HIGHER DIRAC COHOMOLOGY OF MODULES WITH GENERALIZED INFINITESIMAL CHARACTER

We modify the definition of Dirac cohomology in such a way that the standard properties of the usual Dirac cohomology, valid for modules with infinitesimal character, become valid also for modules with only generalized infinitesimal character.     

Systems of oblate molecules. Monte Carlo study

Monte Carlo (MC) simulations were performed for systems of hard oblate spherocylinders with breadth-to-height ratios φ = 0.5–3.5 and packing fractions y = 0.25–0.45 and for Kihara oblate molecule systems of φ = 1 at reduced temperatures T* = 0.75 and 1.0 and y = 0.05–0.45. The compression factors and the dependence of the average correlation functions on the shortest surface-to-surface distance were determined for the case of hard oblate spherocylinders and the compression factors, residual internal energies and average correlation functions for the case of the generalized Kihara molecule systems. In addition, values of the third virial coefficient of the hard oblate spherocylinders were evaluated in the range of φ = 1–3. Results of the MC simulations for the hard oblate spherocylinders compare well with the available data in the literature and theoretical values; thermodynamic functions of the Kihara molecule systems were determined from the second-order perturbation theory. They agree well with our MC values at lower densities and higher reduced temperatures.     

Numerical analysis of subspace-breaking Takens-Bogdanov points

It is assumed that a two-parameter-dependent family of smoothvector fields on R^N leaves a proper subspace u of R^N invariant.Takens-Bogdanov bifurcation points on u are considered. Computationof these points together with their computer-aided asymptoticanalysis are discussed. The asymptotic formulae are appliedas analytical predictors of, for example, Hopf bifurcation pointsthat emanate from a detected Takens-Bogdanov point. Anotherapplication is a local stability analysis of imperfect bifurcationdiagrams.