On Optimal Lattice Decompositions

A lattice decomposition lemma by H. Rosenthal is given an optimal refinement, both in the real and in the complex valued setting.     

A monotone finite volume scheme for advection–diffusion equations on distorted meshes

A new monotone finite volume method with second‐order accuracy is presented for the steady‐state advection–diffusion equation. The method uses a nonlinear approximation for both diffusive and advective fluxes that guarantee the positivity of the numerical solution. The approximation of the diffusive flux is based on nonlinear two‐point approximation, and the approximation of the advective flux is based on the second‐order upwind method with proper slope limiter. The second‐order convergence rate for concentration and the monotonicity of the nonlinear finite volume method are verified with numerical experiments. Copyright © 2011 John Wiley & Sons, Ltd.     

Direct Visualisation of the Surface Atomic Active Sites of Carbon-Supported Co3O4 Nanocrystals via High-Resolution Phase Restoration

The atomic arrangement of the terminating facets on spinel Co₃O₄ nanocrystals is strongly linked to their catalytic performance. However, the spinel crystal structure offers multiple possible surface terminations depending on the synthesis. Thus, understanding the terminating surface atomic structure is essential in developing high-performance Co₃O₄ nanocrystals. In this work, we present direct atomic-scale observation of the surface terminations of Co₃O₄ nanoparticles supported on hollow carbon spheres (HCSs) using exit wavefunction reconstruction from aberration-corrected transmission electron microscopy focal-series. The restored high-resolution phases show distinct resolved oxygen and cobalt atomic columns. The data show that the structure of {100}, {110}, and {111} facets of spinel Co₃O₄ exhibit characteristic active sites for carbon monoxide (CO) adsorption, in agreement with density functional theory calculations. Of these facets, the {100} and {110} surface terminations are better suited for CO adsorption than the {111}. However, the presence of oxygen on the {111} surface termination indicates this facet also plays an essential role in CO adsorption. Our results demonstrate direct evidence of the surface termination atomic structure beyond the assumed stoichiometry of the surface.     

On the dominated convergence theorem for the Kurzweil–Stieltjes integral

This paper is concerned with a version of the Lebesgue dominated convergence theorem (DCT) which has been stated for the Kurzweil–Stieltjes integral of real functions. Our objective in this work is to analyze the extension of this result to include vector functions with values in Banach spaces. We establish that the mentioned convergence theorem for the Kurzweil–Stieltjes integral can be formulated in weaker versions for reflexive and separable Banach spaces, and spaces having the Schur property, nonetheless it is not verified in the general case.     

Conditions for dominated splittings

In this paper, we solve the problem proposed by Lan Wen for the case of dimM = 3. Roughly speaking, we prove that for fixed i, f has C1 persistently no small angles of index i if and only if f has a dominated splitting of index i on the C1 i-preperiodic set P＊i（f）.     

A note on: Quasi-linear quotients and shellability of pure simplicial complexes

The purpose of this note is to point out a careless error in the algebraic criterion of shellability of a pure simplicial complex Δ given in [1 Anwar, I., Raza, Z. (2015). Quasi-linear quotients and shellability of pure simplicial complexes. Commun. Algebra 43:4698–4704.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]].     

A posteriori error estimates of constrained optimal control problem governed by convection diffusion equations

In this paper, we study a posteriori error estimates of the edge stabilization Galerkin method for the constrained optimal control problem governed by convection-dominated diffusion equations. The residual-type a posteriori error estimators yield both upper and lower bounds for control u measured in L ²-norm and for state y and costate p measured in energy norm. Two numerical examples are presented to illustrate the effectiveness of the error estimators provided in this paper.      

Facets of the independent set polytope

Theoretical results pertaining to the independent set polytope P^ISP=conv{x{0,1}ⁿ:Axb} are presented. A conflict hypergraph is constructed based on the set of dependent sets which facilitates the examination of the facial structure of P^ISP. Necessary and sufficient conditions are provided for every nontrivial 0-1 facet-defining inequalities of P^ISP in terms of hypercliques. The relationship of hypercliques and some classes of knapsack facet-defining inequalities are briefly discussed. The notion of lifting is extended to the conflict hypergraph setting to obtain strong valid inequalities, and back-lifting is introduced to strengthen cut coefficients. Preliminary computational results are presented to illustrate the usefulness of the theoretical findings.Mathematics Subject Classification (2000): 90C11, 90C57, 90C35     

Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory

Let {X _k , 1 k n} be n independent and real-valued random variables with common subexponential distribution function, and let {k, 1 k n} be other n random variables independent of {X _k , 1 k n} and satisfying a _k b for some 0 < a b < for all 1 k n. This paper proves that the asymptotic relations P (max_{1 m n k=1} ^m _k X _k > x) P (sum _k=1 ⁿ _k X _k > x) sum _k=1 ⁿ P ( _k X _k > x) hold as x . In doing so, no any assumption is made on the dependence structure of the sequence { _k , 1 k n}. An application to ruin theory is proposed.