Wave Functions and Energy Terms of the SCHR\"Odinger Equation with Two-Center Coulomb Plus Harmonic Oscillator Potential

Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the analytical form.Comment: 4 pages, no figures, LaTeX, submitted to PR

On integration of the Kowalevski gyrostat and the Clebsch problems

For the Kowalevski gyrostat change of variables similar to that of the Kowalevski top is done. We establish one to one correspondence between the Kowalevski gyrostat and the Clebsch system and demonstrate that Kowalevski variables for the gyrostat practically coincide with elliptic coordinates on sphere for the Clebsch case. Equivalence of considered integrable systems allows to construct two Lax matrices for the gyrostat using known rational and elliptic Lax matrices for the Clebsch model. Associated with these matrices solutions of the Clebsch system and, therefore, of the Kowalevski gyrostat problem are discussed. The Kotter solution of the Clebsch system in modern notation is presented in detail.Comment: LaTeX, 24 page

Polarization of Sunyaev-Zeldovich signal due to electron pressure anisotropy in galaxy clusters

We describe polarization of the Sunyaev-Zel'dovich (SZ) effect associated with electron pressure anisotropy likely present in the intracluster medium (ICM). The ICM is an astrophysical example of a weakly collisional plasma where the Larmor frequencies of charged particles greatly exceed their collision frequencies. This permits formation of pressure anisotropies, driven by evolving magnetic fields via adiabatic invariance, or by heat fluxes. SZ polarization arises in the process of Compton scattering of the cosmic microwave background (CMB) photons off the thermal ICM electrons due to the difference in the characteristic thermal velocities of the electrons along two mutually orthogonal directions in the sky plane. The signal scales linearly with the optical depth of the region containing large-scale correlated anisotropy, and with the degree of anisotropy itself. It has the same spectral dependence as the polarization induced by cluster motion with respect to the CMB frame (kinematic SZ effect polarization), but can be distinguished by its spatial pattern. { For the illustrative case of a galaxy cluster with a cold front, where electron transport is mediated by Coulomb collisions, we estimate the CMB polarization degree at the level of 10$^{-8}$ ($\sim 10$ nK). An increase of the effective electron collisionality due to plasma instabilities will reduce the effect. Such polarization, therefore, may be an independent probe of the electron collisionality in the ICM, which is one of the key properties of a high-$\beta$ weakly collisional plasma from the point of view of both astrophysics and plasma theory.Comment: 13 pages, 5 figures, accepted for publication in MNRA

Newest technologies in training on Occupational safety and health

Occupational safety and health - a special discipline: shortcomings and errors due to poor education and no authentic information leading to very serious consequences. New technology training on health and safety in the XXI century beyond lectures and seminars for staff and engineers for safety. Nowadays ensuring industrial safety and health personnel are a key competence of top managers, directors, chief engineers and heads of all departments of companies. Education in the field of labor - an area of special attention because it is addressed to adults. This modern pedagogical aims and science - andragogics branch of science teaching, which reveals the theoretical and practical problems of education and adult education throughout his life.Key words: occupational health and safety, training, education, andragogy, preparation of personnel, lifelong learning, adult education.Охорона праці - особлива дисципліна: недоліки і помилки через неякісне навчання та не достеменну інформацію призводять до дуже тяжких наслідків. Нові технології навчання з охорони праці в XXI столітті виходять за межі лекцій і семінарів для працівників та інженерів з охорони праці. У наші дні забезпечення промислової безпеки та здоров´я персоналу стають однією з ключовими компетенцій топ-менеджерів, директорів, головних інженерів й керівників усіх підрозділів компаній. Навчання у сфері охорони праці - зона особливої уваги, оскільки воно адресовано дорослим людям. На це і спрямована сучасна педагогічна наука – андрагогіка галузь педагогічної науки, яка розкриває теоретичні та практичні проблеми навчання та освіти дорослої людини протягом усього його життя.Ключові слова:охорона праці, навчання, освіта, андрагогіка, підготовка кадрів, безперервне навчання, навчання дорослих.

Relativistic dynamical polarizability of hydrogen-like atoms

Using the operator representation of the Dirac Coulomb Green function the analytical method in perturbation theory is employed in obtaining solutions of the Dirac equation for a hydrogen-like atom in a time-dependent electric field. The relativistic dynamical polarizability of hydrogen-like atoms is calculated and analysed.Comment: 15 pages, 3 figures (not included, but hard copies are available upon request

Operator method in solving non-linear equations of the Hartree-Fock type

The operator method is used to construct the solutions of the problem of the polaron in the strong coupling limit and of the helium atom on the basis of the Hartree-Fock equation. $E_0=-0.1085128052\alpha^2$ is obtained for the polaron ground-state energy. Energies for 2s- and 3s-states are also calculated. The other excited states are briefly discussed.Comment: 7 page