Covering the Plane with Congruent Copies of a Convex Body

It is shown that every plane compact convex set K with an interiorpoint admits a covering of the plane with density smaller thanor equal to 8(23 – 3)/3 = 1.2376043.... For comparison,the thinnest covering of the plane with congruent circles isof density 2 / 27 = 1.209199576.... (see R. Kershner [3]), whichshows that the covering density bound obtained here is closeto the best possible. It is conjectured that the best possibleis 2 / 27. The coverings produced here are of the double-latticekind consisting of translates of K and translates of —K.     

Enantioenriched dihydropyrones from beta-lactone templates

[reaction: see text] Optically active 4-substituted 2-oxetanones provide conduits for preparing 2,3-dihydro-4H-pyrone heterocycles. Enantioenriched beta-lactones are prepared by asymmetric catalytic acyl halide-aldehyde cyclocondensation reactions. Hydrazone anion-mediated beta-lactone ring opening and ensuing cyclization-dehydroamination of the derived beta-ketohydrazone afford the desired dihydropyrones (68-81%). Optimized lactone ring-opening-cyclization reaction conditions render a variety of optically active 4-substituted-2-oxetanones as effective precursors to enantioenriched 2,3-dihydro-4H-pyrones.     

Compaction and tensile forces determine the accuracy of folding landscape parameters from single molecule pulling experiments

We establish a framework for assessing whether the transition state location of a biopolymer, which can be inferred from single molecule pulling experiments, corresponds to the ensemble of structures that have equal probability of reaching either the folded or unfolded states (P(fold)=0.5). Using results for the forced unfolding of a RNA hairpin, an exactly soluble model, and an analytic theory, we show that P(fold) is solely determined by s, an experimentally measurable molecular tensegrity parameter, which is a ratio of the tensile force and a compaction force that stabilizes the folded state. Applications to folding landscapes of DNA hairpins and a leucine zipper with two barriers provide a structural interpretation of single molecule experimental data. Our theory can be used to assess whether molecular extension is a good reaction coordinate using measured free energy profiles.     

n-Type GaAs/AlGaAs heterostructure detector with a 3.2 THz threshold frequency

Terahertz detection using the free-carrier absorption requires a small internal work function of the order of a few millielectron volts. A threshold frequency of 3.2 THz (93 microm or approximately 13 meV work function) is demonstrated by using a 1 x 10(18) cm(-3) Si-doped GaAs emitter and an undoped Al(0.04)Ga(0.96)As barrier structure. The peak responsivity of 6.5 A/W, detectivity of 5.5 x 10(8) Jones, and quantum efficiency of 19% were obtained at 7.1 THz under a bias field of 0.7 kV/cm at 6 K, while the detector spectral response range spans from 3.2 to 30 THz.     

Effect of electrospray ionization conditions on low-energy tandem mass spectra of peptides

The effect of electrospray ionization (ESI) conditions on low-energy tandem mass spectra of peptides in the relative molecular mass range 400–1200 was examined. For singly charged peptide ions the source skimmer potential (which determines the degree of acceleration of the ions through the intermediate pressure region in the source) can strongly influence the extent of fragmentation observed in tandem mass spectra, especially at low collision energies. For each peptide there is an optimum skimmer potential which represents a balance between generating ions with sufficient internal energy for subsequent tandem mass spectrometric experiments and inducing the onset of other processes such as source fragmentation. The fragmentation which can be achieved in tandem mass spectra with high skimmer potentials differs from ESI source fragmentation for the same peptides. We have found that fragmentation in ESI mass spectra depends both on skimmer potential and on solvent pH, presumably because the latter determines the proportion of doubly charged species generated from a given peptide. Low-energy tandem mass spectra of peptides following ESI are equally as sensitive to peptide structure and the type of adduct studied (e.g. [M + H]⁺ vs. [M + NH₄]⁺) as tandem mass spectra obtained following older ionization methods such as fast atom bombardment.     

Method of calculating band shape for molecular electronic spectra

A method for approximating the band shape of molecular electronic transitions based on a single geometric configuration is described. The band shape is modeled using an empirical parameter to estimate the width at half-height for each transition. In addition to generating a shape for allowed transitions, a procedure is developed for approximating the oscillator strength for the symmetry forbidden bands. The results obtained using these two approximations are then compared with experimental spectra and to the results obtained from stochastic methods for simple organic molecules, such as benzene, naphthalene, and the diazobenzenes. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 781–796, 1998