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

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

Teaching Innovations in An Introductory Physics Course for Non-Science Majors

I have made several innovations to Physics 114: Physics of Sound, a course for Communication Disorders and General Education students at the University of Massachusetts. These changes include the use of a network of wireless communication devices called a Personal Response System, on-line tutorials and classnotes, a collaborative discussion section, exam corrections, microthemes, extra-credit papers, group extra-credit projects, and the use of student teaching assistants

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

Quantum Statistics: Is there an effective fermion repulsion or boson attraction?

Physicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins of such exchange force ideas, the validity for them, and the areas where they are highly misleading. We propose that future explanations of quantum statistics should avoid the idea of a effective force completely and replace it with more appropriate physical insights, some of which are suggested here.Comment: 26 pages, 3 figures. Submitted to American Journal of Physic

Angular momentum conservation in measurements on spin Bose-Einstein condensates

We discuss a thought experiment where two operators, Alice and Bob, perform transverse spin measurements on a quantum system; this system is initially in a double Fock spin state, which extends over a large distance in space so that the two operators are far away from each other. Standard quantum mechanics predicts that, when Alice makes a few measurements, a large transverse component of the spin angular momentum may appear in Bob's laboratory. A paradox then arises since local angular momentum conservation seems to be violated. It has been suggested that this angular momentum may be provided by the interaction with the measurement apparatuses. We show that this solution of the paradox is not appropriate, so that another explanation must be sought. The general question is the retroaction of a quantum system onto a measurement apparatus. For instance, when the measured system is entangled with another quantum system, can its reaction on a measurement apparatus be completely changed? Is angular momentum conserved only on average over several measurements, but not during one realization of the experiment?Comment: 11 pages, 3 figure