Elemental technetium as a cosmic-ray clock

Several radioactive isotopes have been proposed as clocks for the study of the mean cosmic ray confinement time, T sub e. Measurements of Be-10 and Al-26 give a value for T sub e of about 10 Myr when one uses a leaky box cosmic ray propagation model. It is important to obtain additional measurements of T sub e from other radioactive isotopes in order to check whether the confinement is the same throughout the periodic table. The possible use of Tc (Z = 43) as a cosmic clock is investigated. Since all isotopes of Tc are radioactive, one might be able to group these isotopes and use the elemental abundance as a whole. The results of the calculations are somewhat inconclusive for two reasons. First, the beta + decay half lives of two of the Tc isotopes relevant to our calculation are not known. Second, the dependence of the Tc abundance on the mean confinement time is rather weak when one considers the number of events expected in 4 trays of plastic track detectors. However, a future, finite measurement of the Beta + half lives and the possible use of the entire collecting area of the HNC to detect Tc nuclei could make the use of Tc as a cosmic ray clock more attractive

Integrable and superintegrable systems with spin

A system of two particles with spin s=0 and s=1/2 respectively, moving in a plane is considered. It is shown that such a system with a nontrivial spin-orbit interaction can allow an 8 dimensional Lie algebra of first-order integrals of motion. The Pauli equation is solved in this superintegrable case and reduced to a system of ordinary differential equations when only one first-order integral exists.Comment: 12 page

Integration of a generalized H\'enon-Heiles Hamiltonian

The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic

From strange to charmed baryons using two-flavour QCD

International audienc

Моніторингові дослідження в університеті: досвід і результати

The article presents the research of the monitoring that has recently been intensified, as well as radical changes in the organization of Ukrainian universities. Thus, we can observe that researches are gradually changing the goals, and as a result their functional features. Initially, the conduction of monitoring research is related to the definition of the degree of subjective perception of the quality of lecturers’ activity, as well as administrative and organizational changes, but afterwards it performs the functions of control and evaluation. Today the monitoring research is becoming an integral part of inner audit of the quality of educational activity. The problems, which arise, concern both, the quality of monitoring tools and the purpose of monitoring; its results are also connected with the results of efficient activity of subjects in educational process, including the university. It should be noted that, except for the purely internal instrumental functions, in the future, monitoring will become the means of the diagnosis of transparent activity in higher educational institutions. One of such steps is the demonstration of the content and the results of monitoring research, which was conducted at Stepan Gzhytskyi National University of Veterinary Medicine and Biotechnologies Lviv during 2008–2016, especially the results since 2010, as they enable us to compare. The authors give emphasis to the monitoring stages, analyzing the objectives, content and results. The data analysis of the research is the basis for the new approaches formation, concerning the university as a subject. This study stimulates the development of similar practices at other universities. First of all, it will encourage the transparency in their activities; secondly, the exchange of experience in the formation of internal system of quality, and finally, this work is essential in the creation of common space for international relations and significant inter-university research.Дослідження моніторингового характеру, що активізувалися в українських університетах одночасно з радикальними змінами в їх організації, поступово змінюють свої цілі, отже, й функціональні риси. Спочатку їх проведення було пов’язане із визначенням ступеня суб’єктивного сприйняття якості діяльності викладачів та адміністративно-організаційних змін, потім вони набули контрольно-оцінних функцій. Зараз моніторингові дослідження стають елементом внутрішнього аудиту якості освітньої діяльності. Проблеми, що при цьому виникають, пов’язані і з якістю засобів моніторингу, і з його метою, і зі зв’язком його результатів та ефективності діяльності суб’єктів освітнього процесу, в тому числі й університету. Слід зазначити, що, крім винятково внутрішніх інструментальних функцій, моніторинг у перспективі стане ще й засобом діагностики транспарентності діяльності вищих навчальних закладів. Одним із таких кроків є оприлюднення змісту й результатів порівнюваних моніторингових досліджень, проведених у Львівському національному університеті ветеринарної медицини та біотехнологій імені С.З. Ґжицького протягом 2008–2016 рр., зокрема результатів починаючи з 2010 р. (пілотний не включений). Авторами виокремлені етапи моніторингу (пілотний і три основні), проаналізовані цілі, зміст, отримані результати. Аналіз відомостей, здобутих у результаті проведених досліджень, є основою формування нових підходів щодо суб’єктивації університету в цілому, зокрема персоналізації управління, індивідуалізації діяльності його суб’єктів. Це дослідження стимулює розвиток аналогічної практики в інших університетах, що сприятиме, по-перше, відкритості у їх діяльності, по-друге, обміну досвідом у побудові внутрішніх систем якості, по-третє, ця робота має важливе значення для створення загального простору для міжнародних зв’язків і значущих міжуніверситетських досліджень

A unified treatment of cubic invariants at fixed and arbitrary energy

Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the invariant generally corresponds to a third rank Killing tensor, whose existence at a fixed energy value forces the metric to satisfy a nonlinear integrability condition expressed in terms of a Kahler potential. Further conditions, leading to a system of equations which is overdetermined except for singular cases, are added when the energy is arbitrary. As solutions to these equations we obtain several new superintegrable cases in addition to the previously known cases. We also discover a superintegrable case where the cubic invariant is of a new type which can be represented by an energy dependent linear invariant. A complete list of all known systems which admit a cubic invariant at arbitrary energy is given.Comment: 16 pages, LaTeX2e, slightly revised version. To appear in J. Math. Phys. vol 41, pp 370-384 (2000

A relativistic quark model for the Omega- electromagnetic form factors

We compute the Omega- electromagnetic form factors and the decuplet baryon magnetic moments using a quark model application of the Covariant Spectator Theory. Our predictions for the Omega- electromagnetic form factors can be tested in the future by lattice QCD simulations at the physical strange quark mass.Comment: 13 pages, 5 figure

SU(3) sextet model with Wilson fermions

We investigate the spectrum and IR properties of the SU(3) "sextet" model with two Dirac fermions in the two-index symmetric representation via lattice simulations. This model is a prime candidate for a realization of Walking Technicolor, which features a minimal matter content and it is expected to be inside or very close to the lower boundary of the conformal window. We use the Wilson discretization for the fermions and map the phase structure of the lattice model. We study several spectral and gradient flow observables both in the bulk and the weak coupling phases. While in the bulk phase we find clear signs of chiral symmetry breaking, in the weak coupling phase there is no clear indication for it, and instead the chiral limit of the model seems compatible with an IR-conformal behavior.Comment: 32 pages, many figure

Third-order superintegrable systems separable in parabolic coordinates

In this paper, we investigate superintegrable systems which separate in parabolic coordinates and admit a third-order integral of motion. We give the corresponding determining equations and show that all such systems are multi-separable and so admit two second-order integrals. The third-order integral is their Lie or Poisson commutator. We discuss how this situation is different from the Cartesian and polar cases where new potentials were discovered which are not multi-separable and which are expressed in terms of Painlev\'e transcendents or elliptic functions