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1.
Marcel Oliver 《Theoretical and Computational Fluid Dynamics》1997,9(3-4):311-324
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 相似文献
2.
Sudoku’s french ancestors 总被引:1,自引:0,他引:1
Christian Boyer 《Mathematical Intelligencer》2007,29(1):37-44
This column is a place for those bits of contagious mathematics that travel from person to person in the community, because
they are so elegant, suprising, or appealing that one has an urge to pass them on.
Contributions are most welcome. 相似文献
3.
Marcel Crabbé 《Comptes Rendus Mathematique》2004,338(6):433-436
We investigate the notion of substitution in an abstract way, without defining it explicitly. We single out the essential features of the operation of performing a substitution in order to define a concept of substitutive structure, called logos. We then prove a completeness theorem making precise and justifying the intuition that formulas true for the usual substitution can be proved from the logos axioms only. To cite this article: M. Crabbé, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
4.
Marcel Erné 《Order》1991,8(2):159-173
We introduce a special type of order-preserving maps between quasiordered sets, the so-called cut-stable maps. These form the largest morphism class such that the corresponding category of quasiordered sets contains the category of complete lattices and complete homomorphisms as a full reflective subcategory, the reflector being given by the Dedekind-MacNeille completion (alias normal completion or completion by cuts). Suitable restriction of the object class leads to the category of separated quasiordered sets and its full reflective subcategory of completely distributive lattices. Similar reflections are obtained for continuous lattices, algebraic lattices, etc. 相似文献
5.
Boris Andreianov Franck Boyer Florence Hubert 《Numerical Methods for Partial Differential Equations》2007,23(1):145-195
Discrete duality finite volume schemes on general meshes, introduced by Hermeline and Domelevo and Omnès for the Laplace equation, are proposed for nonlinear diffusion problems in 2D with nonhomogeneous Dirichlet boundary condition. This approach allows the discretization of non linear fluxes in such a way that the discrete operator inherits the key properties of the continuous one. Furthermore, it is well adapted to very general meshes including the case of nonconformal locally refined meshes. We show that the approximate solution exists and is unique, which is not obvious since the scheme is nonlinear. We prove that, for general W?1,p′(Ω) source term and W1‐(1/p),p(?Ω) boundary data, the approximate solution and its discrete gradient converge strongly towards the exact solution and its gradient, respectively, in appropriate Lebesgue spaces. Finally, error estimates are given in the case where the solution is assumed to be in W2,p(Ω). Numerical examples are given, including those on locally refined meshes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
6.
The syntheses of two rigid organic molecular rods bearing a nitronyl-nitroxide radical and a terminal nitrogen-based functionality like a pyridine or a cyano group are reported. Both new paramagnetic molecules are fully characterized, including crystal structure analysis. Furthermore their magnetic behaviours in the crystalline state are investigated and their spin concentration corroborate their excellent purity. While the pyridine functionalized rod is synthesized by converting the corresponding benzaldehyde to the phenyl-nitronyl-nitroxide radical, the synthesis of the cyano functionalized rod demonstrates the accessibility of highly sophisticated spin-labelled molecules via cross-coupling reaction with a meta-iodo-phenyl-nitronyl-nitroxide moiety. 相似文献
7.
8.
Marek Pękała Jan Mucha Benedicte Vertruyen Rudi Cloots Marcel Ausloos 《Journal of magnetism and magnetic materials》2006
Samples of La0.7Ca0.3Mn1−xGaxO3 with x=0, 0.025, 0.05 and 0.10 were prepared by standard solid-state reaction. They were first characterized chemically, including the microstructure. The magnetic properties and various transport properties, i.e. the electrical resistivity, magnetoresistivity (for a field below 8 T), thermoelectric power and thermal conductivity measured each time on the same sample, are reported. The markedly different behaviour of the x=0.1 sample from those with a smaller Ga content, is discussed. The dilution of the Mn3+/Mn4+ interactions with Ga doping considerably reduces the ferromagnetic double exchange interaction within the manganese lattice leading to a decrease of the Curie temperature. The polaron binding energy varies from 224 to 243 meV with increased Ga doping. 相似文献
9.
Philippe Boyer Gilles Renversez Evgeny Popov Michel Nevière 《Optical and Quantum Electronics》2006,38(1-3):217-230
The present work adapts a recent grating theory called “Fast Fourier factorization” to cylindrical coordinates in order to study microstructured optical fibers (MOFs). Compared with the classical differential method, this new differential method takes into account the truncation of Fourier series and the discontinuities of the fields across the diffracting surface with the help of new factorization rules. The main advantage of this method is that the directrix of the diffracting cylindrical surface is arbitrary and permits anisotropic and inhomogeneous media although its numerical application needs longer computation time, compared with other well-known numerical methods. The S-propagation algorithm is used to avoid numerical contaminations. The numerical results are validated and compared with the well-established Multipole method in the case of a MOF with six circular cylinders. Further, a new cross-sectional profile (with sectorial inclusions) that the Multipole method cannot consider is studied. 相似文献
10.
Wagner SR Hinshaw DA Ong RA Snyder A Abrams G Adolphsen CE Akerlof C Alexander JP Alvarez M Amidei D Baden AR Ballam J Barish BC Barklow T Barnett BA Bartelt J Blockus D Bonvicini G Boyarski A Boyer J Brabson B Breakstone A Brom JM Bulos F Burchat PR Burke DL Butler F Calvino F Cence RJ Chapman J Cords D Coupal DP DeStaebler HC Dorfan DE Dorfan JM Drell PS Feldman GJ Fernandez E Field RC Ford WT Fordham C Frey R Fujino D Gan KK Gidal G Gladney L Glanzman T Gold MS Goldhaber G Green A 《Physical review letters》1990,64(10):1095-1098