The geometry of solvability and duality in linear programming

Solvability and boundedness criteria for dual linear programming problems are given in terms of the problem data and the intersections of the nonnegative orthant with certain complementary orthogonal subspaces. This research was partly supported by the Office of Naval Research, contract Nonr-1228(10), project NR 047-021, and by the National Science Foundation, project G-14102.     

Dispersion of multi-walled carbon nanotubes in poly（p-phenylene） thin films and their electrical characteristics

Dispersion of multi-walled carbon nanotubes in poly（p-phenylene） composite exposed to toluene was experimentally investigated. 3 mg of multi-walled carbon nanotubes with nominal size of 20 nm was compounded with 30 mg of poly（p-phenylene） with the presence of terpineol as binding initiator. To investigate an optimal condition for homogenizing all constituents, ultrasonication with an output power of 750W was employed with compounding time of 3, 10, 20 and 30 min. With FTIR analyses, it could be confirmed that homogeneous composite of multi-walled carbon nanotubes and poly（p-phenylene） could be prepared. SEM analyses were also conducted to examine the dispersion of multi-walled carbon nanotubes in the polymer matrix. Then intrinsic electrical resistance of the composites after being exposed to toluene was also investigated. It was found that the composite film prepared with ultrasonication for 20 min could provide sufficiently sensitive response with respect to varied concentration of toluene.     

Organelle‐Targeted BODIPY Photocages: Visible‐Light‐Mediated Subcellular Photorelease

Photocaging facilitates non‐invasive and precise spatio‐temporal control over the release of biologically relevant small‐ and macro‐molecules using light. However, sub‐cellular organelles are dispersed in cells in a manner that renders selective light‐irradiation of a complete organelle impractical. Organelle‐specific photocages could provide a powerful method for releasing bioactive molecules in sub‐cellular locations. Herein, we report a general post‐synthetic method for the chemical functionalization and further conjugation of meso‐methyl BODIPY photocages and the synthesis of endoplasmic reticulum (ER)‐, lysosome‐, and mitochondria‐targeted derivatives. We also demonstrate that 2,4‐dinitrophenol, a mitochondrial uncoupler, and puromycin, a protein biosynthesis inhibitor, can be selectively photoreleased in mitochondria and ER, respectively, in live cells by using visible light. Additionally, photocaging is shown to lead to higher efficacy of the released molecules, probably owing to a localized and abrupt release.     

Fluorescence anisotropy study of aqueous dispersions of block ionomer complexes

Block ionomer complexes (BIC) of "dual hydrophilic" block copolymers containing ionic and nonionic blocks and oppositely charged surfactants spontaneously form colloidal particles of ca. 80 nm in diameter stable in aqueous dispersions at every composition of the mixture. Packing and dynamics of aliphatic groups of the surfactant in BIC were examined by using the quenching-resolved fluorescence anisotropy (QRFA) method with 1,6-diphenyl-1,3,5-hexatriene (DPH) as a probe. The values of the order parameter and rotational relaxation time in the BIC were higher than those in the surfactant micelles. Incorporation of aliphatic alcohols in the BIC decreased the order parameter and increased the rotational relaxation time. The effects on the order parameter were explained by changes in the surfactant aliphatic group conformation to "fill the gaps" induced by insertion of shorter alcohol molecules. The effects on the relaxation time were attributed to a decrease in repulsion of the surfactant headgroups and expulsion of water from the BIC hydrophobic interior as evidenced by the decrease in micropolarity. The results of this study have implications for potential use of the BIC in pharmaceutics and other fields.     

The geometry of linear separability in data sets

We study the geometry of datasets, using an extension of the Fisher linear discriminant to the case of singular covariance, and a new regularization procedure. A dataset is called linearly separable if its different clusters can be reliably separated by a linear hyperplane. We propose a measure of linear separability, easily computed as an angle that arises naturally in our analysis. This angle of separability assumes values between 0 and π/2, with high [resp. low] values corresponding to datasets that are linearly separable, resp. inseparable.     

Linear equations over cones with interior: a solvability theorem with applications to matrix theory

The solvability of linear equations with solutions in the interior of a closed convex cone is characterized. Corollaries include Lyapunov's theorem characterizing stable matrices and a generalization of Stiemke's theorem of the alternative for complex linear inequalities.