Synthesis and solvent‐dependent micellization of the amphiphilic block copolymer poly(styreneboronic acid)‐block‐polystyrene

The amphiphilic organoboron block copolymer poly (styreneboronic acid)‐block‐polystyrene ( PSBA‐b‐PS ) has been prepared through a postpolymerization modification route from the silicon‐functionalized block copolymer poly(4‐trimethylsilylstyrene)‐block‐polystyrene ( PSSi‐b‐PS ). PSBA‐b‐PS is obtained through highly selective reaction of PSSi‐b‐PS with BBr₃ at room temperature and subsequent hydrolysis of the BBr₂‐functionalized intermediate. Transmission electron microscopy studies demonstrate that PSBA‐b‐PS undergoes pH dependent micellization in aqueous solution. Different morphologies could be realized by using different mixtures of water and organic solvents. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2438–2445, 2010     

Organoboronium amphiphilic block copolymers

A new class of amphiphilic organometallic block copolymers with cationic organoboron pendant groups was developed. Selective replacement of one of the bromine substitutents on each boryl group of the block copolymer PSBBr₂‐b‐PS with an organometallic reagent ArM (ArM = 2,4,6‐trimethylphenyl copper, 4‐t‐butylphenyltrimethyl tin) followed by treatment with 2,2′‐bipyridine gave the novel block copolymers [ 3Ar ](Br)_n as light yellow solid materials that show good stability in air and moisture and high solubility in most organic solvents. Their structure and composition were confirmed by multinuclear NMR, GPC, and elemental analysis. Highly regular micellar aggregates form in block‐selective solvents (e.g., MeOH, toluene) as demonstrated by ¹H NMR, dynamic light scattering, and transmission electron microscopy. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6612–6618, 2009     

Continuity of the Explosion Time in Stochastic Differential Equations

Abstract

Stochastic ordinary differential equations may have solutions that explode in finite time. In this article we prove the continuity of the explosion time with respect to the different parameters appearing in the equation, such as the initial datum, the drift, and the diffusion.     

Time-space white noise eliminates global solutions in reaction-diffusion equations

We prove that perturbing the reaction-diffusion equation u_t=u_xx+(u₊)^p (p>1), with time-space white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model where a positive stationary solution exists.     

Eigenvalues of the p-Laplacian in fractal strings with indefinite weights

In this paper we study the spectral counting function of the weighted p-Laplacian in fractal strings, where the weight is allowed to change sign. We obtain error estimates related to the interior Minkowski dimension of the boundary. We also find the asymptotic behavior of eigenvalues.     

Refined asymptotics for eigenvalues on domains of infinite measure

In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure. Also, we derive some estimates for the spectral counting function of the Laplace operator on unbounded two-dimensional domains.     

On the Existence of Extremals for the Sobolev Trace Embedding Theorem with Critical Exponent

In this paper, the existence problem is studied for extremalsof the Sobolev trace inequality W^1,p()L^p*(), where is a boundedsmooth domain in R^N, p*=p(N–1)/(N–p), is the criticalSobolev exponent, and 1 < p < N. 2000 Mathematics SubjectClassification 35J65 (primary), 35B33 (secondary).