纳米氧化硅表面阴离子接枝聚合苯乙烯

通过正丁基锂(BL)引发甲基丙烯酰氧丙基纳米氧化硅(MAMSN)与苯乙烯共聚,制备了聚苯乙烯表面接枝纳米氧化硅(PS—g—Silica),并考察了正丁基锂加入量对苯乙烯转化率(C)、接枝率(PG)以及聚苯乙烯分子量(Mn)的影响。实验结果表明,阴离子聚合可以获得比自由基聚合更大的分子量和更高的转化率以及接枝率。     

Fredholm alternative and boundary value problems

This note presents a simple proof of A. Lasota's application of the nonlinear Fredholm alternative to the existence proofs of the boundary value problems involving ordinary differential equations. It then uses Lasota's result to get a stronger version of the theorem of Herzog and Lemmert on the Dirichlet boundary value problem for the second-order systems of ordinary differential equations.

     

新型大溶性大π共轭高分子—聚吡咯—{2,5—[双（对二甲氨基苯甲烯）]}？…

该研究合成了一种新型水溶性大π共轭高分子－聚吡咯－｛２,５－〔二（对二甲氨基苯甲烯）〕｝（ＰＰＤＭＡＢ）,它地强酸的水溶液,在１ｍｏｌ／Ｌ的盐酸中溶解度为０．５～１．０g／１００mＬ,通过ＥＡ、ＸＰＳ、ＦＴ－ＩＲ、ＵＶ－Ｖｉｓ－ＮＩＲ、Ｉｎ－ｓｉｔｕＵＶ－Ｖｉｓ－ＮＩＲ对ＰＰＤＭＡＢ进行了结构表征。通过质子化、碘掺杂、浓硫酸（９８％）掺杂等处理,ＰＰＤＭＡＢ的电导率提高２～４个数量组（＆＝１－＾－７     

HgBa2CuO4+δ中载流子分布的研究

我们根据一种结构分块模型,计算了与超导转变温度Tc密切相关的块之间相互作用能,讨论了HgBa2CuO4 δ中载流子分布对相互作用能的影响.通过计算不同氧缺陷下,空穴在不同平面以及空穴在Cu-O平面不同位置上对相互作用能的影响,研究了它们与超导电性的关联.计算表明,空穴在Cu-O面上的位置不仅明显地影响到相互作用能的大小,而且影响相互作用能随氧含量的变化趋势,该结果为我们了解载流子在Cu-O面上分布是否均匀提供了一定的线索.结果还表明,HgBa2CuO4 δ中的载流子主要分布在Cu-O平面上.     

Outer Synchronization of Complex Networks by Impulse

This paper investigates outer synchronization of complex networks, especially, outer complete synchronization and outer anti-synchronization between the driving network and the response network. Employing the impulsive control method which is uncontinuous, simple, efficient, low-cost and easy to implement in practical applications, we obtain some sufficient conditions of outer complete synchronization and outer anti-synchronization between two complex networks. Numerical simulations demonstrate the effectiveness of the proposed impulsive control scheme.     

Additivity rule for electron--molecule total cross section calculations at 50--5000eV: a new geometrical approach

Taking into consideration the changes of the geometric shielding effect in a molecule as the energy of incident electrons varies, this paper presents an empirical fraction, which depends on the energy of incident electrons, the target＇s molecular dimension and the atomic and electronic numbers in the molecule. Using this empirical fraction, it proposes a new formulation of the additivity rule. Employing the new additivity rule, it calculates the total cross sections of electron scattering by C2H4, C6H6, C6H14 and C8H18 over the energy range from 50 to 5000eV. In order to exclude the calculation deviations caused by solving the radial Schrodinger equation of electron scattering by atoms, here the atomic cross sections are derived from the experimental total cross section results of simple molecules （H2, O2, CO） via the inversion algorithm. The quantitative total cross sections are compared with those obtained by experiments and other theories, and good agreement is obtained over a wide energy range, even at energy of several tens of eV.     

On Mixed Pressure-Velocity Regularity Criteria in Lorentz Spaces

In this paper the authors derive regular criteria in Lorentz spaces for LerayHopf weak solutions v of the three-dimensional Navier-Stokes equations based on the formal equivalence relationπ≌|v|²,whereπdenotes the fluid pressure and v denotes the fluid velocity.It is called the mixed pressure-velocity problem(the P-V problem for short).It is shown that if(π/(e-^|(x)|²+|v|^θ∈L^p(0,T;L^q,∞),where 0≤θ≤1 and 2/p+3/q=2-θ,then v is regular on(0,T].Note that,ifΩ,is periodic,e^-|x|2 may be replaced by a positive constant.This result improves a 2018 statement obtained by one of the authors.Furthermore,as an integral part of the contribution,the authors give an overview on the known results on the P-V problem,and also on two main techniques used by many authors to establish sufficient conditions for regularity of the so-called Ladyzhenskaya-Prodi-Serrin(L-P-S for short)type.     

一个阶为2+\sqrt{6}的Newton改进算法

针对非线性方程求单根问题,提出了一种新的Newton预测-校正格式.通过每步迭代增加计算一个函数值和一阶导数值,使得每步迭代需要估计两个函数值和两个一阶导数值.与标准的Newton算法的二阶收敛速度相比,新算法具有更高阶的收敛速度2+\sqrt{6}.通过测试函数对新算法进行测试, 与相关算法比较,表明算法在迭代次数、运算时间及最优值方面都具有较明显的优势. 最后,将这种新格式推广到多维向量值函数, 采用泰勒公式证明了其收敛性,并给出了两个二维算例来验证其收敛的有效性.     

Integrability Aspects and Soliton Solutions for a System Describing Ultrashort Pulse Propagation in an Inhomogeneous Multi-Component Medium

For the propagation of the ultrashort pulses in an inhomogeneousmulti-component nonlinear medium, a system of coupled equations isanalytically studied in this paper. Painlevé analysis shows thatthis system admits the Painlevé property under some constraints.By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pairof this system is derived, and the Darboux transformation (DT) isconstructed with the help of the obtained Lax pair. With symboliccomputation, the soliton solutions are obtained by virtue of the DTalgorithm. Figures are plotted to illustrate the dynamical featuresof the soliton solutions. Characteristics of the solitonspropagating in an inhomogeneous multi-component nonlinear medium arediscussed: (i) Propagation of one soliton and two-peak soliton; (ii) Elastic interactions of the parabolic two solitons; (iii) Overlapphenomenon between two solitons; (iv) Collision of two head-onsolitons and two head-on two-peak solitons; (v) Two different typesof interactions of the three solitons; (vi) Decomposition phenomenonof one soliton into two solitons. The results might be useful in thestudy on the ultrashort-pulse propagation in the inhomogeneousmulti-component nonlinear media.     

Spectral anomalies of diffracted pulsed Hermite--Gaussian beams in dispersive media

This paper derives and uses the recurrence expressions for the power spectra of diffracted pulsed Hermite-Gaussian （HG） beams in dispersive media to study the spectral anomalies of pulsed HG beams in the far field. Numerical results are given to illustrate the dependence of spectral switches on the pulse parameters, truncation parameter and dispersive property of the medium. The potential application of spectral anomalies of ultrashort pulsed beams in information encoding and transmission is discussed.