The unsatisfiability threshold revisited

The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. In this paper, we consider the problem of bounding the threshold value from above using methods that, we believe, are of interest on their own right. More specifically, we show how the method of local maximum satisfying truth assignments can be combined with results for the occupancy problem in schemes of random allocation of balls into bins in order to achieve an upper bound for the unsatisfiability threshold less than 4.571. In order to obtain this value, we establish a bound on the q-binomial coefficients (a generalization of the binomial coefficients). No such bound was previously known, despite the extensive literature on q-binomial coefficients. Finally, to prove our result we had to establish certain relations among the conditional probabilities of an event in various probabilistic models for random formulas. It turned out that these relations were considerably harder to prove than the corresponding ones for unconditional probabilities, which were previously known.     

Rate constants from the reaction path Hamiltonian. I. Reactive flux simulations for dynamically correct rates

As ab initio electronic structure calculations become more accurate, inherent sources of error in classical transition state theory such as barrier recrossing and tunneling may become major sources of error in calculating rate constants. This paper introduces a general method for diabatically constructing the transverse eigensystem of a reaction path Hamiltonian in systems with many degenerate transverse frequencies. The diabatically constructed reaction path Hamiltonian yields smoothly varying coupling constants that, in turn, facilitate reactive flux calculations. As an example we compute the dynamically corrected rate constant for the chair to boat interconversion of cyclohexane, a system with 48 degrees of freedom and a number of degenerate frequencies. The transmission coefficients obtained from the reactive flux simulations agree with previous results that have been calculated using an empirical potential. Furthermore, the calculated rate constants agree with experimental values. Comparison to variational transition state theory shows that, despite finding the true bottleneck along the reaction pathway, variational transition state theory only accounts for half of the rate constant reduction due to recrossing trajectories.     

Nonaqueous capillary electrophoretic separation of basic enantiomers using octakis(2,3-O-dimethyl-6-O-sulfo)-gamma-cyclodextrin, a new, single-isomer chiral resolving agent

The enantiomers of 34 pharmaceutical weak-base analytes were separated by nonaqueous capillary electrophoresis in acidic methanol background electrolytes using the sodium salt of the new, single-isomer chiral resolving agent, octakis(2,3-O-dimethyl-6-O-sulfo)-gamma-cyclodextrin (ODMS). The effective mobilities, separation selectivities and peak resolution values of the weak-base analytes were determined as a function of the ODMS concentration in the 0-40 mM range and were found to follow the theoretical predictions of the charged resolving agent migration model (CHARM model) modified for ionic strength effects. Fast, efficient separations were achieved for both comparatively small and large enantiomers.     

In situ UV-visible spectroscopic measurements of kinetic parameters and active sites for catalytic oxidation of alkanes on vanadium oxides

In situ diffuse reflectance UV-visible spectroscopy was used to measure the dynamics of catalyst reduction and oxidation during propane oxidative dehydrogenation (ODH) on VOx/gamma-Al2O3. Transients in UV-visible intensity in the near-edge region were analyzed using a mechanistic model of ODH reactions. Rate constants per site for the kinetically relevant reduction step (C-H bond activation) measured using this analysis are slightly larger than those obtained from steady-state ODH rates normalized by surface V. The ratio of these values provides a measure of the fraction of the V surface sites that are active for ODH (0.6-0.7, for V surface densities of 2.3-34 V nm(-2)). This suggests that some of the V atoms are either inaccessible or inactive. Reoxidation rate constants, which cannot be obtained from steady-state analysis, are 10(3)-10(5) times larger than those for the C-H bond activation reduction step.     

Regioselective palladium-catalyzed phenylation of ethyl 4-oxazolecarboxylate

The efficient and regioselective palladium-catalyzed C-2 arylation of ethyl 4-oxazolecarboxylate 1 with phenyliodide is described. The different parameters (solvent, base, ligand and catalyst) for the optimal conditions of this arylation process have been screened.     

A growing string method for determining transition states: comparison to the nudged elastic band and string methods

Interpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method.     

Ketendithioacetal-S-imide

Starting from 2-isopropylidene-1,3-dithiane, various ketene-dithioacetal-S-imides have been prepared and characterized by¹H- and¹³C-NMR spectra.

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Ketendithioacetal-S-imideKurze Mitteilung

     

Xylanase production by Trichoderma reesei rut C-30 on rice straw

Xylanase production of Trichoderma reesei Rut C-30 was examined at different initial pH values (4.8, 5.9, and 7.0) on rice straw in shake flasks, and in a fermentor, for the best pH condition. Enzyme performance was tested on ammonia-treated dwarf elephant grass. The maximum xylanase activities, 92 and 122 IU/mL, were obtained at pH 4.8 in the shake flasks and fermentor, respectively, in which good growth of the fungus was observed during the first 24 h and consumption of proteins dissolved from the rice straw caused the pH to rise later to values between 6.4 and 6.7 (optimal for xylanase production). The xylanases from T. reesei were as effective as Multifect XL, a commercial enzyme preparation, in hydrolyzing ammonia-treated elephant grass.