Many pion decays of ρ(770) and ω(782) mesons in chiral theory. Abstract The many particle decays ρ(770) → 4π and ω(782) → 5π are considered in detail in the approach based on the Weinberg Lagrangian or, in a new language, the Lagrangian of hidden local symmetry added with the term induced by the anomalous Lagrangian of Wess and Zumino.

We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit e...

A holomorphic Lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with Lagrangian fibers. It is known (due to Huybrechts) that a given compact manifold admits only finitely many holomorphic symplectic structures, up to deformation. We prove that a given compact manifold with b2 > 7 admits only finitely many deformation types of holomorphic Lagrangian fibrations.

This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a punctured sphere with fixed local monodromy. The submanifold is defined via products of involutions through Lagrangian subspaces. We show that the moduli space of Lagrangian representations is a Lagrangian submanifold of the moduli of unitary representations.

Lagrangian measurements provide a significant portion of the data collected in the ocean. Difficulties arise in their assimilation, however, since Lagrangian data are described in a moving frame of reference that does not correspond to the fixed grid locations used to forecast the prognostic flow variables. A new method is presented for assimilating Lagrangian data into models of the ocean that...

In this paper we develop a numerical procedure using finite element and augmented Lagrangian meth-ods that simulates electro-mechanical pull-in states of both cantilever and fixed beams in microelectromechanical systems (MEMS) switches. We devise the augmented Lagrangian methods for the well-known Euler-Bernoulli beam equation which also takes into consideration of the fringing effect of electr...

In this paper, a step fixed charge transportation problem is developed where the products are sent from the sources to the destinations in existence of both unit and step fixed-charges. The proposed model determines the amount of products in the existing routes with the aim of minimizing the total cost (sum of unit and step fixed-charges) to satisfy the demand of each customer. As the problem i...

Utilizing a first-order perturbative superspace approach, we derive the bosonic equations of motion for the 10D, N = 1 supergravity fields. We give the Lagrangian corresponding to these equations derived from superspace geometry. Moreover, the equivalence of this Lagrangian to the first-order perturbative component level Lagrangian of anomaly-free supergravity is proven. Our treatment covers bo...

This article explains how to construct immersed Lagrangian submanifolds in C2 that are asymptotic at large distance from the origin to a given braid in the 3–sphere. The self-intersections of the Lagrangians are related to the crossings of the braid. These Lagrangians are then used to construct immersed Lagrangians in the vector bundle O(−1)⊕ O(−1) over the Riemann sphere which are asymptotic a...