The Write Approach to Mathematics or How I Found the Middle Way

Revising a course is a multifaceted process. Often, reform efforts are focused on a particular aspect, that of inquiry-based collaborative learning. This article discusses the implementation of another aspect of the reform of a course for pre-service elementary teachers: the use of journals and writing exercises for evaluation and assessment. The evolution of this particular reform is traced, with emphasis on the reactions of students and faculty, the issues raised by these reactions, and the solution and resolution attained by the author is outlined

Process development and fabrication of space station type aluminum-clad graphite epoxy struts

The manufacture of aluminum-clad graphite epoxy struts, designed for application to the Space Station truss structure, is described. The strut requirements are identified, and the strut material selection rationale is discussed. The manufacturing procedure is described, and shop documents describing the details are included. Dry graphite fiber, Pitch-75, is pulled between two concentric aluminum tubes. Epoxy resin is then injected and cured. After reduction of the aluminum wall thickness by chemical milling the end fittings are bonded on the tubes. A discussion of the characteristics of the manufactured struts, i.e., geometry, weight, and any anomalies of the individual struts is included

Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly-periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wavepackets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator which interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.Comment: 4 pages, 3 figures, Optics Letters styl

Modification and updating of the Manned Activity Scheduling System (MASS) for shuttle and shuttle payloads analysis. Volume 2: Space shuttle sortie payload analysis

Space shuttle operations include a significant number of launches with a sortie laboratory serving as a facility for manned experimentation in space. Planning a program of space experiments for a facility of this type requires that both the composition of the laboratory payload and the schedule of experiment operations for each payload be carefully selected. Experiment operations are investigated using the manned activity scheduling system (MASS). Schedules provided by these models assist in selecting experiment groups that efficiently use the laboratory resources and yield the desired experiment accomplishment at the program level. An alternate use of the MASS models provides for establishing the time-dependent supporting resources required for a specified candidate payload. A procedure for defining and analyzing shuttle sortie payloads was developed. This procedure was then applied to the definition of mixed-discipline experiment payloads for an advanced technology laboratory (ATL) supported by two-and three-man crews. The ATL payloads, including schedules of experiment operations, were defined to realize a high percentage of experiment accomplishment. The study considers the sensitivity of experiment accomplishment rate to variations of system parameters such as crew cross training, crew operations, shuttle and laboratory resources, ground target systems, and operational orbits

Static observables of relativistic three-fermion systems with instantaneous interactions

We show that static properties like the charge radius and the magnetic moment of relativistic three-fermion bound states with instantaneous interactions can be formulated as expectation values with respect to intrinsically defined wavefunctions. The resulting operators can be given a natural physical interpretation in accordance with relativistic covariance. We also indicate how the formalism may be generalized to arbitrary moments. The method is applied to the computation of static baryon properties with numerical results for the nucleon charge radii and the baryon octet magnetic moments. In addition we make predictions for the magnetic moments of some selected nucleon resonances and discuss the decomposition of the nucleon magnetic moments in contributions of spin and angular momentum, as well as the evolution of these contributions with decreasing quark mass.Comment: 13 pages, including 2 figures and 3 tables, submitted to Eur.Phys.J.

Squeezing as an irreducible resource

We show that squeezing is an irreducible resource which remains invariant under transformations by linear optical elements. In particular, we give a decomposition of any optical circuit with linear input-output relations into a linear multiport interferometer followed by a unique set of single mode squeezers and then another multiport interferometer. Using this decomposition we derive a no-go theorem for superpositions of macroscopically distinct states from single-photon detection. Further, we demonstrate the equivalence between several schemes for randomly creating polarization-entangled states. Finally, we derive minimal quantum optical circuits for ideal quantum non-demolition coupling of quadrature-phase amplitudes.Comment: 4 pages, 3 figures, new title, removed the fat

Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions

The framework of relativistic energy density functionals is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The effects of triaxial deformation and of $K$-mixing is illustrated in a study of spectroscopic properties of low-spin states in $^{24}$Mg.Comment: 15 pages, 11 figures, 4 tables, accepted for publication in Phys. Rev.

Thermodynamics of small superconductors with fixed particle number

The Variation After Projection approach is applied for the first time to the pairing hamiltonian to describe the thermodynamics of small systems with fixed particle number. The minimization of the free energy is made by a direct diagonalization of the entropy. The Variation After Projection applied at finite temperature provides a perfect reproduction of the exact canonical properties of odd or even systems from very low to high temperature.Comment: 4 pages, 3 figure

Collective Motion of Polarized Dipolar Fermi Gases in the Hydrodynamic Regime

Recently, a seminal STIRAP experiment allowed the creation of 40K-87Rb molecules in the rovibrational ground state [K.-K. Ni et al., Science 322, 231 (2008)]. In order to describe such a polarized dipolar Fermi gas in the hydrodynamic regime, we work out a variational time-dependent Hartree-Fock approach. With this we calculate dynamical properties of such a system as, for instance, the frequencies of the low-lying excitations and the time-of-flight expansion. We find that the dipole-dipole interaction induces anisotropic breathing oscillations in momentum space. In addition, after release from the trap, the momentum distribution becomes asymptotically isotropic, while the particle density becomes anisotropic