Duality between the coordinates and wave functions on noncommutative space

The relation between coordinates and the solutions of the stationary Schrodinger equation in the noncommutative algebra of functions on $R^{2N}$ is discussed. We derive this relation for a certain class of wave functions for which the quantum prepotentials depend linearly on the coordinates similarly to the commutative case. Also, the differential equation satisfied by the prepotentials is given.Comment: Reference added. 8 pages, LATeX fil

The Attitudes of Men Students Toward the Required Physical Education Program at South Dakota State College

The purpose of this investigation was to determine the attitude of male students at South Dakota State College toward the required physical education program. Through this study the author hoped to ascertain the attitude of the male student toward physical education in respect to the total required program, its value to the student, academic credit, facilities, instruction, educational needs, and the activities most desired by the male student. It was hoped that such a study might help to improve the required program of physical education. The descriptive method of research was used in this study in the form of a questionnaire returned by 524 respondents. High school experience in physical education had very little influence on the attitude toward physical education at State College. Benefiting physically was rated second followed b y benefitting mentally, emotionally, and morally in that order. A high percentage of the total sample indicated they enjoyed physical education at State College, and a favorable percent was recorded by the total sample toward having physical education required at State College

The Equivalence Postulate of Quantum Mechanics

The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transform and of its recently observed relation with second-order linear differential equations. This reflects in an intrinsic psi^D-psi duality between linearly independent solutions of the Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even for bound states. No use of any axiomatic interpretation of the wave-function is made. Tunnelling is a direct consequence of the quantum potential which differs from the usual one and plays the role of particle's self-energy. The QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of the extended real line. This is an important feature as the L^2 condition, which in the usual formulation is a consequence of the axiomatic interpretation of the wave-function, directly follows as a basic theorem which only uses the geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunnelling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the non-stationary higher dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the action of SL(2,R) subgroups acting on the reduced action explicitly reveals that the wave-function describes only equivalence classes of Planck length deterministic physics. New derivation of the Schwarzian derivative from the cocycle condition. "Legendre brackets" introduced to further make "Legendre duality" manifest. Introduction now contains examples and provides a short pedagogical review. Clarifications, conclusions, ackn. and references adde

Trajectories in the Context of the Quantum Newton's Law

In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic oscillator. In the classically allowed regions, we show that to each classical trajectory there is a family of quantum trajectories which all pass through some points constituting nodes and belonging to the classical trajectory. We also discuss the generalization to any potential and give a new definition for de Broglie's wavelength in such a way as to link it with the length separating adjacent nodes. In particular, we show how quantum trajectories have as a limit when $\hbar \to 0$ the classical ones. In the classically forbidden regions, the nodal structure of the trajectories is lost and the particle velocity rapidly diverges.Comment: 17 pages, LateX, 6 eps figures, minor modifications, Title changed, to appear in Physica Script

Gestation changes sodium pump isoform expression, leading to changes in ouabain sensitivity, contractility, and intracellular calcium in rat uterus.

Developmental and tissue-specific differences in isoforms allow Na+, K+-ATPase function to be tightly regulated, as they control sensitivity to ions and inhibitors. Uterine contraction relies on the activity of the Na+, K+ATPase, which creates ionic gradients that drive excitation-contraction coupling. It is unknown whether Na+, K+ATPase isoforms are regulated throughout pregnancy or whether they have a direct role in modulating uterine contractility. We hypothesized that gestation-dependent differential expression of isoforms would affect contractile responses to Na+, K+ATPase α subunit inhibition with ouabain. Our aims were therefore: (1) to determine the gestation-dependent expression of mRNA transcripts, protein abundance and tissue distribution of Na+, K+ATPase isoforms in myometrium; (2) to investigate the functional effects of differential isoform expression via ouabain sensitivity; and (3) if changes in contractile responses can be explained by changes in intracellular [Ca2+]. Changes in abundance and distribution of the Na+, K+ATPase α, β and FXYD1 and 2 isoforms, were studied in rat uterus from nonpregnant, and early, mid-, and term gestation. All α, β subunit isoforms (1,2,3) and FXYD1 were detected but FXYD2 was absent. The α1 and β1 isoforms were unchanged throughout pregnancy, whereas α2 and α3 significant decreased at term while β2 and FXYD1 significantly increased from mid-term onwards. These changes in expression correlated with increased functional sensitivity to ouabain, and parallel changes in intracellular Ca2+, measured with Indo-1. In conclusion, gestation induces specific regulatory changes in expression of Na+, K+ATPase isoforms in the uterus which influence contractility and may be related to the physiological requirements for successful pregnancy and delivery

Ulster PD Scheme: Using e-portfolios and professional conversations to evidence recognition claims

Vicky Davies and Sarah Maguire are Professional Development Managers at the University of Ulster. They have many years of experience in delivering and assessing Higher Education Academy claims for recognition via accredited provision for new teaching staff and post-graduate students. More recently they led the development of the University of Ulster’s Professional Development Scheme http://www.ulster.ac.uk/centrehep/pds/ . The core elements of the PD Scheme are the production of an e-portfolio and an assessed professional conversation. This workshop will explore the learning they have acquired through developing this process and piloting it with applicants. You will have the opportunity to discuss this and to identify any transferability to your own practice

High-angle-of-attack pneumatic lag and upwash corrections for a hemispherical flow direction sensor

As part of the NASA F-14 high angle of attack flight test program, a nose mounted hemispherical flow direction sensor was calibrated against a fuselage mounted movable vane flow angle sensor. Significant discrepancies were found to exist in the angle of attack measurements. A two fold approach taken to resolve these discrepancies during subsonic flight is described. First, the sensing integrity of the isolated hemispherical sensor is established by wind tunnel data extending to an angle of attack of 60 deg. Second, two probable causes for the discrepancies, pneumatic lag and upwash, are examined. Methods of identifying and compensating for lag and upwash are presented. The wind tunnel data verify that the isolated hemispherical sensor is sufficiently accurate for static conditions with angles of attack up to 60 deg and angles of sideslip up to 30 deg. Analysis of flight data for two high angle of attack maneuvers establishes that pneumatic lag and upwash are highly correlated with the discrepancies between the hemispherical and vane type sensor measurements

Virtual images and billiards

Students in introductory physics courses struggle to understand virtual image formation by a plane mirror and the proper construction of ray diagrams. This difficulty, if not sufficiently addressed, results in further problems throughout the study of geometric optics. Specifically, students fail to apply proper graphical representation of light rays during investigations of the formation of real images by converging lenses and concave mirrors. We present a guided-inquiry activity based on the research-verified Physics by Inquiry text that incorporates a small and inexpensive billiards table, with billiard balls acting as "light". In this way, we approach the abstract concept of virtual images by relation to the concrete concept of physical reflection.Comment: 6 pages, 2 figures, submitted to Physics Educatio