization reduces the magnitude of the electrostatic interaction to less than 10% of the total int...

The relationship between variable-metric methods derived by norm minimization and those derived by symmetrization of rank-one updates for sparse systems is studied, and an analogue of Dennis's nonsparse symmetrization formula derived. A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed. The sparse BFGS generated by this method...

Let M = (L , ∗) be a GL-monoid. An M-valued preordered set is an L-subset endowed with a reflexive and M-transitive L-relation, it is essentially a category enriched in a quantaloid generated by M. This paper presents a study of M-valued preordered sets with emphasis on symmetrization and the Cauchy completion. The main result states that symmetrization and the Cauchy completion of M-valued pre...

Based on permutation enumeration of the symmetric group and ‘generalized’ barycentric coordinates on arbitrary convex polytope, we develop a technique to obtain symmetrization procedures for functions that provide a unified framework to derive new Hermite-Hadamard type inequalities. We also present applications of our results to the Wright-convex functions with special emphasis on their key rol...