Self-dual Chern–Simons Vortices on Bounded Domains

In this Letter we consider the Abelian Chern–Simons vortices on a bounded simply connected domain. We establish the existence of solutions for the self-duality equations. We prove the uniqueness of solutions when all the vortex points are equal and the domain is star-shaped. We also show the radial symmetry of solutions on balls centered at the vortex point.     

On Vortex Dynamics in the Self-Dual Chern–Simons–Higgs System

The dynamics of n vortices in the self-dual Chern–Simons–Higgs system defined on the infinite plane is investigated. In adiabatic approximation, the vortex dynamics is determined by considering a rigid motion of a vortex configuration and a motion around a fixed center of mass. A motion of two vortices is studied in detail.     

全氟二异丙基膦酸锂的合成及其电化学性能研究

以合成的氯代二异丙基膦为原料, 利用电化学全氟化方法, 得到全氟二异丙基膦酸锂(Li[(C3F7)2PF4]), 并对其物理和电化学性能进行了研究.     

电化学氟化的新进展

电化学氟化是利用电极反应将氟直接引入有机或无机物的一种重要方法。有机物的电化学氟化方法有两种: 一是Simons于1941年发明的, 用镍作阳极, 在无水氟化氢溶液中, 电解制备全氟化合物的方法。此方法在近年来有不少改进。另一是1970年Rozhkov提出的, 以有机溶剂(如含Et3N.3HF的MeCN)为介质, 在铂阳极上,氧化得到单氟化产物的方法。本文全面地综述了这两种方法, 并着重于最新民发展。     

Simons electrochemical fluorination of substituted homopiperazines(hexahydro-1,4-diazepines) and piperazines

Simons electrochemical fluorination (ECF) of 1,4-dimethyl-1,4-homopiperazine, methyl 4-ethylhomopiperazin-1-ylacetate and 1,4-bis(methoxycarbonylmethyl)-1,4-homopiperazine was studied. For comparison, ECF of three piperazines with a N-(methoxycarbonylmethyl) group(s) was also studied. ECF of 1,4-dimethyl-1,4-homopiperazine gave a low yield of corresponding perfluoro(1,4-dimethyl-1,4-homopiperazine) together with perfluoro(2,6-diaza-2,6-dimethylheptane) as the major product. Corresponding perfluoro(homopiperazines) with mono- and/or di-(fluorocarbonyldifluoromethyl) groups [CF₂C(O)F] at the 1- and/or 4-position were formed in low yields from methyl 4-ethylhomopiperazin-1-ylacetate and 1,4-bis(methoxycarbonylmethyl)-1,4-homopiperazine, respectively. These new seven-membered perfluoro(1,4-dialkyl-1,4-homopiperazines) were accompanied by the formation of mono- and/or di-basic linear perfluoroacid fluorides resulting from the CC bond scission at the 2- and 3-positions of the ring. From mono- and/or di-N-(methoxycarbonylmethyl)-substituted piperazines, corresponding perfluoropeperazines having the acid fluoride group(s) were formed in low yields.     

Electrochemical fluorination of N,N-dimethylperfluoroacylamides

The electrochemical fluorination (ECF) of N,N-dimethylperfluoroacylamides gives the corresponding perfluoro-N,N-dimethylacylamides in low yield. With increase of the number of carbon atoms in the perfluoroacyl radical the yield of the required perfluoro-N,N-dimethylacylamides is slightly increased.     

Calderon Projector for the Hessian of the Perturbed Chern-Simons Function on a 3-Manifold with Boundary

The existence and continuity for the Calderón projectorof the perturbed odd signature operator on a 3-manifold is established.As an application we give a new proof of a result of Taubesrelating the modulo 2 spectral flow of a family of operatorson a homology 3-sphere with the difference in local intersectionnumbers of the character varieties coming from a Heegard decomposition.2000 Mathematics Subject Classification 57M27 (primary), 58J32(secondary).     

Global existence for a nonlinear Schroedinger–Chern–Simons system on a surface

Global existence of regular solutions for a nonlinear Schroedinger–Chern–Simons system of equations on a two-dimensional compact Riemannian manifold is proved.     

Existence of self-dual non-topological solutions in the Chern–Simons Higgs model

In this paper we investigate the existence of non-topological solutions of the Chern–Simons Higgs model in R². A long standing problem for this equation is: Given N vortex points and β>8π(N+1), does there exist a non-topological solution in R² such that the total magnetic flux is equal to β/2? In this paper, we prove the existence of such a solution if . We apply the bubbling analysis and the Leray–Schauder degree theory to solve this problem.