Justification of the Shallow-Water Limit for a Rigid-Lid Flow with Bottom Topography

The so-called lake equations arise as the shallow-water limit of the rigid-lid equations—three-dimensional Euler equations with a rigid-lid upper boundary condition—in a horizontally periodic basin with bottom topography. We prove an a priori estimate in the Sobolev space H ^m for m≥ 3 which shows that a solution to the rigid-lid equations can be approximated by a solution of the lake equations for an interval of time which can be estimated in terms of the initial deviation from a columnar configuration and the magnitude of the initial data in H ^m , the gradient of the bottom topography in H ^m+1 , and the aspect ratio of the basin. In particular, any solution to the lake equations remains close to some solution of the rigid-lid equations for an interval of time that can be made arbitrarily large by choosing the aspect ratio of the basin small. Received 10 October 1996 and accepted 15 May 1997     

Dérivés propargyliques,XII et dérivés de la décahydroquinoléine,II Alkynyl-4, alkényl-4 et alkyl-4-décahydroquinolinols-4 N-substitués

The authors describe the synthesis of decahydro-4-quinolinones and N-substituted 4-alkynyl-, 4-allyl- and 4-alkyldecahydro-4-quinolinols and discuss the stereochemical problems of this compounds.     

Cyclisation par amination intramoléculaire dans la série de la pyrazine.

An original one-pot ayntheais of 4,7-diazaindoles is achieved by metalation of methylpyrazines or methylquinoxaline wich are then condensed with an aromatic nitrile: an intermediate imine-enamine is formed which leads, by intramolecular cyclization, to diazaindoles.     

Posets isomorphic to their extensions

A standard extension for a poset P is a system Q of lower ends (descending subsets) of P containing all principal ideals of P. An isomorphism between P and Q is called recycling if [Y]Q for all YQ. The existence of such an isomorphism has rather restrictive consequences for the system Q in question. For example, if Q contains all lower ends generated by chains then a recycling isomorphism between P and Q forces Q to be precisely the system of all principal ideals. For certain standard extensions Q, it turns out that every isomorphism between P and Q (if there is any) must be recycling. Our results include the well-known fact that a poset cannot be isomorphic to the system of all lower ends, as well as the fact that a poset is isomorphic to the system of all ideals (i.e., directed lower ends) only if every ideal is principal.     

Synthèse de dérivés de la benzo[c] quinolizine

The introduction of polar groups in planar polycyclic systems, for the purpose of studying their intercalating action, has been realized in the benzo[c]quinolizinium series. A functionalizing synthesis has been developed from 2-picolyl-and quinaldyllithium. Intermediate ketones or imines were cyclized by a quaternization reaction involving a concerted process. Structure and physico-chemical features of the compounds prepared were studied.     

Asymmetric Synthesis of (S)-5,5,5,5′,5′,5′,5′-Hexafluoroleucine

(S)-5,5,5,5′,5′,5′-Hexafluoroleucine ((S)- 13 ) of 81 % ee is prepared from hexafluoroacetone ( l ) and ethyl bromopyruvate (= ethyl 2-oxopropanoate) in 7 steps with an overall yield of 18% (Schemes 1 and 2). Key step in this sequence is the highly enantioselective reduction of the carbonyl group in α-keto ester 4 either by bakers' yeast (91 % ee) or by ‘catecholborane’ 6 utilizing an oxazaborolidine catalyst, yielding hydroxy ester (R)- 5 with 99% ee. The absolute configuration was determined by X-ray analysis of the HCl adduct (S,R)- 9b of (2S)-N-[(R)- l-phenylethyl]-5,5,5,5′,5′,5′-hexafluoroleucine ethyl ester.     

Vibronic coupling in the excited cationic states of ethylene: simulation of the photoelectron spectrum between 12 and 18 eV

The effect of vibronic coupling on structure and spectroscopy is investigated in the excited cationic states of ethylene. It is found from equation of motion coupled cluster singles and doubles method for ionization potential electronic structure calculations in a triple-zeta plus double polarization basis set that ethylene in its third (B (2)A(g)) and fourth (C (2)B(2u)) ionized states does not have a stable minimum-energy geometry. The potential-energy surfaces of these states are energetically distinct and well separated at the ground-state geometry of ethylene, but in a geometry optimization as the structure of the ion relaxes, these surfaces end up in conical intersections and finally in the stable equilibrium geometry of the second ionized state (A (2)B(3g)). The topology of the potential-energy surfaces can be clearly understood using a vibronic model Hamiltonian. Furthermore, by diagonalizing this model Hamiltonian, the photoelectron spectrum of ethylene corresponding to the second, third, and fourth ionized states (12-18 eV) is simulated. Spectra from vibronic simulations including up to quartic coupling constants and using various normal-mode basis sets are compared to those from vertical Franck-Condon simulations to understand the importance of vibronic coupling and nonadiabatic effects and to examine the influence of individual normal modes on the spectrum.     

Naturstoffe aus Mikroorganismen. 8. Mitteilung [1]. Optimale Gewinnung von Proferrorosamin A aus Pseudomonas roseus fluorescens J. C. MARCHAL 1937

Optimum Obtention of Proferrorosamine A from Pseudomonas roseus fluorescens J. C. MARCHAL 1937. We have developed the best conditions for the culture of Pseudomonas roseus fluorescens, and a quantitative isolation of the Proferrorosamine A produced in the culture solution, in order to study the incorporation of 1-[¹⁴C]-glycerol in this propigment.