Evans functions and bifurcations of standing wave solutions in delayed synaptically coupled neuronal networks

Consider the following nonlinear singularly perturbed system of integral differential equations &\frac{\partial u}{\partial t}+f(u)+w\\ =&(\alpha-au)\int^{\infty}_0\xi(c)\left[\int_{\mathbb R}K(x-y) H\left(u\left(y,t-\frac1c|x-y|\right)-\theta\right){\rm d}y\right]{\rm d}c\\ &+(\beta-bu)\int^{\infty}_0\eta(\tau)\left[\int_{\mathbb R}W(x-y)H\big(u(y,t-\tau)-\Theta\big){\rm d}y\right]{\rm d}\tau,\\ &\frac{\partial w}{\partial t}=\varepsilon[g(u)-w], and the scalar integral differential equation &\frac{\partial u}{\partial t}+f(u)\\ =&(\alpha-a u)\int^{\infty}_0\xi(c)\left[\int_{\mathbb R}K(x-y) H\left(u\left(y,t-\frac1c|x-y|\right)-\theta\right){\rm d}y\right]{\rm d}c\\ &+(\beta-bu)\int^{\infty}_0\eta(\tau)\left[\int_{\mathbb R}W(x-y)H\big(u(y,t-\tau)-\Theta\big){\rm d}y\right]{\rm d}\tau. There exist standing wave solutions to the nonlinear system. Similarly, there exist standing wave solutions to the scalar equation. The author constructs Evans functions to establish stability of the standing wave solutions of the scalar equation and to establish bifurcations of the standing wave solutions of the nonlinear system.     

Synthetic Strategies to Combine High Performance Benzoxazine Thermosets with Polymers

Summary: Polybenzoxazines are newly developed thermosetting polymers exhibiting versatility in a wide range of applications including electronics and aerospace industries. They exhibit highly competitive combination of properties compare to the conventional thermosets. In this paper we present synthetic strategies to incorporate thermally curable benzoxazine functions into polymers as main and side chain groups in order to further improve various properties. The strategies successfully employed include monomer synthesis, macromonomer method, polycondensation, oxidative polymerization, photo-polymerization, click chemistry and hydrosilylation processes. In the case of macromononomer method functional initiators were used in various controlled/living polymerizations to give polymers with benzoxazine end groups. The thermal curing behaviors of the obtained polymers were also demonstrated.     

Asymptotic behaviour of a two‐dimensional differential system with non‐constant delay

The asymptotic behaviour and stability properties are studied for a real two‐dimensional system x^′(t) = A(t)x (t) + B(t)x (θ (t)) + h (t, x (t), x (θ (t))), with a nonconstant delay t ‐ θ (t) ≥ 0. It is supposed that A,B and h are matrix functions and a vector function, respectively. The method of investigation is based on the transformation of the considered real system to one equation with complex‐valued coefficients. Stability and asymptotic properties of this equation are studied by means of a suitable Lyapunov‐Krasovskii functional. The results generalize the great part of the results of J. Kalas and L. Baráková [J. Math. Anal. Appl. 269 , No. 1, 278–300 (2002)] for two‐dimensional systems with a constant delay (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A class of delayed renewal risk processes with a threshold dividend strategy

This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Cerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.     

一类出现在电力系统中的时滞微分方程概周期解的存在唯一性

本文结合运用压缩映射原理,研究一类出现在电力系统中的非线性时滞微分方程的概周期解,所得结果具有实际意义。     

Cross-linked thermoplastic blends of polyethylene with an elastomer 4. Thermorelaxation and adhesion characteristics

The results of an experimental investigation of changes in the thermorelaxation and thermoshrinkage stresses and the strength of adhesion joints with steel of binary blends of high-density polyethylene with an elastomer (ethylene-propylene-dicyclopentadiene terpolymer) in the course of γ-radiation and chemical cross-linking are reported. The interconnection/relationship between the highest values of the stresses, as well as the characteristics of formation processes of the joints, and certain structural characteristics of the blends (content of their cross-linked part, the degree of crystallinity, etc.) is discussed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 265–278, March–April, 2006.     

聚酰胺1010辐射效应的机理及结构

聚酰胺1010;非晶;结晶;辐射损伤;交联机理     

接枝和交联对纳米SiO_2改性NR/PP共混型热塑弹性体的影响

动态硫化制备纳米二氧化硅(SiO2)改性天然橡胶/聚丙烯共混型热塑性弹性体(NR/PP TPE).研究了马来酸酐/苯乙烯/过氧化二异丙苯(MAH/St/DCP)多单体“就地”熔融接枝、交联对TPE力学性能、耐溶剂性能和耐热变形性能的影响,并用SEM分析了TPE的断面形貌.结果表明:纳米SiO2和MAH/St/DCP的最佳质量分数分别为0.03和0.0375/0.0188/0.00375时,MAH/St/DCP接枝、交联改性NR/PP/纳米SiO2TPE的力学性能、耐溶剂性能和耐热变形性能最佳.MAH/St/DCP“就地”接枝、交联通过细化交联NR分散相、改善交联NR分散的均匀性和增加两相之间的共交联,使NR与PP两相界面结合强度明显提高,NR/PP TPE的综合性能得到明显的改善.     

高密度聚乙烯与EPDM磺酸锌盐共混物结构与性能的研究

本文研究了高密度聚乙烯(HDPE)/EPDM磺酸锌盐(Zn-SEPDM)共混物的机械性能、流变行为、形态和相容性。结果表明:加入Zn-SEPDM可使HDPE的熔点和结晶度降低,熔程变窄。当Zn-SEPDM含量超过20％,共混物中Zn-SEPDM呈连续相,冲击强度突增。