Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

New synthesis of 2',3'-didehydro-2',3'-dideoxynucleosides.

The 3'-iodonucleoside 4 and the 3'-O-methylsulfonylthymidine 9 have been synthesized by condensation of silylated uracils 2 with methyl 5-O-tert-butyldiphensilyl-2,3-dideoxy-3-iodo-D-threo-pentofuran oside (3) and methyl 5-O-tert-butyldiphenylsilyl-2-deoxy-3-methylsulfonyl-D-erythro- pentofuranoside (8), respectively. The nucleoside 4 and 9 produced the corresponding 2',3'-didehydro-2',3'-dideoxynucleosides 5 in an elimination reaction on treatment with sodium methoxide. The compounds 5b showed no antiviral activity against HIV-1.     

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals

Slow-light enhanced optical detection in liquid-infiltrated photonic crystals is theoretically studied. Using a scattering-matrix approach and the Wigner–Smith delay time concept, we show that optical absorbance benefits both from slow-light phenomena as well as a high filling factor of the energy residing in the liquid. Utilizing strongly dispersive photonic crystal structures, we numerically demonstrate how liquid-infiltrated photonic crystals facilitate enhanced light–matter interactions, by potentially up to an order of magnitude. The proposed concept provides strong opportunities for improving existing miniaturized absorbance cells for optical detection in lab-on-a-chip systems.     

The Remainder in Ruijsenaars’ Asymptotic Expansion of Barnes Double Gamma Function

We show that the remainder in Ruijsenaars’ asymptotic expansion of the logarithm of Barnes double gamma function gives rise to a completely monotone function. Fourier expansions of the multiple Bernoulli polynomials are also obtained. Research supported by the Carlsberg Foundation.     

Farkas-type results for fractional programming problems

Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant. The desired results are obtained using the Fenchel–Lagrange duality approach applied to an optimization problem with convex or difference of convex (DC) objective functions and finitely many convex constraints. These are obtained from the initial fractional programming problem using an idea due to Dinkelbach. We also show that our general results encompass as special cases some recently obtained Farkas-type results.     

Cyclic and telechelic ladder polymers derived from tetrahydroxytetramethylspirobisindane and 1,4‐dicyanotetrafluorobenzene

5,5′,6,6′‐Tetrahydroxy‐3,3,3′,3′‐tetramethylspirobisindane was polycondensed with 1,4‐dicyanotetrafluorobenzene in four different solvents at 70 °C. In dimethylformamide, N‐methylpyrrolidone, and sulfolane exclusively, cyclic polymers were detectable by matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectrometry up to masses around 13,000 Da. In dimethyl sulfoxide, linear byproducts were also found. Higher temperatures caused degradation reactions catalyzed by potassium carbonate. Polycondensations performed with the addition of 4‐tert‐butyl catechol or 2,2′‐dihydroxy binaphthyl yielded linear telechelic oligomers. Equimolar mixtures of linear and cyclic ladder polymers were examined by MALDI‐TOF mass spectra to determine how the end groups and the cyclic structure influenced the signal‐to‐noise ratio. The results suggested a preferential detection of the linear chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5344–5352, 2006