A ``universal' dynamical system generated by a continuous map of the interval

In this paper we show that there is a continuous map of the interval such that any -limit set of any continuous map can be transformed by a homeomorphism to an -limit set of . Consequently, any nowhere-dense compact set and any finite union of compact intervals is a homeomorphic copy of an -limit set of .

     

Controlled grafting of cellulose esters using SET‐LRP process

Here, we present the first example of application of single‐electron transfer living radical polymerization (SET‐LRP) process to a controlled grafting of cellulose esters, cellulose diacetate (CDA), and cellulose acetate butyrate (CAB). The cellulose ester macroinitiators with various functionality densities have been prepared by acylation of the backbones with 2‐bromoisobutyryl (BrIB) and dichloroacetyl (DCA) groups, respectively. Methacrylate monomers were polymerized using DCA‐functionalized macroinitiators in the presence of pentamethyldiethylene triamine as a ligand. At 30 °C, the reaction is rather slow, reaching about 10% conversion after 3 to 6 h of polymerization, whereas the higher temperature (60 °C) perceptibly speeds up the polymerization so that methyl methacrylate (MMA) conversion is ～30% after 5 h. Graft copolymers with random‐type and diblock‐type grafts having amphiphilic character were also synthesized. For acrylate grafting (BuA and t‐BuA), BrIB‐functionalized macroinitiators are more convenient in a combination with a low concentration of Cu(0) and Me₆TREN as a ligand and polymerization is detectably faster even at the lower temperature than that of MMA. Kinetic studies show “living” character of both the graftings. Important advantages of SET‐LRP, compared with classic ATRP, are (i) higher polymerization rate, (ii) lower extent of recombination of the growing grafts and (iii) negligible coloration of the products with catalytic residua, so that the prepared polymers do not require additional careful purification. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Development and Validation of an LC–ESI-MS Ion-Trap Method for Analysis of Impurities in Transkarbam 12, a Novel Transdermal Accelerant

A new, sensitive LC–MS method for evaluation of the purity of Transkarbam 12 (T12), a novel and highly effective accelerant of transdermal penetration, has been developed and validated. T12 and its impurities (6-aminohexanoic acid, AH, ε-caprolactam, CA, and dodecyl 6-(6-aminohexanamido)hexanoate, DAH) were characterized by MS and MS–MS analysis. Separation was achieved on a 150 mm × 3 mm, 5-μm particle, phenyl–hexyl column. The mobile phase was a gradient prepared from water, formic acid, and acetonitrile. The method was validated within the concentration range 50–250 ng mL^?1; correlation coefficients were >0.998. The accuracy of the method was from 98.6–105.0% for AH, 102.6–104.8% for CA, and 97.9–100.9% for DAH. Precision was in the range 3.19–4.42% for AH, 3.22–5.81% for CA, and 4.8–8.78% for DAH. The selectivity of the method and sample stability were also confirmed. The practical applicability of the method was proven by analysis of T12 bulk substance.     

Light scattering by optically heterogeneous materials: Structural aspects of dichromatic laser speckle patterns

An analysis is given of dichromatic speckle patterns formed by small-angle scattered light in the illumination of optically heterogeneous systems with light of two nearby wavelengths. The existence of the radial-fibrillar appearance of the speckle patterns is explained; it is shown that the occurrence of the radial-fibrillar “structure” corresponds to the measurable correlation of dichromatic speckle patterns as specified by the spectral spatial cross-correlation function of intensity fluctuations. A measurement of speckle-pattern correlation to determine σ_z (the standard deviation of optical path fluctuations due to the passage of coherent light through a layer of heterogeneous material) is described, and the relations between σ_z and the structural parameters for two simple types of heterogeneous materials are discussed. Experimental results obtained with a series of samples of polyethylene filled with CaCO₃ are in comparatively good agreement with theoretical values.     

An acceleration of Erlenkotter-Körkel’s algorithms for the uncapacitated facility location problem

This contribution is focused on an acceleration of branch and bound algorithms for the uncapacitated facility location problem. Our approach is based on the well-known Erlenkotters’ procedures and Körkels’ multi-ascent and multi-adjustment algorithms, which have proved to be the efficient tools for solving the large-sized instances of the uncapacitated facility location problem. These two original approaches were examined and a thorough analysis of their performance revealed how each particular procedure contributes to the computational time of the whole algorithms. These analyses helped us to focus our effort on the most frequent procedures. The unique contribution of this paper is a new dual ascent procedure. This procedure leads to considerable acceleration of the lower bound computation process and reduces the resulting computational time. To demonstrate more efficient performance of amended algorithms we present the results of extensive numerical experiments.