Copolymerization of N‐vinylcaprolactam and glycidyl methacrylate: Reactivity ratio and composition control

Free‐radical copolymerizations of N‐vinylcaprolactam (VCL) and glycidyl methacrylate (GMA) were investigated to synthesize temperature‐responsive reactive copolymers with minimized compositional heterogeneity. The average copolymer composition was determined by Fourier transform infrared and nuclear magnetic resonance techniques. The reactivity ratios for VCL and GMA were found to be 0.0365 ± 0.0009 and 6.44 ± 0.36 by the Fineman–Ross method and 0.039 ± 0.006 and 6.75 ± 0.29 by the Kelen–Tudos method, respectively. When prepared by batch polymerization, VCL–GMA copolymers had a highly heterogeneous composition and fractions of different solubilities in water. The use of a gradual feeding technique, which included the sequential addition of more reactive GMA monomer into the reaction, yielded copolymers with much more homogeneous composition. The produced copolymers with 0.9 and 0.11 fractional GMA contents preserved their temperature‐responsive properties and precipitated from aqueous solutions when the temperature exceeded 31 °C. The GMA units in the VCL–GMA copolymers were capable of reacting with amino end‐functionalized poly(ethylene oxide) at room temperature to produce poly(N‐vinylcaprolactam)–poly(ethylene oxide) graft copolymers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 183–191, 2006     

Living anionic polymerization of N‐methoxymethyl‐N‐isopropylacrylamide: Synthesis of well‐defined poly(N‐isopropylacrylamide) having various stereoregularity

Anionic polymerization of N‐methoxymethyl‐N‐isopropylacrylamide ( 1 ) was carried out with 1,1‐diphenyl‐3‐methylpentyllithium and diphenylmethyllithium, ‐potassium, and ‐cesium in THF at ?78 °C for 2 h in the presence of Et₂Zn. The poly( 1 )s were quantitatively obtained and possessed the predicted molecular weights based on the feed molar ratios between monomer to initiators and narrow molecular weight distributions (M_w/M_n = 1.1). The living character of propagating carbanion of poly( 1 ) either at 0 or ?78 °C was confirmed by the quantitative efficiency of the sequential block copolymerization using N,N‐diethylacrylamide as a second monomer. The methoxymethyl group of the resulting poly( 1 ) was completely removed to give a well‐defined poly(N‐isopropylacrylamide), poly(NIPAM), via the acidic hydrolysis. The racemo diad contents in the poly(NIPAM)s could be widely changed from 15 to 83% by choosing the initiator systems for 1 . The poly(NIPAM)s obtained with Li⁺/Et₂Zn initiator system possessed syndiotactic‐rich configurations (r = 75–83%), while either atactic (r = 50%) or isotactic poly(NIPAM) (r = 15–22%) was generated with K⁺/Et₂Zn or Li⁺/LiCl initiator system, respectively. Atactic and syndiotactic poly(NIPAM)s (42 < r < 83%) were water‐soluble, whereas isotactic‐rich one (r < 31%) was insoluble in water. The cloud points of the aqueous solution of poly(NIPAM)s increased from 32 to 37 °C with the r‐contents. These indicated the significant effect of stereoregularity of the poly(NIPAM) on the water‐solubility and the cloud point in water © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4832–4845, 2006     

Bounds on the inverses of nonnegative triangular matrices with monotonicity properties

Some bounds on the entries and on the norm of the inverse of triangular matrices with nonnegative and monotone entries are found. All the results are obtained by exploiting the properties of the fundamental matrix of the recurrence relation which generates the sequence of the entries of the inverse matrix. One of the results generalizes a theorem contained in a recent article of one of the authors about Toeplitz matrices.     

Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

A remark on partial linear spaces of girth 5 with an application to strongly regular graphs

We derive a lower bound on the number of points of a partial linear space of girth 5. As an application, certain strongly regular graphs with=2 are ruled out by observing that the first subconstituents are partial linear spaces.     

酚醛型吸附树脂对水体系中吡啶和N,N-二甲基苯胺的吸附性能研究

研究了酚醛型吸附树脂在水体系中对吡啶和N，N-二甲基苯胺的静态和动态吸附行为．结果表明，在水中树脂对吡啶和N，N-二甲基苯胺的吸附主要以疏水吸附机理进行；吸附吡啶和N．N-二甲基苯胺的初始阶段，即达到38．3～48．9％平衡吸附时，吸附速率数据和半经验速率方程很吻合：酚醛型吸附树脂等温吸附吡啶和N，N-二甲基苯胺的平衡吸附数据符合Langmuir方程，相关系数在0．99以上，酚醛型吸附树脂吸附吡啶和N，N-二甲基苯胺属单分子层吸附：用80％的乙醇溶液作洗脱剂来洗脱吸附吡啶已达饱和的JDW-2树脂，效果是很理想的．在3．6个床体积内洗脱率达91．52％，4．8个床体积内洗脱率达到94．85％。表明酚醛型吸附树脂具有优良的洗脱性能．     

A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen

Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu _h in the norm of a suitable space . Sufficient conditions for the uniform boundedness u _{h Z} =O(1) ash0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain . The approximating subspaces are finite element spaces. Especially the caseX=W ₀ ^{m, p} (), 1<p<,Y=W ₀ ^{m. 2} (),Z=W ₀ ^{m. max (2,p)} ()W^m, () is treated. Some examples for 1<p<2 are considered. Forp2 a refined technique is introduced in the author's paper [7].

     

Conductance studies in amide-water mixtures. II. Sodium salts inN,N-dimethylformamide-water mixtures at 35°C

Conductance data for sodium nitrite, chloride, and acetate in water andN,N-dimethylformamide (DMF)-water mixtures (74.82D42.48) for the concentration range 0.001–0.04N, as well as the densities, viscosities, and dielectric constants of the solvent mixtures at 35°C, are reported. The data have been analyzed by the Fuoss (1975) equation. The existence of a maximum in the viscosity at a 13 mole ratio of DMF and water is indicated. The Walden products for all the three salts pass through a maximum while the equivalent conductances show a minimum with increasing DMF content. The maxima in the Walden product are attributed to the dehydration of ions by the cosolvent (DMF).Part I:Indian J. Chem. 14A, 1015 (1976).Deceased.     

Symmetric Skorohod topology onn-variable functions and hierarchical Markov properties ofn-parameter processes

Summary We introduce a new Skorohod topology for functions of several variables. Since ann-variable function may be viewed as a one-variable function with values in the set of (n–1)-variable functions, this topology is defined by induction from the classical Skorohod topology for one-variable functions. This allows us to define the notion of completen-parameter symmetric Markov processes: Such processes are, for any 1pn, rawp-parameter Markov processes (in the sense of our previous paper [17]) with values in the space of (n–p)-variable functions. We prove, for these processes and their Bochner subordinates, a maximal inequality which implies the continuity of additive functionals associated with finite energy measures. We finally present several important examples.     

Reflected Brownian motion in a cone: Semimartingale property

Summary In this paper, the object of study is reflected Brownian motion in a cone ind-dimensions (d3) with nonconstant oblique reflection on each radial line emanating from the vertex of the cone. The basic question considered here is When is this process a semimartingale?. Conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by Kwon, which is resolved in terms of a real parameter depending on the cone and the direction of reflection. It is shown that starting from any point of the cone, the process is a semimartingale if < 1, + 0 and not a semimartingale if < < 2.This research is supported by KOSEF grant 941-0100-011-1