Depth profiling of latex blends of fluorinated and fluorine‐free acrylates with laser‐induced secondary mass spectrometry

We explored phase separation and self‐assembly of perfluoroalkyl segments at the surface of polymer films obtained from latices of semifluorinated acrylate copolymers and the corresponding latex blends of nonfluorinated and semifluorinated polyacrylates. With laser‐induced secondary mass spectrometry the fluorine distribution was measured after annealing above the minimum film‐forming temperature of the polymers up to a depth of several micrometers. Depth profiles of a semifluorinated acrylate homopolymer and latex blends thereof with fluorine‐free alkylacrylates with 25, 50, and 75 mol % semifluorinated acrylate as well as a copolymer comprised of alkyl acrylate and semifluorinated acrylate (50/50 mol %) were investigated. In the case of latex blends containing both semifluorinated polyacrylates and fluorine‐free or low‐fluorine polymers, self‐assembly accounted for enrichment of the perfluoroalkyl segments at the surface. Coatings exhibiting low surface energy and having a substantially reduced total fluorine content were obtained. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 360–367, 2003     

Differentiation of chiral phosphorus enantiomers by P and H NMR spectroscopy using amino acid derivatives as chemical solvating agents

The ability of commercially available amino acid derivatives, especially Fmoc-Trp(Boc)-OH, to differentiate enantiomers of chiral phosphonates, phosphinates, phosphates, phosphine oxides, and phosphonamidates is demonstrated with (31)P, (13)C, and (1)H NMR spectroscopy. The chiral differentiation provided a rapid and convenient method for measuring the enantiomeric purity of these phosphorus compounds.     

Combinatorial Characterizations of Authentication Codes II

For any authentication code for k source states and v messages having minimum possible deception probabilities (namely, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaaS% baaSqaaiaadsgaaeqaaOWaaSbaaSqaaiaaicdaaeqaaOGaeyypa0Za% aSGbaeaacaWGRbaabaGaamODaaaaaaa!3F28!\[P_d _0 = {k \mathord{\left/ {\vphantom {k v}} \right. \kern-\nulldelimiterspace} v}\] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9qq-f0-yqaqVeLsFr0-vr% 0-vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbWaaS% baaSqaaiaadsgaaeqaaOWaaSbaaSqaaiaaigdaaeqaaOGaeyypa0Ze% xLMBb50ujbqeguuDJXwAKbacfaGae8hkaGIaam4AaiabgkHiTiaaig% dacqWFPaqkcqWFVaWlcqWFOaakcqWF2bGDcqGHsislcaaIXaGae8xk% aKIae8xkaKcaaa!4CD1!\[P_d _1 = (k - 1)/(v - 1))\], we show that there must be at least v encoding rules. (This can be thought of as an authentication-code analogue of Fisher's Inequality.) We derive several properties that an extremal code must satisfy, and we characterize the extremal codes for equiprobable source states as arising from symmetric balanced incomplete block designs. We also present an infinite class of extremal codes, in which the source states are not equiprobable, derived from affine planes.Dedicated to Gus Simmons     

Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity

We consider the nonlinear Schrödinger equation: (1) $${{i\partial u} \mathord{\left/ {\vphantom {{i\partial u} {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} = - \Delta u - \left| u \right|^{{4 \mathord{\left/ {\vphantom {4 N}} \right. \kern-\nulldelimiterspace} N}} uandu\left( {0,.} \right) = \varphi \left( . \right),$$ whereu:[0,T)×? ^N →?. For any given pointsx ₁,x ₂,...,x _k in ? ^N , we construct a solution of Eq. (1),u(t), which blows up in a finite timeT at exactlyx ₁,x ₂,...,x _k . In addition, we describe the precise behavior of the solutionu(t) whent→T, at the blow-up points {x ₁,x ₂,...,x _k } and in ? ^N ?{x ₁,x ₂,...,x _k }.