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41.
Dorota G?azowska Janusz Matkowski 《Journal of Mathematical Analysis and Applications》2007,331(2):1187-1199
The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g. 相似文献
42.
In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with the Hausdorff measure of noncompactness. 相似文献
43.
Various tests have been carried out in order to compare the performances of several methods used to solve the non-symmetric linear systems of equations arising from implicit discretizations of CFD problems, namely the scalar advection-diffusion equation and the compressible Euler equations. The iterative schemes under consideration belong to three families of algorithms: relaxation (Jacobi and Gauss-Seidel), gradient and Newton methods. Two gradient methods have been selected: a Krylov subspace iteration method (GMRES) and a non-symmetric extension of the conjugate gradient method (CGS). Finally, a quasi-Newton method has also been considered (Broyden). The aim of this paper is to provide indications of which appears to be the most adequate method according to the particular circumstances as well as to discuss the implementation aspects of each scheme. 相似文献
44.
In this paper we deal with nonlinear second-order boundary value problems with impulses. The impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear. In both cases functional dependence on the solution is allowed. The existence results follow from the existence of a pair of well-ordered lower and upper solutions. 相似文献
45.
François Loiseau Jean-Mary Simone David Carcache Pavel Bobal Reinhard Neier 《Monatshefte für Chemie / Chemical Monthly》2007,138(2):121-129
Summary. Free radical couplings from furan, as cheap starting material, were studied in view of developing a rapid strategy en route to the synthesis of derivatives of nonactin. The chain containing the alcohol function was introduced in one or two steps
in 86% yield. For the introduction of the second chain with the ester function two different coupling methods were tested.
Starting from the advanced intermediates obtained nonactin derivatives can be prepared by catalytic hydrogenation of the furan
ring. 相似文献
46.
A palladium‐TPPTS catalyst heterogenized on KF/alumina has been shown to be effective and recyclable for the selective formation of monooctadienylxylopyranosides via the telomerization of butadiene with D ‐xylose. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
47.
S?awomir Solecki 《Topology and its Applications》2007,154(12):2462-2464
Let I0 be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I0 and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Ros?anowski-Shelah stating that I0 on N2 strongly violates the countable chain condition. 相似文献
48.
49.
R. Knizikevi?ius 《Applied Surface Science》2006,253(3):1581-1583
The ion-beam-assisted etching of silicon in Cl2 environment is considered. The theoretically calculated dependences of silicon etching rate on the flux of Cl2 molecules at different ion current densities are compared with experimentally measured. The composition of the adsorbed layer is determined. It is found that SiCl2 molecules prevail in the adsorbed layer. The reciprocal of relative concentration of SiCl2 molecules in the adsorbed layer linearly depends on the ion-to-neutral flux ratio. 相似文献
50.
We establish a combinatorial interpretation for various operations on symmetric functions, such as plethysm, scalar product, and derivation. Thus we obtain proofs of formulas involving symmetric functions in term of combinatorial constructions on permutations. 相似文献