Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints

We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The covariance of the construction with respect to the change of the constraint basis is provided by introducing a connection in the ``constraint bundle'', which becomes a key ingredient of the conversion procedure for the non-scalar constraints. Unlike in the case of scalar second-class constraints, no Abelian conversion is possible in general. Within the BRST framework, a systematic procedure is worked out for converting non-scalar second-class constraints into non-Abelian first-class ones. The BRST-extended system is quantized, yielding an explicitly covariant quantization of the original system. An important feature of second-class systems with non-scalar constraints is that the appropriately generalized Dirac bracket satisfies the Jacobi identity only on the constraint surface. At the quantum level, this results in a weakly associative star-product on the phase space.Comment: LaTeX, 21 page

Symplectic connections, Noncommutative Yang Mills theory and Supermembranes

In built noncommutativity of supermembranes with central charges in eleven dimensions is disclosed. This result is used to construct an action for a noncommutative supermembrane where interesting topological terms appear. In order to do so, we first set up a global formulation for noncommutative Yang Mills theory over general symplectic manifolds. We make the above constructions following a pure geometrical procedure using the concept of connections over Weyl algebra bundles on symplectic manifolds. The relation between noncommutative and ordinary supermembrane actions is discussed.Comment: 18 page

Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles

We provide a method of converting Lagrange and Finsler spaces and their Legendre transforms to Hamilton and Cartan spaces into almost Kaehler structures on tangent and cotangent bundles. In particular cases, the Hamilton spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on effective phase spaces. This allows us to define the corresponding Fedosov operators and develop deformation quantization schemes for nonlinear mechanical and gravity models on Lagrange- and Hamilton-Fedosov manifolds.Comment: latex2e, 11pt, 35 pages, v3, accepted to J. Math. Phys. (2009

СИСТЕМА УПРАВЛІННЯ ЯКІСТЮ НФаУ: ДОСВІД І ПЕРСПЕКТИВИ

The aim of the work – to highlight the importance of creating a quality management system, taking into account the experience of the National University of Pharmacy, and outline its perspectives. The main body. In order to support the functioning of the internal quality management system at the National Pharmaceutical University, a completely new structural unit for the university was created – the Quality Management Department. The functions of Quality Management Department include the planning of the University’s activities, organizational and methodological support for internal and external audits, the procedure for rating departments and NPP, monitoring the effectiveness of the quality management system processes, introducing risk-oriented approaches to the functioning of the quality management system, personnel training, document management coordination, etc. The informative model of the quality management system National Pharmaceutical University is represented by a cascade planning system, which involves the gradual elaboration of plans from the Mission and Policy University to the plans of individual performers. Conclusions. The University leadership believes that the implemented quality management system is an effective mechanism for preventing the emergence of internal and reducing the impact of external risks. The established quality management system of the National University of Pharmacy is a meaningful basis for the development of an internal quality assurance system for higher education in pharmacy.Мета роботи – висвітлити значення створення системи управління якістю, враховуючи досвід НфаУ, та окреслити її перспективи. Основна частина. Для підтримки функціонування внутрішньої системи управління якістю у НФаУ створено абсолютно новий для університету структурний підрозділ – відділ управління якістю. До функцій ВУЯ належать планування діяльності університету, організаційно-методичний супровід внутрішніх і зовнішніх аудитів, проведення процедури рейтингування кафедр та НПП, моніторинг результативності процесів СУЯ,  впровадження ризик-орієнтованих підходів до функціонування процесів СУЯ, навчання персоналу, координація документообігу тощо. Змістовна модель СУЯ НФаУ представлена каскадною системою планування, яка передбачає поступову деталізацію планів від Місії й Політики університету до планів окремих виконавців. Висновки. Керівництво університету вважає запроваджену систему управління якістю дієвим механізмом, що попереджає виникнення внутрішніх та зменшує вплив зовнішніх ризиків. Створена система управління якістю Національного фармацевтичного університету є змістовним підґрунтям для розбудови внутрішньої системи забезпечення якості вищої фармацевтичної освіти

Preclinical study of the efficacy and safety of wound healing gel containing chitosan, taurine and allantoin

Objectives: To develop gel containing chitosan, taurine, allantoin, and to experimentally investigate its wound healing properties in preclinical studies on laboratory animal

Deformation quantization of cosmological models

The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is applied to cosmological models in the minisuperspace. The quantization procedure is performed explicitly for quantum cosmology in a flat minisuperspace. The de Sitter cosmological model is worked out in detail and the computation of the Wigner functions for the Hartle-Hawking, Vilenkin and Linde wave functions are done numerically. The Wigner function is analytically calculated for the Kantowski-Sachs model in (non)commutative quantum cosmology and for string cosmology with dilaton exponential potential. Finally, baby universes solutions are described in this context and the Wigner function is obtained.Comment: 37 pages, 16 figure

Weyl-Wigner Formulation of Noncommutative Quantum Mechanics

We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform and to the Seiberg-Witten map we construct an isomorphism between the operator and the phase space representations of the extended Heisenberg algebra. This map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space. We construct the extended starproduct, Moyal bracket and propose a general definition of noncommutative states. We study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of Seiberg-Witten map. Our approach unifies and generalizes all the previous proposals for the phase space formulation of noncommutative quantum mechanics. For concreteness we rederive these proposals by restricting our formalism to some 2-dimensional spaces.Comment: Revtex4, 3 diagrams, 32 page

Weyl's symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics

The knowledge of quantum phase flow induced under the Weyl's association rule by the evolution of Heisenberg operators of canonical coordinates and momenta allows to find the evolution of symbols of generic Heisenberg operators. The quantum phase flow curves obey the quantum Hamilton's equations and play the role of characteristics. At any fixed level of accuracy of semiclassical expansion, quantum characteristics can be constructed by solving a coupled system of first-order ordinary differential equations for quantum trajectories and generalized Jacobi fields. Classical and quantum constraint systems are discussed. The phase-space analytic geometry based on the star-product operation can hardly be visualized. The statement "quantum trajectory belongs to a constraint submanifold" can be changed e.g. to the opposite by a unitary transformation. Some of relations among quantum objects in phase space are, however, left invariant by unitary transformations and support partly geometric relations of belonging and intersection. Quantum phase flow satisfies the star-composition law and preserves hamiltonian and constraint star-functions.Comment: 27 pages REVTeX, 6 EPS Figures. New references added. Accepted for publication to JM

Cohomologies of the Poisson superalgebra

Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on $R^{2n}$ ($C^{2n}) are investigated under suitable continuity restrictions on cochains. The first and second cohomology spaces in the trivial representation and the zeroth and first cohomology spaces in the adjoint representation of the Poisson superalgebra are found for the case of a constant nondegenerate Poisson superbracket for arbitrary n>0. The third cohomology space in the trivial representation and the second cohomology space in the adjoint representation of this superalgebra are found for arbitrary n>1.Comment: Comments: 40 pages, the text to appear in Theor. Math. Phys. supplemented by computation of the 3-rd trivial cohomolog