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71.
72.
Pierre de la Harpe A. Guyan Robertson Alain Valette 《Israel Journal of Mathematics》1993,81(1-2):65-96
Let Γ be a finitely generated group. In the group algebra ℂ[Γ], form the averageh of a finite setS of generators of Γ. Given a unitary representation π of Γ, we relate spectral properties of the operator π(h) to properties of Γ and π.
For the universal representationπ
un
of Γ, we prove in particular the following results. First, the spectrum Sp(π
un
(h)) contains the complex numberz of modulus one iff Sp(π
un
(h)) is invariant under multiplication byz, iff there exists a character
such that η(S)={z}. Second, forS
−1=S, the group Γ has Kazhdan’s property (T) if and only if 1 is isolated in Sp(π
un
(h)); in this case, the distance between 1 and other points of the spectrum gives a lower bound on the Kazhdan constants. Numerous
examples illustrate the results. 相似文献
73.
Nguyen Thanh Long Pham Ngoc Dinh Alain 《Mathematical Methods in the Applied Sciences》1993,16(4):281-295
We study the following initial and boundary value problem: In section 1, with u0 in L2(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L2(0, T; H ∩ H2) ∩ L∞(0, T; H) if we assume u0 in H and f in C1(?,?). Numerical results are given for these two cases. 相似文献
74.
Max Robba Jean-Charles Lancelot Daniel Maume Alain Rabaron 《Journal of heterocyclic chemistry》1978,15(7):1159-1163
1,2,4-Triazino[4,5-b]indazol-1(2H)one and its derivatives were prepared by transposition of 3-[2-(-1,3,4-oxadiazolyl)]indazole or by ring closure of indazole ethoxymethylidenehydrazides. The synthesis of 1,2,3,4-tetrahydro-l,2,4-triazino[4,5-b]indazole-1,4-dione was achieved by cyclising the N-carbethoxyhydrazide of indazole-3-carboxylic acid and the synthesis of 1,2,4-triazino-[4,5-b]indazol-4(3H)one was made by cyclising the N-carbethoxy-hydrazone of indazole-3-carboxaldehyde. The Oxydation of 1,2,4-triazino[4,5-b]indazole-l(2H)thione gave 1,2,4-triazino-[4,5-b]indazoles. Nmr spectral data are reported. 相似文献
75.
The composition of the essential oil of Bifora radians, an aldehyde-producing weed, has been investigated by capillary gas chromatography, coupled gas chromatography – mass spectrometry, on-line catalytic hydrogenation and coupled gas chromatography – infrared spectrometry. The nineteen compounds identified included eighteen aldehydes: seven alkanals (C6, C9, C10, C11, C12, C13, and C14), ten alkenals, including five (E)-2-alkenals (C12, C13, C14, C15, and C16), and one (E,E)-2,4-alkadienal (C13). Typical Bifora odors were attributed to three major (E)-2-alkenals, C12, C13, and C14. 相似文献
76.
A successful application of microwave irradiation, in which phthalocyanines were synthesized under solventless conditions from 1,2-phthalonitrile or phthalic anhydride and urea in the presence of metal templates is described. It was found that in comparison with conventional heating, the microwave process is a very useful alternative for cyclotetramerization processes because of reduction of the reaction time, better yield, and easy-to-perform procedure. 相似文献
77.
Graziano Bonetti Patrick Pibarot Alain Chaintreau Jean Paul Marion 《Journal of separation science》1992,15(5):305-306
The use of diethylene glycol monoethyl ether as a flavor solvent is restricted. Since existing methods of quantitation are tedious or require sophisticated multi-dimensional GC instrumentation, a simple method has been developed using low cost GC-MS. Monitoring of ions 31 and 45 enables quantitation of DEGEE in essential oils at levels down to 1 μg/g with accuracy equal to or better than 15%. 相似文献
78.
José Elguero Alain Fruchier El Mostafa Tjiou Sviatoslav Trofimenko 《Chemistry of Heterocyclic Compounds》1995,31(9):1006-1026
The carbon-13 chemical shifts and some selected coupling constants of 183 indazoles are reported. The main conclusions of the original references are briefly summarized.Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1159–1179, September, 1995. 相似文献
79.
Alain H. Roux Daniel Hétu Gérald Perron Jacques E. Desnoyers 《Journal of solution chemistry》1984,13(1):1-25
Mixed micelles can be formed in water between various pairs of hydrophobic solutes such as surfactants, alcohols and hydrocarbons. These systems can often be studied through the thermodynamic functions of transfer of one of the solutes, usually kept near infinite dilution, from water to an aqueous solution of the other solute. When mixed micelles are formed, these functions change significantly, and often go through extrema, in the region where the binary system micellizes or undergoes some microphase transition.Three main effects are responsible for the observed trends: pair-wise interactions between both solutes in the monomeric form, a distribution of the reference solute between the aqueous and micellar phases and a shift in the monomer-micelle equilibrium in the vicinity of the reference solute. Simple equations can be derived for these three effects which can account for the sign and magnitude of the observed trends using parameters which are derived for the most part from the two binary systems. 相似文献
80.
Weeber JC Finot E Legay G Cathelat A Lacroute Y Dereux A 《Langmuir : the ACS journal of surfaces and colloids》2004,20(23):10179-10185
We report on the near-field imaging of microstructured polymer layers deposited on an homogeneous metal thin film on which a surface plasmon mode is excited. The microstructures in the polymer layers are designed by electron beam lithography, and the near-field imaging is performed with a photon scanning tunneling microscope (PSTM). We show that, despite their very small height, the microstructures can be conveniently imaged with a PSTM thanks to the field enhancement at the surface of the metal thin film supporting the surface plasmon. The influence of the illumination conditions on the contrast of the PSTM images is discussed. In particular, we show that both the field enhancement and the near-field intensity distribution around the microstructures depend dramatically upon the illumination conditions, leading to the conclusion that the PSTM is well suited for spatially resolved near-field surface plasmon sensing purposes. 相似文献