On uniform distribution of double sequences

In this paper a new notion of uniform distribution of double sequences is introduced. In the most elementary case a double sequence (x_mn)_{m, nN} is called uniformly distributed in this sense if all finite matrices of equal size appear with the same frequency as submatrices of the infinite matrix (x_mn). Some special double sequences with such a distribution property are studied and metric theorems are proved.     

Molecular weight distribution studies. I. Radiation-induced polymerization of liquid α-methylstyrene

The concentration of water in purified and BaO-dried α-methylstyrene was found to be 1.1 × 10^?4M. The radiation-induced bulk polymerization of the α-methylstyrene thus prepared was studied in the temperature range of ?20°C to 35°C. The polymerization rate varied as the 0.55 power of the dose rate. The theoretical molecular weights and molecular weight distribution were calculated from a proposed kinetic scheme and these values were then compared with those found experimentally. The agreement between these two was reasonably close, and therefore it was concluded that, from the molecular weight distribution point of view, the proposed kinetic scheme for the cationic polymerization of α-methylstyrene is an acceptable one. The rate constant for chain transfer to monomer k_f changed with temperature and was found to be responsible for the decrease in the molecular weight of the polymer with increase in temperature. k_f and k_p at 20°C were found to be 0.95 × 10⁴ l./mole-sec and 0.99 × 10⁶ l./mole-sec, respectively.     

Preparation and reactions of [2,2-bis(carbethoxy)propyl]cyclopentadienyldicarbonyliron

Although

, (Fp  η-C₅H₅Fe(CO)₂) (I) is stable and characterizable, the lower homologue FpCH₂CH(CO₂CH₃)₂ (II) is not; this we attribute to a facile elimination reaction resulting from the relatively acidic β-hydrogen of II. Formation of I from Fp^? and XCH₂CE₂CH₃ (X  Br, Cl; E  CO₂CH₂CH₃) and cleavage of its FeC bonds (using H⁺, Br₂, Ce^IV and Hg^II) occur without major amounts of ester group migrations, even though ·CH₂CE₂CH₃ radicals are involved in some of these reactions.     

Stacking due to ionic transport number mismatch during sample sweeping on microchips

Sample stacking can occur in isoconductive buffer systems as a result of ion transport mismatches that cause changes in buffer conductivity during electrophoresis. Fluorescence imaging was used to examine this effect in the sweeping of hydrophobic dyes with sodium dodecyl sulfate (SDS) on microchips. Imaging revealed the occurrence of a stacking effect in a sodium borate buffer system in which the sample buffer and SDS-containing run buffer had the same initial conductivity. Injected sample plugs were first swept by SDS micelles and the swept band was then stacked at the trailing end of the sample zone. This effect is due to changes in conductivity at both the front and back interfaces of the injected sample plug and can be modeled by moving boundary equations. Maximum signal enhancements of 86-, 160- and 560-fold were obtained for Rhodamine 560, Rhodamine B and Rhodamine 6G, respectively, by the combination of sweeping and stacking within a 1 cm section of microchannel. Based on sample sweeping/stacking and manipulation of the electric field polarity, a method of trapping and concentrating analyte from multiple injections was also demonstrated.     

Unexpected conversion of a polycyclic thiophene to a macrocyclic anhydride

Oxygenation of 2,5,9,12-tetra(tert-butyl)diacenaphtho[1,2-b:1′,2′-d]-thiophene (1, C₄₀H₄₄S) by peracids gave the cyclic sulfonic ester 4 (2,7,10,13-tetra(tert-butyl)diacenaphtho[1,2-c:1′,2′-e]oxathiin 5,5-dioxide, C₄₀H₄₄O₃S) which, when heated in nitrobenzene, is converted into a complex, macrocyclic anhydride 3 (C₈₀H₈₈O₃), which is derived from two molecules of 4. Further investigation found a likely intermediate in this reaction, 4,4′,7,7′-tetra(tert-butyl)-1,1′-biacenaphthylenylidene-2,2′-dione (5, C₄₀H₄₄O₂), apparently formed from 4 by additional oxidation. Anhydride 3 plausibly arises by Diels-Alder reaction of 4 and 5 followed by several ring fragmentations. The structures of 3, 4, and 5 were unambiguously established by X-ray crystallography.     

