摘要:

A survey of basic concepts of the theory of unconstrained higher order variational principles in fibered spaces is given, and selected open problems, related to the variational sequence theory, are discussed. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814712

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

This lecture brings a survey of topics and results concerning differential equations which arise as equations for extremals of higher‐order variational functionals on fibered manifolds. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814713

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

In this paper we give a general compatibility theorem for overdetermined systems of scalar partial differential equations of complete intersection type in terms of generalized Mayer brackets. As an applications we propose a generalization of the classical Lagrange‐Charpit method for integration of a single scalar PDE. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814714

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

This paper introduces various geometric optimization problems and explores their relationship with motion coordination algorithms for networks of mobile agents. For each problem, the objective is the optimization of an appropriate multi‐center function encoding the sensing task to be achieved by the mobile network in a dynamic environment. We present five different scenarios: the expected value scenario, the expected value scenario with limited range interactions, the area scenario, the worst‐case scenario and the non‐interference scenario. We carefully analyze the smoothness properties and gradient information of the multi‐center functions. Based on this investigation, we propose distributed motion coordination algorithms specifically tailored for each scenario. The multi‐center functions play the role of network aggregate cost functions certifying the validity of the coordination algorithms. Various numerical simulations illustrate the results. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814715

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

&zgr;‐regularization of the Jacobian of scaling transformation of an infinite dimensional integral is derived. It simplifies mathematical justification of the appearance of the Ray‐Singer determinant in the Gaussian path integral given in our previous paper “Regularized Calculus: An application of zeta regularization to infinite dimensional Geometry and Analysis, Int.J.Geo, Meth. Mod. Phys., 1(2004)”. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814716

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

The fractional calculus is the name for the theory of integrals and derivatives of arbitrary order, which generalize the notions of n‐fold integration and integer‐order differentiation.Differential equations of fractional order appear in certain applied problems and in theoretical researches. In this paper, the Euler‐Lagrange equations of the Lagrangians linear in velocities were derived using the fractional calculus. Two examples of constrained systems possessing a gauge invariance are investigated in details, the explicit solutions of Euler‐Lagrange equations are obtained, and the recovery of the classical results is discussed. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814717

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

In the framework of geometrized jet spaces of first order endowed with a Lagrange structure, is discussed the existence of Lagrangian canonic nonlinear connections. The Euler‐Lagrange equations for certain Kronecker‐type Lagrangian cases are derived, and extensions of the known results are provided. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814718

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

Killing‐Yano and Killing tensors are investigated corresponding to a set of two dimensional superintegrable systems. A suitable surface term is added to the corresponding free Lagrangian describing the motion of a particle on a 2‐sphere of unit radius and we analyze the symmetries of the obtained geometries. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814719

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

Spinning point particle theories accommodate non‐generic supercharges in connection with the existence of Killing‐Yano tensors. Killing‐Yano tensors of order two and three and their corresponding Killing tensors are found for a subclass of generalized pp‐wave metrics. These metrics include the pp‐wave itself, its possible generalizations and the Siklos metric which is conformal to that. The compatibility between geometric duality and non‐generic symmetries is discussed within the context of the metric solutions. It is found that some of the metric solutions admit anti‐de Sitter spacetimes while some are found to be purely radiative. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814720

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

Conformal Killing and Ricci collineation equations for (2+1)‐dimensional Friedmann‐Robertson‐Walker (FRW) spacetimes are solved. These spacetimes are classified according to their Ricci conformal collineations (RCCs) and Ricci collineations (RCs). In the non‐degenerate and degenerate cases of the Ricci tensor (the casesdet(Rab) ≠ 0 anddet(Rab) = 0, respectively), the general forms of the vector fields generating RCCs and RCS are obtained. When the Ricci tensor is degenerate, the special cases are classified and it is shown that there are many cases of RCCs and RCs with infinite degrees of freedom. Furthermore, it is found that when the Ricci tensor is non‐degenerate, the groups of RCCs and RCs are finite‐dimensional, and we have always 10‐parameter group of RCCs and 6‐parameter group of RCs which are the maximal possible dimension for three‐dimensional spacetime manifold. The results obtained are compared with conformal Killing vectors and Killing vectors. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814721

出版商:AIP    

年代:1904

数据来源: AIP