Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

We study the continuity of an abstract generalization of the maximum-entropy inference - a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for $3\times 3$ matrices.Comment: 27 page

Development of International Law in the Western Hemisphere

It is almost axiomatic to say that any development of International Law in the Western Hemisphere must come as a development of the Monroe Doctrine—that all-elastic and heretofore unilateral policy of the United States of America towards Central and South America. This is because no major development of International Law is possible in the Western Hemisphere without the agreement or even leadership of the most powerful nation of that hemisphere. If the United States is to, lead, and past and present movements indicate this fact beyond question, its leadership has always been and is now being expressed in terms of the Monroe Doctrine

Algebras of Almost Periodic Functions with Bohr-Fourier Spectrum in a Semigroup: Hermite Property and its Applications

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener--Hopf type of rectangular matrix functions and the Toeplitz corona problem in the context of almost periodic functions of several variables.Comment: 18 page

Compressions of linearly independent selfadjoint operators

The following question is considered: What is the smallest number gamma(k) with the property that for every family {X-1,..., X-k} of k selfadjoint and linearly independent operators on a real or complex Hilbert space H there exists a subspace H-0 subset of H of dimension gamma(k) such that the compressions of X-1,..., X-k to H-0 are still linearly independent? Upper and lower bounds for gamma(k) are established for any k, and the exact value is found for k = 2, 3. It is also shown that the set of all gamma(k)-dimensional subspaces H-0 with the desired property is open and dense in the respective Grassmannian. The k = 3 case is used to prove that the ratio numerical range W(A/B) of a pair of operators on a Hilbert space either has a non-empty interior, or lies in a line or a circle. (C) 2011 Elsevier Inc. All rights reserved

Analysis of Fluorinated Polyimides Flown on the Materials International Space Station Experiment

This Technical Memorandum documents the results from the Materials on International Space Station Experiment (MISSE) series involving fluorinated polyimide films analyzed at NASA Marshall Space Flight Center. These films may be used in thermal control, sunshield, solar sail, solar concentrator, and other lightweight polymer film applications. Results include postflight structural integrity, visual observations, determination of atomic oxygen erosion yield, and optical property changes as compared to preflight values

On common invariant cones for families of matrices

The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable matrices of any size. Families of matrices with a shared dominant eigenvector are considered under some additional conditions