Nonnegative integral generalized inverses

Necessary and sufficient conditions are given for a nonnegative integral matrix to have nonnegative integral generalized inverses of various types, and the possible ranks of these inverses are determined. More generally, conditions are also given for matrices to have generalized inverses over certain subsets of the nonnegative reals forming monoids under addition and multiplication. Many of our results are adapted from results of Berman and Plemmons [3–6] on real matrices.     

Preferred frames and oscillating universes

A metric theory of gravitation is presented. It is based on the existence of a preferred ‘cosmic’ time. It agrees with all present experimental facts regarding gravitation and leads to singularity-free oscillating universes.     

Quasi-phase-matching in chiral materials

The second-order nonlinear optical coefficients associated with chirality differ in sign for the two mirror-image forms (enantiomers) of a chiral material. Structures comprised of alternating stacks of the enantiomers can therefore be used for quasi-phase-matched frequency conversion, as we demonstrate here by second-harmonic generation from Langmuir-Blodgett films of a helicenebisquinone. Such structures could lead to new types of frequency converters in which both the second-order nonlinear response and quasi-phase-matching arise from the chirality of a material rather than its polar order.     

Grand unification signal from ultrahigh energy cosmic rays?

The spectrum of ultrahigh energy (above approximately 10(9) GeV) cosmic rays is consistent with the decay of grand unification scale particles. The predicted mass is m(X) = 10(b) GeV, where b = 14.6(+1.6)(-1.7).     

Boundary case of equality in optimal Loewner-type inequalities

We prove certain optimal systolic inequalities for a closed Riemannian manifold , depending on a pair of parameters, and . Here  is the dimension of , while is its first Betti number. The proof of the inequalities involves constructing Abel-Jacobi maps from to its Jacobi torus  , which are area-decreasing (on -dimensional areas), with respect to suitable norms. These norms are the stable norm of , the conformally invariant norm, as well as other -norms. Here we exploit -minimizing differential 1-forms in cohomology classes. We characterize the case of equality in our optimal inequalities, in terms of the criticality of the lattice of deck transformations of  , while the Abel-Jacobi map is a harmonic Riemannian submersion. That the resulting inequalities are actually nonvacuous follows from an isoperimetric inequality of Federer and Fleming, under the assumption of the nonvanishing of the homology class of the lift of the typical fiber of the Abel-Jacobi map to the maximal free abelian cover.

     

Biomolecule-nanoparticle hybrid systems for bioelectronic applications

Recent advances in nanobiotechnology involve the use of biomolecule-nanoparticle (NP) hybrid systems for bioelectronic applications. This is exemplified by the electrical contacting of redox enzymes by means of Au-NPs. The enzymes, glucose oxidase, GOx, and glucose dehydrogenase, GDH, are electrically contacted with the electrodes by the reconstitution of the corresponding apo-proteins on flavin adenine dinucleotide (FAD) or pyrroloquinoline quinone (PQQ)-functionalized Au-NPs (1.4 nm) associated with electrodes, respectively. Similarly, Au-NPs integrated into polyaniline in a micro-rod configuration associated with electrodes provides a high surface area matrix with superior charge transport properties for the effective electrical contacting of GOx with the electrode. A different application of biomolecule-Au-NP hybrids for bioelectronics involves the use of Au-NPs as carriers for a nucleic acid that is composed of hemin/G-quadruplex DNAzyme units and a detecting segment complementary to the analyte DNA. The functionalized Au-NPs are employed for the amplified DNA detection, and for the analysis of telomerase activity in cancer cells, using chemiluminescence as a readout signal. Biomolecule-semiconductor NP hybrid systems are used for the development of photoelectrochemical sensors and optoelectronic systems. A hybrid system consisting of acetylcholine esterase (AChE)/CdS-NPs is immobilized in a monolayer configuration on an electrode. The photocurrent generated by the system in the presence of thioacetylcholine as substrate provides a means to probe the AChE activity. The blocking of the photocurrent by 1,5-bis(4-allyldimethyl ammonium phenyl)pentane-3-one dibromide as nerve gas analog enables the photoelectrochemical analysis of AChE inhibitors. Also, the association CdS-NP/double-stranded DNA hybrid systems with a Au-electrode, and the intercalation of methylene blue into the double-stranded DNA, generates an organized nanostructure of switchable photoelectrochemical functions. Electrochemical reduction of the intercalator to the leuco form, -0.4 V vs. SCE, results in a cathodic photocurrent as a result of the transfer of photoexcited conduction-band electrons to O(2) and the transport of electrons to the valance-band holes by the reduced intercalator units. The oxidation of the intercalator, E 0 V (vs. SCE), yields in the presence of triethanolamine, TEOA, as sacrificial electron donor, an anodic photocurrent by the transport of conduction-band electrons, through intercalator units, to the electrodes, and filling the valance-band holes with electrons supplied by TEOA. The systems reveal potential-switchable directions of the photocurrents, and reveal logic gate functions.     

Hydroxy-terminated organic semiconductor-based field-effect transistors for phosphonate vapor detection

Organic field-effect transistors (OFETs) with a hydroxy-functionalized semiconductor incorporated into a receptor layer were fabricated and shown to respond strongly to the analyte dimethyl methylphosphonate (DMMP) that simulates phosphonate nerve agents. Large and reproducible source-drain current changes were observed upon exposure to DMMP vapor. Compared to single component transistors, OFETs with a mixed hydroxylated and nonhydroxylated semiconductor upper layer exhibited higher sensitivity. We further investigated the selectivity of the heterostructured OFETs by comparing responses upon exposure to different interference vapors with response to DMMP exposure. Much higher response was observed in the case of DMMP, even when the concentration of DMMP vapor was much lower than other analytes. Microstructures of OSC were characterized by scanning electron microscopy (SEM) and X-ray diffraction (XRD), revealing that the organic mixture has similar crystal structure and surface morphology to those of single component OSC films, indicating that the enhanced performance of the mixture is due to its chemical properties, rather than microstructural effects.