Optimally scaled matrices,necessary and sufficient conditions

Summary We shall in this paper consider the problem of determination a row or column scaling of a matrixA, which minimizes the condition number ofA. This problem was studied by several authors. For the cases of the maximum norm and of the sum norm the scale problem was completely solved by Bauer [1] and Sluis [5]. The condition ofA subordinate to the pair of euclidean norms is the ratio /, where and are the maximal and minimal eigenvalue of (A ^H A)^1/2 respectively. The euclidean case was considered by Forsythe and Strauss [3]. Shapiro [6] proposed some approaches to a numerical solution in this case. The main result of this paper is the presentation of necessary and sufficient conditions for optimal scaling in terms of maximizing and minimizing vectors. A uniqueness proof for the solution is offered provided some normality assumption is satisfied.     

Reactivity comparison for selenophen,thiophen, and their methyl derivatives via hydrogen-isotope exchange

Deuteration measurements have been made with t-C₄H₉OK and with 4 moles of CH₃COOH mixed with one mole of CF₃COOH against 2D-selenophen, 3D-selenophen, 3CH₃, 2D-selenophen and 5CH₃, 2D-selenophen. Reactivity in the selenohpen-thiopen series is examined via protophilic and electrophilic isotopic-exchange reactions. The factors for the partial exchange rates with acid and base for heterocyclics with D at position 2 and CH₃ at position 3, 4, or 5 are compared with those factors for isomers of monodeuterotoluene; it is found that the electronic effect of the CH₃ group is transmitted similarly for these heterocyclics and for the benzene ring. Reasonably good agreement is found between the relative constants for deuterium exchange in thiophen, selenophen, and methyl derivatives of these as catalyzed by alkali-metal t-butylates in dimethylsulfoxide (DMSO) and in t-butanol mixed with diethylene glycol dimethyl ether. This shows that the results with DMSO correctly characterize the reactivity in protophilic hydrogen exchange.     

Theory of the two step enantiomeric purification of 1,3 dimethylallene

An application of a recently proposed [P. Kral et al., Phys. Rev. Lett. 90, 033001 (2003)] two step optical control scenario to the purification of a racemic mixture of 1,3 dimethylallene is presented. Both steps combine adiabatic and diabatic passage phenomena. In the first step, three laser pulses of mutually perpendicular linear polarizations, applied in a "cyclic adiabatic passage" scheme, are shown to be able to distinguish between the L and D enantiomers due to their difference in matter-radiation phase. In the second step, which immediately follows the first, a sequence of pulses is used to convert one enantiomer to its mirror-imaged form. This scenario, which only negligibly populates the first excited electronic state, proves extremely useful for systems such as dimethylallene, which can suffer losses from dissociation and internal conversion upon electronic excitation. We computationally observe conversion of a racemic mixture of dimethylallene to a sample containing approximately 95% of the enantiomer of choice.     

1H NMR Self-Diffusion Study of Morphology and Structure of Polyvinyl Alcohol Cryogels

The multicomponent self-diffusion of the polyvinyl alcohol (PVA) cryogels prepared by a freezing-thawing treatment of aqueous and water-DMSO solutions of PVA has been studied with the NMR FT-PGSE method. The temperature dependencies of the self-diffusion coefficients, Ds, for the PVA chains have a maximum at 45 degrees C due to the syneresis of cryogels. They are quite different from the monotonous increase of Ds for the aqueous solutions of PVA. Evaluated apparent activation energies, Ea, of the self-diffusion for the PVA chains in the PVA solutions and cryogels in D2O are practically the same and equal 22-24 kJ/mol below the crucial point. The proton spin-lattice relaxation times, T1, of the PVA chain also coincide with one another for solutions and cryogels. This means that molecular packing in cryogels depends mainly on the dimensions of the ice and polymer microcrystallites formed by freezing the solution. Above the crucial point polymer compartments become firmer, and the chain mobility somewhat reduces. The strength of cryogels also increases along with growing the DMSO contents and decreases by the BSA addition. For estimation of the cryogel morphology, effects of the restricted diffusion of both the water and PVA in a q-space have been taken into account. By the introduction of DMSO to cryogels the solvent filled pores become smaller, and channels become much shorter. The diameter of the PVA filaments is similar to those for all the cryogels, but the length of filaments with D2O is twice that for cryogels with a mixed solvent. Entrapment of BSA in the cryogel matrix by preparation leads to the increase of an average diameter of the water filled pores and destroys molecular packing the cryogel. Copyright 1999 Academic Press.     

Synthesis of Isodehydroilludin M

Isodehydroilludin M was synthesized from carbonyl ylid 1,3-dipolar cycloaddition product that was further elaborated with an unusual PCC-mediated double oxidation reaction.     

Photoelectric response of thiamonomethinecyanine J-aggregate nanoribbons deposited via dielectrophoresis technique

Different dyes can produce the two-dimensional self-assembled structures called J- and H-aggregates that make them attractive material for various nano-electronics applications. This paper shows that electrokinetic deposition technique of cyanine dye J-aggregates is appropriate for the photoelectric devices production. The influence of excitation in visible on conductivity is observed in J-aggregate channel structure deposited using dielectrophoresis technique. The effect was observed in self-assembled thiamonomethinecyanine nanostructures. Samples were analyzed using AFM and micro-Raman spectroscopy methods. Analysis shows that photoelectric response must be the result of conductive channel formation in the structure of J-aggregate between the electrodes. The observed increase in conductivity manifold exceeds the structure dark conductivity: maximal increase comprised 6.3 times.