A type of closed exterior algebra in R3 under the cross product is revealed to hold between differential forms from the three Whittaker scalar potentials, associated with the fields of a moving electron. A special algebraic structure is revealed in the context of Clebsch reparametrization of these scalars, and a special prescription for the construction of permutation invariant electromagnetic ...

An efficient implementation technique for the Lagrange interpolation is derived. This formulation called the Farrow structure leads to a version of Lagrange interpolation that is well suited to time varying FD filtering. Lagrange interpolation is mostly used for fractional delay approximation as it can be used for increasing the sampling rate of signals and systems. Lagrange interpolation is on...

Abstract: This paper addresses a stability analysis problem and synthesis problem for pendulum-like systems with multiple nonlinearities. A method for analysing the Lagrange stability of a pendulum-like system with multiple nonlinearities is proposed. In order to study the synthesis problem, the paper develops an Extended Strict Bounded Real Lemma for unstable systems. A sufficient condition fo...

The regularity of Lagrange multipliers for state-constrained optimal control problems belongs to the basic questions of control theory. Here, we investigate bottleneck problems arising from optimal control problems for PDEs with certain mixed control-state inequality constraints. We show how to obtain Lagrange multipliers in L p-spaces for linear problems and give an application to linear parab...

In this paper we interpret chaos synchronization schemes within the framework of Lagrange programming networks, which form a class of continuous-time optimization methods for solving constrained nonlinear optimization problems. From this study it follows that standard synchronization schemes can be regarded as a Lagrange programming network with soft constraining, where synchronization between ...

It is well known that equations of motions and equations which describe the dynamics of physical elds can be deduced from the condition the action S (determined by the corresponding Lagrange function) is optimal. In other words, there is an optimality criterion on the set of all trajectories, and the actual trajectory is optimal with respect to this criterion. The next reasonable question is: w...

The subject of this paper are two Hopf algebras which are the non-commutative analogues of two different groups of formal power series. The first group is the set of invertible series with the group law being multiplication of series, while the second group is the set of formal diffeomorphisms with the group law being composition of series. The motivation to introduce these Hopf algebras comes ...