Investigation on the Tribological Properties of POM Modified by Nano-PTFE

The tribological properties of polyoxymethylene (POM) modified by nano-polytetrafluorethylene (nano-PTFE) were investigated by a block-on-ring wear tester. For comparison, modified POM with micro-polytetrafluoroethylene (micro-PTFE) was also studied. The modified POM with a much lower concentration of nano-PTFE showed the similar tribological properties compared with POM modified by micro-PTFE. The friction coefficient decreased with the increase of nano-PTFE, while the wear rate showed the lowest value when the concentration of nano-PTFE was 2%. Scanning electron microscope (SEM) micrographs revealed that transfer films played an important role in the friction process. The transfer films decreased and stabilized the friction coefficient. Comparing to POM/2%nano-PTFE, when the concentration of nano-PTFE reached 4%, the mechanical properties decreased significantly, possibly due to poor dispersion of nano-PTFE.     

一类二阶多点边值问题正解的存在性

利用锥上不动点定理讨论了二阶常微分方程组多点边值问题正解的存在性，所得结论推广了最近的一些结果．     

Exact Analytical Solution to Equations of Perihelion Advance in General Relativity

Previously the perihelion advance in binary system was computed approximately. We will present an exact analytical solution to nonlinear differential equation of perihelion advance by method of Jacobian elliptic function and the advanced angle between successive perihelions. Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars from Ministry of Education, China (Grant No. [2004]527) and the Natural Science Foundation of Hunan Province, China (Grant No. 06JJ2026)     

Traveling waves for a reaction–diffusion–advection predator–prey model

In this paper we study a reaction–diffusion–advection predator–prey model in a river. The existence of predator-invasion traveling wave solutions and prey-spread traveling wave solutions in the upstream and downstream directions is established and the corresponding minimal wave speeds are obtained. While some crucial improvements in theoretical methods have been established, the proofs of the existence and nonexistence of such traveling waves are based on Schauder’s fixed-point theorem, LaSalle’s invariance principle and Laplace transform. Based on theoretical results, we investigate the effect of the hydrological and biological factors on minimal wave speeds and hence on the spread of the prey and the invasion of the predator in the river. The linear determinacy of the predator–prey Lotka–Volterra system is compared with nonlinear determinacy of the competitive Lotka–Volterra system to investigate the mechanics of linear and nonlinear determinacy.     

Tuning the sugar‐response of boronic acid block copolymers

A detailed study of the pH‐ and sugar‐responsive behavior of poly(3‐acrylamidophenylboronic acid pinacol ester)‐b‐poly(N,N‐dimethylacrylamide) (PAPBAE‐b‐PDMA) block copolymers is presented. Reversible addition‐fragmentation chain transfer (RAFT) polymerization of the pinacol ester of 3‐acrylamidophenylboronic acid resulted in homopolymers with molecular weights between 12,000 and 37,000 g/mol. The resulting homopolymers were employed as macro‐chain transfer agents during the polymerization of N,N‐dimethylacrylamide (DMA). Successful chain extension and removal of the pinacol protecting groups to yield poly(3‐acrylamidophenylboronic acid)‐b‐PDMA (PAPBA‐b‐PDMA) with free boronic acid moieties resulted in pH‐ and sugar‐responsive block copolymers that were subsequently investigated for their behavior in aqueous solution. The PAPBA‐b‐PDMA block copolymers were capable of solution self‐assembly due to the PAPBA block being water‐insoluble below its pK_a. The resulting aggregates were demonstrated to solubilize and release model hydrophobic compounds, as demonstrated by fluorescence studies. Dissociation of the aggregates was induced by raising the pH above the pK_a of the boronic acid residues or by adding sugars capable of forming boronate esters. Aggregate size, dissociation kinetics, and the effect of various sugars were considered. The critical sugar concentration needed to induce aggregate dissociation was tuned by incorporation of hydrophilic DMA units within the PAPBA responsive segment to yield PDMA‐b‐poly(3‐acrylamidophenylboronic acid‐co‐DMA) block copolymers. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

具有5个不同素因子的Nicol数数数

通过计算机辅助,利用元素的阶、欧拉函数、因子和函数等数论函数的性质,继续研究了具有5个不同素因子的Nicol数,证明了具有5个不同素因子的Nicol数只能是3-Nicol数和4-Nicol数.     

Accelerating electromagnetic magic field from the C-metric

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the “magic field” of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr–Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the “accelerating magic field” represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born’s solution for two uniformly accelerated monopole charges.     

On reachable set of singularly perturbed differential inclusions and optimal control problems

Asymptotic properties of reachable sets of singularly perturbed differential inclusions are given. Their applications to optimal control problems are also studied