We have derived the most general chirally invariant Lagrangian L 6 for the meson sector at order p 6. The result provides an extension of the standard Gasser-Leutwyler Lagrangian L 4 to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms ...

I promised a second part. Here it is. I hesitated, because I don’t like being destructive, and unfortunately, to deal with the current state of affairs in quantum theory means just doing this: I show you that the current gauge theory is fundamentally ill-designed, along with it fall Weinberg model and Wightman theory. 1. Continuing with the Lagrangian Formalism Let me continue from where I left...

This paper suggests an inverse optimal proportional–integral–derivative (PID) control design method to track trajectories in Lagrangian systems. The inverse optimal PID controller exists if and only if the Lagrangian system is extended disturbance input-to-state stable. First, we find the Lyapunov function and the control law that satisfy the extended disturbance input-to-state stability by usi...

The vortex-wave system is a version of the vorticity equation governing the motion of 2D incompressible fluids in which vorticity is split into a finite sum of Diracs, evolved through an ODE, plus an L part, evolved through an active scalar transport equation. Existence of a weak solution for this system was recently proved by Lopes Filho, Miot and Nussenzveig Lopes, for p > 2, but their result...

A Lagrangian for flat domain walls in spaces with Cartan torsion and electromagnetic fields is proposed.The Lagrangian is very similar to a recently proposed Lagrangian for domain walls in a Chern-Simons electrodynamics in 2+1 dimensions.We show that in the first approximation of the torsion scalar potential the field equations are reduced to a Klein-Gordon type field equation for the torsion p...

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of the damped Benjamin-Ono equation. The structure of the dispersive shock is considered in this method.

In this review paper we present a stable Lagrangian numerical method for computing plane curves evolution driven by the fourth order geometric equation. The numerical scheme and computational examples are presented.

We derive a priori interior Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher dimensions. Our unified approach leads to sharper estimates even for the previously known three dimensional and convex solution cases.

We introduce a new method for studying the Cauchy problem for systems of conservation laws in one space dimension. This method is based on the equivalence of the Cauchy problems in Eulerian and Lagrangian coordinates, as regards the existence and uniqueness of entropy solutions. The main idea is to solve the problem in Lagrangian coordinates and determine the transformation linking the two coor...

The present paper aims at investigating the manner of two dissipative massive scalar fields. Two massive scalar fields that interact with a reservoir were considered and a reservoir was modeled by continuum Klein-Gordon fields. The Lagrangian of the total system was canonically quantized and the dynamics of the system was determined using the Euler-Lagrange equation. Then, the explicit form of the...