Degenerate nonlinear hyperbolic conservation laws: Non classical geometrical theory

Kinetic selection principles have been shown to be useful and physically reasonable in nonlinear hyperbolic problems with large amplitude phase transitions. We refer to Abeyaratne and Knowles, [A-K], for discussion on the subject. They also have been used for degenerate nonlinear problems, where the genuine nonlinearity property of Lax is violated. This is the framework of Liu, [Li], in the kinetic situation of Hayes and Le Floch, [H-L], where their so-called non classical shocks may be seen as small amplitude phase transitions. Here, we describe the local geometry generated by the generic non genuinely nonlinear assumption. A geometric kinetic criterion can be used to select indeterminate simple waves and obtain the well-posedness of the local Riemann problem. A particular case is the entropic kinetic criterion of Hayes and Le Floch.

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Sunto Principi di selezione cinetica sono stati mostrati utili e fisicamente ragionevoli in problemi iperbolici con transizioni di fase di grande ampiezza. Ci riferiamo ad Abeyaratne e Knowles, [A-K], per discussioni sull'argomento. Detti principi sono stati usati per problemi nonlineari degeneri, dove la proprietà di genuina nonlinearità di Lax è violata. Questo è la prospettiva di Liu, [Li], nella situazione cinetica di Hayes e Le Floch, [H-L], dove i loro così detti urti non classici possono essere considerati come transizioni di fase di piccola ampiezza. Qui, descriviamo la geometria locale generata dall'ipotesi generica genuinamente nonlineare. Un criterio di geometria cinetica può essere usato per selezionare onde semplici indeterminate ed ottenere la buona posizione per il problema locale di Riemann. Un caso particolare è il criterio di entropia cinetico di Hayes e Le Floc.

     

Assembly of the Entire Carbon Backbone of a Stereoisomer of the Antitumor Marine Natural Product Hemicalide

A strategy for the assembly of the entire carbon backbone of a stereoisomer of the antitumor marine natural product hemicalide has been investigated. The devised convergent approach relies on Horner–Wadsworth–Emmons and Julia–Kocienski olefination reactions for the construction of the C6=C7 and C34=C35 double bonds, respectively, an aldol reaction to create the C27−C28 bond, and a Suzuki–Miyaura cross-coupling as the endgame to form the C15−C16 bond.     

Stabilité de la structure d'une solution de Riemann à deux grands chocs

Sunto Costruiamo una soluzione debole di un problema di Cauchy iperbolico conservativo globale in tempo, vicino a un problema di Riemann che presenta due urti di grande ampiezza. Sotto delle ipotesi di stabilità e di smorzamento, un adattamento dello schema di Bressan permette di conservare la struttura a due urti, con delle stime fini della soluzione nei settori definiti da questi urti.

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Stability of the structure of a Riemann wave with two large shocks. We construct a global weak solution of an hyperbolic system of conservation laws, close to a Riemann problem which contains two large shock waves. Under some stability and damping conditions, we define a version of the scheme of A. Bressan which maintains the structure with two shocks in the solution and leads to refined estimates.

     

Existence pour un problème de l'élastodynamique Neumann non linéaire en dimension 2

Sans résumé Présenté par H. Brézis     

Isolation and Structural Elucidation of Armeniaspirols A–C: Potent Antibiotics against Gram‐Positive Pathogens

In an antibiotic lead discovery program, the known strain Streptomyces armeniacus DSM19369 has been found to produce three new natural products when cultivated on a malt‐containing medium. The challenging structural elucidation of the isolated compounds was achieved by using three independent methods, that is, chemical degradation followed by NMR spectroscopy, a computer‐assisted structure prediction algorithm, and X‐ray crystallography. The compounds, named armeniaspirol A–C ( 2 – 4 ), exhibit a compact, hitherto unprecedented chlorinated spiro[4.4]non‐8‐ene scaffold. Labeling experiments with [1‐¹³C] acetate, [1,2‐¹³C2] acetate, and [U‐¹³C] proline suggest a biosynthesis through a rare two‐chain mechanism. Armeniaspirols displayed moderate to high in vitro activities against Gram‐positive pathogens such as methicillin‐resistant S. aureus (MRSA) or vancomycin resistant E. faecium (VRE). As analogue 2 was active in vivo in an MRSA sepsis model, and showed no development of resistance in a serial passaging experiment, it represents a new antibiotic lead structure.     

Le n-ondes de lax pour le probleme mixte (the n-waves of lax for initial-boundary value problem)

We Confirm two conjectures of Lax about Glimm's weak solutions for initial boundary value problem whose data have compact support; asmptotic decay as t^-1/2 of the total variation in the genuinely nonlinear case and L¹ -approximation by N-waves or travelling-waves in general case; it is boundary's version of Liu's results [Li2].     

2′,3′‐Dide­hydro‐3′‐deoxy­thymidine N‐methyl‐2‐pyrrolidone solvate (D4T·NMPO)

The title compound, 1‐(2′,3′‐di­deoxy‐β‐d ‐glycero‐pent‐2‐eno­furan­osyl)­thymine 1‐methyl‐2‐pyrrolidone solvate, C₁₀H₁₂N₂O₄·­C₅H₉NO, is an NMPO solvate of the anti‐AIDS agent D4T. In its crystal structure, both the pyrimidine and the furan­ose rings are planar and approximately perpendicular [82.1 (4)°]. The value of the torsion angle defining the orientation of the thymine with respect to the joined furane, χ = ?100.8 (4)°, and that of the torsion angle giving the orientation of the hydroxyl group linked to the furane ring, γ = 52.9 (5)°, show that the gly­cosyl­ic link adopts the so‐called high‐anti conformation and the 5′‐hydroxyl group is in the +sc position. The NMPO solvate is linked to the nucleoside through a fairly strong hydrogen bond.     

Kinetic Stabilization¶of a Nonlinear Sonic Phase Boundary

We consider a system arising in the study of phase transitions in elastodynamics – a system of two conservation laws, in a single space dimension. The system has two hyperbolic regions with an elliptic zone in between. A phase boundary is a strong discontinuity in a solution, with left and right states belonging to different hyperbolic regions. We call such a solution a phase wave. We first address the Riemann problem for initial states close to a fixed sonic phase wave, in the genuinely nonlinear case. This problem is naturally underdetermined. We propose two essentially different types of Reimann problems: a sonic one, which is smooth, and a kinetic one, which is only Lipschitz-continuous. Both problems are well posed owing to a shared stability condition that is of a purely sonic nature. In the kinetic case we prove the global existence of solutions to the Cauchy problem for initial data having small variation and close to a sonic kinetic wave. The crucial issue is the interaction of the phase boundary with a small wave of the same mode. The introduction of a pertinent quantity, called here detonation potential, ensures a balance between ingoing and outgoing waves. The proof is based on a Glimm-type scheme; we define a potential, which includes the detonation potential, along the strong discontinuity, and this potential controls the outbreak of unusual shocks. Accepted: June 9, 1999