在对称群Sm中解循环方程组

本文研究了在对称群S_m中解循环方程组:x_mX_(m+1)…x_(ω+k-1)σ_m,其中σ_m∈S_m,ω=1,2,…,s,确定了这个循环方程组有解的充分必要条件和解的个数,而且给出了求解过程。     

A density functional theory computational study of the role of ligand on the stability of CuI and CuII species associated with ATRP and SET‐LRP

Atom transfer radical polymerization (ATRP) and single electron‐transfer living radical polymerization (SET‐LRP) both utilize copper complexes of various oxidation states with N‐ligands to perform their respective activation and deactivation steps. Herein, we utilize DFT (B3YLP) methods to determine the preferred ligand‐binding geometries for Cu/N‐ligand complexes related to ATRP and SET‐LRP. We find that those ligands capable of achieving tetrahedral complexes with Cu^I and trigonal bipyramidal with axial halide complexes with [Cu^IIX]⁺ have higher energies of stabilization. We were able to correlate calculated preferential stabilization of [Cu^IIX]⁺ with those ligands that perform best in SET‐LRP. A crude calculation of energy of disproportionation revealed that the same preferential binding of [Cu^IIX]⁺ results in increased propensity for disproportionation. Finally, by examining the relative energies of the basic steps of ATRP and SET‐LRP, we were able to rationalize the transition from the ATRP mechanism to the SET‐LRP mechanism as we transition from typical nonpolar ATRP solvents to polar SET‐LRP solvents. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4950–4964, 2007     

A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

Literal‐paraconsistent and literal‐paracomplete matrices

We introduce a family of matrices that define logics in which paraconsistency and/or paracompleteness occurs only at the level of literals, that is, formulas that are propositional letters or their iterated negations. We give a sound and complete axiomatization for the logic defined by the class of all these matrices, we give conditions for the maximality of these logics and we study in detail several relevant examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stereocontrol of diene polymers by topochemical polymerization of substituted benzyl muconates and their crystallization properties

We report the stereocontrol of diene polymers by the topochemical polymerization of alkoxy-substituted benzyl muconates in the solid state. A monomer stacking structure is controlled by the weak intermolecular interactions in the monomer crystals, depending on the structure and position of the alkoxy-substituent. The translational and alternating types of molecular stacking structures in a column provide diisotactic and disyndiotactic polymers, respectively, by the solid-state polymerization under UV and γ-ray irradiation. On the other hand, the meso and racemo structures of the resulting polymers are determined by the molecular symmetry of the used muconate monomers. The various substituted benzyl ester polymers are transformed into the same ethyl ester polymers with the four types of tacticities. The structure and crystallization behavior of the substituted benzyl ester polymers as well as the ethyl ester polymers have been revealed in detail. We clarify the effects of the tacticity on the crystallization property of the stereoregular polymuconates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4952–4965, 2006     

Thermochemically induced binding of methyl orange to polycations containing primary amine groups

The thermochemical transformation of electrostatically formed complexes of methyl orange (MO) with polycations containing primary amine groups such as ammonium salts afforded new polymers with a high concentration of covalently bound 4‐N,N‐dimethylaminoazobenzene groups in the side chain. Poly(allylamine hydrochloride) and poly(β‐aminoethylene acrylamide hydrochloride) were employed as support polycations for MO. The transformation of sulfonate–ammonium ion pairs into sulfonamide bonds, via heating at an elevated temperature, was supported by the polymer properties before and after the thermal treatment. The polymer structure changes were monitored with elemental analysis, Fourier transform infrared, ¹H NMR, and ultraviolet–visible absorption spectroscopy, and thermogravimetric analysis. The spacer length between the backbone and azobenzene structures used as side chains strongly influenced the polymer properties before and after the heat‐induced reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5898–5908, 2006     

Poly(ortho‐phenylene ethynylene)s: Synthetic accessibility and optical properties

Poly(ortho‐phenylene ethynylene)s (PoPEs) have been synthesized via an in situ activation/coupling AB′ polycondensation protocol. The resulting polymers have been characterized by several analytical methods and are shown to have no structural defects. Although the Sonogashira–Hagihara polycondensation reaction is less efficient than for the preparation of the corresponding meta‐ and para‐linked polymers, presumably because of steric hindrance caused by the ortho substituents, the process can be accelerated by the use of microwave irradiation. Optical spectroscopy indicates solvent‐dependent conformational changes between extended transoid and helical cisoid conformations, providing the first experimental evidence for solvophobically driven folding of the PoPE backbone. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1619–1627, 2006     

Design,synthesis, and characterization of main‐chain,aromatic polyesters based on 3,4‐ethylenedioxythiophene

A series of new thermoplastic polyesters based on 3,4‐ethylenedioxythiophene (EDOT) with flexible aliphatic spacers have been synthesized and characterized for the first time. The thermal properties of these polyesters based on EDOT are comparable to those of conventional polyesters based on the 1,4‐phenyl unit, indicating that EDOT is a viable replacement for the phenyl units. The glass‐transition and melting‐transition temperatures decrease monotonically with an increase in the spacer length. Theoretical calculations have revealed that the core angle for EDOT is comparable to that of unsubstituted thiophene and hence should be compatible with the formation of the mesophase. This has been confirmed experimentally by the synthesis of a main‐chain, thermotropic, liquid‐crystalline polyester based on EDOT that exhibits fluid birefringence. In fact, this is the first report in which a main‐chain, liquid‐crystalline polymer based on 3,4‐disubstituted thiophene has been successfully designed and synthesized. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3479–3486, 2006     

Mathematical modeling of crystallization analysis fractionation (Crystaf) of polyethylene

Four polyethylene samples (PE) with different molecular weight distributions (MWD) were analyzed by crystallization analysis fractionation (Crystaf) at several cooling rates to investigate the effect of MWD and cooling rate on their Crystaf profiles. Using these results, we developed a mathematical model for Crystaf that considers crystallization kinetic effects, which are ignored in all previous Crystaf models. The Crystaf model we proposed can fit the experimental Crystaf profiles of the 4 polyethylene resins very well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2749–2759, 2006     

USING A SYSTEM DYNAMICS APPROACH TO MODEL SUSTAINABILITY INDICATORS FOR IRRIGATION SYSTEMS IN AUSTRALIA

ABSTRACT. An indicator defined as a function of the total water diversion through the Coleambally canal and the potential irrigation demand is selected to represent the sustainability of the irrigation water system in the Coleambally irrigation area, Australia. A simulation procedure using a system dynamics approach was developed to evaluate the indicator. The procedure includes water diversion assessment, potential crop water demand and total gross margin. Three cases of water supply options (surface water, ground water pumping and water trading), two cases of changes in the total agricultural area and three cropping pattern scenarios were simulated to better understand their impact on sustainability. The simulated results indicate that increasing the agricultural area reduces the sustainability of the irrigation system because the demand of water increased despite increase in the gross margin. The scenarios show that imposed water trading and ground water pumping would considerably increase the supply system having a positive impact on the sustainability. The paper concludes that a multi‐objective sustainability indicator taking account of economic and environmental issues could be more useful.