On the Exponentials of Some Structured Matrices

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra isomorphism and basic Lie theory. When used in conjunction with structure preserving similarities, such as Givens rotations, these techniques extend to dimensions bigger than four.Comment: 19 page

The Journal of the Center for Interdisciplinary Teaching and Learning

IMPACT: The Journal of the Center for Interdisciplinary Teaching & Learning is a peer-reviewed, biannual online journal that publishes scholarly and creative non-fiction essays about the theory, practice and assessment of interdisciplinary education. Impact is produced by the Center for Interdisciplinary Teaching & Learning at the College of General Studies, Boston University (www.bu.edu/cgs/citl).In this issue, podcasts are looked at as a pedagogical game changer. Using the award-wining podcast Serial as their catalyst, this issue's essayists look at podcast's emerging role in higher education, how multimodal learning can help students find their voices, the podcast's place in the curriculum at a criminal justice college, and how podcasts can inspire students to reflectively assess their own writing. Our reviewers take a critical look at the podcasts Welcome to Night Vale and Revisionist History

Concerted [4 + 2] and Stepwise (2 + 2) Cycloadditions of Tetrafluoroethylene with Butadiene: DFT and DLPNO-UCCSD(T) Explorations.

Tetrafluoroethylene and butadiene form the 2 + 2 cycloadduct under kinetic control, but the Diels-Alder cycloadduct is formed under thermodynamic control. Borden and Getty showed that the preference for 2 + 2 cycloaddition is due to the necessity for syn-pyramidalization of the two CF2 groups in the 4 + 2 transition state. We have explored the full potential energy surface for the concerted and stepwise reactions of tetrafluoroethylene and butadiene with density functional theory, DFT (B3LYP and M06-2X), DLPNO-UCCSD(T), and CASSCF-NEVPT2 methods and with the distortion/interaction-activation strain model to explain the energetics of different pathways. The 2 + 2 cycloadduct is formed by an anti-transition state followed by two rotations and a final bond formation transition state. Energetics are compared to the reaction of maleic anhydride and ethylene

The diagnosis of malaria infection using a solid-phase radioimmunoassay for the detection of malaria antigens: Application to the detection of Plasmodium berghei infection in mice

A method has been devised to show that malaria parasites can be detected serologically in infected blood with a high degree of sensitivity. Using a murine malaria model, parasites were demonstrated in a solid-phase radio-immunoassay which measured antibody-binding inhibition. Lysed red blood cells (r.b.c.) were incubated with labelled specific antibody and were then reacted in antigen-coated tubes. The degree of inhibition of antibody binding in the tubes correlated with the level of parasitaemia in the test blood. Using homologous antisera the test detected infection at a level of 1 parasite/million r.b.c. The specificity of the method was shown by comparison of antibody-binding inhibition in normal and infected r.b.c. and in r.b.c. from non-infected mice with induced reticulocytosis. The sensitivity was shown in vitro in tests of serially diluted blood of high parasitaemia and in vivo for the detection of early infection. The presence of antibody in the test blood did not significantly affect the sensitivity of parasite detectio

Group projector generalization of dirac-heisenberg model

The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is applied to the system of identical particles with spin independent interaction, to derive the Dirac-Heisenberg hamiltonian and its effective space for arbitrary orbital occupation numbers and arbitrary spin. This gives transparent insight into the physical contents of this hamiltonian, showing that formal generalizations with spin greater than 1/2 involve nontrivial additional physical assumptions.Comment: 10 page

Models of the circumstellar medium of evolving, massive runaway stars moving through the Galactic plane

At least 5 per cent of the massive stars are moving supersonically through the interstellar medium (ISM) and are expected to produce a stellar wind bow shock. We explore how the mass loss and space velocity of massive runaway stars affect the morphology of their bow shocks. We run two-dimensional axisymmetric hydrodynamical simulations following the evolution of the circumstellar medium of these stars in the Galactic plane from the main sequence to the red supergiant phase. We find that thermal conduction is an important process governing the shape, size and structure of the bow shocks around hot stars, and that they have an optical luminosity mainly produced by forbidden lines, e.g. [OIII]. The Ha emission of the bow shocks around hot stars originates from near their contact discontinuity. The H$\alpha$ emission of bow shocks around cool stars originates from their forward shock, and is too faint to be observed for the bow shocks that we simulate. The emission of optically-thin radiation mainly comes from the shocked ISM material. All bow shock models are brighter in the infrared, i.e. the infrared is the most appropriate waveband to search for bow shocks. Our study suggests that the infrared emission comes from near the contact discontinuity for bow shocks of hot stars and from the inner region of shocked wind for bow shocks around cool stars. We predict that, in the Galactic plane, the brightest, i.e. the most easily detectable bow shocks are produced by high-mass stars moving with small space velocities.Comment: 22 pages, 24 figure

An augmented moment method for stochastic ensembles with delayed couplings: I. Langevin model

By employing a semi-analytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E {\bf 67}, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics of an $N$-unit ensemble described by linear and nonlinear Langevin equations with delays. In AMM, original $N$-dimensional {\it stochastic} delay differential equations (SDDEs) are transformed to infinite-dimensional {\it deterministic} DEs for means and correlations of local as well as global variables. Infinite-order DEs arising from the non-Markovian property of SDDE, are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), which yields $(3+m)$-dimensional deterministic DEs. Model calculations have been made for linear and nonlinear Langevin models. The stationary solution of AMM for the linear Langevin model with N=1 is nicely compared to the exact result. The synchronization induced by an applied single spike is shown to be enhanced in the nonlinear Langevin ensemble with model parameters locating at the transition between oscillating and non-oscillating states. Results calculated by AMM6 are in good agreement with those obtained by direct simulations.Comment: 18 pages, 3 figures, changed the title with re-arranged figures, accepted in Phys. Rev. E with some change