20 research outputs found
Courant-Dorfman algebras and their cohomology
We introduce a new type of algebra, the Courant-Dorfman algebra. These are to
Courant algebroids what Lie-Rinehart algebras are to Lie algebroids, or Poisson
algebras to Poisson manifolds. We work with arbitrary rings and modules,
without any regularity, finiteness or non-degeneracy assumptions. To each
Courant-Dorfman algebra (\R,\E) we associate a differential graded algebra
\C(\E,\R) in a functorial way by means of explicit formulas. We describe two
canonical filtrations on \C(\E,\R), and derive an analogue of the Cartan
relations for derivations of \C(\E,\R); we classify central extensions of
\E in terms of H^2(\E,\R) and study the canonical cocycle
\Theta\in\C^3(\E,\R) whose class obstructs re-scalings of the
Courant-Dorfman structure. In the nondegenerate case, we also explicitly
describe the Poisson bracket on \C(\E,\R); for Courant-Dorfman algebras
associated to Courant algebroids over finite-dimensional smooth manifolds, we
prove that the Poisson dg algebra \C(\E,\R) is isomorphic to the one
constructed in \cite{Roy4-GrSymp} using graded manifolds.Comment: Corrected formulas for the brackets in Examples 2.27, 2.28 and 2.29.
The corrections do not affect the exposition in any wa
Comparison of quantum mechanical and classical trajectory calculations of cross sections for ion-atom impact ionization of negative - and positive -ions for heavy ion fusion applications
Stripping cross sections in nitrogen have been calculated using the classical
trajectory approximation and the Born approximation of quantum mechanics for
the outer shell electrons of 3.2GeV I and Cs ions. A large
difference in cross section, up to a factor of six, calculated in quantum
mechanics and classical mechanics, has been obtained. Because at such high
velocities the Born approximation is well validated, the classical trajectory
approach fails to correctly predict the stripping cross sections at high
energies for electron orbitals with low ionization potential.Comment: submitted to Phys. Rev.
Analysis of resonance structure in the above-threshold ionization photoelectron spectra of magnesium
Institutional and interpersonal trust as an indicator of the health of modern society
In modern society an important role was played by trust as a necessary condition for social communication in society, for understanding, harmony and cooperation. The article set relatively low levels of social and institutional trust in Russian society. As a result of changes for the last twenty years there has been disappointment with the population of the liberal economy. Distrust of all important social institutions means failure of the government institutions to provide effective positive impact on socio-economic processes in society