Approximation of the Hausdorff distance by the distance of continuous surjections

The aim of this paper is to answer the following question: let (X,?) and (Y,d) be metric spaces, let A,B⊂Y be continuous images of the space X and let be a fixed continuous surjection. When is the inequality

     

A Trigonal‐Pyramidal Erbium(III) Single‐Molecule Magnet

Given the recent advent of mononuclear single‐molecule magnets (SMMs), a rational approach based on lanthanides with axially elongated f‐electron charge cloud (prolate) has only recently received attention. We report herein a new SMM, [Li(THF)₄[Er{N(SiMe₃)₂}₃Cl]?2 THF, which exhibits slow relaxation of the magnetization under zero dc field with an effective barrier to the reversal of magnetization (ΔE_eff/k_B=63.3 K) and magnetic hysteresis up to 3 K at a magnetic field sweep rate of 34.6 Oe s^?1. This work questions the theory that oblate or prolate lanthanides must be stabilized with the appropriate ligand framework in order for SMM behavior to be favored.     

Effect of high pressure on the organocatalytic asymmetric Michael reaction: highly enantioselective synthesis of γ-nitroketones with quaternary stereogenic centers

The significant effect of hydrostatic pressure on the difficult organocatalytic 1,4-conjugate addition of nitroalkanes to prochiral sterically congested β,β-disubstituted enones is demonstrated. This approach allows for the synthesis of γ-nitroketones containing quaternary stereogenic centers with good yields, excellent enantioselectivity, and low loading (1-5 mol %) of simple chiral primary amine catalysts.     

Evidence for magnetic anisotropy of [Nb(IV)(CN)8]4- in a pillared-layered Mn2Nb framework showing spin-flop transition

The first example of the [Nb(CN)(8)]-based pillared-layered-type framework system {[Mn(II)(2)(bpdo)(H(2)O)(4)][Nb(IV)(CN)(8)]·6H(2)O}(n) (bpdo = 4,4'-bipyridyl-N,N'-dioxide) has been obtained and characterized structurally and magnetically. The presented results provide the first evidence for substantial magnetic anisotropy of [Nb(IV)(CN)(8)].     

Theory Assessment and Final Theory Claim in String Theory

String theory has by now maintained a highly influential position in high energy physics for more than a quarter of a century. The present article analyses the reasons for the considerable trust exponents of string theory have in their theory even though it has neither found empirical confirmation nor a complete formulation up to this point. It is argued that this trust can be understood in terms of an emerging new conception of theory assessment that relies strongly on the identification of limitations to the underdetermination of scientific theory building. The second part of the paper makes the point that another conspicuous element of string theoretical reasoning, the prominent role of the notion of a final theory, can be understood in terms of this altered notion of theory assessment as well.     

Diffusion and aggregation of adatoms on faceted Pd/Mo(111) surface

Diffusion of Pd adatoms on faceted Pd/Mo(111) surface with hill and valley structure is studied by kinetic Monte Carlo method. The surface consists of {211} channeled facets separated by concave and convex edges. It is shown that diffusion on the faceted surface is significantly reduced with comparison to diffusion on (112) surface by the presence of concave edges. A simple formula for the diffusion coefficient is proposed. The growth of linear structures, studied at low coverage θ = 0.1, depends on the cross-channel diffusion, although the cross-channel diffusion coefficient is by 6–8 orders of magnitude smaller than the in-channel diffusion coefficient. We observed that most of atomic structures grow in valleys and the average size of the structure increases with increase of facet size.     

High-pressure accelerated asymmetric organocatalytic Friedel-Crafts alkylation of indoles with enones: application to quaternary stereogenic centers construction

An organocatalytic Friedel-Crafts alkylation of indoles with α,β-unsaturated ketones was found to be efficiently accelerated under high-pressure conditions with a low loading of chiral primary amine salts with good yield and enantioselectivity up to 90%. This approach also allows, for the first time, selected indole derivatives containing quaternary stereogenic centers to be obtained from prochiral β,β-disubstituted enones with an enantioselectivity up to 80%.