DENSENESS OF RADIAL-BASIS FUNCTIONS IN L^2（R^n） AND ITS APPLICATIONS IN NEURAL NETWORKS

The authors discuss problems of approximation to functions in L2(Rn) and operators fromL2(Rn1) to L2(Rn2) by Radial-Basis Functions. The results obtained solve the problem ofcapability of RBF neural networks, a basic problem in neural networks.     

ON PERIODIC DYNAMICAL SYSTEMS

The authors investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the results obtained are universal.     

刚体转动实验中的误差估计和数据处理

在刚体转动定律研究的实验理论中，常做某种简化，本文将对这种简化产生的系统误差做以估计；本文还将论及如何进行最小二乘法数据处理的教学。     

LOCAL L^p ESTIMATE FOR THE SOLUTION OF $\bar \partial-NEUMANN$ PROBLEM OVER $D_t={(w,z):Rew\leq \frac{|z^m-tw|^2}{m}}$

Assume that a distribution u satisfies conditions:$\[\bar \partial u = f,u \bot H({D_t})\]$ on domain $D_t,u\in Dom(\bar \partial _0^*),\bar \partial u \in \bar \partial _1^*;\bar \partial f=0,f\bot H^{0,1}$. It is proved that $\phi_1u\inL_{\beta +\frac{1}{2m}-\epsilon}^p$ if $\phi _2f\inL_\beta ^p$,where is the potential space defined in [14]; $\phi _1,\phi _2\in C_c^\infinity(U),\phi _2=1$ on suppt \phi_1;U is a neighbourhood of the origin; \epsilon is a small positive number. This result contains a result of D.C. Chang (in [3]) by setting t = 0.     

A note on the hyper Cochrane sum

The main purpose of this paper is using the analytic methods to study the upper bound of the hyper Cochrane sum, and obtain an interesting result which generalized the main theorem of Liu [2].     

Boundedness and synchronization of y-coupled Lorenz systems with or without controllers

The purpose of this paper is to investigate the boundedness and synchronization of y-coupled Lorenz systems. When the coupling term is only added to the second variable, we call them y-coupled Lorenz systems. In this paper, we first prove the boundedness of y-coupled Lorenz systems, which ensures the existence and uniqueness of the solution when t→∞. Based on the boundedness, we prove that for y-coupled Lorenz systems, QUAD condition is satisfied. It should be pointed out that QUAD condition plays an essential role in the discussion of synchronization. Based on the boundedness and QUAD condition, we prove that if the coupling is strong enough, the y-coupled Lorenz systems can achieve the complete synchronization globally and exponentially.     

X波段高功率微波对介质窗材料的破坏现象

 在X波段微波源（频率9.4 GHz,功率1 GW）下,对4种典型介质窗材料（聚四氟乙烯、有机玻璃、低密度聚乙烯及高密度聚乙烯）在真空中进行了微波放电击穿实验,同时考虑了材料的不同表面处理工艺（表面刻槽和抛光）对其击穿特性的影响,对微波击穿后样品的表面形貌进行了宏观和微观分析,实验观测到:介质表面出现了沿微波电场方向的明显树枝状破坏现象,且材料表面处理工艺对其击穿破坏程度有显著影响,认为树枝状破坏通道与施加的微波场有着密切的关系。通过观察透明有机玻璃内部的树枝状破坏,发现树枝既沿介质表面生长,同时也向介质内部发展。提出了微波作用下介质窗击穿破坏的物理模型,认为微波电场导致树枝状破坏沿电场方向发展,而微波磁场导致树枝状向介质内部发展,并进一步给出了树枝状破坏起始和发展的可能原因。     

Consensus problem in directed networks of multi-agents via nonlinear protocols

In this Letter, the consensus problem via distributed nonlinear protocols for directed networks is investigated. Its dynamical behaviors are described by ordinary differential equations (ODEs). Based on graph theory, matrix theory and the Lyapunov direct method, some sufficient conditions of nonlinear protocols guaranteeing asymptotical or exponential consensus are presented and rigorously proved. The main contribution of this work is that for nonlinearly coupled networks, we generalize the results for undirected networks to directed networks. Consensus under pinning control technique is also developed here. Simulations are also given to show the validity of the theories.     

Vanillin‐derived phosphorus‐containing compounds and ammonium polyphosphate as green fire‐resistant systems for epoxy resins with balanced properties

Flame retardants from vanillin when utilized together with ammonium polyphosphate (APP) yield excellent synergistic flame retardancy toward epoxy resins. Bisphenol A epoxy resins have been widely used due to their excellent mechanical properties, chemical resistance, electrical properties, adhesion, etc., while they are flammable. Environment‐friendly and bio‐based flame retardants have captured increasing attention due to their ecological necessity. In this paper, 3 bio‐based flame retardants were synthesized from abundant and more importantly renewable vanillin, and their chemical structures were determined by ¹H NMR and ¹³C NMR. They were used together with APP (an environment‐friendly commercial flame retardant) to improve the fire resistance of bisphenol A epoxy resin. With the addition APP content of 15 phr, the modified bisphenol A epoxy resin could reach UL‐94V0 rating during vertical burning test and limit oxygen index values of above 35%, but reducing APP content to 10 phr, the flame retardancy became very poor. With the total addition content of 10 phr, the epoxy resins modified by 7 to 9 phr APP and 1 to 3 phr bio‐based flame retardants with epoxy groups or more benzene rings showed excellent flame retardancy with UL‐94V0 rating and limit oxygen index values of around 29%. The T_gs of the epoxy resins could be remained or even increased after introducing bio‐based flame retardants, as the control; those of APP alone‐modified epoxy resins compromised a lot. The green synergistic flame‐retardant systems have a great potential to be used in high‐performance materials.