Revisiting the Concentration Problem of Vector Fields within a Spherical Cap: A Commuting Differential Operator Solution

We propose a novel basis of vector functions, the mixed vector spherical harmonics that are closely related to the functions of Sheppard and Török and help us reduce the concentration problem of tangential vector fields within a spherical cap to an equivalent scalar problem. Exploiting an analogy with previous results published by Grünbaum, Longhi and Perlstadt, we construct a differential operator that commutes with the concentration operator of this scalar problem and propose a stable and convenient method to obtain its eigenfunctions. Having obtained the scalar eigenfunctions, the calculation of tangential vector Slepian functions is straightforward.     

Microstructure and performance of AZO thin films prepared by sol–gel processing

Al-doped zinc oxide (AZO) films were prepared by a wet-chemical coating technique, their microstructure and crystal growth were characterized as a function of the single layer thickness. When similar final thicknesses are attained by more multiple subsequent coating-firing cycles, film porosity is reduced from over 14 to 2 %. Simultaneously the AZO crystallite size is increased from approximately 23 to 60 nm, a preferential c-axis oriented growth is observed. Different substrates (soda-lime glass, soda-lime glass with a SiO₂ barrier coating, borosilicate glass and alkali-free display glass) were used and the resulting AZO films were compared. It is found that the substrate composition primarily affects grain growth and subsequently the electrical performance of the AZO films.     

Continuous loading of a conservative potential trap from an atomic beam

We demonstrate the fast accumulation of 52Cr atoms in a conservative potential from a guided atomic beam. Without laser cooling on a cycling transition, a dissipative step involving optical pumping allows us to load atoms at a rate of 2×10(7) s(-1) in the trap. Within less than 100 ms we reach the collisionally dense regime, from which we produce a Bose-Einstein condensate with subsequent evaporative cooling. This constitutes a new approach to degeneracy where Bose-Einstein condensation can be reached without a closed cycling transition, provided that a slow beam of particles can be produced.     

Tandem Anionic oxy‐Cope Rearrangement/Oxygenation Reactions as a Versatile Method for Approaching Diverse Scaffolds

Tandem anionic oxy‐Cope rearrangement/radical oxygenation reactions provide δ,?‐unsaturated α‐(aminoxy) carbonyl compounds, which serve as convenient precursors to diverse compound classes. Functionalized carbocycles are accessible by very rare all‐carbon 5‐endo‐trig cyclizations, but also common 5‐exo‐trig radical cyclizations, based on the persistent radical effect. The tandem reactions can be further extended by highly diastereoselective allylation or reduction steps to give complex scaffolds.     

Reference point approximation method for the solution of bicriterial nonlinear optimization problems

This paper presents a reference point approximation algorithm which can be used for the interactive solution of bicriterial nonlinear optimization problems with inequality and equality constraints. The advantage of this method is that the decision maker may choose arbitrary reference points in the criteria space. Moreover, a special tunneling technique is given for the computation of global solutions of certain subproblems. Finally, the proposed method is applied to a mathematical example and a problem in mechanical engineering.