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.     

Automated sample preparation method for suspension arrays using renewable surface separations with multiplexed flow cytometry fluorescence detection

In this paper, we describe a new method of automated sample preparation for multiplexed biological analysis systems that use flow cytometry fluorescence detection. In this approach, color-encoded microspheres derivatized to capture particular biomolecules are temporarily trapped in a renewable surface separation column to enable perfusion with sample and reagents prior to delivery to the detector. This method provides for separation of the biomolecules of interest from other sample matrix components as well as from labeling solutions. After sample preparation, the beads can be released from the renewable surface column and delivered to a flow cytometer for direct on-bead analysis one bead at a time. Using mixtures of color-encoded beads derivatized for various analytes yields suspension arrays for multiplexed analysis. Development of this approach required a new technique for automated capture and release of the color-encoded microspheres within a fluidic system. We developed a method for forming a renewable filter and demonstrate its use for capturing microspheres that are too small to be easily captured in previous flow cells for renewable separation columns. The renewable filter is created by first trapping larger beads in the flow cell, and then smaller beads are captured either within or on top of the bed of larger beads. Both the selective microspheres and filter bed are automatically emplaced and discarded for each sample. A renewable filter created with 19.9 μm beads was used to trap 5.6 μm optically encoded beads with trapping efficiencies of 99%. The larger beads forming the renewable filter did not interfere with the detection of color-encoded 5.6 μm beads by the flow cytometer fluorescence detector. The use of this method was demonstrated with model reactions for a variety of bioanalytical assay types including a one-step capture of a biotinylated label on Lumavidin beads, a two-step sandwich immunoassay, and a one-step DNA binding assay. A preliminary demonstration of multiplexed detection of two analytes using color-encoded beads was also demonstrated. The renewable filter for creating separation columns containing optically encoded beads provides a general platform for coupling renewable surface methods for sample preparation and analyte labeling with flow cytometry detectors for suspension array multiplexed analyses.