Banana-shaped side chain liquid crystalline siloxanes

Eight banana-shaped side chain liquid crystalline oligomers and polymers have been synthesized by hydrosilylation of vinyl-terminated bent-core mesogens with trimethylsilyl-terminated siloxanes. The synthesized oligomers and polymers, and their olefinic precursors, were investigated by polarizing optical microscopy (POM), differential scanning calorimetry, X-ray diffraction (XRD), electro-optical experiments and Maldi-Tof. The short-tailed olefins form a Col_r mesophase, whereas those with longer chains exhibit the SmCP_A mesophase. All the oligomers and polymers studied show liquid crystalline properties and do not crystallize upon cooling. Most oligomers with around four repeating siloxane units, show a lamellar (layer) structure and antiferroelectric switching properties, the SmCP_A phase. XRD shows that the layer spacings are hardly influenced by the length of the terminal tails. The oligomer prepared from the smallest olefinic precursor, having the shortest alkyl tail, shows an XRD pattern reminiscent of a columnar phase, although POM displays domains of opposite chirality, and no switching behaviour could be detected. The polymers with around 35 repeating siloxane units are liquid crystalline, but due to their high viscosity a thorough characterization of the liquid crystalline phases was impossible.     

On asymptotic theory for multivariate GARCH models

The paper investigates the asymptotic theory for a multivariate GARCH model in its general vector specification proposed by Bollerslev, Engle and Wooldridge (1988) [4], known as the VEC model. This model includes as important special cases the so-called BEKK model and many versions of factor GARCH models, which are often used in practice. We provide sufficient conditions for strict stationarity and geometric ergodicity. The strong consistency of the quasi-maximum likelihood estimator (QMLE) is proved under mild regularity conditions which allow the process to be integrated. In order to obtain asymptotic normality, the existence of sixth-order moments of the process is assumed.     

Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer

A moiré interferometer is used to measure the thermal expansion of two ferroelectric crystals, LiNbO₃ and KTiOPO₄. The crystal samples are patterned with a chromium reflective grating and used as a diffractive component in a reflective grating interferometer. The thermal expansion of all the three axes of congruent LiNbO₃ and of x and y axes of the flux-grown KTiOPO₄ were measured from room temperature to 200 °C. For this temperature range the thermal expansion coefficient has been modeled by a second-order polynomial and its coefficients have been estimated by accurate analysis of the resulting moiré fringe pattern.     

Hybrids of the hemiasterlin analogue taltobulin and the dolastatins are potent antimicrotubule agents

The targeting of microtubules is an important mechanism for cancer chemotherapy. However, there is still a need for improved antimicrotubule agents. A number of seemingly structurally disparate peptidic natural products inhibit tubulin polymerization by binding to a region of the tubulin heterodimer close to the vinca binding site. An analogue of the naturally occurring tripeptide hemiasterlin, taltobulin (HTI-286, 3), has advanced to clinical trials. Structure-activity relationship studies of 3 have revealed critical structural elements necessary for antimicrotubule activity that correspond to comparable groups in the amino terminus tripeptide region of the dolastatins. To investigate the structural relationship between the hemiasterlins and the more complex dolastatins, hybrid compounds composed of 3 and the carboxy terminus dipeptides of dolastatin 10, or the dolastatin 15 analogue cemadotin, were synthesized. The resulting hybrid compounds were potent antimicrotubule agents, thus establishing a structural relationship between the hemiasterlins and the dolastatins. This relationship may be useful in the design of analogues having improved activity in resistant cell lines expressing the P-glycoprotein transporter, for establishing structural relationships with other classes of peptidic antimicrotubule agents, or for modeling studies of the tubulin binding site of these agents.     

Redox-active pH-responsive molecules: ferrocenylphosphonic acid, ferrocenylmethylphosphonic acid and 1,1'-ferrocenylbisphosphonic acid. Structural determination of FcPO3Na2.5H2O

The acidity constants of the reduced and oxidized species of ferrocenylphosphonic acids FcPO3H2, FcCH2PO3H2 and fc(PO3H2)2 (Fc = (eta5-C5H5)Fe(eta5-C5H4), fc = (eta5-C5H4)Fe(eta5-C5H4)) in water have been evaluated by potentiometric, 31P NMR, and electrochemical methods. The oxidized forms are more acidic than the reduced ones. The interaction between the redox centre and the charged oxygen atoms of the phosphonate group is shown to be electrostatic. The maximum oxidation shift DeltaE between the protonated and unprotonated species increases with the number of charges of the substrate and decreases with the increase of the distance between the ferrocenyl centre and the oxygen atoms of the phosphonate group. The structure of FcPO3Na2.5H2O is determined. The compound crystallizes in the monoclinic system. It is lamellar with an inorganic layer formed by tetramers Na4O14, the ferrocenyl groups occupying the interlamellar space.     

Intensity of the ν3 band of ozone from a study of its anomalous dispersion at 10 μm

An apparatus, consisting of a Michelson interferometer and a tunable CO₂ laser, is used to measure the anomalous dispersion of ozone in the 10-μm region. A line by line analysis leads to a new determination of the ν₃ band intensity of ozone which is independent of earlier measurements.     

On the solution of discrete bottleneck problems

We consider a class of discrete bottleneck problems which includes bottleneck integral flow problems. It is demonstrated that a problem in this class, with k discrete variables, can be optimized by solving atmost k problems with real valued variables.     

On products of two nilpotent subgroups of a finite group

LetG be a finite group with an abelian Sylow 2-subgroup. LetA be a nilpotent subgroup ofG of maximal order satisfying class (A)≦k, wherek is a fixed integer larger than 1. Suppose thatA normalizes a nilpotent subgroupB ofG of odd order. ThenAB is nilpotent. Consequently, ifF(G) is of odd order andA is a nilpotent subgroup ofG of maximal order, thenF(G)?A.