Both particle physics and all the approaches to gravity make use of variational principles employing singular Lagrangians [1]. As a consequence the Euler-Lagrange equations cannot be put in normal form, some of them may be non independent equations (due to the contracted Bianchi identities) and a subset of the original configuration variables are left completely or partially indetermined. Moreo...

In our present paper we study the duality theory and linear identities for real polynomials and functions on Banach spaces, which allows for a unified treatment and generalization of some classical results in the area. The basic idea is to exploit point evaluations of polynomials, as e.g. in [Rez93]. As a by-product we also obtain a curious generalization of the well-known Hilbert lemma on the ...

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

The credit for introducing the geometry of Lagrange spaces and their subspaces goes to the famous Romanian geometer Miron 1 . He developed the theory of subspaces of a Lagrange space together with Bejancu 2 . Miron and Anastasiei 3 and Sakaguchi 4 studied the subspaces of generalized Lagrange spaces GL spaces in short . Antonelli and Hrimiuc 5, 6 introduced the concept of φ-Lagrangians and stud...

We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.

We write the field equations of torsion gravity theories and Noether identity they obey directly in terms metric contorsion tensor components expressed with respect to natural coordinates, i.e., without using vierbien but Lagrange multipliers. Then we obtain explicit solutions these equations, under specific ans\"atze for field, by assuming be respectively Bertotti-Robinson, pp-wave, Friedmann-...

Kyparisis proved in 1985 that a strict version of the MangasarianFromovitz constraint qualification (MFCQ) is equivalent to the uniqueness of Lagrange multipliers. However, the definition of this strict version of MFCQ requires the existence of a Lagrange multiplier and is not a constraint qualification (CQ) itself. In this note we show that LICQ is the weakest CQ which ensures (existence and) ...

In the present paper, some finite element softwares about interaction of dam and reservoir during earthquake in time domain are discussed. Impedance option is used as boundary condition of absorbent of reservoir and wave. For each software, time history analysis of pressure and displacement are done and finally suitable elements for dam structure and reservoir fluid are introduced comparing the...

This paper is devoted to a sharp investigation of the notion of Lagrange's resolvent and his connections with Galois Theory.

in this paper we demonstrate the existence of a set of polynomials pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in thelagrange interpolation process. in other words, if a  a1  an  b is a given finite sequence of realnumbers, then pi (a j )  ij (ij is the kronecker delta symbol ) ; moreover, the sum of ...