Schwinger approach of unitary geometry for a finite-dimensional Hilbert space is interpreted in terms of a magnonic qudit — a hypothetic elementary unit of memory of a quantum computer. The space is interpreted within the Heisenberg model for a magnetic ring, its calculational basis as the classical configuration space for a single spin deviation, treated as a Bethe pseudoparticle, and the dual basis corresponds to quasimomenta, so that the classical phase space spans the quantum algebra of observables. Effects of the Schur-Weyl duality and Bethe ansatz exact eigenstates of the Heisenberg Hamiltonian for the XXX model on properties of the magnonic qudit are presented.

In the paper two chosen features of the comet 103P/Hartley 2 are studied. The first one are 'cometary geysers' which have been recorded by the camera on Deep Impact spacecraft. The numerical calculations related with this phenomenon have been carried out for large number of values of probable cometary characteristics. Our calculations confirm the assumption what also has been observed by NASA's scientists that the jets of carbon dioxide from the geysers are able to lift large chunks of water ice from the comet. The second discussed feature of the comet 103P/Hartley 2 is the lack of impact holes on the surface of its nucleus. The expected rate of impact holes on the surface of the nucleus of 103P/Hartley 2 is discussed. These holes could be the product of impacts between this comet and other small bodies orbiting in the main asteroid belt. The probability of such impacts, the total number of expected perceptible holes and changes in the luminosity of the comet caused by collisions are examined. We conclude that indeed the number of visible holes on its surface should be negligible.

We propose the system of 1 8 N -= mutually commuting operators which classify all eigenstates of the Heisenberg Hamiltonian for the linear magnetic chain of N = 9 nodes, each with the spin 1/2. These eigenstates, determined exactly by Bethe Ansatz and classified combinatorially by rigged string configurations of Kerov, Kirillov and Reshetikhin, can be also associated with the spectrum of this set of commuting operators.