Transformation of macromonomers into ring‐opening polymerization macroinitiators: A detailed initiation efficiency study

In the present study, n‐butyl acrylate macromonomer (BAMM) (M_n = 1900 g mol^?1; PDI = 1.96) has been synthesized via a high‐temperature polymerization process. Subsequently, the olefinic termini of the BAMM have been transformed into a diol via a dihydroxylation process using KMnO₄ as an oxidizing agent. The OH‐terminated macroinitiator pBA(OH)₂ has subsequently been employed for the ring‐opening polymerization (ROP) of ε‐caprolactone via various catalytic systems, that is, organo‐(1,5,7‐triazabicyclo[4.4.0]dec‐5‐ene), metal (tin(II) 2‐ethylhexanoate), and enzymatic catalysis (Novozym® 435). The obtained pBA‐b‐pCL block copolymers and the initiation efficiency of the BAMM macroinitiator have been investigated via size exclusion chromatography (SEC), electrospray ionization–mass spectrometry (ESI‐MS) hyphenated with SEC and liquid chromatography at the critical conditions of both poly(ε‐caprolactone) (pCL) and pBA. The in vitro enzyme catalysis (eROP) approach proved to be the most efficient catalysis system due to minor transesterification side reactions during the polymerization process. However, side reactions such as transesterifications occur in each catalytic system and—while they cannot be suppressed—they can be minimized. The species generated during the eROP process include the desired block copolymer pBA‐b‐pCL as main species as well as pCL homopolymer and residual macroinitiator pBA(OH)₂. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

The use of high-frequency filters in the investigation of the coloured-random-noise properties of cosmic-ray data

Summary This paper investigates the influence of high-frequency filtering the background white noise on the determination of the coloured-random-noise properties of cosmic-ray experimental signals. We consider fractal methods (Grassberger-Procaccia method, scaling exponent method and fractal length method) and statistical methods (comparison with the Gaussian curve, and the multivariate scaling-analysis technique). The investigation is carried out using two experimental time series with differentcolour (spectral indices α=1.6 and α=1.2) and their computer simulations of pure noise-freecoloured-random-noise signals. The results of the investigation is that the use of high-frequency filtering allows the algorithms employed in the various analyses to see the physical characteristics of the particular data set; the procedure should be reserved, however, to researchers with a good experience in the methods of fractal analysis so that they can identify and discard the artifacts introduced by the truncation applied to the power spectrum.     

高掺镁LiNbO3晶体折射率温度系数的表示式

推导了掺５ｍｏｌ％ＭｇＯ的ＬｉＮｂＯ３晶体折射率温度系数的表示式。利用这些表示式可以计算２９３～４２８Ｋ温度和０．５３９８μｍ～１．３４１４μｍ波长范围内的折射率温度系度，结果表明：计算值和实验值的最大相对偏差是１２％，用具有最大相对偏差的折射率温度系数的计算值，计算１．０７９５μｍ波长的非临界相位匹配温度，其值为３８２．４Ｋ，它与实验值仅差６Ｋ。因此，本文得到的表示式，对于采用这种晶体，设计在上     

标量场与电磁场相互作用体系中的Gasimir效应

摘要本文用Feynmann路径积分方法,研究了一种U(1)规范场理论中的Casimir效应。在一圈图近似下,计算了带电标量场在两个平行的理想金属板之间的Casimir能,并对低维情况进行了讨论。     

Some peculiar boundary phenomena for extremes of rth nearest neighbor links

Let D_n,r denote the largest rth nearest neighbor link for n points drawn independently and uniformly from the unit d-cube C_d. We show that according as r < d or r>d, the limiting behavior of D_n,r, as n → ∞, is determined by the two-dimensional ‘faces’ respectively one-dimensional ‘edges’ of the boundary of C_d. If d = r, a ‘balance’ between faces and edges occurs. In case of a d-dimensional sphere (instead of a cube) the boundary dominates the asymptotic behavior of D_n,r if d 3 or if d = 2, r 3.     

Cooperative equilibria in discounted stochastic sequential games

This paper addresses the problem of computation of cooperative equilibria in discounted stochastic sequential games. The proposed approach contains as a special case the method of Green and Porter (developed originally for repeated oligopoly games), but it is more general than the latter in the sense that it generates nontrivial equilibrium solutions for a much larger class of dynamic games. This fact is demonstrated on two examples, one concerned with duopolistic economics and the other with fishery management.     

Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

The smallest point of a polytope

This note suggests new ways for calculating the point of smallest Euclidean norm in the convex hull of a given set of points inR ⁿ . It is shown that the problem can be formulated as a linear least-square problem with nonnegative variables or as a least-distance problem. Numerical experiments illustrate that the least-square problem is solved efficiently by the active set method. The advantage of the new approach lies in the solution of large sparse problems. In this case, the new formulation permits the use of row relaxation methods. In particular, the least-distance problem can be solved by Hildreth's method.     

Prophet inequalities for cost of observation stopping problems

Comparisons are made between the expected gain of a prophet (an observer with complete foresight) and the maximal expected gain of a gambler (using only non-anticipating stopping times) observing a sequence of independent, uniformly bounded random variables where a non-negative fixed cost is charged for each observation. Sharp universal bounds are obtained under various restrictions on the cost and the length of the sequence. For example, it is shown for X₁, X₂, … independent, [0, 1]-valued random variables that for all c ≥ 0 and all n ≥ 1 that E(max_{1 ≤ j ≤ n}(X_j − jc)) − sup_{t Tn} E(X_t − tc) ≤ 1/e, where T_n is the collection of all stopping times t which are less than or equal to n almost surely.     

The Perturbation of the Interface of the Two-dimensional Diffraction Problem and an Approximating Muskat Modal

ln this paper, a new transformation is found out to straighten the interface Γ_2 x = f(y), f ∈ C^{2+a}([0, a]), f_y|_y =0, δ < f < l-δ,δ > 0,δ,l=constants and a perturbation of the interface is considered for a two dimensional diffraction problem. And the existence, uniqueness and regularity of an appeoximating Muskat model are proved.