Representation of integral quantales by tolerances

The central result of the paper claims that every integral quantale \(\mathbf {Q}\) has a natural embedding into the quantale of complete tolerances on the underlying lattice of \(\mathbf {Q}\). As an application, we show that the underlying lattice of any finite integral quantale is distributive in 1 and dually pseudocomplemented. Besides, we exhibit relationships between several earlier results. In particular, we give an alternative approach to Valentini’s ordered sets and show how the ordered sets are related to tolerances.     

Recoupling of residual dipolar couplings in single-domain polymer-stabilized liquid crystals undergoing magic-angle spinning

Measurement of dipolar couplings, chemical shift anisotropies, and quadrupole couplings in oriented media such as liquid crystals are of great importance for extraction of structural parameters in biological macromolecules. Here, we introduce a new technique, SAD-REDOR, that consists of recoupling heteronuclear dipolar couplings in molecules dissolved in a single-domain liquid crystal or other oriented medium through the combined use of magic-angle spinning and rotor-synchronized radiofrequency pulses. This application of the REDOR pulse sequence to oriented media offers several advantages such as selectivity over the type of coupling recovered and tunable scaling of the interaction. The effectiveness of the technique is demonstrated both theoretically and experimentally, using the recently developed polyacrylamide-stabilized Pf1 phage medium and 15N-labeled benzamide as the aligned molecule.     

On highly palindromic words

We study some properties of palindromic (scattered) subwords of binary words. In view of the classical problem on subwords, we show that the set of palindromic subwords of a word characterizes the word up to reversal.Since each word trivially contains a palindromic subword of length at least half of its length-a power of the prevalent letter-we call a word that does not contain any palindromic subword longer than half of its length minimal palindromic. We show that every minimal palindromic word is abelian unbordered, that is, no proper suffix of the word can be obtained by permuting the letters of a proper prefix.We also propose to measure the degree of palindromicity of a word w by the ratio |rws|/|w|, where the word rws is minimal palindromic and rs is as short as possible. We prove that the ratio is always bounded by four, and construct a sequence of words that achieves this bound asymptotically.     

Syntheses and crystal structures of three novel Cu(II) coordination polymers of different dimensionality constructed from Cu(II) carboxylates (carboxylate = malonate (mal), 2 acetate (ac), fumarate (fum)) and conformationally flexible 1,4-bis(imidazole-1-yl-methylene)benzene (IX)

We herein report three new coordination polymers generated from Cu(II) carboxylates (mal, 2ac, fum) and conformationally flexible bifunctional IX as building blocks. All the three complexes adopt unique structures in the solid state. The complex [Cu₂(mal)₂(IX)₂(H₂O)₆]_n crystallizes as orthorhombic co-linear rods with space group P2(1) P2(1) P2(1). Each rod is further formed of two tightly intertwined strings. The second polymer [Cu₂(ac)₄(IX)₂]_n crystallizes with space group P1 which consists of two sets of intersecting 2D sheets composed of parallel rods which interpenetrate to form a fully interlocked 3D structure. In both these complexes IX coordinates in the anti mode. The third polymer [Cu₂(fum)₂(IX)₂(H₂O)₂]_n possesses a monoclinic crystal system with space group C₂/c and crystallizes as 1D straps. Cu–fum–Cu forms the base of the string which is alternatively garlanded by a macrocycle derived from Cu₂(IX)₂ unit, where IX coordinates in the syn fashion. The present study suggests that the use of a rigid building block with a flexible organic ligand leads to a better prediction of the final structure of the polymeric array.     

Solubilization of polyaniline in water by interpolymer complexation

Water solubility of electro-active polymers in their doped state may provide a possibility for environmentally feasible manufacturing processes. Because previous results in this direction require expensive modifications or impractical template polymerization methods, we created a simple method of mixing components with a large molecular weight difference. The polymer which acts as an acidic dopant and provides water solubility, has to have the higher molecular weight. The formed complex resembles a block copolymer but in this case the polyaniline block is attached to the sulfonated polystyrene chain by strong physical interactions instead of chemical end-to-end linkage.     

Reactivation of a Poisoned Metallocene Catalyst by Irradiation with Visible Light

Both oxygen and carbon dioxide are efficient catalyst poisons, remarkably reducing the ethylene polymerisation rate, increasing the molecular weight of the resulting polyethylene, and broadening its molecular weight distribution (MWD). By introducing visible light into the contaminated polymerisation system, the catalyst activity was totally recovered. The molecular weight and MWD became similar to those of a non‐poisoned system, supporting the formation of new active sites during poisoning that are responsible for the lower activity and broader MWD.     

Effect of Ground Rubber Powder on Properties of Natural Rubber

Ground rubber powder (GRP) with three different sizes was incorporated into nature rubber matrix with different loading. Cure characteristics, swelling behaviour, crosslink density, tensile fractured surface, and mechanical properties have been studied. Based on the cure characteristics, it is evident that the processability of the rubber compounds has not changed obviously with the different GRP loading. The introduction of GRP in virgin rubber leads to the increase in swelling degree and the decrease in crosslink density. Tensile strength, hardness and abrasion resistant deteriorate with the increase of GRP loading, but the tear resistance gets better. If the ground rubber particles are smaller, the properties are more similar to the virgin rubber. Because of the phase separation of the GRP and matrix, the properties get worse with the bigger ground rubber powder.