Chemometrics-based approach to enhancing the usefulness of time domain reflectometry in investigating properties of granular materials.

Sets of time domain reflectometry waveforms analyzed with appropriate chemometric methods, instead of typical single waveform analysis, enable one to detect and quantify differences between waveforms, even if they appear at the level of several orders of magnitude below the scale of the measurements. Typical applications of such an approach to samples of healthy and damaged grain showed that differences contributing five orders of magnitude below the scale are still detectable. Under more rigorous experimental conditions, the level of detectable differences can be expected to be even lower.     

Lower bound technique in the theory of a stochastic differential equation

We establish a criterion for the existence of an invariant measure for Markov processes acting on measures defined on an arbitrary complete separable metric space. This criterion is applied to time-homogeneous Markov processes associated with a nonlinear heat equation driven by an impulsive noise.     

Synthesis of poly(glycidol)‐block‐poly(N‐isopropylacrylamide) copolymers using new hydrophilic poly(glycidol) macroinitiator

New, water soluble poly(glycidol) (PGl) macroinitiators for atom transfer radical polymerization (ATRP) were synthesized. This new class of macroinitiators were prepared in a three‐step process. First, series of well‐defined ω‐hydroxyl functional poly(glycidol acetal)s with different molecular weights was synthesized via anionic polymerization followed by quantitative termination of anionically growing active sites. End capping was achieved by treatment of living chain ends with water. The living nature of the system and termination reaction is discussed. In the second stage, monofunctional poly(glycidol acetal)s were functionalized by esterification with 2‐chloropropionyl chloride. Finally, selective deprotection (hydrolysis) of acetal protective groups was performed. As simultaneous partial cleavage of ester bond of attached ATRP moieties was unavoidable, the final functionality of macroinitiator calculated from ¹H NMR varied in the range 85–95%. The obtained (2‐chloropropionyl) poly(glycidol) macroinitiator with DP = 55 and 90% functionality was successfully used in ATRP polymerization of N‐isopropylacrylamide (NIPAAm) at room temperature in the DMF/water mixture. Linear block copolymers with relatively narrow molecular weight distribution and controlled composition were obtained and characterized with ¹H NMR and SEC‐MALLS measurements. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2488–2499, 2008     

The smooth cohomology ofN=2 supersymmetric Landau-Ginzburg field theories

We compute the smooth cohomology (both unrestricted and compactly supported) of the supercharge of an ultraviolet cutoffN=2 supersymmetric Landau-Ginzburg field theory.Supported in part by the National Science Foundation under grant DMS-9206936.Supported in part by the Department of Energy under grant DE-FG02-88ER25065.     

Asymptotic Stability of Some Nonlinear Boltzmann-Type Equations

A generalized version of the Tjon-Wu equation is considered. It describes the evolution of the energy distribution in a model of gas in which simultaneous collisions of many particles are permitted. Using the technique of Zolotarev metrics we show that the stationary solution is exponentially stable.     

Initial-boundary value problems for non-linear equations of generalized thermoelasticity and elasticity

We formulate a local existence theorem for the initial-boundary value problems of generalized thermoelasticity and classical elasticity. We present a unified approach to such boundary conditions as, for example, the boundary condition of traction, pressure or place combined with the boundary condition of heat flux or temperature.