The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

Large Scale Linear Programs and Heuristics for the Design of Survivable Telecommunication Networks

We consider the problem of providing a minimum cost multi-service network subject to one link failure scenarios. We assume our network is fully meshed and demand is satisfied by using direct or two hop-paths. We provide a large scale linear programming formulation and propose and test two effective heuristics.     

Fast atom bombardment mass spectra of keto acid and keto ester phosphoranes

Positive-ion fast atom bombardment mass spectra of 13 keto acid and keto ester phosphoranes were examined. All compounds gave a protonated molecular ion and characteristic peaks at m/z 303, 279, 262 and 201.     

Separation index of a graph

The concepts of separation index of a graph and of a surface are introduced. We prove that the separation index of the sphere is 3. Also the separation index of any graph faithfully embedded in a surface of genus g is bounded by a funtion of g. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 53–61, 2002     

Emission and sputtering characteristics of Ne-Ar mixed gas glow discharge plasmas.

The emission characteristics of several Cu lines emitted from a Ne-Ar mixed gas glow discharge plasma were investigated. The addition of small amounts of Ar to a Ne plasma increases the sputtering rate of a Cu sample because Ar ions, which work as the impinging ions for cathode sputtering, are predominantly produced through Penning ionization collisions between Ne metastables and Ar atoms. Ar addition also elevates the number density of electrons in the plasma. These changes occurring in the Ne-Ar mixed gas plasma result in enhanced emission intensities of the Cu lines. The Cu II 270.10-nm and the Cu II 224.70-nm lines yield different intensity dependence on the Ar partial pressure added. This phenomenon is because these Cu II lines are excited principally through different charge transfer processes: collisions with Ne ions for the Cu II 270.10-nm line and collisions with Ar ions for the Cu II 224.70-nm line. The shape of sputtered craters in the Ne-Ar glow discharge plasma was measured. The depth resolution was improved when Ar was added to a Ne plasma because the crater bottoms were flatter with larger Ar partial pressures.     

Continuity of the Solution Map in Parametric Affine Variational Inequalities

A systematic study of the upper semicontinuity and the lower semicontinuity of the solution map in parametric affine variational inequalities is given in this paper. Several examples are constructed to analyze the results. This work was supported by Korea Research Foundation Grant (KRF 2001-015-DP0049), the APEC Postdoctoral Fellowships Program, and the KOSEF Brain Pool Program.     

Positive Schatten(-Herz) Class Toeplitz Operators on the Half-space

On the harmonic Bergman space of the half-space, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten (or Schatten-Herz) class operator in terms of averaging functions and Berezin transforms. Examples are provided to show that various results are sharp. This research was supported by KOSEF(R01-2003-000-10243-0).