Toward the synthesis of reidispongiolide a: stereocontrolled synthesis of the C17-C22 and C23-C35 degradation fragments

[structure: see text] By relying on the asymmetric aldol reactions of chiral ketones, a highly stereocontrolled synthesis of each of the C(17)-C(22) and C(23)-C(35) degradation fragments of reidispongiolide A has been achieved. This permits a configurational assignment of the complete C(17)-C(36) region of this antimitotic macrolide, along with providing advanced intermediates for a projected total synthesis.     

Upper and lower bounds for a serial dilution test

A Poisson-binomial model estimates the concentration of a target microbe from a serial dilution test. The maximum likelihood procedure gives an equation whose solution equals the estimate of the concentration. This paper gives bounds for the solution to this equation that require only minimal calculations.     

Concerning atomic radii

The identification of the atomic radius with the distance from the nucleus to the position of the minimum in the internuclear electronic density is studied. It is shown that a set of statistically significant radii may be defined for the atoms of a given column of the periodic table bound to any of the atoms of another column. Sets of radii calculated by modified Anderson-Parr relations are presented. The values obtained are consistent with radii obtained using a minimum in electronic density criterion with electron densities calculated from molecular orbital wave functions or approximated by a sum of atomic densities.     

OptiDock: virtual HTS of combinatorial libraries by efficient sampling of binding modes in product space

Products from combinatorial libraries generally share a common core structure that can be exploited to improve the efficiency of virtual high-throughput screening (vHTS). In general, it is more efficient to find a method that scales with the total number of reagents (Sigma growth) rather with the number of products (Pi growth). The OptiDock methodology described herein entails selecting a diverse but representative subset of compounds that span the structural space encompassed by the full library. These compounds are docked individually using the FlexX program (Rarey, M.; Kramer, B.; Lengauer, T.; Klebe, G. J. Mol. Biol. 1995, 251, 470-489) to define distinct docking modes in terms of reference placements for combinatorial core atoms. Thereafter, substituents in R-cores (consisting of the core structure substituted at a single variation site) are docked, keeping the core atoms fixed at the coordinates dictated by each reference placement. Interaction energies are calculated for each docked R-core with respect to the target protein, and energies for whole compounds are calculated by finding the reference core placement for which the sum of corresponding R-core energies is most negative. The use of diverse whole compounds to define binding modes is a key advantage of the protocol over other combinatorial docking programs. As a result, OptiDock returns better-scoring conformers than does serially applied FlexX. OptiDock is also better able to find a viable docked pose for each library member than are other combinatorial approaches.     

Acceleration of convergence in Monte Carlo simulations of aqueous solutions using the metropolis algorithm. Hydrophobic hydration of methane

Convergence problems encountered in the computer simulations of aqueous solutions are discussed. Solute–solvent radial distribution functions are shown to converge very poorly when the standard Metropolis Monte Carlo procedure is applied. To overcome this difficulty, several modifications are made in the Metropolis method. Optimum maximum step sizes are determined for simulations of liquid water. A scheme is employed for preferential sampling of both the solvent and the solute molecules. To test these modifications, a simulation is carried out for pure liquid water, treating a single water molecule as a “solute.” The convergence of the radial distribution functions is found to be accelerated significantly. A further test is made by simulating an aqueous solution of methane, consisting of one methane molecule (using the EPEN /2 potential for methane–water interactions) and 124 water molecules (using the MCY potential for water–water interactions). Again, the convergence of solute–solvent radial distribution functions is found to be accelerated. The computation of partial molar thermodynamic quantities, however, still suffers from convergence difficulties. This problem is discussed in detail. The EPEN /2 potential is found to yield structural and thermodynamic features of hydrophobic hydration that are consistent with available experimental and theoretical results for aqueous solutions of methane.