New upper bounds on the minimum size of covering designs

Let D = {B₁, B₂,…, B_b} be a finite family of k-subsets (called blocks ) of a v-set X(v) = {1, 2,…, v} (with elements called points ). Then D is a (v, k, t) covering design or covering if every t-subset of X(v) is contained in at least one block of D. The number of blocks, b, is the size of the covering, and the minimum size of the covering is called the covering number , denoted C(v, k, t). This article is concerned with new constructions of coverings. The constructions improve many upper bounds on the covering number C(v, k, t) © 1998 John Wiley & Sons, Inc. J Combin Designs 6:21–41, 1998     

Consistent lattice Boltzmann method

Lack of energy conservation in lattice Boltzmann models leads to unrealistically high values of the bulk viscosity. For this reason, the lattice Boltzmann method remains a computational tool rather than a model of a fluid. A novel lattice Boltzmann model with energy conservation is derived from Boltzmann's kinetic theory. Simulations demonstrate that the new lattice Boltzmann model is the valid approximation of the Boltzmann equation for weakly compressible flows and microflows.     

Stilbene derivatives from two species of Gnetaceae

Five new stilbene oligomers (gnemonols A, B and C, gnemonoside E and gnetal) were isolated together with 2b-hydroxyampelopsin F and gnetin E from Gnetum gnemon and G. gnemonoides. The structures of the compounds were elucidated on the basis of spectral evidence.     

On semiclassical four‐point correlators in AdS5 × S5

Following the recent advances in the holographic calculation of n‐point correlation functions with two “heavy” (with large quantum numbers) states at strong coupling, we extend these findings by computing specific contributions to four‐point correlators of four heavy BMN operators in �� = 4 supersymmetric Yang–Mills theory.     

Synthesis and Properties of Hydrophilized Tertiaryamine Polymers Obtained by Graphitide-Initiated Anionic Copolymerization of a N,N-Disubstituted Aminothiirane with Oxiranes

Abstract

New functional aliphatic copolymers have been synthesized by an-ionic ring opening polymerization of N-methyl-N-sec-butyl-N-(thii-rane-2-ylmethyl) amine (Me-sBu, ESA) with either trimethylsilyl protected glycidol (TMSGE) or ethylene oxide (EO) using potassium graphitide KC₂₄ or sodium metal as initiators. Whenever TMSGE was present, TMSGE chain growing was perturbed by transfer reactions. Branched TMSGE homopolymers and Me-sBu, ESA/TMSGE copolymers were obtained with both the expected 1–3 polyglycidol and the unusual 1-4 poly(3-hydroxyoxetane) enchainments, as shown by ¹³C NMR. Copolymers of different compositions obtained by varying the Me-sBu, ESA/TMSGE feed composition from 85/15 to 35/65 or the Me-sBu, ESA/EO one from 76/24 to 64/36 were amorphous and random, as shown by DTA and ¹³C NMR studies. Copolymers with less than 20% of EO or TMSGE-derived units in the chain were soluble in water at pH < 4. Potentiometric titration curves showed the presence of a plateau (for the degree of neutralization α in the range 0.15 < α < 0.9) due to phase separation, as in the case of Me-sBu, ESA homopolymers. Copolymers with more than 50% of TMSGE units in the chain were soluble in water at pH < 7 and exhibited normal potentiometric titration curves with pH increasing progressively in the range 0.15 < α < 0.9. From these data, it is concluded that TMSGE- or EO-derived hydrophilic repeat units are unable to promote globular structure, in contrast to quaternary ammonium repeat units.     

N,N,N-trimethylchitosan iodide complexes with a weak or a strong polyacid and nanoparticles thereof

Polyelectrolyte complexes (PECs) were prepared from N,N,N-trimethylchitosan iodide (TMCh) of different molar mass and a weak polyacid-poly(acrylic acid) (PAA) or a strong polyacid-poly(2-acrylamido-2-methylpropanesulfonic acid) (PAMPS). The quaternization of the amino groups of chitosan enabled the formation of water-insoluble PECs in a broad pH range—from 3 to 12 and from 1 to 12 for TMCh/PAA and TMCh/PAMPS, respectively. Whereas the stoichiometry of the TMCh/PAA complex was pH dependant, the stoichiometry of the TMCh/PAMPS complex did not depend on pH. The stoichiometry and the yield of the complexes were influenced by the molar mass of TMCh. PEC nanoparticles were produced by mixing dilute solutions of the oppositely charged polyelectrolytes as revealed by dynamic light scattering analyses. The size of the particles was in the range of 135–924 nm and depended on the polyelectrolyte molar mass, the initial polyelectrolyte concentration, and the molar fraction of the TMCh units. Microbiological screening against Staphylococcus aureus and Escherichia coli revealed that PECs between TMCh and PAA or PAMPS have a good antibacterial effect, which is more slowly pronounced than that of the starting TMCh of different molar mass.     

A method for efficiently computing the number of codewords of fixed weights in linear codes

The problem of computing the number of codewords of weights not exceeding a given integer in linear codes over a finite field is considered. An efficient method for solving this problem is proposed and discussed in detail. It builds and uses a sequence of different generator matrices, as many as possible, so that the identity matrix takes disjoint places in them. The efficiency of the method is achieved by optimizations in three main directions: (1) the number of the generated codewords, (2) the check whether a given codeword is generated more than once, and (3) the operations for generating and computing these codewords. Since the considered problem generalizes the well-known problems “Weight Distribution” and “Minimum Distance”, their efficient solutions are considered as applications of the algorithms from the method.     

Darstellung von isotaktischem Polystyrol auf bin?ren K- Graphit-Inklusions-Verbindungen

Ohne Zusammenfassung     

Electrospun chitosan-coated fibers of poly(L-lactide) and poly(L-lactide)/poly(ethylene glycol): preparation and characterization

Fibrous poly(L-lactide) (PLLA) and bicomponent PLLA/poly(ethylene glycol) mats were prepared by electrospinning and then were coated with chitosan. The presence of chitosan coating was proved by scanning electron microscopy and by fluorescence microscopy. On contact with blood, the chitosan coating led to changes in erythrocyte shape and in their aggregation. The haemostatic activity of the mats increased with increasing chitosan content. Microbiological studies against Staphylococcus aureus revealed that the chitosan coating imparts antibacterial activity to the hybrid mats. The combined haemostatic and antibacterial activities render these novel materials suitable for wound-healing applications.