On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

Turbulence ahead: disputes within the Russian ruling elite are gathering force. OSW Commentary No. 91, 2012-09-27

The last month has seen a public confrontation between Igor Sechin, the president of Rosneft, and Arkady Dvorkovich, the deputy prime minister, concerning the consolidation of the energy sector. This is the latest in a series of disputes between the Kremlin & businessmen from Putin’s inner circle on one side, and the government & Prime Minister Medvedev on the other. These disputes have been wide-ranging in nature, concerning economic policy, the scope of competency of individual members of the elite, but also the ‘tough line’ adopted by the Kremlin since Vladimir Putin’s return to the presidency. The Kremlin, which is still the main decision-making centre in Russia, has been effectively forcing its opinions through in its short-term disputes with the government. However, a new element in the ongoing conflicts, which is unfavourable to President Putin, is their exceptional strength, their much more public nature, and their wide range (which has included criticism of the president himself) and ever-changing context, especially the worsening socio-economic situation. These conflicts have been overlapping with signs of dissent among Putin’s business supporters, and their declining political willingness to support the leader unconditionally. The Kremlin’s response to the unrest consists of intensifying efforts to discipline the elite and weakening those groups in which Vladimir Putin has limited confidence. The elite’s support is crucial to the stability of his government; to maintain this support, the Kremlin is ready to introduce restrictive and repressive actions against both parliamentarians and government officials. In the short term, such a policy will force the Kremlin’s supporters back into obedience, but fears of a further increase in repression are also starting to be expressed on the sidelines.

Meteorological measurements from 8 dropsondes released during POLAR 4 flight on 1993-03-04 along a track orthogonal to the pack ice edge north west of Svalbard

Different parameterizations of subgrid-scale fluxes are utilized in a nonhydrostatic and anelastic mesoscale model to study their influence on simulated Arctic cold air outbreaks. A local closure, a profile closure and two nonlocal closure schemes are applied, including an improved scheme, which is based on other nonlocal closures. It accounts for continuous subgrid-scale fluxes at the top of the surface layer and a continuous Prandtl number with respect to stratification. In the limit of neutral stratification the improved scheme gives eddy diffusivities similar to other parameterizations, whereas for strong unstable stratifications they become much larger and thus turbulent transports are more efficient. It is shown by comparison of model results with observations that the application of simple nonlocal closure schemes results in a more realistic simulation of a convective boundary layer than that of a local or a profile closure scheme. Improvements are due to the nonlocal formulation of the eddy diffusivities and to the inclusion of heat transport, which is independent of local gradients (countergradient transport).