The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest's theorem is shown to be Lie-Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying P...

Ġ = {G,H}. In particular, the DV F is called an integral if it has zero PB with the Hamiltonian {F,H} = 0. In this case F does not depend on t. In many problems of the classical mechanics DV form elegant algebraic structures which are closed with respect to PB. The Poisson structures with non-linear PB were discussed in [9] and [6]. Sklyanin introduced [9] the so-called quadratic Poisson algebr...

Let K be a compact connected Lie group and M a compact Hamiltonian K-manifold, i.e., a symplectic K-manifold equipped with a moment map μ : M → k. In this paper, we determine Col(M): the set of all functions on M which Poisson commute with all Kinvariant functions. For this, we construct a finite reflection group WM and show that Col(M) is completely determined by μ(M) and WM . More precisely, ...

The control and treatment of rheumatoid arthritis is a challenge in today's world. Therefore, the pursuit of natural disease-modifying antirheumatic drugs (DMRDs) remains a top priority in rheumatology. The present study focused on curcumin and its derivatives in the search for new DMRDs. We focused on prominent p38 mitogen-activated protein (MAP) kinase p38α which is a prime regulator of tumor...

The success of recombinant virus-like particles (VLPs) for human papillomavirus and hepatitis B demonstrates the potential of VLPs as safe and efficacious vaccines. With new modular designs emerging, the effects of antigen module insertion on the self-assembly and structural integrity of VLPs should be clarified so as to better enabling improved design. Previous work has revealed insights into ...

This paper deals with solutions to the Vlasov-Poisson system with an infinite mass. The solution to the Poisson equation cannot be defined directly because the macroscopic density is constant at infinity. To solve this problem, we decompose the solution to the kinetic equation into a homogeneous function and a perturbation. We are then able to prove an existence result in short time for weak so...