Synthesis of various stimuli‐responsive gradient copolymers by living cationic polymerization and their thermally or solvent induced association behavior

Stimuli‐responsive gradient copolymers, composed of various monomers, were synthesized by living cationic polymerization in the presence of base. The monomers included thermosensitive 2‐ethoxyethyl vinyl ether (EOVE) and 2‐methoxyethyl vinyl ether (MOVE), hydrophobic isobutyl vinyl ether (IBVE) and 2‐phenoxyethyl vinyl ether (PhOVE), crystalline octadecyl vinyl ether (ODVE), and hydrophilic 2‐hydroxyethyl vinyl ether (HOVE). The synthesis of gradient copolymers was conducted using a semibatch reaction method. Living cationic polymerization of the first monomer was initiated using a conventional syringe technique, followed by an immediate and continuous addition of a second monomer using a syringe pump at regulated feed rates. This simple method permitted precise control of the sequence distribution of gradient copolymers, even for a pair of monomers with very different relative monomer reactivities. The stimuli‐responsive gradient, block and random copolymers exhibited different self‐association behavior. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6444–6454, 2008     

Effect of side groups of polymer glycol on microphase‐separated structure and mechanical properties of polyurethane elastomers

The effect of side methyl and dimethyl groups of the soft segment component on the microphase‐separated structure and mechanical properties of polyurethane elastomers (PUEs) was investigated. Poly(oxytetramethylene) glycol (PTMG), and PTMG incorporating dimethyl groups (PTG‐X) and methyl side groups (PTG‐L) were used as a polymer glycol, which forms a soft segment in the PUEs. The PUEs were synthesized with 4,4′‐dipheylmethane diisocyanate [1,1′‐methylenebis(4‐isocyanatobenzene)], 1,4‐butane diol, and 1,1,1‐trimethylol propane by a prepolymer method. The degree of microphase separation of the PUEs became weaker with increasing side group content in polymer glycols. Dynamic viscoelastic properties measurement showed reorganized‐crystallization and melting of the soft segment for the PUEs based on PTMG, PTG‐L, and PTG‐X with a lower content of the side groups, but not for a PTG‐L and PTG‐X with higher content of the side groups. Tensile testing revealed that increasing methyl group concentration made the PUEs soften and weaken. The PTMG‐based PUEs obviously exhibited strain‐induced crystallization of the soft segment chains during elongation process. In contrast, for the PTG‐L and PTG‐X‐based PUEs, crystallinity decreased with increasing side group content, and the PUEs with PTG‐L and PTG‐X with highest methyl group content did not crystallize even at a large strain. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2054–2063, 2008     

Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M₀ in containing M such that .     

一种结合Mean—shift和粒子滤波的视频跟踪算法

提出一种结合均值偏移算法和粒子滤波理论的视频跟踪算法,解决了目标旋转、部分遮挡和运动速度过快的问题．通过均值偏移对粒子滤波中的粒子集进行进一步寻优,增加了粒子的有效性,极大减少了粒子采样的数量,且解决了经过多次重采样后粒子多样性降低的问题．新的粒子通过与观测值之间的巴氏系数来决定重要性权重．实验证明：本算法可以完成实时地对视频目标进行部分遮挡以及目标旋转下的跟踪,具有较强的鲁棒性．     

DE-Sinc methods have almost the same convergence property as SE-Sinc methods even for a family of functions fitting the SE-Sinc methods

In this paper, the theoretical convergence rate of the trapezoidal rule combined with the double-exponential (DE) transformation is given for a class of functions for which the single-exponential (SE) transformation is suitable. It is well known that the DE transformation enables the rule to achieve a much higher rate of convergence than the SE transformation, and the convergence rate has been analyzed and justified theoretically under a proper assumption. Here, it should be emphasized that the assumption is more severe than the one for the SE transformation, and there actually exist some examples such that the trapezoidal rule with the SE transformation achieves its usual rate, whereas the rule with DE does not. Such cases have been observed numerically, but no theoretical analysis has been given thus far. This paper reveals the theoretical rate of convergence in such cases, and it turns out that the DE’s rate is almost the same as, but slightly lower than that of the SE. By using the analysis technique developed here, the theoretical convergence rate of the Sinc approximation with the DE transformation is also given for a class of functions for which the SE transformation is suitable. The result is quite similar to above; the convergence rate in the DE case is slightly lower than in the SE case. Numerical examples which support those two theoretical results are also given.     

AnL 1 smoothing spline algorithm with cross validation

We propose an algorithm for the computation ofL ₁ (LAD) smoothing splines in the spacesW _M (D), with . We assume one is given data of the formy _i =(f(t _i ) + _i , i=1,...,N with {itt_i} _i=1 ^{N D} , the _i are errors withE( _i )=0, andf is assumed to be inW _M . The LAD smoothing spline, for fixed smoothing parameter0, is defined as the solution,s , of the optimization problem (1/N) _i=1 ^N ¦y _i –g(t _i ¦+J _M (g), whereJ _M (g) is the seminorm consisting of the sum of the squaredL ₂ norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s , would be expected to give robust smoothed estimates off in situations where the _i are from a distribution with heavy tails. The solution to such a problem is a thin plate spline of known form. An algorithm for computings is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The data driven selection of the smoothing parameter is achieved by minimizing aCV() score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in 0 taken on the above SQPs parametrized in, with the optimal smoothing parameter taken to be that value of at which theCV() score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.     

The endomorphism spectrum of an ordered set

Theendomorphism spectrum of an ordered setP, spec(P)={|f(P)|:f End(P)} andspectrum number, sp(P)=max(spec(P)\{|P|}) are introduced. It is shown that |P|>(1/2)n(n – 1) ^{n – 1} implies spec(P) = {1, 2, ...,n} and that if a projective plane of ordern exists, then there is an ordered setP of size 2n ²+2n+2 with spec(P)={1, 2, ..., 2n+2, 2n+4}. Lettingh(n)=max{|P|: sp(P)n}, it follows thatc ₁ n ²h(n)c ₂ n ⁿ⁺¹ for somec ₁ andc ₂. The lower bound disproves the conjecture thath(n)2n. It is shown that if |P| – 1 spec(P) thenP has a retract of size |P| – 1 but that for all there is a bipartite ordered set with spec(P) = {|P| – 2, |P| – 4, ...} which has no proper retract of size|P| – . The case of reflexive graphs is also treated.Partially supported by a grant from the NSERC.Partially supported by a grant from the NSERC.     

A Construction of Difference Sets in High Exponent 2-Groups Using Representation Theory

Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Menon difference sets (or Hadamard), and they have parameters (2^2d+2, 2^2d+1±2 ^d , 2^2d ±2 ^d ). In the abelian case, the group has a difference set if and only if the exponent of the group is less than or equal to 2 ^d+2. In [14], the authors construct a difference set in a nonabelian group of order 64 and exponent 32. This paper generalizes that result to show that there is a difference set in a nonabelian group of order 2^2d+2 with exponent 2 ^d+3. We use representation theory to prove that the group has a difference set, and this shows that representation theory can be used to verify a construction similar to the use of character theory in the abelian case.