Estimating the complexity of a class of path-following methods for solving linear programs by curvature integrals

In this paper we study a particular class of primal-dual path-following methods which try to follow a trajectory of interior feasible solutions in primal-dual space toward an optimal solution to the primal and dual problem. The methods investigated are so-called first-order methods: each iteration consists of a long step along the tangent of the trajectory, followed by explicit recentering steps to get close to the trajectory again. It is shown that the complexity of these methods, which can be measured by the number of points close to the trajectory which have to be computed in order to achieve a desired gain in accuracy, is bounded by an integral along the trajectory. The integrand is a suitably weighted measure of the second derivative of the trajectory with respect to a distinguished path parameter, so the integral may be loosely called a curvature integral.     

Study of cross-conjugated iso-polytriacetylenes and related oligoenynes

Two series of monodisperse cross-conjugated oligomers based on enyne repeat units have been realized. The first class of molecules, iso-polytriacetylenes (iso-PTAs, 2), was divergently synthesized using an iterative sequence of palladium-catalyzed cross-coupling reactions of vinyl triflate 5 with terminal alkynes. The second series of oligoenynes (17-20) are based on an octatetrayne backbone, and result from homocoupling of the differentially protected iso-PTA oligomers 8-11. The longest member of this series, 20, spans ca. 5.6 nm from Si atom to Si atom and is composed of a contiguous sequence of 44 sp and sp(2) carbons. The lowest energy electronic absorption band for iso-PTA dimers in the progression 13 --> 9 --> 16 is consistently red-shifted as a result of extending the cross-conjugated structure. A similar comparison within each series (i.e., 16, 6-7, or 17-20), however, suggests little effect on the electronic characteristics of these molecules as oligomer length is increased. The solid-state properties of one derivative, 17, are also described.     

Theoretical approach and the practice to the evaluation of structural parameters characterizing concentration polarization alongside ion-exchange membranes by means of dielectric measurement

As the application of a dielectric theory proposed previously (J Membrane Sci 64:153–161 (1991)), theoretical formulation and the practical procedure of dielectric analysis are developed to calculate the structural parameters such as the conductivity gradient and the thickness of the concentration polarization layer, the capacitances and the conductances of the two adjoining aqueous phases from the observed dielectric parameters. The procedure of calculation consequent upon the theoretical formulation was applied to double relaxation data observed for cation-exchange membrane systems under application of d.c. bias voltage. As a consequence, the structural parameters of concentration polarization were readily obtained with accuracy.     

The uranium-Xylidyl Blue I complex and its application in linear sweep polarography

The linear sweep polarographic wave of the uranium-Xylidyl Blue I complex in ethylenediamine-1,10-phenanthroline-hydrochloric acid medium has been studied. The complex, corresponding to UO(2)(XBI)(2-)(2) with log beta' = 9.09 (by polarography), 8.81 (by spectrophotometry), is strongly adsorbed on the surface of the mercury electrode. The polarographic wave is attributed to the reduction of Xylidyl Blue I in the complex. The method is very sensitive with a detection limit of 3 x 10(-8)M. The wave height is proportional to the concentration of uranium over the range 8 x 10(-8)-7 x 10(-6)M. Solvent extraction is used to separate possible interferences. The recommended procedure has been applied to the determination of trace amounts of uranium in ores.     

Noble gas-transition metal complexes: coordination of ScO+ by multiple Ar, Kr, and Xe atoms in noble gas matrixes

The combination of matrix isolation infrared spectroscopic and density functional calculation results provides strong evidence that the transition metal monoxide cation, ScO+, coordinates five noble gas atoms in forming the [ScO(Ng)5]+ (Ng = Ar, Kr, or Xe) complexes in noble gas matrixes.     

Synthesis of substituted carbazoles by a vinylic to aryl palladium migration involving domino C-H activation processes

Substituted carbazoles are readily prepared in good yields by the palladium-catalyzed cross-coupling of alkynes and N-(3-iodophenyl)anilines. This process proceeds by carbopalladation of the alkyne, heteroatom-directed vinylic to aryl palladium migration, and ring closure involving two consecutive C-H activation processes. The process has also been expanded to the synthesis of an indole. [Structure: see text]     

Rheological properties of the aqueous mixtures of cationic-anionic surfactants

The rheological properties of the aqueous mixtures of cationic-anionic surfactants, both in single-phase systems and in aqueous two-phase systems, have been studied. Bizarre rheological properties —negative thixotropy, viscoelasticity and hihg viscosity of shear rate dependent at relatively low concentration — have been observed. An unusual viscosity change, that is, viscosity lowering with increasing concentration, was obtained. The negative thixotropy might be due to the existence of lamellar or sheet-like micelles, viscoelasticity might be induced by rodlike and lamellar or sheet-like micelles, the high viscosity might be a consequence of the formation of network by long rodlike micelles and the concentration-induced viscosity lowering could be interpreted in terms of the decrease of micellar dimensions with concentration.