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

Some Sharp Estimates for Convex Hypersurfaces of Pinched Normal Curvature

For a convex domain D bounded by the hypersurface ∂D in a space of constant curvature we give sharp bounds on the width R - r of a spherical shell with radii R and r that can enclose ∂D, provided that normal curvatures of ∂D are pinched by two positive constants. Furthermore, in the Euclidean case we also present sharp estimates for the quotient R/r. From the obtained estimates we derive stability results for almost umbilical hypersurfaces in the constant curvature spaces.В пространствах постоянной кривизны получены точные оценки для ширины R — r сферического слоя с радиусами R и r, в который можно поместить гиперповерхность ∂D, ограничивающую выпуклую область D, при учете, что нормальные кривизны ∂D зажаты между двумя положительными константами. В евклидовом случае также приведена точная оценка для отношения R/r. Из найденных оценок получены результаты по устойчивости почти омбилических гиперповерхностей в пространствах постоянной кривизны.У просторах сталої кривини отримано точні оцінки для ширини R — r сферичного шару з радіусами R та r, в який можна помістити гіперповерхнго ∂D, що обмежує опуклу область D, за умови, що нормалвні кривини ∂D, зажаті між двома додатними константами. У випадку евклідового простору також наведена точна оцінка для відношення R/r. 3 оцінок, що були знайдені, отримано результати зі стійкості майже омбілічних гіперповерхонв у просторах сталої кривини

The dynamics of complex box mappings

In holomorphic dynamics, complex box mappings arise as first return maps to well-chosen domains. They are a generalization of polynomial-like mapping, where the domain of the return map can have infinitely many components. They turned out to be extremely useful in tackling diverse problems. The purpose of this paper is: -To illustrate some pathologies that can occur when a complex box mapping is not induced by a globally defined map and when its domain has infinitely many components, and to give conditions to avoid these issues. -To show that once one has a box mapping for a rational map, these conditions can be assumed to hold in a very natural setting. Thus we call such complex box mappings dynamically natural. -Many results in holomorphic dynamics rely on an interplay between combinatorial and analytic techniques: (*)the Enhanced Nest by Kozlovski-Shen-van Strien; (*)the Covering Lemma by Kahn-Lyubich; (*)the QC-Criterion, the Spreading Principle. The purpose of this paper is to make these tools more accessible so that they can be used as a 'black box', so one does not have to redo the proofs in new settings. -To give an intuitive, but also rather detailed, outline of the proof of the following results by Kozlovski-van Strien for non-renormalizable dynamically natural box mappings: (*)puzzle pieces shrink to points; (*)topologically conjugate non-renormalizable polynomials and box mappings are quasiconformally conjugate. -We prove the fundamental ergodic properties for dynamically natural box mappings. This leads to some necessary conditions for when such a box mapping supports a measurable invariant line field on its filled Julia set. These mappings are the analogues of Lattes maps in this setting. -We prove a version of Mane's Theorem for complex box mappings concerning expansion along orbits of points that avoid a neighborhood of the set of critical points

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

Nucleon scalar matrix elements with Nf=2+1+1N_f=2+1+1 twisted mass fermions

The XXIX International Symposium on Lattice Field Theory, Lattice 2011We investigate scalar matrix elements of the nucleon using $N_f=2+1+1$ flavors of maximally twisted mass fermions at a fixed value of the lattice spacing of $a\approx 0.078{\rm fm}$. We compute disconnected contributions to the relevant three-point functions using an efficient noise reduction technique. Using these methods together with an only multiplicative renormalization applicable for twisted mass fermions, allows us to obtain accurate results in the light and strange sector

Overlap Valence Quarks on a Twisted Mass Sea

7 pages, 14 figures, presented at the XXVIII International Symposium on Lattice Field Theory (Lattice 2010), Villasimius, Sardinia, Italy, 14-19 June 2010We present the results of an investigation of a mixed action approach of overlap valence and maximally twisted mass sea quarks. Employing a particular matching condition on the pion mass, we analyze the continuum limit scaling of the pion decay constant and the role of chiral zero modes of the overlap operator in this process. We employ gauge field configurations generated by the European Twisted Mass Collaboration with linear lattice size $L$ ranging from 1.3 to 1.9 fm. The continuum limit is taken at a fixed value of $L=1.3$ fm, employing three values of the lattice spacing and two values of the pion mass constructed from sea quarks only

Looking at the gluon moment of the nucleon with dynamical twisted mass fermions

7 pages, 3 figures, talk given at the 31st International Symposium on Lattice Field Theory (Lattice 2013), July 29-August 3 2013, Mainz, GermanyTo understand the structure of hadrons it is important to know the PDF of their constituents, the quarks and gluons. In our work we aim to compute the first moment of the gluon PDF $\langle x \rangle_g$ for the nucleon. We follow two possible approaches in order to extract the gluon moment: the Feynman-Hellmann theorem and a direct method with smearing of the gluon operator. We present preliminary results computed on $24^3 \times 48$ lattices for the case where the Feynman-Hellman theorem is used and $32^3 \times 64$ lattices for the direct method, employing $N_f=2+1+1$ maximally twisted mass fermions

Canonical transformations of the extended phase space, Toda lattices and Stackel family of integrable systems

We consider compositions of the transformations of the time variable and canonical transformations of the other coordinates, which map completely integrable system into other completely integrable system. Change of the time gives rise to transformations of the integrals of motion and the Lax pairs, transformations of the corresponding spectral curves and R-matrices. As an example, we consider canonical transformations of the extended phase space for the Toda lattices and the Stackel systems.Comment: LaTeX2e + Amssymb, 22p