In this note we prove a generalization of the flat extension theorem of Curto and Fialkow [4] for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free setting, this gives an equivalent result for truncated Hankel operators.

In this work, the optimization calculations were carried out on quetiapine hemifumarat, 4, and its analogues, 1-5. These calculations were carried out using the B3LYP/6-31G(d) level of theory. The DFT calculations clarified a boat structure for dibenzothiazepine moiety of the molecule which piperazine moiety has a chair conformation. Thermal energies (E), enthalpies (H), and free energies (G) o...

In lecture 29, we introduced the Euler angles as a framework for formulating and solving the equations for conservation of angular momentum. We applied this framework to the free-body motion of a symmetrical body whose angular momentum vector was not aligned with a principal axis. The angular moment was however constant. We now apply Euler angles and Euler’s equations to a slightly more general...

In 2005, Nualart and Peccati [12] showed the so-called Fourth Moment Theorem asserting that, for a sequence of normalized multiple Wiener-Itô integrals to converge to the standard Gaussian law, it is necessary and sufficient that its fourth moment tends to 3. A few years later, Kemp et al. [8] extended this theorem to a sequence of normalized multiple Wigner integrals, in the context of the fre...

The crossover between a free magnetic moment phase and a Kondo phase in low-dimensional disordered metals with dilute magnetic impurities is studied. We perform a finite-size scaling analysis of the distribution of the Kondo temperature obtained from a numerical renormalization group calculation of the local magnetic susceptibility for a fixed disorder realization and from the solution of the s...

We discuss a dynamical theory for nematic liquid crystals describing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolution proceeds via diffusive motion of the orientational degrees of freedom. This diffusion induces a slow motion of singularities of the order parameter field. Using asymptotic methods for gradient flows, we establish...