Superconvergence error estimates of discontinuous Galerkin time stepping for singularly perturbed parabolic problems

Numerical Algorithms - A parabolic convection-diffusion-reaction problem is discretized by the non-symmetric interior penalty Galerkin (NIPG) method in space and discontinuous Galerkin (DG) method...     

On sparse spanners of weighted graphs

Given a graphG, a subgraphG' is at-spanner ofG if, for everyu,v V, the distance fromu tov inG' is at mostt times longer than the distance inG. In this paper we give a simple algorithm for constructing sparse spanners for arbitrary weighted graphs. We then apply this algorithm to obtain specific results for planar graphs and Euclidean graphs. We discuss the optimality of our results and present several nearly matching lower bounds.The work of G. Das and D. Joseph was supported by NSF PYI Grant DCR-8402375. The work of D. Dobkin was supported by NSF Grant CCR-8700917. The work of J. Soares was supported by CNPq proc 203039/87.4 (Brazil) and NSF Grant CCR-9014562. This research was accomplished while G. Das was a student at the University of Wisconsin-Madison. A preliminary version was presented at the Second Scandinavian Workshop on Algorithm Theory, Bergen, Norway, 1990, under the title Generating Sparse Spanners for Weighted Graphs, and proceedings appear in the series Lecture Notes in Computer Science, Springer-Verlag. The preliminary version also appears as Princeton University Technical Report CS-TR-261-90, and as University of Wisconsin-Madison Computer Sciences Technical Report 882.     

Guest excitation energy in dilute organic mixed crystals with chemically distinct guests

Philpott's theory of vibronic transitions of substitutional impurities in molecular crystals has been examined. The lowest energy guest transition in a number of mixed crystals has been calculated and compared with experiment. Satisfactory agreement is achieved. In some cases consideration of charge overlap of the guest and nearest host gives better agreement.     

A single amino acid Gly-tag enables metal-free protein purification

Analytically pure proteins are indispensable for diverse applications, including therapeutics. Here, we report a methodology where a single amino acid, glycine, enables metal-free protein purification. This robust platform is enabled by a Gly-tag resin for site-specific capture, enrichment, and release through chemically triggered C–C bond dissociation by resonance-assisted electron density polarization.

Gly-tag resin precisely captures and releases a protein with one glycine at the N-terminus. The user-friendly protocol delivers analytically pure protein free of metal contaminants.     

DMSO/N2H4.H2O/I2/H2O/CH3CN: a new system for selective oxidation of alcohols in hydrated media

A new alternative system for the oxidation of secondary alcohols to ketones with DMSO/N2H4.H2O/I2/H2O/CH3CN in hydrated media has been developed. The system also selectively oxidizes the secondary alcoholic groups to the corresponding ketones in the presence of primary alcoholic groups present within the same molecule in moderate to very good yields at reflux temperature.     

Krichever-Novikov global operator formalism: NSR superstring in curved background

The Neveu-Schwarz-Ramond type II closed superstring is considered to evolve in a curved space-time manifold. The Krichever-Novikov global operator formalism is used to construct the generators of a super-conformal algebra on a Riemann surface . The computation for the quantum algebra of these generators is explicitly presented. It is shown that the theory is free from super-conformal anomalies if the target manifold is ten dimensional and satisfies the Ricci flatness condition.     

Mode of termination in the copolymerization of vinyl acetate–isobutyl methacrylate and methyl methacrylate–methyl acrylate at 60°C

The mode of termination in the vinyl acetate–isobutyl methacrylate (VA–IBMA) and methyl methacrylate–methyl acrylate (MMA–MA) copolymerization systems has been investigated at 60°C. by using the dye-interaction technique for functional endgroup estimation. The results show that pairs of poly(vinyl acetate) radicals interact almost exclusively through a disproportionation mechanism. In the homopolymerization of methyl methacrylate and methyl acrylate, about 1.16 and 1.22 carboxyl-containing endgroups per polymer molecule have been estimated, which shows the predominance of disproportionation over combination in these termination reactions. In poly(isobutyl methacrylate) about 1.55 tagged initiator fragments per chain indicate that 29% of the total radicals terminate through the disproportionation mechanism. Cross termination in the (VA–IBMA) copolymerization system occurs almost entirely through combination for monomer feeds richer in isobutyl methacrylate content while for the MMA–MA system, combination is more important at intermediate monomer feed ratios. These results have been discussed in the light of different explanations for the reaction mechanism.     

The oblique chiral nematic phase in calamitic bimesogens

ABSTRACT

The discovery of the oblique chiral (or, the twist-bend, N_TB) nematic phase predicted for bent-core mesogens has engendered much interest due to its unique structure and physical properties, and the possibility of use in the next generation of fast electro-optic technology. Bimesogenic calamitic as well as bent-core mesogens are found to form the N_TB phase. Here, we report direct measurements of the temperature dependence of the conical tilt and the evidence of volcano-like orientational distribution of molecules in the N_TB phase. Optical and x-ray scattering investigations of two single-component calamitic bimesogens and their mixtures show that, while the Maier–Saupe orientational distribution function (ODF) is valid for the higher temperature nematic phase, a generalised expansion in terms of even Legendre functions is needed for the N_TB phase. Temperature dependence of the ODFs and the order parameters 〈P₂(cosβ)〉, 〈P₄(cosβ)〉, and 〈P₆(cosβ)〉 has been measured in both phases. The parameters 〈P₂(cosβ)〉 and 〈P₄(cosβ)〉 increase/decrease in the N/N_TB phase with decreasing temperature, while 〈P₆(cosβ)〉 remains vanishingly small for all samples. The value of 〈P₄(cosβ)〉 becomes negative in the N_TB phase confirming a conical distribution of molecules as they follow a helical trajectory keeping the local director tilted at an angle α wrt the macroscopic director. The heliconical tilt calculated from ODFs, exhibits a power law behaviour with temperature, vanishing at the transition to the N phase.     

Synthesis of Unsymmetrically Substituted Hexahydroimidazo [4,5-d] Imidazole-2,5-diones and Elucidation of Reaction Pathways

We have reported the synthesis and structural elucidation of a series of hexahydroimidazo [4,5-d] imidazole-2,5-diones and hydantoins from glyoxal and substituted ureas.^1,2 The general equation of this condensation reaction and a few representative compounds: those reported, current and hypothetical, are depicted in Scheme 1.