Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

Semileptonic (Λ b → Λcev) decay in a field theoretic quark model

The semileptonic decay width of heavy baryons such as (Λ _b → Λcev) has been estimated in the framework of a nonrelativistic field theoretic quark model where four component quark field operators along with a harmonic oscillator wave function are used to describe translationally invariant hadronic states. The present estimation does not make an explicit use of heavy quark symmetry and has a reasonable agreement with the experimentally measured decay width, polarisation ratio and form factors with the harmonic oscillator radii and quark momentum distribution inside the hadron as free parameters.     

Characterization of supported membranes on topographically patterned polymeric elastomers and their applications to microcontact printing

This article describes the fluorescence microscopy and imaging ellipsometry-based characterization of supported phospholipid bilayer formation on elastomeric substrates and its application in microcontact printing of spatially patterned phospholipid bilayers. Elastomeric stamps, displaying a uniformly spaced array of square wells (20, 50, and 100 mum linear dimensions), are prepared using poly(dimethyl)siloxane from photolithographically derived silicon masters. Exposing elastomeric stamps, following UV/ozone-induced oxidation, to a solution of small unilamellar phospholipid vesicles results in the formation of a 2D contiguous, fluid phospholipid bilayers. The bilayer covers both the elevated and depressed regions of the stamp and exhibits a lateral connectivity allowing molecular transport across the topographic boundaries. Applications of these bilayer-coated elastomeric stamps in microcontact printing of lipid bilayers reveal a fluid-tearing process wherein the bilayer in contact regions selectively transfers with 75-90% efficiency, leaving behind unperturbed patches in the depressed regions of the stamp. Next, using cholera-toxin binding fluid POPC bilayers that have been asymmetrically doped with ganglioside Gm1 ligand in the outer leaflets, we examine whether the microcontact transfer of bilayers results in the inversion of the lipid leaflets. Our results suggest a complex transfer process involving at least partial bilayer reorganization and molecular re-equilibration during (or upon) substrate transfer. Taken together, the study sheds light on the structuring of lipid inks on PDMS elastomers and provides clues regarding the mechanism of bilayer transfer. It further highlights some important differences in stamping fluid bilayers from the more routine applications of stamping in the creation of patterned self-assembled monolayers.