On the normalized eigenvalue problems for nonlinear elliptic operators

This paper solves the following form of normalized eigenvalue problem:

     

Analytic Extension of Functions from Analytic Hilbert Spaces

Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd).     

New segmented poly(ester‐urethane)s from renewable resources

The physical and mechanical properties of aliphatic homopolyesters from monomers obtainable from renewable resources, namely, 1,3‐propanediol and succinic acid, were improved by their combination with aromatic urethane segments capable of establishing strong intermolecular hydrogen bonds. Segmented poly(ester‐urethane)s were synthesized from dihydroxy‐terminated oligo(propylene succinate)s chain‐extended with 4,4′‐diisophenylmethane diisocyanate. The newly synthesized materials were exhaustively characterized by ¹H NMR spectroscopy, size exclusion chromatography, differential scanning calorimetry, dynamic mechanical analysis, and with respect to their main static mechanical properties, an Instron apparatus was used. The average repeat number of the hard segments, evaluated by NMR, ranged from 4 to 9, whereas that of the flexible segments was about 14. The degree of crystallinity, glass‐transition temperature, melting point, tensile strength, elongation, and Young's modulus were influenced by the ratio between hard and soft segments of the segmented copolymer in a predictable way. The results demonstrated that poly(ester‐urethane)s from 1,3‐propanediol and succinic acid are promising thermoplastics. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 630–639, 2001     

A method for establishing generalized variational principle

A method for establishing generalized variational principle is proposed in this paper. It is based on the analysis of mechanical meaning and it can be applied to problems in which the variational principles are needed but no corresponding variational principle is available. In this paper, the Hu-Washizu ’s generalized variational principle and the Hu’s generalized principle of complementary energy are derived from the mechanical meaning instead of from the generalization of the principle of minimum potenlial energy and the correct proofs of these two generaleed variational principles are given. It is also proved that this is wrong if one beleives that σ_ij, e_ij and ui are independent variables each other based on the reason that these three kinds of variables are all contained in these two generalized variational principles. The condition of using these two variational principles in a correct manner is also explained.     

Singular point perturbation of an odd operator in ℤ2-Graded space

In the paper we study supersymmetric models for point interaction perturbations of operators of Dirac type and their spectral properties. Such models are considered in the class of odd self-adjoint operators in ℤ₂-graded Pontryagin space. We present in detail the previously considered realization method of strongly singular perturbation by means of their embedding into the theory of self-adjoint extensions. We describe odd self-adjoint extensions of odd symmetric operators with deficiency indices (1,1) in ℤ₂-graded Pontryagin space and squares of such extensions using Krein’s formula for the resolvent. The results obtained are refined in application to singular perturbations of odd self-adjoint differential operators. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 924–940, December, 1999.     

Carboxyl Terminated Polymer Chain Extension Using a Bisoxazoline Coupling Agent: Monte Carlo Simulation

Summary: The kinetics of the chain extension reaction of a carboxyl‐terminated polymer using a bisoxazoline coupling agent was simulated by the Monte Carlo method based on the master equation. The effects of temperature and stepwise addition of the chain extender was examined. A comparison between simulated results and those calculated by an amended kinetic model was made. The results show that the highest coupling efficiency and the highest can be obtained when the initial concentrations of carboxyl and oxazoline groups are equal, which is in good agreement with the experiments. It is found that a higher reaction temperature could lead to a bigger coupling efficiency, a higher and narrower MWDs. The stepwise addition of the chain extender can only postpone the chain extension reaction, but cannot affect the final coupling efficiency and the MWDs when the concentration of the oxazoline group is lower than that of the carboxyl group. However, stepwise addition of the chain extender favors bigger coupling efficiency and narrower MWDs when the concentration of the oxazoline group exceeds that of the carboxyl group.

The relationship among three group of polymers, r and ratios of k₂ to k₁. The dots are the data simulated by MC and solid lines are relative data calculated by the kinetic model.     

