Addition–fragmentation chain transfer: Molecular weight distributions and retardation in the system methyl methacrylate/methyl α‐(bromomethyl)acrylate

A detailed investigation of addition–fragmentation chain transfer (AFCT) in the free‐radical polymerization of methyl methacrylate (MMA) in the presence of methyl α‐(bromomethyl)acrylate (MBMA) was carried out to elucidate mechanistic details with efficient macromonomer synthesis as an underlying goal. Advanced modeling techniques were used in connection with the experimental work. Curve fitting of simulated and experimental molecular weight distributions with respect to the rate coefficient for addition of propagating radicals to MBMA (k_add) over 60–120 °C resulted in E_add = 21.7 kJ mol^?1 and A_add = 2.18 × 10⁶ M^?1 s^?1 and a very weak temperature dependence of the chain‐transfer constant (E_add ≈ E_p). The rate coefficient for fragmentation of adduct radicals at 60 °C was estimated as k_f ≈ 39 s^?1 on the basis of experimental data of the MMA conversion and the concentration of 2‐carbomethoxy‐2‐propenyl end groups. The approach developed is generic and can be applied to any AFCT system in which copolymerization does not occur and in which the resulting unsaturated end groups do not undergo further reactions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2640–2650, 2004     

在几何和参数上表示同一条曲线的两条有理NURBS曲线的权与控制顶点之间的关系

The paper discusses the relationship between weights and control vertices of two rational NURBS curves of degree two or three with all weights larger than zero when they represent the same curve parametrically and geometrically, and gives sufficient and necessary conditions for coincidence of two rational NURBS curves in non-degeneracy case.     

ON A SET OF h-HARMONIC HOMOGENEOUS POLYNOMIALS

1　IntroductionLet Sd- 1 bethe unitsphere of Rd,Πdthe space of allpolynomialsofd variables,and x(i)= (x1 ,… ,xi) (i=1 ,… ,d) .In this paper,we are concerned with the homogeneous polyno-mials orthogonal with the weightfunction h(x(d) ) =x2 k11 …x2 kdd on Sd- 1 ,where ki≥ 0 (i=1 ,… ,d) .Connected with the weightfunction h(x(d) ) are the following differential-differenceoperators introduced by Charles F. Dunkl in [3 ] ,Dip(x(d) ) = p(x(d) ) xi+ di=1kip(x(d) ) -p(x1 ,… ,-xi,… ,xd)xi,Δ…     

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.     

RANDOM EDGE can be exponential on abstract cubes

We prove that RANDOM EDGE, the simplex algorithm that always chooses a random improving edge to proceed on, can take a mildly exponential number of steps in the model of abstract objective functions (introduced by Williamson Hoke [Completely unimodal numberings of a simple polytope, Discrete Appl. Math. 20 (1988) 69-81.] and by Kalai [A simple way to tell a simple polytope from its graph, J. Combin. Theory Ser. A 49(2) (1988) 381-383.] under different names). We define an abstract objective function on the n-dimensional cube for which the algorithm, started at a random vertex, needs at least exp(const·n^1/3) steps with high probability. The best previous lower bound was quadratic. So in order for RANDOM EDGE to succeed in polynomial time, geometry must help.     

A Construction of Optimal Constant Composition Codes

In this paper, a construction of optimal constant composition codes is developed, and used to derive some series of new optimal constant composition codes meeting the upper bound given by [13].     

加权Herz—type Triebel—Lizorkin空间的特征及应用

当s∈ R,0,〈q, p〈∈∞,0,〈β≤∞且 max{-n/q,-nδ2/qδ1}〈a时，定义了加权Herz—type　Triebel-Lizorkin空间kq^q,pF^s β（R^n,ω1，ω2）和Kq^a,pF^sβ（R^n，ω1，ω2），并给出这些空间的一些特征及在这些空间上的Hard—Littlewood极大算子不等式．     

一个改进的Hardy-Hilbert不等式

通过建立权系数的不等式,得到一个改进的Hardy-Hilbert不等式.     

一个推广的Hardy-Hilbert型不等式及其逆式

本文引入单参数λ及应用Beta函数,给一个Hardy-Hilbert型不等式以具有最佳常数因子的推广,作为应用,给出了它的逆向形式．     

关于多线性振荡奇异积分在加权Hardy-型空间上的一致估计

本文对一类具有光滑位相函数的多线性振荡奇异积分算子建立了一致的加权（H^1(R^n),L^1(R^n))估计及一致的加权（HKp(R^n),Kp(R^n)估计。