The PCA-seq method applied to analyze of the dynamics of COVID-19 epidemic indicators

In time series analysis using the SSA method, a univariate series is converted into the multivariate one by shifts. The resulting trajectory matrix is subjected to principal component analysis (PCA). However, the principal components can also be computed using the PCA-Seq method if segments of the original series are selected as objects. The matrix of Euclidean distances between the objects can be obtained using any method, which offers additional opportunities for time series analysis compared to the conventional SSA. In this study, the PCA-Seq method was used to analyze the dynamics of COVID-19 epidemic indicators

Integrable magnetic geodesic flows on Lie groups

Right-invariant geodesic flows on manifolds of Lie groups associated with 2-cocycles of corresponding Lie algebras are discussed. Algebra of integrals of motion for magnetic geodesic flows is considered and necessary and sufficient condition of integrability in quadratures is formulated. Canonic forms for 2-cocycles of all 4-dimensional Lie algebras are given and integrable cases among them are separated.Comment: 16 page

Differential Form of the Skornyakov--Ter-Martirosyan Equations

The Skornyakov--Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.Comment: 4 pages, 2 figure

On orientational relief of inter-molecular potential and the structure of domain walls in fullerite C60

A simple planar model for an orientational ordering of threefold molecules on a triangular lattice modelling a close-packed (111) plane of fullerite is considered. The system has 3-sublattice ordered ground state which includes 3 different molecular orientations. There exist 6 kinds of orientational domains, which are related with a permutation or a mirror symmetry. Interdomain walls are found to be rather narrow. The model molecules have two-well orientational potential profiles, which are slightly effected by a presence of a straight domain wall. The reason is a stronger correlation between neighbour molecules in triangular lattice versus previously considered square lattice A considerable reduction (up to one order) of orientational interwell potential barrier is found in the core regions of essentially two-dimentional potential defects, such as a three-domain boundary or a kink in the domain wall. For ultimately uncorrelated nearest neighbours the height of the interwell barrier can be reduced even by a factor of 100.Comment: 11 pages, 13 figures, LaTeX, to appear in Low Temperature Physic