We develop a numerical method for solving shape optimization of functionals involving Steklov eigenvalues and apply it to the problem maximization k-th eigenvalue, under volume constraint. A similar study in planar case was already addressed literature using boundary integral equation method. Here we extend that 3D 4D cases, Method Fundamental Solutions as forward solver.

 ‎In this paper we study the existence of nontrivial‎ solutions for a variational inequality on the half-line‎. ‎Our‎ ‎approach is based on the non-smooth critical point theory‎ ‎for Szulkin-type functionals.

In this work, we dissect the performance of  two modern Perdew-Burke-Ernzerhof (PBE)-based double-hybrid (DH) density functionals to predict the isotropic and anisotropic polarizabilities of water nanoclusters (H2O)n [n = 2-6]. The considered models include the cubic integrand (CI) and quadratic integrand (QI) functions as well as the spin-opposite-scaled...

Abstract Let $B^n\subset \mathbb{R} ^{n}$ and $\mathbb{S} ^n\subset ^{n+1}$ denote the Euclidean $n$-dimensional unit ball sphere, respectively. The extrinsic $k$-energy functional is defined on Sobolev space $W^{k,2}\left (B^n,\mathbb{S} ^n \right )$ as follows: $E_{k}^{{\textrm{ext}}}(u)=\int _{B^n}|\Delta ^s u|^2\ dx$ when $k=2s$, _{B^n}|\nabla \Delta $k=2s+1$. These energy functionals are a...

Flow equations describe the evolution of the effective action Γk in the process of varying an infrared cutoff k. The presence of the infrared cutoff explicitly breaks gauge and hence BRS invariance. We derive modified Slavnov-Taylor identities, which are valid for nonvanishing k. They guarantee the BRS invariance of Γk for k → 0, and hence allow the study of non-abelian gauge theories by integr...

A generalization of the the flat extension theorems of Curto and Fialkow and Laurent and Mourrain is obtained by seeing the problem as one of ideal projection. Some other results on ideal projection are generalized, and it is seen that a linear functional on the k-variate polynomials over C is finitely atomic if and only if its moment matrix has finite rank, a fact previously known for positive...

We present a characterization of the approximation errors of the PostWidder and the Gamma operators in Lp(0,∞), 1 ≤ p ≤ ∞, with a weight x0(1 + x)γ∞−γ0 with arbitrary real γ0, γ∞. Two types of characteristics are used – weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on simple modifications of it. 2000 Mathematics Subject Classi...

For R or T , a strong converse inequality of type A (in the terminology of Ditzian and Ivanov (J. Anal. Math. 61 (1993) 61)) is obtained for the high order averages on balls and the K-functionals generated by the high order Laplacian, which answers a problem raised by Ditzian and Runovskii (J. Approx. Theory 97 (1999) 113). © 2004 Elsevier Inc. All rights reserved. MSC: Primary 41A25; 41A50

A lemma of Micchelli’s, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback’s more recent extension of this lemma and Schaback’s result concerning interpolation by radial polynomials. Schaback’s interpolant is explored. In his most-cited paper, [M], Micchelli supplies the following interesting auxiliary lemma (h...

Properties of increasing-weakly lower semicontinuous (LSC) sublinear functionals on the positive cone L 1 + are of importance for study miscellaneous non-controlled factors from a uniied viewpoint based on the notion of sublinear expectation 3, 4 and 5]. For every such functional N there are deened the class is proved and their description is given. The orders induced in L 11 by convex cones co...