In this survey we address the Björling problem for various classes of surfaces associated to the Euler–Lagrange equation of the Helfrich elastic energy subject to volume and area constraints.

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts (the Ricci tensor and the term proportional to the curvature scalar) with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, wit...

The transformation of an Euler-Lagrange system into a state affine system in order to solve some interesting problem as the design of observer, the output tracking control, is considered in this paper. A necessary and a sufficient condition is given as well as a method to compute this transformation.

We present a new numerical scheme for solving a conservative Allen–Cahn equation with a space–time dependent Lagrange multiplier. Since the well-known classical Allen–Cahn equation does not have mass conservation property, Rubinstein and Sternberg introduced a nonlocal Allen–Cahn equation with a time dependent Lagrange multiplier to enforce conservation of mass. However, with their model it is ...

Abstract It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The ...

In (Kosmol, 1991; Kosmol and Pavon, 1993) a new elementary approach to optimal control problems relying on the Lagrange lemma was described which appears to be technically, and conceptually, much simpler than existing methods, and, furthermore, provides a unified variational approach. In (Kosmol and Pavon, 1992) this method was further clarified and developed for linear Lagrangefunctionals. We ...

We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as h → 0 is either the nonlinear von Kármán plate equation or the linear fourth order Germain-Lagrange equa...

The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject, the main results being Agrawal’s necessary optimality conditions of Euler-Lagrange and respective transversality conditions. Using Agrawal’s Euler-Lagrange equation and the Lagrange multiplier technique, we obtain here a Noether-like theorem for fractional optimal control problems in the se...

Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard's algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange mu...