Links between the Slater Index and the Ryser Index of Tournaments

Given a tournament T, the Slater index i(T) of T is the minimum number of arcs that must be reversed to make T transitive. The Ryser index (T) of T, defined from the out-degrees of T, measures a remoteness between T and the transitive tournaments of same order. In this paper, we study some links between i(T) and (T). More precisely, calling I(n, ) the maximum value of i(T) over the set of tournaments on n vertices and such that (T)=, we compute an upper bound of I(n,) for every value of . Then we use this upper bound to study a conjecture stated by J.-C. Bermond on the regularity (i.e., the fact that all the out-degrees are equal or almost equal) of the tournaments with a maximum Slater index by showing that the out-degrees of such tournaments cannot be too far from the ones of the regular tournaments.     

Constructing complete tables of quartic fields using Kummer theory

We explain how to construct tables of quartic fields of discriminant less than or equal to a given bound in an efficient manner using Kummer theory, instead of the traditional (and much less efficient) method using the geometry of numbers. As an application, we describe the computation of quartic fields of discriminant up to , the corresponding table being available by anonymous ftp.     

β-Cyano meso-unsubstituted porphyrins for intramolecular charge transfer

β-Cyano meso-unsubstituted porphyrin 10, synthesized via a ‘3+1’ condensation using a bromotripyrrane, shows an effective charge transfer interaction across the porphyrin between electron-acceptor and -donor groups in β-positions.     

Iterative oxime bond chemistry leads to protease inhibitors

[structure: see text] In the present paper, we have looked at iterative coupling as a strategy to form new druglike molecules. We have developed an iterative coupling chemistry based on oxime bond formation between hydroxyaromatic aldehyde building blocks to form linear oxime oligomers. The strategy is validated by the discovery of micromolar protease inhibitors.     

Total synthesis of the reputed structure of alcyonin and reassignment of its structure

Introduction of the C4 hydroxyl group by an epoxy ester rearrangement is a pivotal step in the first total synthesis of the purported structure of alcyonin. As the spectral data for diol acetate 3 do not match those reported for alcyonin, the structure of this marine diterpene must be revised. Reexamination of NMR spectra, MS data, and chemical transformations of natural alcyonin suggests that the structure of this marine metabolite is allylic peroxide 15.[structure: see text]     

Rational improvement of centrifugal partition chromatographic settings for the production of 5-n-alkylresorcinols from wheat bran lipid extract. I. Flooding conditions--optimizing the injection step

A dedicated CPC prototype permits direct flow pattern visualization in the partition cells of a CPC column. It was used to understand "flooding", a frequent phenomenon associated with large injections. A general strategy was developed to optimize the injection step in the framework of a particular preparative separation: the purification of 5-n-alkylresorcinols from a wheat bran lipid extract on a several hundred milligram scale. The construction of the "mobile phase/stationary phase/sample" pseudo ternary diagram characterizes the effect of the injected solution on mobile and stationary phases. The position of the binodal curve maximum indicates if the biphasic system is "robust" towards a large injection or not, and can be used for optimum mass load determination.     

Influence of the correlation,aggregation, and solvation on ab initio computed Li-C,Li-N,and Li-Li NMR coupling constants

The (1)J and (3)J(C-Li), (1)J(N-Li), and (2)J(Li-Li) NMR coupling constants have been calculated for various homogeneous and heterogeneous aggregates of methyllithium and lithium dimethylamide at the HF and MP2 levels of calculation. Ethereal solvation has also been taken into account either through a continuum model or through the explicit introduction of Me(2)O molecules. The results obtained are in good general agreement with the experimental data available for methyllithium itself or model alkyllithiums and supports the empirical rule proposed by Bauer, Winchester, and Schleyer to evaluate (1)J(C-Li) provided that calculations include solvent and/or aggregation effects.     

A 6 pi + 6 pi potentially antiaromatic zwitterion preferred to a quinoidal structure: its reactivity toward organic and inorganic reagents

A straightforward synthesis of the zwitterionic benzoquinonemonoimine 8 is reported. This molecule is a rare example of a zwitterion being more stable than its canonical forms. It is shown that 8 is best described as constituted of two chemically connected but electronically not conjugated 6 pi electron subunits. Its reactivity with electrophiles such as H(+), CH(3)(+), and metal salts leads to the synthesis of new 12 pi electron molecules 12 (H(+)), 14 (CH(3)(+)), and 20 (Pd(2+)), respectively, in which one or both 6 pi electron subsystems localize into an alternation of single and double bonds, as established by X-ray diffraction. The acidity of the N[bond]H protons of 8 can be modulated by an external reagent. Dependent on the electrophile used, the control of the pi system delocalization becomes possible. When the electrophile simply adds to the zwitterion as in 12, 14, or 15, there is no more negative charge to be delocalized and only the positive charge remains delocalized between the nitrogen atoms. Furthermore, when a reaction with the electrophilic reagent results in deprotonation, as in 17-21, there remains no charge in the system to be delocalized. DFT calculations were performed on models of 8, 12, 14, 20, and on other related zwitterions 9 and 10 in order to examine the influence of the fused cycles on the charge separation and on the singlet-triplet energy gap. An effect of the nitrogen substituents in 8 is to significantly stabilize the singlet state. The dipole moment of 8 was measured to be 9.7 D in dichloromethane, in agreement with calculated values. The new ligands and complexes described in this article constitute new classes of compounds relevant to many areas of chemistry.     

Monotone Methods for Markovian Equilibrium in Dynamic Economies

In this paper, we provide an overview of an emerging class of monotone map methods in analyzing distorted equilibrium in dynamic economies. In particular, we focus on proving the existence and characterization of competitive equilibrium in non-optimal versions of the optimal growth models. We suggest two alternative methods: an Euler equation method for a smooth, strongly concave environment, and a value function method for a non-smooth supermodular environment. We are able to extend this analysis to study models that allow for unbounded growth or a labor–leisure choice.