ON THE SMARANDACHE FUNCTION AND THE FIXED - POINT THEORY OF NUMBERS

This brief note points out several basic connections between the Smarandache function, fixed-point theory and prime-number theory. First recall that fixed-point theory in function spaces provides elegent, if not short, proofs of the existence of solutions to many kinds of differential equations, integral equations, optimization problems and game-theoretic problems

OAST space power technology program

The current research and technology (R and T) base program is first described, then special attention is directed toward outlining a new system technology specifically oriented toward providing the utility power plant technology base for semi-permanent earth orbital facilities expected to be needed in the middle to late 1980's. The R and T program involves five areas of research: (1) photovoltaic energy conversion; (2) chemical energy conversion and storage; (3) thermal-to-electric conversion; (4) environment interactions; and (5) power systems management and distribution. The general objectives and planned direction of efforts in each of these areas is summarized

Quantum-Monte-Carlo Calculations for Bosons in a Two-Dimensional Harmonic Trap

Path-Integral-Monte-Carlo simulation has been used to calculate the properties of a two-dimensional (2D) interacting Bose system. The bosons interact with hard-core potentials and are confined to a harmonic trap. Results for the density profiles, the condensate fraction, and the superfluid density are presented. By comparing with the ideal gas we easily observe the effects of finite size and the depletion of the condensate because of interactions. The system is known to have no phase transition to a Bose-Einstein condensation in 2D, but the finite system shows that a significant fraction of the particles are in the lowest state at low temperatures.Comment: six pages, two figures; Contribution to QFS98; To be published in Journ. Low. Temp. Phy

The Two-Dimensional Bose-Einstein Condensate

We study the Hartree-Fock-Bogoliubov mean-field theory as applied to a two-dimensional finite trapped Bose gas at low temperatures and find that, in the Hartree-Fock approximation, the system can be described either with or without the presence of a condensate; this is true in the thermodynamic limit as well. Of the two solutions, the one that includes a condensate has a lower free energy at all temperatures. However, the Hartree-Fock scheme neglects the presence of phonons within the system, and when we allow for the possibility of phonons we are unable to find condensed solutions; the uncondensed solutions, on the other hand, are valid also in the latter, more general scheme. Our results confirm that low-energy phonons destabilize the two-dimensional condensate.Comment: 8 pages, 3 figures, REVTeX 4. To appear in J. Low Temp. Phys. Corrected a mistake in a calculation and changed the conclusions accordingl

Book review: Questioning secularism: Islam, sovereignty, and the rule of law in modern Egypt

"Questioning Secularism: Islam, Sovereignty, And The Rule Of Law In Modern Egypt." Hussein Ali Agrama. University of Chicago Press. November 2012. --- The central questions of the Arab uprisings—what is the appropriate relationship between religion and politics and what is the function of the national security state —have developed into a vigorous debate amongst actors from across the political spectrum. But what, exactly, is secularism? What is its relationship to the ‘deep state’ in Egypt? In Questioning Secularism, Hussein Ali Agrama focuses on the Fatwa councils and family law courts of Egypt just prior to the revolution, to argue that secularism is a historically contingent phenomenon that works through a series of paradoxes that it creates. He probes the meaning of secularism and the ambiguities that lie at its heart. Reviewed by Corinna Mullin