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91.
Rossella Bartolo Anna Germinario Miguel Sánchez 《Annals of Global Analysis and Geometry》2002,21(1):63-84
In this paper the problem of the geodesic connectedness and convexity ofincomplete Riemannian manifolds is analyzed. To this aim, a detailedstudy of the notion of convexity for the associated Cauchy boundary iscarried out. In particular, under widely discussed hypotheses,we prove the convexity of open domains (whose boundaries may benondifferentiable) of a complete Riemannian manifold. Variationalmethods are mainly used. Examples and applications are provided,including a result for dynamical systems on the existence oftrajectories with fixed energy. 相似文献
92.
A simple model consisting of two electronic levels and one vibrational mode (phonon) was theoretically studied. The electronic-vibrational interaction was linear in the vibrational displacement. The vibrational mode was taken in the harmonic approximation and was attached to the thermal bath formed by the ambient environment. The kinetic constants of the vibrational dissipation were of the second order in the vibrational-bath coupling and were taken in the Markovian limit. Although, depending on the parameters of the model, different curves of the non-radiative vibration-induced excited state decay were obtained, in general, three time intervals, corresponding to different physical behaviour, were found. In the short-time interval, small oscillations superimposed on the excited state decay were observed. They were determined by the vibrational frequency and influenced by electronic-vibrational coupling. In the middle-time interval, almost quasi-exponential decay was detected; its rate constant increased with stronger electronic-vibrational interaction and speed of vibrational relaxation. In the long-time interval, the decay was very slow and, under special conditions, even an asymptotic non-zero excited state population was observed. Its value increased with the strength of the off-diagonal electron-vibrational coupling. Links of the parameters of the model with quantum chemical terms were estimated. 相似文献
93.
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process. 相似文献
94.
Jerónimo Rodríguez 《Comptes Rendus Mathematique》2004,339(6):445-450
In the present Note we introduce an extension of the conservative space–time mesh refinement method presented by Fouquet et al. We also propose a post-treatment of the solution that reduces the spurious phenomena due to the non-conformity between the time meshes. A reinterpretation of the equations in terms of new unknowns leads to a new scheme with second order consistent coupling equations. Numerical experiments in 2D and a plane wave analysis for the 1D model show that the method is second order accurate for an arbitrary refinement. To cite this article: J. Rodríguez, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
95.
Enrique Fernández-Cara Sergio Guerrero Oleg Yurievich Imanuvilov Jean-Pierre Puel 《Comptes Rendus Mathematique》2004,338(5):375-380
This Note deals with the controllability of Stokes and Navier–Stokes systems with distributed controls with support in possibly small subdomains. We first present a new global Carleman inequality for the solutions to Stokes-like systems that leads to the null controllability at any time T>0. Then, we present a local result concerning exact controllability to trajectories of the Navier–Stokes system. To cite this article: E. Fernández-Cara et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
96.
I. M. Kolthoff S. R. Cooper V. J. Tulane F. Reimers H. A. J. Pieters K. Höppner V. H. Matula C. B. Macek W. N. Skworzow J. S. Schepelewa F. Čuta K. Kámen S. Cohen R. E. Oesper D. S. Narayanamurthi T. R. Seshadri H. M. State A. W. Kirssanow W. M. Tscherkassow D. M. Mukherjee T. Akiyama Y. Mine S. Yabe Y. Volmar M. Déribéré 《Analytical and bioanalytical chemistry》1937,111(5-6):192-197
97.
In order to investigate the relative effects of the differences between the structures and lipophilicities of 1, 10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TA-18-crown-6) and the tetrabenzyl derivative of 1,10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TBTA-18-crown-6) on their extraction-abilities and -selectivities for transition metal cations, constants of the overall extraction (logK
ex) of 1:1 (M:L) complexes, the distribution (K
D) for two diluents (CH2Cl2 and CHCl3) with different dielectric constants have been determined at 25 ± 0.1 °C. The magnitude of logK
ex is largely determined by that of K
D. The equilibrium constants of TA-18-crown-6 have been compared with those of TBTA-18-crown-6. It is found that:(i) logK
ex sequences of TA-18-crown-6 and TBTA-18-crown-6 for transition metals in CH2Cl2 lie in order: Fe3+ > Cu2+ > Mn2+ > Co2+ > Cd2+ > Ni2+ > Zn2+ and Fe3+ > Cu2+ > Co2+ > Mn2+ > Ni2+ > Cd2+ > Zn2+ respectively; (ii) the stability sequences of two types of tetra-aza-crown ethers with the transition metal cations in CHCl3 are the same as follows: Fe3+ > Ni2+ > Cu2+ > Co2+ > Zn2+ > Cd2+ > Mn2+, and (iii) unusual selectivities are observed for transition metal-tetra-aza-crowns, e.g. the high Fe3+/M
n+ selectivity factors (Sf) of TA-18-crown-6, except for the competitive-extractions for the special case in CHCl3 of TBTA-18-crown-6, it was found that the Mn2+/M
n+ values were relatively higher according to the other transition metal cations. A systematic sequence in these two types of solvents is not found for a given transition metal cation in terms of the variation of selectivity with the tetra-aza-crown ethers. The results provide alternatives for the rational design of other specific ligands on the transition metal cations. 相似文献
98.
Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the
groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even
if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set
system consisting of sufficiently many sets contains at least one of these structures with many sets. 相似文献
99.
100.