The effect of fluorine substituents on the polymerization mechanism of 2-methylene-1,3-dioxolane and properties of the polymer products

Perfluoro-2-methylene-1,3-dioxolane (III) was synthesized and polymerized with an initiator, perfluoro dibenzoyl peroxide, and a white solid product III-P was quantitatively isolated. The polymer was insoluble in organic solvents including fluorinated solvents such as Fluorinert FC 75 and hexafluorobenzene, but dissolved in hexafluorobenzene by heating at around 140 °C in a sealed ampoule. The X-ray measurement showed that III-P was semi-crystalline and melted at 230 °C. The IR spectrum of III-P indicated that the polymer obtained did not show carbonyl peak and it was the vinyl addition product. When the solid product was heated above the melting temperature and pressed under 100-200 kg/cm², we obtained an amorphous and flexible film, which is transparent from the UV region to the near IR region. The glass transition temperature was 110 °C and refractive indexes were 1.3443, 1.3434 and 1.3373 at 633, 839 and 1544 nm, respectively. The film did not degrade in concentrated sulfuric acid and aqueous sodium hydroxide solutions even heated at 80-90 °C for 2 days. The film was thermally stable and began to decompose at 300 °C under air atmosphere.     

Positive definite symmetric functions on finite dimensional spaces. I. Applications of the Radon transform

An n-dimensional random vector X is said (Cambanis, S., Keener, R., and Simons, G. (1983). J. Multivar. Anal., 13 213–233) to have an α-symmetric distribution, α > 0, if its characteristic function is of the form φ(|ξ₁|^α + … + |ξ_n|^α). Using the Radon transform, integral representations are obtained for the density functions of certain absolutely continuous α-symmetric distributions. Series expansions are obtained for a class of apparently new special functions which are encountered during this study. The Radon transform is also applied to obtain the densities of certain radially symmetric stable distributions on ⁿ. A new class of “zonally” symmetric stable laws on ⁿ is defined, and series expansions are derived for their characteristic functions and densities.     

带有负指数 Kirchhoff 方程稳定解的Liouville型定理

In this paper, we consider the Liouville-type theorem for stable solutions of the following Kirchhoff equation ■,where M(t) = a + bt~θ, a 0, b, θ≥ 0, θ = 0 if and only if b = 0. N ≥ 2, q 0 and the nonnegative function g(x) ∈ L_(loc)~1(R~N). Under suitable conditions on g(x), θ and q, we investigate the nonexistence of positive stable solution for this problem.     

THE VOLTERRA MODEL FOR THREE SPACIES PREDATOR-PREY SYSTEMS IN LOOPS

We consider the three species predator-prey model with the same intrinsic growth rates, where species 3 feeds on species 2, species 2 feeds on species 1, species 1 feeds on species 3. An open question raised by Nishan Krikorian is answered: We obtain the necessary and sufficient conditions for all the orbits to be unbounded. We also obtain the necessary and sufficient conditions for the positive equilibrium to be globally stable. It is shown that there exists a family of neutrally stable periodic orbits, in which we extend Darboux method to three-species models for the first time.     

Rapid additive‐free TEMPO‐mediated stable free radical polymerizations of styrene

The stable free radical polymerization (SFRP) of styrene, initiated with benzoyl peroxide in the presence of TEMPO, under bulk conditions, is demonstrated to proceed rapidly without the need for any rate enhancing additives such as camphorsulfonic acid, 2‐fluoro‐1‐methyl pyridinium p‐toluenesulfonate, or acetic anhydride. Monomer conversions as high as 70% can be achieved in 5 h or less while maintaining polydispersity indexes of 1.15. These results stand in stark contrast to earlier reactions that required 70 h to achieve similar conversions. This study demonstrates that the single largest factor governing the rates of polymerization is the molar concentration of excess TEMPO remaining in solution after initiation. A reduction in the TEMPO to BPO ratio is required when large amounts of BPO are used to target low molecular weight polystyrenes. However, when a lower molar amount of BPO is used to obtain high molecular weight polystyrenes, a higher TEMPO to BPO ratio is required. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5487–5493, 2007     

依赖凝聚函数求解非线性互补问题的一种微分方程方法

利用凝聚函数一致逼近非光滑极大值函数的性质,将非线性互补问题转化为参数化光滑方程组.然后,对此方程组给出了一种微分方程解法,并且证明了非线性互补问题的解是微分方程系统的渐进稳定平衡点.在适当的假设条件下,证明了所给出的算法具有二次收敛速度.数值结果表明了此算法的有效性.     

CUSUM,GLR,GEWMA以及RFCuscore控制图监测稳定过程均值漂移的效果比较(英)

本文给出了累积和控制图(CUSUM)监测稳定过程均值漂移的平均运行长度(ARL)的区间估计,并采用数字模拟的方法对CUSUM,GLR,GEWMA以及RFCuscore四种控制图监测稳定过程均值漂移的效果进行比较,结果显示CUSUM效果最好.     

On stability of the hamiltonian index under contractions and closures

The hamiltonian index of a graph G is the smallest integer k such that the k‐th iterated line graph of G is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an A_G(F)‐contractible subgraph F of a graph G nor the closure operation performed on G (if G is claw‐free) affects the value of the hamiltonian index of a graph G. AMS Subject Classification (2000): 05C45, 05C35. © 2005 Wiley Periodicals, Inc. J Graph Theory     

KdV方程的一类本性并行差分格式

对三阶KdV方程给出了—组非对称的差分公式,并用这些差分公式和对称的Crank-Nicolson型公式构造了一类具有本性并行的交替差分格式．证明了格式的线性绝对稳定性．对—个孤立波解、二个孤立波解和三个孤立波解的情况分别进行了数值试验,并对—个孤立波解的数值解的收敛阶和精确性进行了试验和比较．     

n维可投影LOtka-Volterra竞争系统的渐近性

对于二维和三维的Lotka-Volterra竞争系统,已有文献证明:当每一个坐标轴上的平衡点均为渐近稳定时,该系统几乎所有解趋于坐标轴上平衡点所组成的点集,即,不趋于坐标轴上平衡点的解集,其测度为零.由此, van den Driessche和Zeeman于1998年提出猜测:对n(n>3)维Lotka-Volterra竞争系统,当每一个坐标轴上的平衡点均为渐近稳定时,该系统几乎所有解趋于坐标轴上平衡点所组成的点集,即,不趋于坐标轴上平衡点的解集,其在n维空间的测度为零.本文证明当n维Lotka-Volterra竞争系统可被逐维投影到一维系统时,该猜测成立,并给出了可投影条件的代数判据.本文所得结论包含了已有文献的结果.