Block designs signed over groups of order 2n3m

We introduce a new piecewise construction technique for generalised Bhaskar Rao designs and the concepts of generalised Bhaskar Rao block design pieces and holey generalised Bhaskar Rao block designs. We prove composition theorems for these designs. Using this construction technique and the theory of group representations, and the representations of $2$-groups over the field with $3$ elements, we show that the established necessary conditions for the existence of generalised Bhaskar Rao designs of block size $3$ are sufficient for all groups of order $2^n{3}^m$.     

Synthesis of microsequential methylvinylsiloxane–dimethylsiloxane copolymers by nonequilibrium copolymerization

Nonequilibrium anionic ring-opening copolymerization of 1,3,5,7-tetramethyl-1,3,5,7-tetravinylcyclotetrasiloxane (V₄) with hexamethylcyclotrisiloxane (D₃) was examined as a route to methylvinyl–dimethylsiloxane microsequential copolymers. The copolymerization was carried out in toluene and was initiated with Me₃SiCH₂Li using DMSO as the promoter. Distribution of siloxane units obtained from kinetic analysis based on first-order Markovian statistics was compared with that found from analysis by ²⁹Si NMR spectroscopy. Results showed that although chain transfer and back-biting play some role in this system, the kinetics of copolymerization may be described to a reasonable approximation by the first-order Markov model. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 137–145, 1998     

Perchloropolysilane: X-Ray Structure,Solid-State 29Si NMR Spectroscopy,and Reactions of [SiCl2]n

The silicon backbone is all- trans in the crystal structure of perchloropolysilane [SiCl₂]_n (see structure on the right). The Cl atoms can be substituted by nucleophiles to form polymers such as peralkoxy- and peraminopolysilanes.     

Evolution processes of coupled thermal qubits

We investigate the quantum speed limit time (QSLT) of quantum evolution before thermal equilibrium of two coupled qubits each of which is coupled to a separate thermal bath at the same temperature within the Born-Markov approximation. The evolution process in one particular initial state can change between speed-up and speed-down two times before reaching equilibrium. We call this double cusp behaviour. This behaviour is an anomalous phenomenon in evolution processes in the weak-coupling Markovian regime. We study QSLT corresponding to all pure initial energy eigenstates and categorise them. In addition, we also display the conditions for double cusp behaviour in terms of temperature, qubit interaction and frequency.     

Multiparameter kinetic analysis of alkaline hydrolysis of a series of aryl diphenylphosphinothioates: models for P=S neurotoxins

Alkaline hydrolysis of a series of X‐substituted‐phenyl diphenylphosphinothioates ( 2a‐i ) in 80 mol%/20 mol% DMSO at 25.0 ± 0.1°C has been studied kinetically and assessed through a multiparameter approach. Substrates 2a to 2i are approximately 12 to 22 times less reactive than their P=O analogues 1a to 1i (ie, the thio effect). The Brønsted‐type plot for the reactions of 2a to 2i is linear with β_lg = ?0.43, consistent with a concerted mechanism. Hammett plots correlated with σ^o and σ^? constants also support a concerted mechanism; the Yukawa‐Tsuno plot results in an excellent linear correlation with ρ_X = 1.26 and r = 0.30, indicating that expulsion of the leaving group occurs in the rate‐determining step (RDS). The ΔH^? value increases from 10.5 to 11.7 and 13.9 kcal/mol as substituent X in the leaving group changes from 3,4‐(NO₂)₂ to 4‐NO₂ and H, in turn, while TΔS^? remains constant at ?6.0 kcal/mol. The strong dependence of ΔH^? on the electronic nature of substituent X also indicates that the leaving group departs in the RDS. The reaction mechanism and origin of the thio effect are discussed by comparison of the current kinetic results with those reported for the reactions of 1a to 1i . The results suggest that for useful OP neurotoxins the mechanism of abiotic hydrolysis is concerted (with varying degrees of asynchronicity) when the substrate bears good leaving groups.     

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.     

Macrocyclic Tetramers—Structural Investigation of Peptide-Peptoid Hybrids

Outstanding affinity and specificity are the main characteristics of peptides, rendering them interesting compounds for basic and medicinal research. However, their biological applicability is limited due to fast proteolytic degradation. The use of mimetic peptoids overcomes this disadvantage, though they lack stereochemical information at the α-carbon. Hybrids composed of amino acids and peptoid monomers combine the unique properties of both parent classes. Rigidification of the backbone increases the affinity towards various targets. However, only little is known about the spatial structure of such constrained hybrids. The determination of the three-dimensional structure is a key step for the identification of new targets as well as the rational design of bioactive compounds. Herein, we report the synthesis and the structural elucidation of novel tetrameric macrocycles. Measurements were taken in solid and solution states with the help of X-ray scattering and NMR spectroscopy. The investigations made will help to find diverse applications for this new, promising compound class.     

Ultrasonic Spectrometry of Aqueous Solutions of Alkyl Maltosides: Kinetics of Micelle Formation and Head‐Group Isomerization

At frequencies between 100 kHz and 400 MHz, ultrasonic attenuation spectra are measured at 25 °C for aqueous solutions of hexyl‐, heptyl‐, octyl‐, nonyl‐, and decyl‐β‐D ‐maltopyranoside as well as of decyl‐α‐D ‐maltopyranoside. The spectra with surfactant concentration c above the relevant critical micelle concentration (cmc) display three relaxation terms with discrete relaxation times. That with a relaxation time between 0.1 and 1.2 μs is due to exchange of monomers between micelles and the suspending phase. It is discussed in the light of the Teubner–Kahlweit–Aniansson–Wall model of the formation/decay kinetics of systems with Gaussian size distribution of micelles. The relaxation parameters are compared to those for solutions of other non‐ionic surfactants, such as alkyl monoglycosides and poly(ethylene glycol) monoalkyl ethers. At c<cmc this low‐frequency relaxation term is missing and at c≈cmc it is broadened, as is characteristic of solutions of oligomeric molecular structures rather than proper micelles. The relaxation terms with relaxation times between 6 and 15 ns and 0.7 and 2.3 ns reveal head‐group rotations around glycosidic angles and isomerization of the exocyclic hydroxymethyl group, respectively. These unimolecular reactions are also examined with a view to solutions of alkyl monoglycosides as well as of glucose and maltose.     

Existence of (2, 8) GWhD( v) and (4, 8) GWhD( v) with $${ v \equi v 0,1 (mod 8)}$$

(2, 8) Generalized Whist tournament Designs (GWhD) on v players exist only if . We establish that these necessary conditions are sufficient for all but a relatively small number of (possibly) exceptional cases. For there are at most 12 possible exceptions: {177, 249, 305, 377, 385, 465, 473, 489, 497, 537, 553, 897}. For there are at most 98 possible exceptions the largest of which is v = 3696. The materials in this paper also enable us to obtain four previously unknown (4, 8)GWhD(8n+1), namely for n = 16,60,191,192 and to reduce the list of unknown (4, 8) GWhD(8n) to 124 values of v the largest of which is v = 3696.