The Influence of Intergovernmental Organizations on Main Determinants of the Open Systems Model with Correlation Analysis Method Application.

The paper aims at analyzing the nature of relations between Intergovernmental Organizations and International Corporations. In first instance the study concentrates on identifying the key determinants of Intergovernmental Organizations behaviours. The following section is a description of business environment of International Companies based on the Open Systems Model. Three levels of interrelations have been mentioned, including the Operating Environment, the Host – Country Environment and the Global Environment. The solution proposal provides an analysis of the influence of determinants of Intergovernmental Organizations behaviours on the determinants of business environment of International Corporations with use of correlation analysis method

Supercloseness of Orthogonal Projections onto Nearby Finite Element Spaces

We derive upper bounds on the difference between the orthogonal projections of a smooth function $u$ onto two finite element spaces that are nearby, in the sense that the support of every shape function belonging to one but not both of the spaces is contained in a common region whose measure tends to zero under mesh refinement. The bounds apply, in particular, to the setting in which the two finite element spaces consist of continuous functions that are elementwise polynomials over shape-regular, quasi-uniform meshes that coincide except on a region of measure $O(h^\gamma)$, where $\gamma$ is a nonnegative scalar and $h$ is the mesh spacing. The projector may be, for example, the orthogonal projector with respect to the $L^2$- or $H^1$-inner product. In these and other circumstances, the bounds are superconvergent under a few mild regularity assumptions. That is, under mesh refinement, the two projections differ in norm by an amount that decays to zero at a faster rate than the amounts by which each projection differs from $u$. We present numerical examples to illustrate these superconvergent estimates and verify the necessity of the regularity assumptions on $u$

Atomic-state diagnostics and optimization in cold-atom experiments

We report on the creation, observation and optimization of superposition states of cold atoms. In our experiments, rubidium atoms are prepared in a magneto-optical trap and later, after switching off the trapping fields, Faraday rotation of a weak probe beam is used to characterize atomic states prepared by application of appropriate light pulses and external magnetic fields. We discuss the signatures of polarization and alignment of atomic spin states and identify main factors responsible for deterioration of the atomic number and their coherence and present means for their optimization, like relaxation in the dark with the strobe probing. These results may be used for controlled preparation of cold atom samples and in situ magnetometry of static and transient fieldsComment: 15 pages and 9 figures (including supplementary information

A Backward Stable Algorithm for Computing the CS Decomposition via the Polar Decomposition

We introduce a backward stable algorithm for computing the CS decomposition of a partitioned $2n \times n$ matrix with orthonormal columns, or a rank-deficient partial isometry. The algorithm computes two $n \times n$ polar decompositions (which can be carried out in parallel) followed by an eigendecomposition of a judiciously crafted $n \times n$ Hermitian matrix. We prove that the algorithm is backward stable whenever the aforementioned decompositions are computed in a backward stable way. Since the polar decomposition and the symmetric eigendecomposition are highly amenable to parallelization, the algorithm inherits this feature. We illustrate this fact by invoking recently developed algorithms for the polar decomposition and symmetric eigendecomposition that leverage Zolotarev's best rational approximations of the sign function. Numerical examples demonstrate that the resulting algorithm for computing the CS decomposition enjoys excellent numerical stability