Some Z2\mathbf{Z}_2-invariant Variables: Constructed of the Scalars Dilaton and Axion

Using the dilaton scalar and axion pseudoscalar fields we construct a number of scalars and differential forms which are symmetric under the $\mathbf{Z}_2$-subgroup of the group $SL(2, \mathbf{R})$. These invariants enable us to establish various 10-dimensional invariant actions. Other invariants which are not independent from the previous ones will be detached.Comment: 11 pages, Latex, No figure. In the revised version some interpretations have been improve

T-duality and Noncommutative DBI Action

In this article we study the noncommutative description of the DBI Lagrangian and its T-dual counterpart. We restrict the freedoms of the noncommutativity parameters of these Lagrangians. Therefore the noncommutativity parameter, the effective metric, the effective coupling constant of the string and the extra modulus ${\tilde \Phi}$ of the effective T-dual theory, can be expressed in terms of the closed string variables $g$, $B$, $g_s$ and the noncommutativity parameter of the effective theory of open string.Comment: 8 pages, Latex, no figure, Some formulas have been cancele

Analysis of moving least squares approximation revisited

In this article the error estimation of the moving least squares approximation is provided for functions in fractional order Sobolev spaces. The analysis presented in this paper extends the previous estimations and explains some unnoticed mathematical details. An application to Galerkin method for partial differential equations is also supplied.Comment: Journal of Computational and Applied Mathematics, 2015 Journal of Computational and Applied Mathematic