The orbit method of Kirillov is used to derive the p-mechanical brackets [25]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder–Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with G...

We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in socalled ”quantized spaces”. Our main result is a description of the motion of a particle in the corresponding Kepler-Coulomb problem.

It is shown how to introduce a geometric description of the algebraic approach to the non-relativistic quantum mechanics. It turns out that the GNS representation provides not only symplectic but also Hermitian realization of a ‘quantum Poisson algebra’. We discuss alternative Hamiltonian structures emerging out of different GNS representations which provide a natural setting for quantum bi-Ham...

The orbit method of Kirillov is used to derive the p-mechanical brackets [25]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder–Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with G...

Recently, the development of Src/Abl (c-Src/Bcr-Abl tyrosine kinases) dual inhibitors has attracted considerable attention from the research community for treatment of malignancies. In order to explore the different structural features impacting the Src and Abl inhibitory activities of N(9)-arenethenyl purines and to investigate the molecular mechanisms of ligand-receptor interactions, a molecu...

Accurate methods of computing the affinity of a small molecule with a protein are needed to speed the discovery of new medications and biological probes. This paper reviews physics-based models of binding, beginning with a summary of the changes in potential energy, solvation energy, and configurational entropy that influence affinity, and a theoretical overview to frame the discussion of speci...

This paper develops a reduction theory for Dirac structures that includes in a unified way, reduction of both Lagrangian and Hamiltonian systems. It includes the reduction of variational principles and in particular, the Hamilton–Pontryagin variational principle. It also includes reduction theory for implicit Lagrangian systems that could be degenerate and have constraints. In this paper we foc...

Electrostatic potentials around DNA are obtained by solving the nonlinear Poisson-Boltzmann (PB) equation. The detailed charge distribution of the DNA and the different polarizabilities of the macromolecule and solvent are included explicitly in the calculations. The PB equation is solved using extensions of a finite difference approach applied previously to proteins. Electrical potentials and ...