We study bosonization of the sine-Gordon theory in the presence of boundary interactions at the free fermion point. In this way we obtain the boundary S-matrix as a function of physical parameters in the boundary sine-Gordon Lagrangian. The boundary S-matrix can be matched onto the solution of Ghoshal and Zamolodchikov, thereby relating the formal parameters in the latter solution to the physic...

and there are no inequality constraints (i.e. there are no fi(x) i = 1, . . . , m). We simply write the p equality constraints in the matrix form as Cx− d = 0. The basic idea in Lagrangian duality is to take the constraints in (1) into account by augmenting the objective function with a weighted sum of the constraint functions. We define the Lagrangian L : R ×R ×R → R associated with the proble...

in this article, modeling and optimization of power consumption of two–stage compressed airsystem has been investigated. to do so, the two – stage compressed air cycle with intercooler offajr petroleum company was considered. this cycle includes two centrifugal compressors, ashell, and a tube intercooler. for modeling of power consumption, actual compressors isentropicefficiencies and intercool...

We consider the local convergence properties of the class of augmented Lagrangian methods for solving nonlinear programming problems whose global convergence properties are analyzed by Conn et al. (1993a). In these methods, linear constraints are treated separately from more general constraints. These latter constraints are combined with the objective function in an augmented Lagrangian while t...

A bi-isotropic magneto-electric metamaterials is modeled by two independent reservoirs. The reservoirs contain a continuum of three dimensional harmonic oscillators, which describe polarizability and magnetizability of the medium. The paper aimed to investigate the effect of electromagnetic field on bi-isotropic. Starting with a total Lagrangian and using Euler-Lagrange equation, researcher cou...

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.

In this paper, we focus on the decentralized optimization problem over Stiefel manifold, which is defined a connected network of $d$ agents. The objective an average local functions, and each function privately held by agent encodes its data. agents can only communicate with their neighbors in collaborative effort to solve p...

This paper extends to dimension 4 the results in the article " Second Order Families of Special Lagrangian 3-folds " by Robert Bryant. We consider the problem of classifying the special Lagrangian 4-folds in C 4 whose fundamental cubic at each point has a nontrivial stabilizer in SO(4). Points on special Lagrangian 4-folds where the SO(4)-stabilizer is nontrivial are the analogs of the umbilica...

We determine the number of functionally independent components of tensors involving higher–order derivatives of a Riemannian metric. A central problem in Riemannian geometry is to determine the number of functionally independent invariants which can be constructed out from a Riemannian metric and its derivatives up to a given order. Due to the inmediate applications of these invariants as Lagra...