Synthesis and properties of thermally reversible polyesters

Thermally reversible polyesters were obtained by the ester formation reaction of thermoplastic polyesters with hydroxyl end groups and the diacid anhydride of tetra carboxylic acid as a thermally reversible chain extender. Typical example of the thermally reversible polyesters was obtained by the reaction of PBT (polyburylene terephthalate) and PMA (pyromellitic dianhydride). This material having twice as large molecular weight as the original PBT exhibited almost the same melt viscosity as the original. Also that thermally reversible chain extension reaction occurred without unfavorable side reaction such as cross-linking. This material shows both good processability and superior mechanical properties due to its thermally reversible characters.     

SIR phasing by combination of SOLVE/RESOLVE and dual-space fragment extension involving OASIS

A new phasing procedure has been proposed for dealing with single isomorphous replacement (SIR) x-ray diffraction data. The procedure combines {SOLVE/RESOLVE} with the dual-space fragment extension involving {OASIS}. Two sets of SIR data at 0.28~nm resolution taken from the protein (R)-phycoerythrin (PDB code: 1LIA) were used in the test. For one of the two SIR data sets, a default run of {SOLVE/RESOLVE} based on the heavy-atom substructure found by {SHLEXD} led automatically to an interpretable electron density map. {OASIS} could not effectively improve the result. For the other set of SIR data, {SOLVE/RESOLVE} resulted in a fragmented model consisting of 454 of the total 668 residues, in which only 29 residues were docked into the sequence. Based on this model, 7 iteration cycles of {OASIS-DM-RESOLVE} (build only) yielded automatically a model of 547 residues with 133 residues docked into the sequence. The overall-averaged phase error decreased considerably and the quality of electron density map was improved significantly. Two more cycles of iterative {OASIS}-{DM}-{RESOLVE} were carried out, in which the output phases and figures of merit from {DM} were merged with that from the original run of {SOLVE/RESOLVE} before they were passed onto {RESOLVE} (build only). This led automatically to a model containing 452 residues with 173 docked into the sequence. The resultant electron density map is manually traceable. It is concluded that when results of {SOLVE/RESOLVE} are not sufficiently satisfactory, the combination of {SOLVE/RESOLVE} and {OASIS}-{DM}-{RESOLVE} (build only) may significantly improve them.     

区间有限元方法及其在抗滑稳定性分析中的应用

通过区间值函数和实值函数的关系探讨了区间相关性导致的区间扩张的问题,给出了保证区间计算获得足够精度的计算方法;提出了基于单元的子区间摄动有限元计算方法,并给出了提高计算效率的一些方法和获得较好计算精度时的子区间数目的近似计算公式．结合工程实例,基于单元的子区间有限元方法和抗滑稳定性分析方法给出了稳定性的区间范围,为更合理地估计和评价结构的抗滑稳定性提供一定的依据．     

Preparation and properties of aniline chain-extended thermoplastic epoxy resin using triphenylphosphine as catalyst

Thermoplastic resins have been widely used in fiber reinforced polymer composites because of its recyclability and short cycle times. However, the high viscosity after heating and melting restricts its infiltration on the surface of fiber. In this study, a series of thermoplastic epoxy resins were prepared via the chain extension reaction of epoxy groups with liquid aniline using triphenylphosphine (TPP) as catalyst. The relationship between polymer network structure and performance was comprehensively investigated. The solubility tests indicated that excessive aniline or TPP facilitated the crosslinking of resins. Besides, on the premise of thermoplasticity, appropriate TPP could increase the degree of chain extension, molecular weight, and glass transition temperature of resins. Furthermore, the in-situ polymerization process facilitated infiltration between epoxy resin and the fibers before chain extension reaction. The bending test showed that the flexural performance of the sample with 2 phr of TPP was improved by 38.8%. Therefore, this work provides a feasible method to prepare the thermoplastic epoxy resins and its fiber-reinforced composites with good mechanical properties.