Coset extensions of <Emphasis Type=”Italic”>S</Emphasis>-sets

Summary Three weak variants of compactness which lie strictly between compactness and quasicompactness, are introduced. Their basic properties are studied. The interplay with mapping and their direct and inverse preservation under mappings are investigated. In the process three decompositions of compactness are observed.     

Free probability and the von Neumann algebrasof free groups

This short note summarizes the circumstances of the birth of free probability theory andsome of the recent achievements.     

The mesa problem for Neumann boundary value problem

In this paper, we study the singular limit of the Porous Medium equation u_t=Δu^m+g(x,u), as m→∞, in a bounded domain with Neumann boundary condition.     

CAP-子群与p-幂零性

设G是有限群。H是G的一个正规子群。P是|H|的一个素因子。P是H的一个Sylow p-子群。若下列条件之一满足。则H是p-幂零：1)P的极大子群都是G的CAP-子群且(|H|，P-1)=1；2)P的二次极大子群都是G的CAP-子群且(|H|，P^2-1)=1。特别地，若进一步假设G／H为P-幂零且(|G|，P-1)=1或(|G|，P^2-1)=1。则G自身亦为P-幂零。     

Equivariant Spectral Triples on the Quantum SU(2) Group

We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L ₂-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SU_q(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L ₂-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India.     

Preparation of macromonomers by copolymerization of methyl acrylate dimer involving β fragmentation

The unsaturated dimer of methyl acrylate [CH₂C(CO₂CH₃)CH₂CH₂CO₂CH₃, or MAD] was copolymerized with various monomers to prepare copolymers bearing the ω-unsaturated end group [CH₂C(CO₂CH₃)CH₂ ] arising from β fragmentation of the MAD propagating radical. Copolymerizations of MAD with cyclohexyl and n-butyl acrylate resulted in copolymers with ω-unsaturated end groups, and increasing the temperature up to 180 °C resulted in an increase in the rate of β fragmentation of MAD radicals relative to propagation. Only a small amount of unsaturated end groups was introduced by copolymerization with ethyl methacrylate (EMA), and the EMA content in the copolymer increased with temperature. These findings could be explained by the reversible addition of the poly(EMA) radical to MAD. The copolymerization with ethyl α-ethyl acrylate (EEA) did yield a copolymer containing unsaturated end groups with MAD units as part of the main chain, although the steric hindrance of the ethyl group suppressed homopropagation and crosspropagation of EEA, resulting in low polymerization rates. Therefore, the copolymerization of MAD with acrylic esters at high temperatures was noted as a convenient route for obtaining acrylate–MAD copolymers bearing unsaturated end groups at the ω end (macromonomer). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 597–607, 2004     

Synthesis,characterization, and biological activity of [2‐oxo‐2‐(4‐acetyl) phenyl amino] ethylene methacrylate and its derivatives

A new type of methacrylate monomer, [2‐oxo‐2‐(4‐acetyl) phenyl amino] ethylene methacrylate (APEMA), was synthesized. The oxime, 2,4‐dinitrophenylhydrazone, and thiosemicarbazone derivatives of poly{[2‐oxo‐2‐(4‐acetyl) phenyl amino] ethylene methacrylate} [poly(APEMA)] were prepared with hydroxylamine hydrochloride, 2,4‐dinitrophenylhydrazine, and thiosemicarbazone hydrochloride, respectively. The radical homopolymerization of APEMA was performed at 65 °C in a 1,4‐dioxane solution with benzoyl peroxide as an initiator. The monomer and its homopolymer were characterized with Fourier transform infrared and NMR techniques. The thermal stabilities of poly(APEMA) and its derivatives were investigated with thermogravimetric analysis and differential scanning calorimetry. The ultraviolet stability of the polymers were compared. The solubility and inherent viscosity of the polymers were also determined. The number‐average and weight‐average molecular weights and polydispersity index of the polymers were determined with gel permeation chromatography. The antibacterial and antifungal effects of the monomer and the polymer and its derivatives were also investigated on various bacteria and fungi. The activation energies of the thermal degradation of the polymers were calculated with the Ozawa method. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3157–3169, 2004     

Novel,organosoluble, light‐colored fluorinated polyimides based on 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)biphenyl or 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)‐1,1′‐binaphthyl

Two series of fluorinated polyimides were prepared from 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)biphenyl ( 2 ) and 2,2′‐bis(4‐amino‐2‐trifluoromethylphenoxy)‐1,1′‐binaphthyl ( 4 ) with various aromatic dianhydrides via a conventional, two‐step procedure that included a ring‐opening polyaddition to give poly(amic acid)s, followed by chemical or thermal cyclodehydration. The inherent viscosities of the polyimides ranged from 0.54 to 0.73 and 0.19 to 0.36 dL/g, respectively. All the fluorinated polyimides were soluble in many polar organic solvents, such as N,N‐dimethylacetamide and N‐methylpyrrolidone, and afforded transparent and light‐colored films via solution‐casting. These polyimides showed glass‐transition temperatures in the ranges of 222–280 and 257–351 °C by DSC, softening temperatures in the range of 264–301 °C by thermomechanical analysis, and a decomposition temperature for 10% weight loss above 520 °C both in nitrogen and air atmospheres. The polyimides had low moisture absorptions of 0.23–0.58%, low dielectric constants of 2.84–3.61 at 10 kHz, and an ultraviolet–visible absorption cutoff wavelength at 351–434 nm. Copolyimides derived from the same dianhydrides with an equimolar mixture of 4,4′‐oxydianiline and diamine 2 or 4 were also prepared and characterized. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2416–2431, 2004     

The large scale topology and algebraic K-theory of arithmetic groups

New compactifications of symmetric spaces of noncompact type X are constructed using the asymptotic geometry of the Borel–Serre enlargement. The controlled K-theory associated to these compactifications is used to prove the integral Novikov conjecture for arithmetic groups.