Synthesis and mass spectrometry characterization of centrally and terminally amine‐functionalized polyisobutylenes

This article reports the facile synthesis of novel terminally and centrally functionalized polyisobutylenes (PIBs) and the detailed characterization of the products by various mass spectrometry techniques. Specifically, H? PIB? CH₂? C(OH)CH₃? CH₂? NHCH₃ and [H? PIB? CH₂? CH(OH)CH₃? CH₂]₂? NCH₃ were synthesized by the quantitative epoxidation of H? PIB? CH₂? C(CH₃)?CH₂ and the subsequent conversion of the resulting epoxide with excess CH₃NH₂. Quaternization with CH₃Cl of these mixtures of secondary and tertiary amines yielded exclusively H? PIB? CH₂? C(OCH₃)CH₃? CH₂? N(CH₃)₂ from the secondary amine, whereas the tertiary (centrally functionalized) amine remained unchanged. Tandem mass spectrometry experiments provided unique insight into the precise connectivity of the functional end groups added to the PIB frame. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 946–958, 2005     

Spectral Densities and Partition Functions of Modular Quantum ystems as Derived from a Central Limit Theorem

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite number of subsystems. Even for only small numbers of subsystems we find good accordance with some known, exact results.     

Issues of stability and accuracy in identifying the principal axis of inertia of an inhomogeneous rigid body with a rotating Hooke’s joint

The paper addresses issues of real-world operation of a device designed to experimentally identify the principal central axes of inertia of an arbitrary inhomogeneous rigid body. The effect of external and internal dissipation on the stability and accuracy of the device is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 131–143, November 2006.     

The central warehouse location problem revisited

This paper is concerned with the optimal location of a centralwarehouse, given a fixed number and the locations of the localwarehouses. We investigate whether the solution determined bythe traditional model that minimizes total transportation costdiffers from the one determined by a model that also takes intoaccount the inventory and service costs. We build simple modelsto address this question. Numerical results show that ignoringinventory costs in modelling location models may lead to inferiorlocation solutions.     

On the Central Limit Theorem and Its Weak Invariance Principle for Strongly Mixing Sequences with Values in a Hilbert Space via Martingale Approximation

In this paper we not only prove an extension to Hilbert spaces of a sharp central limit theorem for strongly real-valued mixing sequences, but also slightly improve it. The proof is mainly based on the Bernstein blocking technique and approximations by martingale differences. Moreover, we derive also the corresponding functional central limit theorem.     

Graded Lie Algebras and Dynamical Systems

We define the graded Lie algebras generated by ergodic transformation with invariant measure. This algebra is the central extension of Lie algebras which is associated with the usual crossed product. At the same time, it is the special case of algebras with continuum root systems which were defined by the author and M. Saveliev at the beginning of Nineties. Examples of systems with a discrete spectrum are considered.     

载流回路受磁场作用的一般运动趋势

本文根据学生学习的实际需求，从磁场做功和能量转换的角度论证了载流回路受磁场作用的一般运动趋势．     

A Multivariate CLT for Decomposable Random Vectors with Finite Second Moments

Stein's method is used to derive a CLT for dependent random vectors possessing the dependence structure from Barbour et al. J. Combin. Theory Ser. B 47, 125–145, but under the assumption of second moments only. This allows us to derive Lindeberg–Feller type theorems for sums of random vectors with certain dependence structures. We apply the main theorem to the study of three problems: local dependence, random graph degree statistics and finite population statistics. In particular, we consider U-statistics of independent observations as well as of observations drawn without replacement.     

中心代数上的矩阵方程组

设Ω是一个特征非2的具有对合反自同构的有限维中心代数.本文研究Ω上的两个矩阵方程组,分别给出了其有一般解和次(斜)自共轭解的充要条件.     

Testing Epidemic Changes of Infinite Dimensional Parameters

To detect epidemic change in the mean of a sample of size n of random elements in a Banach space, we introduce new test statistics DI based on weighted increments of partial sums. We obtain their limit distributions under the null hypothesis of no change in the mean. Under alternative hypothesis our statistics can detect very short epidemics of length log^γ n, γ > 1. We present applications to detect epidemic changes in distribution function or characteristic function of real valued observations as well as changes in covariance matrices of random vectors. Final version 27 October 2004