Truncated K-moment problems in several variables

Let $\beta\equiv\beta^{(2n)}$ be an N-dimensional real multi-sequence of degree 2n, with associated moment matrix $\mathcal{M}(n)\equiv \mathcal{M}(n)(\beta)$, and let $r:=rank \mathcal{M}(n)$. We prove that if $\mathcal{M}(n)$ is positive semidefinite and admits a rank-preserving moment matrix extension $\mathcal{M}(n+1)$, then $\mathcal{M}(n+1)$ has a unique representing measure \mu, which is r-atomic, with supp \mu$equal to$\mathcal{V}(\mathcal{M}(n+1))$, the algebraic variety of$\mathcal{M}(n+1)$. Further, \beta has an r-atomic (minimal) representing measure supported in a semi-algebraic set$K_{\mathcal{Q}}$subordinate to a family$\mathcal{Q}% \equiv\{q_{i}\}_{i=1}^{m}\subseteq\mathbb{R}[t_{1},...,t_{N}]$if and only if$\mathcal{M}(n)$is positive semidefinite and admits a rank-preserving extension$\mathcal{M}(n+1)$for which the associated localizing matrices$\mathcal{M}_{q_{i}}(n+[\frac{1+\deg q_{i}}{2}])$are positive semidefinite$(1\leq i\leq m)$; in this case, \mu (as above) satisfies supp \mu\subseteq K_{\mathcal{Q}}$, and \mu has precisely rank \mathcal{M}(n)-rank \mathcal{M}_{q_{i}}(n+[\frac{1+\deg q_{i}}{2}])$atoms in$\mathcal{Z}(q_{i})\equiv {t\in\mathbb{R}^{N}:q_{i}(t)=0}$,$1\leq i\leq m$.Comment: 33 pages; to appear in J. Operator Theor

Is There a Disc in the Superluminal Quasars?

We present a new evidence of the accretion disc in active galactic nuclei, by examining the properties of the Ha emission line versus viewing angle, in a sample of superluminal (SL) quasars. Both line velocity width (FWHM) and rest equivalent width (EW) correlate with viewing angle. These correlations are quantitatively consistent with a disc geometry for both the line and the underlying continuum source.Comment: 18 pages with 6 figures, accepted for publication in MNRA

Assessing the Effectiveness of Farm Supply Cooperatives: A Comparison of Farmer and Manager Viewpoints

This paper reports the results of a survey of attitudes of commercial farmers and supply cooperative managers about agricultural supply cooperatives. Cooperative managers and farmers frequently made significantly different responses to questionnaire statements. With a few expectations, farm size and farmer age did not appear to influence perceptions about supply cooperatives. Whether a farmer was a cooperative member was important in some cases. Lower prices in lieu of easy credit and patronage refunds were found to be acceptable to farmers, but not at the expense of good service. Managers placed great importance on member loyalty to the supply cooperative without regard to price consideration.Agribusiness,

Addressing technical, social and economic constraints to rice fish culture in Laos, emphasising women’s involvement: DFID Aquaculture Research Programme Project R6380Cb, final technical report

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The Federal Administrative Court Proposal: An Examination of General Principals

Simulations of relativistic hydrodynamics often need both high accuracy and robust shock-handling properties. The discontinuous Galerkin method combines these features—a high order of convergence in regions where the solution is smooth and shock-capturing properties for regions where it is not—with geometric flexibility and is therefore well suited to solve the partial differential equations describing astrophysical scenarios. We present here evolutions of a general-relativistic neutron star with the discontinuous Galerkin method. In these simulations, we simultaneously evolve the spacetime geometry and the matter on the same computational grid, which we conform to the spherical geometry of the problem. To verify the correctness of our implementation, we perform standard convergence and shock tests. We then show results for evolving, in three dimensions, a Kerr black hole; a neutron star in the Cowling approximation (holding the spacetime metric fixed); and, finally, a neutron star where the spacetime and matter are both dynamical. The evolutions show long-term stability, good accuracy, and an improved rate of convergence versus a comparable-resolution finite-volume method

Evolving relativistic fluid spacetimes using pseudospectral methods and finite differencing

We present a new code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved on one grid using pseudospectral methods, while the fluids are evolved on another grid by finite differencing. We discuss implementation details, such as the communication between the grids and the treatment of stellar surfaces, and present code tests.Comment: To appear in the Proceedings of the Eleventh Marcel Grossmann Meetin