Minimum boundary touching tilings of polyominoes

We study the problem of tiling a polyomino P with as few squares as possible such that every square in the tiling has a non‐empty intersection with the boundary of P . Our main result is an algorithm which given a simply connected polyomino P computes such a tiling of P . We indicate how one can improve the running time of this algorithm for the more restricted row‐column‐convex polyominoes. Finally we show that a related decision problem is in NP for rectangular polyominoes. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic NMR study of the flexibility of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts

Dynamic NMR investigations of a number of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts were carried out. The barrier to rotation of the partial C, N double bond was determined and proved to be in the range of 62 to 63 kJ/mol. Quantum chemical calculations of bond orders and electron densities of the different atoms in the molecules show the distinct double bond character of the exocyclic C, N bond. This is in agreement with the relatively high barrier to rotation. By quantum chemical ab initio 3-21G calculations, the dynamic behaviour of this kind of compounds was simulated; two pairs (image and mirror image) of ground state conformations, in coincidence with the experiment, were obtained. Received: 10 May 1996 / Revised: 1 July 1996 / Accepted: 4 July 1996     

A note to the paper “An efficient algorithm for linear programming” of V Ch Venkaiah

In Venkaiah [1] an algorithm for solving linear optimization problems based on the idea of the projective algorithm of Karmarkar, is proposed. The essential simplification in the new algorithm is the use of a fixed projection operator. In this way the algorithm requires onlyO(n ² ) operations to obtain a sufficient exact solution. In this note it is shown that in some special cases the algorithm of Venkaiah yields a feasible solution that is far from the optimal one.     

Metal Complexes with Macrocyclic Ligands. Part XXIX.. Structural and kinetic studies of two isomeric Cu2+ complexes with 1,4-dimethyl-8-[2-(2-pyridyl)ethyl]-1,4,8,11-tetraazacyclotetradecane

The synthesis and complexation properties of 1,4-dimethyl-8-[2-(2-pyridyl)ethyl]-1,4,8,11-tetraazacyclotetra-decane ( 2 ) are described. This ligand forms with Cu²⁺ two complexes, one of which has been characterized by X-ray structure analysis. The structural, spectral, and kinetic studies indicate that the two Cu²⁺ complexes are isomers with the macrocycle in the trans-III and trans-I configuration. The rate of the interconversion of the trans-I isomer to the thermodynamically more stable trans-III species is proportional to [OH^?]. A mechanism for this reaction is proposed.     

Synthesis and blending behavior of an oligoarylenevinylene. Design towards processable materials for LED applications

A bisstyrenebenzene with improved solubility can be obtained by a lateral phenyl substituent on the phenylene ring. The phenyl substituted bisstyrenebenzene (PBSB) was synthesized by Pd-catalyzed coupling of 2,5-dibromobiphenyl and styrene. PBSB exhibits blue fluorescence in solution. Blends of PBSB and polystyrene or polycarbonate are homogeneous over a wide concentration range of PBSB, based on differential scanning calorimetry (DSC) and scanning electron microscopy (SEM). The results were compared with the blending behavior of unsubstituted bisstyrenebenzene.