A Multidimensional Branch-and-Prune Method for Interval Global Optimization

In this paper a new multidimensional extension of the recently developed one-dimensional enclosure method called kite is given for interval global optimization. A more sophisticated version of the pruning technique based on the kite method is introduced. By the new componentwise approach all the one-dimensional theoretical results and procedures can be used in the higher-dimensional case. The possibilities in the implementation of the new algorithm together with numerical results on 40 standard test problems are presented.     

Hydrogen-bonded block mesogens derived from semiperfluorinated benzoic acids and the non-mesogenic 1,2-bis(4-pyridyl)ethylene

Thermal properties of benzoic acids carrying one or two semiperfluorinated alkoxy tails on the aromatic core have been investigated in binary mixtures with the non-liquid crystalline bidirectional trans-1,2-bis(4-pyridyl)ethylene. The hydrogen bonded complexes built from the complementary molecular species show a significantly enhanced mesophase stability compared with the fluorinated acids in their pure states. The mesophase morphologies of the complexes are governed mainly by the number of the partially fluorinated chains grafted to the acid component. Mixed systems comprising the one-chain acids exhibit a smectic C phase followed by a smectic A phase at more elevated temperatures. Incorporation of a second semiperfluorinated chain into the acid leads to the formation of columnar mesophases. These columnar phases of the H-bonded complexes should represent ribbon phases resulting from the collapse of the smectic layers.     

New disc-shaped mesogens based on pentakis(phenylethynyl)benzene derivatives

First examples of amphiphilic alkyl pentakis(phenylethynyl)benzene ethers containing functional groups at the terminal position of their alkoxy chains were synthesized by etherification of pentabromophenol with 11-bromoundecan-1-ol and 11-bromoundecanoic acid ethyl ester, respectively, and subsequent palladium catalyzed, fivefold coupling reactions with the substituted phenylacetylene. Two undecanoic acid derivatives with different pentakis(phenylethynyl)phenoxy substituents in the ω-position were prepared by ester cleavage from the corresponding ethyl esters. The thermal behaviours of five penta-alkynes in their pure states, as well as of their charge transfer complexes formed from mixtures with 2,4,7-tri-nitrofluorenone, were examined.