共查询到20条相似文献,搜索用时 15 毫秒
1.
A. V. Shchepetilov 《Theoretical and Mathematical Physics》1996,109(3):1556-1564
Quantum mechanical problems are considered for potentials satisfying Bertrand's problem in Lobachevsky space. The self-adjointness of the corresponding Schrödinger operators is proved. The energy levels are calculated both from the Schrödinger equation and by means of the Bohr-Sommerfeld method. The effect of the quantum binding of classically infinite motion was discovered and is presented for the first time. It is shown that the quasi-classical limit is equivalent, in a sense, to the Euclidean limit.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 395–405, December, 1996. 相似文献
2.
V. T. Fomenko 《Mathematical Notes》1996,59(2):201-204
It is proved that conformal infinitesimal deformations of a surfaceF
kin Riemannian space, and they only, are areally recurrent infinitesimal deformations. All areally recurrent deformations of the hypersphereS
n–1 inE
n are described.Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 284–290, February, 1996.This research was partially supported by the Russian Foundation for Basic Research under grant No. 95-01-00228a. 相似文献
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We describe the class of Archimedean polyhedra in the three-dimensional Lobachevsky space, which technically reduces to studying
Archimedean tilings of the Lobachevsky plane. We analyze the possibility of obtaining Archimedean tilings by methods that
are usually applied on the sphere and in the Euclidean plane. It is pointed out that such tilings can be constructed by using
certain types of Fedorov groups in the Lobachevsky plane. We propose a general approach to the problem of classifying Archimedean
tilings of the Lobachevsky plane. 相似文献
4.
A. A. Borisenko 《Journal of Mathematical Sciences》1991,54(1):675-678
Translated from Ukrainskii Geometricheskii Sbornik, No. 31, pp. 14–19, 1988. 相似文献
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Frank Morgan 《Rendiconti del Circolo Matematico di Palermo》2004,53(3):469-477
For the cylindrical norm onR
3, for which the isoperimetric shape is a cylinder rather than a round ball, there are analogs of the classical Delaunay surfaces
of revolution of constant mean curvature. 相似文献
7.
V. T. Lisitsa 《Journal of Mathematical Sciences》1994,69(1):874-875
A definition of l -dimensional k-cylindrical metrics is introduced and it is proved that k-cylindrical metrics admit an immersion in the form of k-cylindrical surfaces into Lobachevsky space Ll+p, where codimension p of the immersion coincides with the codimension of the immersion of the base of the cylindrical metric into a Euclidean or Lobachevsky space.Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 66–69, 1991. 相似文献
8.
A. A. Borisenko 《Journal of Mathematical Sciences》1990,51(2):2191-2196
The structure ofk-convex multidimensional surfaces in Euclidean space is studied. The classes ofk-asymptotic surfaces are introduced. A sufficient condition is found for an asymptotic distribution on a multidimensional surface to be holonomic.Translated from Ukrainskií Geometricheskií Sbornik, Issue 29, 1986, pp. 5–12. 相似文献
9.
M. Boutat S. Hilout J.-E. Rakotoson J.-M. Rakotoson 《Nonlinear Analysis: Theory, Methods & Applications》2008
This paper deals with the existence and nonnegativity of the weak periodic-domain solution for a degenerate fourth-order parabolic equation modeling the evolution of thin films. This study in the multidimensional domain follows the recent results related to the resolution in one-dimensional space [J.E. Rakotoson, J.M. Rakotoson, C. Verbeke, Generalized lubrification models blow-up and global existence, RACSAM 99 (2) (2005) 235–241; C. Verbeke, Quelques modèles d’équations d’évolution de surfaces: Explosion en temps fini et diverses propriétés qualitatives, Thèse de doctorat de l’Université de Poitiers (15 Décembre 2005); J.E. Rakotoson, J.M. Rakotoson, C. Verbeke, Higher-order equations related to thin film: Blow up and global existence, the influence of the initial data, (submitted for publication)]. 相似文献
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A. A. Borisenko 《Siberian Mathematical Journal》1990,31(3):379-387
Khar'kov. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 3, pp. 19–29, May–June, 1990. 相似文献
13.
Translated from Ukrainskii Geometricheskii Sbornik, No. 31, pp. 19–26, 1988. 相似文献
14.
Urs Lang 《Mathematische Zeitschrift》1992,210(1):581-592
15.
Johan Deprez 《Journal of Geometry》1985,25(2):192-200
Semi-parallel immersions are defined as extrinsic analogue for semi-symmetric spaces and as a direct generalization of parallel immersions. Using results of Backes on Euclidean Jordan triple systems, the totally geodesic immersions are shown to be the only minimal semi-parallel immersions into a Euclidean space. Semi-parallel immersions of surfaces into Em are studied and a classification of semi-parallel immersions with pointwise planar normal sections of surfaces in Em is given.Research Assistant of the National Fund of Scientific Research 相似文献
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Rafael López 《Calculus of Variations and Partial Differential Equations》2010,39(3-4):333-359
A stationary rotating surface is a compact surface in Euclidean space whose mean curvature H at each point x satisfies 2H(x) = a r(x)2 + b, where r(x) denotes the distance from x to a fixed straight-line L, and a and b are constants. These surfaces are solutions of a variational problem that describes the shape of a drop of incompressible fluid in equilibrium by the action of surface tension when it rotates about L with constant angular velocity. The effect of gravity is neglected. In this paper we study the geometric configurations of such surfaces, focusing the relationship between the geometry of the surface and the one of its boundary. As special cases, we will consider two families of such surfaces: axisymmetric surfaces and embedded surfaces with planar boundary. 相似文献
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20.
I. Dobson 《Journal of Nonlinear Science》1993,3(1):307-327
Summary Engineering and physical systems are often modeled as nonlinear differential equations with a vector λ of parameters and operated
at a stable equilibrium. However, as the parameters λ vary from some nominal value λ0, the stability of the equilibrium can be lost in a saddle-node or Hopf bifurcation. The spatial relation in parameter space
of λ0 to the critical set of parameters at which the stable equilibrium bifurcates determines the robustness of the system stability
to parameter variations and is important in applications. We propose computing a parameter vector λ* at which the stable equilibrium bifurcates which is locally closest in parameter space to the nominal parameters λ0. Iterative and direct methods for computing these locally closest bifurcations are described. The methods are extensions
of standard, one-parameter methods of computing bifurcations and are based on formulas for the normal vector to hypersurfaces
of the bifurcation set. Conditions on the hypersurface curvature are given to ensure the local convergence of the iterative
method and the regularity of solutions of the direct method. Formulas are derived for the curvature of the saddle node bifurcation
set. The methods are extended to transcritical and pitchfork bifurcations and parametrized maps, and the sensitivity to λ0 of the distance to a closest bifurcation is derived. The application of the methods is illustrated by computing the proximity
to the closest voltage collapse instability of a simple electric power system. 相似文献