Hamiltonian Gromov-Witten invariants

In this paper we introduce invariants of semi-free Hamiltonian actions of S¹ on compact symplectic manifolds using the space of solutions to certain gauge theoretical equations. These equations generalise both the vortex equations and the holomorphicity equation used in Gromov-Witten theory. In the definition of the invariants we combine ideas coming from gauge theory and the ideas underlying the construction of Gromov-Witten invariants.     

Application of the Volterra filter in experimental diffraction data processing

The effective signal in x-ray diffraction analysis of material properties often contains high frequency (noise) and low frequency (trend) components as additive parts. It is necessary to extract the effective signal from the noise to ensure high quality of signal processing. Digital filters of Volterra type are proposed for filtering purposes and a comparison of Volterra filtration implemented on x-ray diffraction data versus results from a set of other digital filters is given.     

Vorticity-velocity-pressure formulation for Stokes problem

We propose a three-field formulation for efficiently solving a two-dimensional Stokes problem in the case of nonstandard boundary conditions. More specifically, we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary. The proposed computational methodology consists in reformulating the considered boundary value problem via a mixed-type formulation where the pressure and the vorticity are the principal unknowns while the velocity is the Lagrange multiplier. The obtained formulation is then discretized and a convergence analysis is performed. A priori error estimates are established, and some numerical results are presented to highlight the perfomance of the proposed computational methodology.

     

On classification of conformally flat spaces

Classification of conformally flat n-dimensional pseudo-Riemannian spaces via Plebanski's method is discussed. It is based on embedding these spaces into a flat (n + 2)-dimensional space and on finding their minimal isometry groups which are subgroups of the conformal group. In particular, the case n = 4 is given in full detail and compared with incomplete results known in the literature. The found conformally flat spacetimes are identified with the associated solutions of the Einstein equations and with the spacetimes used in various cosmological considerations.     

trans-Bis(azido-κN)bis(pyridine-2-carboxamide-κ2N1,O2)nickel(II)

In the title compound, [Ni(N₃)₂(C₆H₆N₂O)₂], the Ni^II atom lies on an inversion centre. The distorted octahedral nickel(II) coordination environment contains two planar trans-related N,O-chelating picolinamide ligands in one plane and two monodentate azide ligands perpendicular to this plane. Molecules are linked into a three-dimensional framework by N—H...N hydrogen bonds.