We explain a general approximation technique for nonholonomic systems by discussing in detail a special example, chosen so as to illustrate some of the technical aspects of the general construction. The example considered is that of an extension of a two-input system obtained by adding a single bracket of degree ve. This bracket is suuciently complicated to exhibit some phenomena, such as multi...

In this paper we consider the optimal structure of double bracket flows and generalisations of these flows to more complex gradient flows. We discuss different notions of optimality and the relationship of the flows to the structure of convex polytopes.

In a Hamiltonian system with first class constraints observables can be defined as elements of a quotient Poisson bracket algebra. In the gauge fixing approach observables form a quotient Dirac bracket algebra. We show that these two algebras are isomorphic. A new realization of the observable algebras through the original Poisson bracket is found.Generators, brackets and pointwise products of ...

We present a Hamiltonian derivation of a class of reduced plasma two-dimensional fluid models, an example being the Charney–Hasegawa–Mima equation. These models are obtained from the same parent Hamiltonian model, which consists of the ion momentum equation coupled to the continuity equation, by imposing dynamical constraints. It is shown that the Poisson bracket associated with these reduced m...

We study the classical current algebra for principal chiral model defined on two dimensional world-sheet with general metric. We develop the Hamiltonian formalism and determine the form of the Poisson brackets between currents. Then we determine the Poisson bracket for Lax connection and we show that this Possion bracket does not depend on the world-sheet metric. We also study the Nambu-Gotto f...

BACKGROUND Technological advances in wire selection and bracket design have led to improved treatment efficiency and allowed longer time intervals between appliance adjustments. The wires remain in the mouth for a longer duration and are subjected to electrochemical reactions, mechanical forces of mastication and generalized wear. These cause different types of corrosion. This study was done to...

modern integrated circuits consist of millions of standard cells and routing paths. in nano-scale designs, mis-prediction is a dominant problem that may diminish the quality of physical design algorithms or even result in the disruption of the convergence of the design cycle. in this paper, a new planning methodology is presented in which a master-plan of the chip is constructed at the early le...

In his celebrated proof of Szemerédi’s theorem that a set of integers of positive density contains arbitrarily long arithmetic progressions, W. T. Gowers introduced a certain sequence of norms ‖ · ‖U 2[N ] ≤ ‖ · ‖U 3[N ] ≤ . . . on the space of complex-valued functions on the set [N ]. An important question regarding these norms concerns for which functions they are ‘large’ in a certain sense. ...