In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the complete solution in terms of ultraelliptic functions and quadratures.

A classical result of Tchakaloff on the existence of exact quadrature formulae up to a given degree is extended to positive measures without compact support. A criterion for the existence of Gaussian quadratures for a class of such measures is also derived from the main proof.

In this paper, we study the extended Hamilton–Jacobi Theory in context of dynamical systems with symmetries. Given an action a Lie group G on manifold M and G-invariant vector field X M, construct complete solutions equation (HJE) related to (and given fibration M). We do that along each open subset U⊆M, such πU has structure πU:U→πU, restriction U canonical projection π:M→M/G, is surjective su...

We investigate a family of integrable Hamiltonian systems on Lie–Poisson spaces L+(5) dual to Lie algebras soλ,α(5) being two-parameter deformations of so(5). We integrate corresponding Hamiltonian equations on L+(5) and T ∗R5 by quadratures as well as discuss their possible physical interpretation.

The main purpose of this paper is the construction of explicit Gauss-Turán quadrature formulas: they are relative to some classes of weight functions, which have the peculiarity that the corresponding s-orthogonal polynomials, of the same degree, are independent of s. These weights too are introduced and discussed here. Moreover, highest-precision quadratures for evaluating Fourier-Chebyshev co...

A novel scheme to realize the whole class of quantum nondemolition (QND) measurements of a field quadrature is suggested. The setup requires linear optical components and squeezers, and allows optimal QND measurements of quadratures, which minimize the information gain versus state disturbance trade-off.

We study a bosonic Gaussian channel with classical additive noise and memory effects. In particular we consider correlations in the added noise which are asymmetric in the phase space quadratures and show in such a case the usefulness of entangled codewords for reliable communication. We explicitly demonstrate that optimal rates can be achieved with multiparty entangled codewords.