The existence of non-topological solitons in the self-dual Chern-Simons theory

In the recently discovered (2+1)-dimensional relativistic Chern-Simons model, self-duality can be achieved when the Higgs potential density assumes a special form for which both the asymmetric and symmetric vacua are ground state solutions. This important feature may imply the coexistence of static topological and non-topological vortex-like solutions inR ² but the latter have been rather elusive to a rigorous construction. Our main purpose in this paper is to prove the existence of non-topological radially symmetricN-vortex solutions in the self-dual Chern-Simons model. By a shooting method, we obtain a continuous family of gauge-distinctN-vortex solutions. Moreover, we are also able to classify all possible bare (or 0-vortex) solutions.     

A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

Syntheses and properties of 4-hydroxy-3,5-dibromobenzyl phosphonates and their flame-retarding effects on ABS copolymer

4-Hydroxy-3,5-dibromobenzyl phosphonates (HDBBP) were synthesized by reacting phosphites with 4-hydroxy-3,5-dibromobenzyl bromide (HDBBB) which was prepared in advance by photobromination of 2,6-dibromo-p-cresol (DBPC) produced by bromination of p-cresol. In the reactions between HDBBB and phosphites, the rate of formation of dimethyl 4-hydroxy-3,5-dibromobenzyl phosphonate (HDBBP_m) was greater than that of diphenyl 4-hydroxy-3,5-dibromobenzyl phosphonate (HDBBP_P); however, quantitative yields for both products were obtainable. The addition of HDBBP as bromine and phosphorus containing flame-retardants to ABS copolymer showed better results than the addition of the same amount of brominated compound, or mixtures of both two compounds. It was also proved that compound containing both bromine and phosphorus exhibited more apparent synergistic effects on flame retardancy than the mixtures of brominated compound and phosphorous containing compound     

Synthesis of monodisperse polymers from proteins

Proteins are functional biopolymers; viewed as molecules, they are also monodisperse polyamides with chemically reactive side chains. This paper describes the use of proteins as starting materials for the synthesis of monodisperse polymers with nonbiological functionalities attached to the side chains. It demonstrates the complete derivatization of amine groups (lysine side chains and N-termini) on three different proteins by addition of activated carboxylate reagents in aqueous solutions containing sodium dedecyl sulfate (SDS), under denaturing conditions. Several different acylating reagents were used to generate derivatized proteins; the resulting compounds constitute a new class of monodisperse, semisynthetic polymers, having the potential for wide variation in the structure of the backbone and of the side chains. Modification of lysozyme on a gram scale demonstrated that the method can generate useful quantities of material.     

Comparative studies of the photoinduced reactions in the Mg+-SCNC2H5 and Mg+-NCSC2H5 complexes

The photoinduced reactions of the complexes Mg+-SCNC2H5 and Mg+-NCSC2H5 are studied comparatively in the spectral range of 230-440 nm. One-photon excitation of the complexes through the Mg+ chromophore (3 2P <-- 3 2S) gives rise to the evaporative fragment as well as the molecular activation and charge transfer products. The action spectra of the complexes consist of three broad peaks for Mg+-SCNC2H5 and two for Mg+-NCSC2H5, which accord with the structures obtained from quantum mechanics calculations. These calculations reveal two association isomers for Mg+-SCNC2H5: one is with Mg+ being linked to the S atom and the other to the N atom. The former is more stable than the latter by only 0.23 eV. Both of the isomers have been shown to exist in the complex source employed in our experiments. On the other hand, only one stable structure is found for the complex Mg+-NCSC2H5 characterized by the Mg+-N linkage. In general, the photofragments are dominated by Mg+ at lambda > 400 nm, which decreases with decreasing wavelength accompanied by the increase in other photoproducts. In addition, the branching ratios of Mg+ to other photoproducts are nearly constant in the short wavelength region but decrease with decreasing wavelength. The observed photoreactions have been reasonably explained.