Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

Mechanism of formation and decay of the compound nuclei150Gd produced by two entrance channels (16O+134Ba) and (40Ar+110Pd)

Excitation functions have been drawn for evaporation residues issued from¹⁵⁰Gd, a compound nucleus produced either by¹⁶O ions on¹³⁴Ba, or by⁴⁰Ar on¹¹⁰Pd. Absolute cross sections were measured for^145–147Gd,^145–147Eu,^141m Sm,^143m Sm,^140m Pm and^139m Nd. Complete fusion cross sections have been obtained and compared to calculated estimations based, at low energies, on the simple expressionσ _CF=πR _Fuss ² (1?V _Fus/E) whereR _Fus andV _Fus are respectively the distance and the potential for fusion atdV/dr=0. For high energies σ_CF=πR _cr ² (1?V_cr/E) with the model of critical distanceR _cr and critical potentialV _cr. Thresholds energies have been determined with a particular care. The analysis of the shape and the width of excitation functions, particularly for the emission of 4 and 5 neutrons, has been carried out and compared to calculated values. The difference between argon and oxygen induced reactions has been attributed to the difference inl population in the entrance channel.     

Elemental speciation by chromatographic separation with inductively coupled plasma mass spectrometry detection

Separation techniques coupled to inductively coupled plasma mass spectrometry (ICP-MS) is reviewed. ICP-MS technique is described briefly. Coupling of the different separation techniques are described, together with the most common applications used for each technique that has been described in the literature. An overview for the future of separation techniques coupled to ICP-MS with regard to elemental speciation is discussed.     

Reaktive E = C(p-p)π-Systeme. XLII [1]. Neue Koordinationsverbindungen des 2-(Diisopropylamino)-1-phosphaethins: [{η4-(iPr2NCP)2}Ni{η2-(iPr2NCP)}], [(Ph3P)2Pt{η2-(iPr2NCP)}] und [Co2(CO)6{η2-η2-(iPr2NCP)}]

Reactive E = C(pp)π-Systems. XLII [1]. Novel Coordination Compounds of 2-(Diisopropylamino)-1-phosphaethyne: [{η⁴-(iPr₂NCP)₂}Ni{η²-(iPr₂NCP)}], [(Ph₃P)₂Pt{η²-(iPr₂NCP)}], and [Co₂(CO)₆{η²-μ²-(iPr₂NCP)}] 2-(Diisopropylamino)-phosphaethyne iPr₂N? C?P ( 2 ) reacts with the Ni(0)-complexes [Ni(1,5-cyclooctadiene)₂] and [Ni(CO)₃(1-azabicyclo[2.2.2]octane)], respectively, to give the novel complex [{η⁴-(iPr₂NCP)₂}Ni{η²-(iPr₂NCP)}] ( 5 ), with the 1,3-diphosphacyclobutadiene derivative and 2 (side-on) as π-ligands. The molecular structure of 5 determined by X-ray diffraction on single crystals proves the spin systems and rotational barriers deduced from NMR-data (¹H, ¹³C-, ³¹P). The PC distances of the four-membered ring of 1.817(2) and 1.818(2) Å – as expected – are considerably longer than the PC bond of the η²-coordinated phosphaalkyne 2 [1.671(2) Å]. – In the reactions of 2 with [(Ph₃P)₂Pt(C₂H₄)] or [Co₂(CO)₈] the ligand properties of 2 resemble those of alkynes affording the complexes [(Ph₃P)₂Pt{η²-(iPr₂NCP)}] ( 7 ) with side-on coordinated 2 and [Co₂(CO)₆{η²-μ²-(iPr₂NCP)}] with 2 acting as a 4e donor bridge in quantitative yield. In attempts to prepare copper(I) complexes of the aminophosphaalkyne 2 by reaction with CuCl or CuI the only isolable product formed in reasonable amounts under the influence of air and moisture is the 1 λ³, 3 λ⁵-diphosphetene (iPr₂N) ( 10 ) (isolated yield: ca. 20%). The crystal structure analysis of 10 indicates a strong structural relationship to the diamino-2-phosphaallyl cation [Me(iPr₂N)]⁺ ( 12 ), the 1,3-diphosphacyclobutadiene ligand (iPr₂NCP)₂ in the binuclear complex [{η¹, μ²-(iPr₂NCP)₂}Ni₂(CO)₆] ( 3a ) as well as to the heterocycles (dme)₂LiOE₂′ (E′ = S, 11a ; E′ = Se, 11b ) prepared by Becker et al. [11b, 35].     

