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.     

Analysis and Prbability over Infinite Extensions of a Local Field

We consider an infinite extension K of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. K is equipped with an inductive limit topology; its conjugate K; is a completion of K with respect to a topology given by certain explicitly written semi-norms. We construct and study a Gaussian measure, a Fourier transform, a fractional differentiation operator and a cadlag Markov process on K. If we deal with Galois extensions then all these objects are Galois-invariant.     

弦图扩张与最优排序

弦图是一类特殊的完美图,以具有完美消去顺序为特征．由弦图扩张引出一系列序列性组合优化问题,沟通了图论、数值分析及最优排序等领域的若干研究课题．本文将论述我们的一些观点和研究结果．     

Kan Extensions of Internal Functors. Algebraic Approach

We investigate the question of the Kan extension in the case when all categories and functors are internal in the category of groups. Under certain assumptions we establish the necessary and sufficient conditions for the existence of internal Kan extensions. Questions related to this problem are also discussed.     

A N. Bourbaki type General Theory and the Properties of Contracting Symbols and Corresponding Contracted Forms

A system of contracting symbols is introduced for a N. Bourbaki type general mathematical theory corresponding to a general classical mathematical theory T.