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...

We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether’s theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energymomentum current and the hypermomentum current. In particular, the propagation equations allow for a ...

We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether’s theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energymomentum current and the hypermomentum current. In particular, the propagation equations allow for a ...

The paper is concerned with mechanical systems which are controlled by implementing a number of time-dependent, frictionless holonomic constraints. The main novelty is due to the presence of additional non-holonomic constraints. We develop a general framework to analyze these problems, deriving the equations of motion and studying the continuity properties of the “input-to-trajectory” maps. Var...

We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether’s theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energymomentum current and the hypermomentum current. In particular, the propagation equations allow for a ...

In the first part of the paper we present a new point of view on the geometry of nonholonomic mechanical systems with linear and affine constraints. The main geometric object of the paper is the nonholonomic connection on the distribution of constraints. By using this connection we obtain the Newton forms of Lagrange–d’Alembert equations for nonholonomic mechanical systems with linear and affin...

We present an new system of ordinary differential equations with affine Weyl group symmetry of type E (1) 6 . This system is expressed as a Hamiltonian system of sixth order with a coupled Painlevé VI Hamiltonian. Introduction The Painlevé equations PJ (J = I, . . . ,VI) are ordinary differential equations of second order. It is known that these PJ admit the following affine Weyl group symmetri...

Traditional affine models of the term structure are eminently tractable, but suffer from empirical difficulties. Random field models offer great flexibility in fitting the data, but are widely considered non-implementable unless they are approximated by a low-dimensional system. I develop a state-space estimation framework where both random field and affine models can be estimated by MCMC using...