More on superintegrable models on spaces of constant curvature

A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic oscillator or a generalised Kepler potential. The angular components, on the contrary, are given implicitly by a transcendental, in general, equation. In the present note, devoted to the previously less studied models with the radial potential of the generalised Kepler type, a new two-parameter family of relevant angular potentials is constructed in terms of elementary functions. For an appropriate choice of parameters, the family reduces to an asymmetric spherical Higgs oscillator.Comment: 18 page

The evolution of the political vision of Polish energy security

Artykuł jest próbą porównania stanowisk głównych sił politycznych w Polsce w kwestii kierunków rozwoju polityki energetycznej RP i szeroko pojętego bezpieczeństwa energetycznego. Szczególny nacisk położono na analizę wizji przyszłości bezpieczeństwa politycznego RP zawartych w programach wyborczych najważniejszych partii politycznych przed wyborami parlamentarnymi 2015 roku. Tekst stanowi także próbę wskazania ewolucji poglądów partii politycznych wobec wyzwań bezpieczeństwa energetycznego w okresie po 2010 roku.The article is an attempt to compare the attitudes of the major Polish political powers in terms of energy policy and energy security future development. Special attention was paid to the analysis of the political program of the major political parties before the parliamentary elections in 2015. The text tries to indicate the evolution of political attitudes towards the challenges of energy security in the period after 2010

Classification of the popliteofibular ligament

The purpose of this study was to characterize the morphological variations in the distal attachment of the popliteofibular ligament (PFL) and create an accurate classification for use in planning surgical procedures in this area and in evaluating radiological imaging. One hundred and thirty-seven lower limbs of body donors fixed in 10% formalin solution were examined for the presence and course of the PFL. The PFL was present in 88.3% of cases. We propose the following three-fold classification: type I (72.3%), the most common type, characterized by the attachment onto the apex of the head of the fibula, type II (8.7%), characterized by a bifurcation, with the dominant band inserting on the anterior slope of the styloid process of the fibula and the smaller band onto the posterior surface of the styloid process of the fibula and type III (7.3%), characterized by a double PFL: the first PFL (main) originated from the popliteus tendon and inserted onto the anterior slope of the styloid process of the fibula, while the second originated from the musculotendinous junction of the popliteus muscle and inserted on the posterior surface of the styloid process of the fibula. The PFL was characterized by high morphological variation, as reflected in our proposed classification. This variation may present clinical and biomechanical issues for both medical personnel and researchers. Our proposed classification may be valuable for clinicians who evaluate and perform surgical procedures within the knee joint area.Depto. de Anatomía y EmbriologíaFac. de MedicinaTRUEpu