Spin mixing in colliding spinor condensates

F = 1 spinor condensates initially prepared in a double-well potential are studied in the mean field approach. First, the decoupling of the dipolar oscillation and the internal dynamics is presented. Second, the dynamical consequences of a small seed of m = 0 atoms on a system with initially well separated m = 1 and −1 condensates is explored. It is found that such a seed drives the dynamics of the m = ±1 condensates, thus departing dramatically from the behavior of binary mixtures. Original Text ? Astro, Ltd., 2009. The article is published in the original.     

Finite Laurent Developments and the Logarithmic Residue Theorem in the Real Non-analytic Case

This paper develops a general abstract non-holomorphic operator calculus under minimal regularity requirements on the family of operators through the concept of algebraic eigenvalue and the use of a, very recent, transversalization theory. Further, it analyzes under what conditions the inverse of a non-analytic family admits a finite Laurent development, and employs the new findings to calculate the multiplicity of a real non-analytic family through a logarithmic residue, so extending the applicability of the classical theory of I. C. Gohberg and coworkers. Applications to matrix families and Nonlinear Analysis are also explained.     

关于局部对称伪黎曼流形中的2-调和类空子流形

研究局部对称伪黎曼流形中的2-调和类空子流形,得到了这类子流形成为极大的Pinching现象及推广的J．Simons型积分不等式．     

Spatial versus non-spatial dynamics for diffusive Lotka–Volterra competing species models

This paper studies the dynamics of the diffusive Lotka–Volterra competition model under small dispersion rates and Dirichlet boundary conditions. Its main goal is ascertaining the connections between the qualitative behavior of the positive solutions of the parabolic model for small diffusions and the dynamics of its associated non-spatial model given by switching them off. After sharpening very substantially some previous results of Furter and López-Gómez (Proc R Soc Edinb 127A:281–336, 1997), we characterizes the singular limit, as diffusions go to zero, of any sequence of coexistence steady-state solutions. It turns out that they must approximate, point-wise in the inhabiting territory, the global attractor of the non-spatial model, uniformly on compact subsets of the habitat zones where a global hyperbolic attractor exist. As a very special consequence of our general theorem, the Dirichlet counterpart of the singular perturbation theorem of Hutson et al. (World Sci Ser Appl Anal 4:501–533, 1995) holds. Further, a multiplicity result is given when the underlying non-spatial model exhibits a founder control competition somewhere in the territory. This is the first multiplicity theorem available in the literature for small diffusivities.     

The singular perturbation problem for the periodic-parabolic logistic equation with indefinite weight functions

In this paper we investigate the singular perturbation problem for the periodic-parabolic logistic equation with indefinite weight functions subject to Dirichlet boundary conditions at the boundary. We show that the positive periodic solution of the diffusion model tends to the periodic solution of the purely kinetic model as the diffusion coefficient goes to zero, uniformly in time on compact subsets of the domain.On leave from the Math. Institut, Universität Zürich, Rämistrasse 74, CH-8001 Zürich, Switzerland.     

Nickel‐Catalyzed Chemo‐, Regio‐ and Diastereoselective Bond Formation through Proximal CC Cleavage of Benzocyclobutenones

The first catalytic intermolecular proximal C1? C2 cleavage of benzocyclobutenones (BCB) without prior carbonyl activation or employing noble metals has been developed. This protocol operates at room temperature and is characterized by an exquisite chemo‐, regio‐ and diastereoselectivity profile, constituting a unique platform for preparing an array of elusive carbocyclic skeletons.     

Synthesis of Diacyl Sulfides by Phase Transfer Catalysis

The symmetrical monothioanhydrides or diacyl sulfides have been synthesized by several methods. They are formed by acylation of free monothioacids or their anions¹, by acylation of potassium² or lithium³ sulfide, from the reaction of monothiocarboxylic acids with dicyclohexylcarbodiimide⁴ or by treatment of trimethylsilyl thiocarboxylates with acyl chlorides⁴. The recent publication about diacyl disulfides synthesis using phase transfer catalysis⁵ promted us to communicate our own results applying this technique to the preparation of the closely related diacyl sulfides. These compounds may be obtained by a more simple procedure than the published methods and in very high yields by the reaction of acylchlorides (1) with sodium sulfide nonahydrate in a solid-liquid system consisting of dichloromethane, the mentioned salt and hexadecyltributylphosphonium bromide as a phase transfer catalyst.     

New poly(phenylenevinylene)‐methyl methacrylate‐based photonic crystals

Monodisperse colloids have been prepared efficiently by copolymerization of methyl methacrylate and fluorescent first‐ and second‐generation poly(phenylenevinylene) dendrons under surfactant‐free emulsion polymerization conditions. The copolymers were characterized by UV–vis and fluorescence spectroscopy and size exclusion chromatography. Transmission electron microscopy revealed that the copolymers were microspheres with smooth surfaces and narrow dispersity. The bead diameter could be varied by changing the monomer/water ratio. The materials could be crystallized to give polymer opal photonic crystals. The emission was not affected by the periodic structure because of the large spectral distance between the emission and the pseudogap position. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2659–2665, 2010