Evaluation of Ptitsyn-Eizner λ parameter in dilute solutions of poly(N-vinylcarbazole) and its variation in conformational transitions of poly(methyl methacrylate)

The Ptitsyn-Eizner λ flexibility parameter for poly(N-vinylcarbozole) solutions under theta conditions has been found to be 6.31, demonstrating the rigidity imparted to the polymer chain by the carbazole group. A study has been made of the variation of this parameter with solvent and temperature. A study has been made of the variation of λ in a conformational transition of poly(methyl methacrylate).     

Chiral conformations induced by cyclodextrin

Studies of chiroptical properties need separation or at least enrichment of enantiomers. The separation is difficult with chiral conformers of molecules with very low barriers of internal rotation. However, in association with cyclodextrin, these labile molecules can exhibit a strong Cotton effect in solution: one chiral conformer is favoured by complexation. The cyclodextrins have the advantage to yield inclusion complex in solution as well as crystalline clathrates. Therefore, the absolute configuration of the guest can be obtained by determining the structure of the cyclodextrin. In this work, the first CD spectrum of 4-helicene is recorded and crystal structures of several clathrates of labile molecules are studied.     

Characteristics of immunosorbents used as a new approach to selective solid-phase extraction in environmental analysis

Summary The trace-level determination of organic pollutants in complex matrices is difficult and often not reliable because theccurrent extraction procedures are non-selective. New extraction sorbents involving antigen-antibody interactions, called immunosorbents (ISs), have been synthesised in order to trap a group of structurally related pollutants. The IS capacity is always high for the analyte-antigen used to make the antibodies, but can be low for some related compounds. In this work, we show the relationship that exists between capacity, break-through volume and recovery of analytes because of the competition between the structurally related compounds for antibody sites. Breakthrough due to the overloading of the column should be avoided because calibration curves are no longer linear. The capacity of two ISs, one made for trapping the triazine pesticide group and the second for the phenylurea, group, have been optimised by selecting silica with 50 nm pore size. Calibration curves are linear for all the compounds in a mixture of ten phenylureas up to a concentration of 5 to 10 μg L⁻¹ for each compound when handling 50 mL water samples through a precolumn packed with 0.22 g of IS. Under these conditions, reliable quantitative results are obtained because calibration curves are similar when compounds are alone or in a mixture. Application to the clean-up of soil extracts illustrates the high selectivity and the high potential of these new sorbents in environmental analysis. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

Gould-Jacobs reaction of 6-amino-2,3-diphenylquinoxaline

Summary Catalytic hydrogenation of 2,3-diphenyl-6-nitroquinoxaline led to the corresponding amine1 which in turn afforded products3a-i on reaction with alkoxymethylene derivatives2a-i. Thermal cyclization of3b and3f yielded substituted pyrazinoquinolones5b and5f, respectively. Optimal conditions for the successful hydrolysis of ester5b were found. The structures of all products were deduced from their IR, UV,¹H, and¹³C NMR spectroscopic data.Dedicated to Prof.F. Sauter on the occasion of his 65th birthday     

New fluorescent probes for testing combinatorial catalysts with phosphodiesterase and esterase activities

Combinatorial development of new catalysts with phosphodiesterase and esterase activities requires specific fluorescent probes for rapid visual detection of hydrolytic activity. Such fluorescent probes have been synthesized with special attention to solubility in water and stability towards spontaneous hydrolysis at a given pH. The probes reported here include compound 5 based on a fluorescein fluorophore, compound 12 for FRET-detection of phosphodiester hydrolysis and compound 25 based on a quinolinium fluorophore.     

Méthylène-indolines,indolénines et indoléniniums—XIII: L'hydroxy-16 déhydro-1 vincadifformine,intérmédiaire dans le réarrangement biomimétique de la vincadifformine en vincamine

The title compound is a crucial intermediate in the biomimetic conversion of vincadifformine 1 into vincamine 7. Its configuration at C-16 is established by a combination of chemical and spectroscopic evidence. Iodine oxidation converts 14 into the bridged lactam 18, thus proving a β configuration for the hydroxy group at C-16. The same reaction applied to vindoline 19 gives 21 identical with one of the compounds obtained by microbiological transformation of 19. The ¹³C NMR spectra of derivatives 3 and 8 (obtained by oxidation of vincadifformine) show that oxidation proceeds with introduction of the substituent at C-16, with a β-configuration. The alcohol 3 however, posesses a different conformation due to strong hydrogen bonding with N-4.