Kinetic features of ethylene polymerization over supported catalysts [2,6‐bis(imino)pyridyl iron dichloride/magnesium dichloride] with AlR3 as an activator

The effects of polymerization temperature, polymerization time, ethylene and hydrogen concentration, and effect of comonomers (hexene‐1, propylene) on the activity of supported catalyst of composition LFeCl₂/MgCl₂‐Al(i‐Bu)₃ (L = 2,6‐bis[1‐(2,6‐dimethylphenylimino)ethyl] pyridyl) and polymer characteristics (molecular weight (MW), molecular‐weight distribution (MWD), molecular structure) have been studied. Effective activation energy of ethylene polymerization over LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a value typical of supported Ziegler–Natta catalysts (11.9 kcal/mol). The polymerization reaction is of the first order with respect to monomer at the ethylene concentration >0.2 mol/L. Addition of small amounts of hydrogen (9–17%) significantly increases the activity; however, further increase in hydrogen concentration decreases the activity. The IRS and DSC analysis of PE indicates that catalyst LFeCl₂/MgCl₂‐Al(i‐Bu)₃ has a very low copolymerizing ability toward propylene and hexene‐1. MW and MWD of PE produced over these catalysts depend on the polymerization time, ethylene and hexene‐1 concentration. The activation effect of hydrogen and other kinetic features of ethylene polymerization over supported catalysts based on the Fe (II) complexes are discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5057–5066, 2007     

多线性Calderón-Zygmund算子的加权有界性

建立了多线性Calderón-Zygmund算子在比幂权空间更一般的Herz空间和Herz型Hardy空间上的有界性.作为推论,得到了该算子的幂权估计.在这些幂权估计中,权指标可以突破Ap权的指标限制,显示出和经典Calderón-Zygmund算子本质的区别.     

一类最高权向量环的Krull维数

本文给出Om×GLn作用于Cm,n上的复多项式环上的最高权向量环的Krull维数公式,从而改正了Aslaksen,Tan及Zhu的一个错误.     

Relations among eigenvalues of Sturm-Liouville problems with different types of leading coefficient functions

For any Sturm-Liouville problem with a separable boundary condition and whose leading coefficient function changes sign (exactly once), we first give a geometric characterization of its eigenvalues λn using the eigenvalues of some corresponding problems with a definite leading coefficient function. Consequences of this characterization include simple proofs of the existence of the λn's, their Prüfer angle characterization, and a way for determining their indices from the zeros of their eigenfunctions. Then, interlacing relations among the λn's and the eigenvalues of the corresponding problems are obtained. Using these relations, a simple proof of asymptotic formulas for the λn's is given.     

2‐Cyanoprop‐2‐yl dithiobenzoate mediated reversible addition–fragmentation chain transfer polymerization of acrylonitrile targeting a polymer with a higher molecular weight

The reversible addition–fragmentation chain transfer (RAFT) polymerization of acrylonitrile (AN) mediated by 2‐cyanoprop‐2‐yl dithiobenzoate was first applied to synthesize polyacrylonitrile (PAN) with a high molecular weight up to 32,800 and a polydispersity index as low as 1.29. The key to success was ascribed to the optimization of the experimental conditions to increase the fragmentation reaction efficiency of the intermediate radical. In accordance with the atom transfer radical polymerization of AN, ethylene carbonate was also a better solvent candidate for providing higher controlled/living RAFT polymerization behaviors than dimethylformamide and dimethyl sulfoxide. The various experimental parameters, including the temperature, the molar ratio of dithiobenzoate to the initiator, the molar ratio of the monomer to dithiobenzoate, the monomer concentration, and the addition of the comonomer, were varied to improve the control of the molecular weight and polydispersity index. The molecular weights of PANs were validated by gel permeation chromatography along with a universal calibration procedure and intrinsic viscosity measurements. ¹H NMR analysis confirmed the high chain‐end functionality of the resultant polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1272–1281, 2007     

对期望理论的两个重要推进——损失厌恶系数λ及参考点研究

行为金融学是近20年来最为重要的新兴金融理论,期望理论更是其中的亮点,其运用领域之广超乎人们的想象,所以对它的完善改进具有非常重要的意义。本文对期望理论中的损失厌恶系数和参考点问题进行了深入研究,并且得出了创新性的结果:损失厌恶系数不是常数而是动态变量;得出了内生且纳入更多投资者行为特征的参考点。这些结果是对期望理论的重要改善和推进,对其在大量金融领域和涉及到财富偏好的问题的解决中都大有裨益。     

On the Use of the Restitution Condition in Flexible Body Dynamics

The difference between the classical treatment offlexible body impact and the treatment of impact in flexiblemultibody dynamics is due to several fundamental reasons. Inthe classical impact theory, simple structures such as beamsand plates are used. Infinite dimensional models can bedeveloped for these simple structural elements to study theimpact dynamics and the wave propagation problem. Flexiblemultibody impact problems, on the other hand, involve bodieswith complex geometry that cannot be modeled using infinitenumber of degrees of freedom. Furthermore, the classicalimpact theory has been mainly concerned with the impactbetween a rigid mass that moves without constraints beforeit impacts a simple flexible structure. This is not amultibody simulation scenario in which the impact occursbetween kinematically constrained bodies that are subjectedto impulsive constraint forces in addition to the impactforces. These constraint forces can influence the motion ofthe two bodies immediately after impact, and as aconsequence, the simple classical theory scenario of impactdoes not apply. It is the objective of this paper to discussthe use of the restitution condition in flexible multibodyimpact problems and demonstrate that the use of thisapproach does not exclude the classical formulation.Nonetheless, the impulse momentum balance approach can serveas an effective and efficient procedure for solving theimpact problem in finite dimensional models that do not obeythe classical wave theory. Energy results of simplestructural elements are presented in order to demonstratethe consistency of using the impulse momentum balanceapproach in solving impact problems in finite dimensionalflexible body applications.     

Identification of a dissipation coefficient by a variational method

A generalized inverse problem for the identification of the absorption coefficient for a hyperbolic system is considered. The well-posedness of the problem is examined. It is proved that the regular part of the solution is an L ₂ function, which reduces the inverse problem to minimizing the error functional. The gradient of the functional is determined in explicit form from the adjoint problem, and approximate formulas for its calculation are derived. A regularization algorithm for the solution of the inverse problem is considered. Numerical results obtained for various excitation sources are displayed.     

相关系数与相关性度量

研究了度量相关性的两个主要工具:线性相关系数和尾部相关系数.线性相关系数反映了变量间的线性相关性,这对于一般的椭圆型分布是合适的.但如果随机变量具有不对称的尾部变化特征时,要用尾部相关系数描述它们之间的相关性.通过相关函数C opu la,对沪深股市的尾部相关系数进行了定量分析.结果表明:沪深股市具有较强的相关性.     

Optimal reconstruction of the solution of the wave equation from inaccurate initial data

In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from l ₂, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors.