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Second-order Lagrangians depending on a surface which are parameter-invariant and also invariant under rigid motions of Euclidean 3-space are classified.texto impreso
The complex of s-horizontal forms of a smooth foliation F on a manifold M is proved to be exact for every s = 1, . . . , n = codim F, and the cohomology groups of the complex of its global sections, are introduced. They are then compared with ot[...]texto impreso
Castrillón López, Marco ; Díaz-Cano Ocaña, Antonio ; Etayo Gordejuela, J. Javier ; Folgueira, Marta ; Infante del Río, Juan Antonio ; Pozo Coronado, Luis Miguel ; Rey Cabezas, Jose María | No publicado | 2013Material elaborado por profesores de la UCM para la asignatura de este nombre del grado en Ingeniería Matemáticas, el grado en Matemáticas y el grado en Matemáticas y Estadística. Contenidos: - Números enteros. Dígitos de control y criptografía[...]texto impreso
The global inverse problem of the calculus of variations for the particular case of first-order quasi-linear PDEs is solved. Some examples in the field theory are discussed.texto impreso
The variational problem on spatial curves defined by the integral of the squared curvature, whose solutions are the elasticae or nonlinear splines, is analyzed from the Hamiltonian point of view, using a procedure developed by Munoz Masqueand Po[...]texto impreso
Muñoz Masqué, Jaime ; Pozo Coronado, Luis Miguel | Natsional. Akad. Nauk Ukraïni, Inst. Mat., Kiev | 2000The authors use the procedure developed in [9] to develop a Hamiltonian structure into the variational problem given by the integral of the squared curvature on the spatial curves. The solutions of that problem are the elasticae or nonlinear spl[...]texto impreso
Higher-order Lagrangians on T*(M) invariant under the natural representation of gauge fields of M x U(1) on the cotangent bundle are determined.texto impreso
We summarize und analyze several results concerning the variational character of a set of first order quasi-linear PDEs. A local characterization of the problem is given, and the global obstructions to the problem are obtained.texto impreso
The deparametrization problem for parameter-invariant Lagrangian densities defined over J(1)(N, F), is solved in terms of a projection onto a suitable jet bundle. The Hamilton-Cartan formalism for such Lagrangians is then introduced and the pre-[...]texto impreso
A projection is defined such that a second-order Lagrangian density factors through this projection module contact forms if and only if it is parameter invariant. In this way, a geometric interpretation of the parameter invariance conditions is [...]texto impreso
Parameter invariance of the variational problem associated to the squared curvature Lagrangian, whose extremals are the elasticae, allows us to find an equivalent,nonparametric variational problem which is regular. Hamiltonian formalism is then [...]texto impreso
The notion of unrolling of a spherical curve is proved to coincide with its development into the tangent plane. The development of a curve in an arbitrary surface in the Euclidean 3-space is then studied from the point of view of unrolling. The [...]texto impreso
Grifone, Joseph ; Muñoz Masqué, Jaime ; Pozo Coronado, Luis Miguel | Institute of Mathematics and Informatics.University of Debrecen | 2001The systems of first-order quasilinear partial differential equations defined on the 1-jet bundle of a fibred manifold which come from a variational problem defined by an affine Lagrangian are characterized by means of the Hamilton-Cartan formal[...]
