Nonlinear equations with unbounded heat conduction and integrable data

We consider a class of quasi-linear diffusion problems involving a matrix A(t,x,u) which blows up for a finite value m of the unknown u. Stationary and evolution equations are studied for L ¹ data. We focus on the case where the solution u can reach the value m. For such problems we introduce a notion of renormalized solutions and we prove the existence of such solutions.      

Structural investigation and elucidation of new communesins from a marine‐derived Penicillium expansum Link by liquid chromatography/electrospray ionization mass spectrometry

Penicillium expansum is a ubiquitous species for which there are only few reports for chemical investigation in marine environments. Among the numerous secondary metabolites produced by this species, communesins represent a new class of cytotoxic and insecticidal indole alkaloids. In this study, we investigated a marine P. expansum strain exhibiting neuroactivity on a Diptera larvae bioassay. Bio‐guided purification led to the isolation and the identification of communesin B as the main active compound by HRMS and ¹H and ¹³C NMR. Liquid chromatography analyses with detection by electrospray ionization coupled with tandem mass spectrometry (LC/ESI‐MS/MS) and high‐resolution tandem mass spectrometry (LC/HRMS/MS) allowed the identification and characterization of four other known communesins (A, D, E and F) in the crude extract. A fragmentation model for dimethyl epoxide communesins was proposed after detailed interpretation of their MS/MS spectra. Further analyses of the extract using the modelled fragmentations led to the detection of seven new communesins found as minor compounds. Chemical structural elucidation of these new derivatives is discussed based on their fragmentation characteristics. Copyright © 2009 John Wiley & Sons, Ltd.     

Hartmann wave-front scanner

A wave-front sensor is described that uses a programmable moving aperture to scan an incoming wave front. The position of the diffraction spot is recorded behind an objective lens with a two-dimensional sensor and gives an estimate of the local slope at the aperture position. Then the wave front is reconstructed by processing of the slope data. The device is basically a programmable Hartmann wave-front sensor. Compared with a microlens Shack-Hartmann wave-front sensor, its much longer focal length provides higher resolution, although real-time operation is lost. A practical implementation of the new scanner with a liquid-crystal television as the programmable aperture is presented.     

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.     

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.     

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.