Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent \Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and multi-vectors, and give closed formulas for the higher Courant brackets.Comment: 42 pages, LaTeX. v2: Added remarks in Section 5. v3: Added further explanation. v4: Minor adjustments. v5: Section 5 completely rewritten to include covariant construction. v6: Minor adjustments. v7: Added references and explanation to Section

КЛАССИФИКАЦИЯ НАРУШЕНИЙ ФУНКЦИОНАЛЬНОЙ АКТИВНОСТИ МОЗГА У БОЛЬНЫХ С ОПУХОЛЯМИ ГОЛОВНОГО МОЗГА

This paper is devoted to the automatic classification of functional disorders of brain activity in patients with brain tumors on the basis of the reference groups. The test of statistical hypotheses set made crisp classification. Functional activity of the brain abnormality is assessed indicators of the frequency spectrum of the EEG. We describe the scheme of the algorithm and an analysis of the results. The publication is intended for IT-professionals and clinicians who are actively applying them in their work. Статья посвящена автоматической классификации нарушений функциональной активности мозга у больных с опухолями головного мозга на основе эталонных групп. Проверкой статистических гипотез устанавливается четкость выполненной классификации. Функциональную активность мозга оценивают посредством индикаторов аномальностей частотного спектра электроэнцефалограммы. Описана схема алгоритма, и представлен анализ получаемых результатов. Публикация рассчитана на специалистов по информационным технологиям и клиницистов, активно применяющих их в своей работе.

Research of sanitary, chemical and toxicological properties of silicone material «Silast-M» for removable dentures

Objective: to conduct sanitary, chemical and toxicological testing of the domestic cold-curing silicone material «Silast-M» for removable dentures. The object of the study included samples of silicone material «Silast-M» developed by CJSC «MEDSIL» in cooperation with the Department of Moscow State Medico-Stomatological University n.a. A. I. Evdokimov. Laboratory studies were carried out in the department of toxicology testing and researching materials and medical products VNIIIMT in accordance with the instructions on the sanitary, chemical and toxicological studies, developed and approved by the Ministry of Health of the Russian Federation. The results showed that all samples did not exceed the limit values. Conclusion. After successfully passed sanitary, chemical and toxicological studies clinical trials of the material have been started

Colloidal and Chemical Properties of Polyesters Based on Glutamic Acid and Diols of Different Nature

The paper describes synthesis method and colloid-chemical properties of novel α-amino acid based polyesters with controllable hydrophilic-lipophillic balance. Glutamic acid and diols of different nature based polyesters were obtained via low-temperature activated polyesterefication. Such polymers are able to form micellar structures in self-stabilized water dispersion. Solubilization of water insoluble dyes Sudan and toluene in polymer water solution was studied. Due to micelle forming ability and prognosticated biodegradability to non-toxic products, obtained polymers are promising materials for formation of novel dispersed drug delivery systems. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3507

Schwinger-Dyson equation for non-Lagrangian field theory

A method is proposed of constructing quantum correlators for a general gauge system whose classical equations of motion do not necessarily follow from the least action principle. The idea of the method is in assigning a certain BRST operator $\hat\Omega$ to any classical equations of motion, Lagrangian or not. The generating functional of Green's functions is defined by the equation $\hat\Omega Z (J) = 0$ that is reduced to the standard Schwinger-Dyson equation whenever the classical field equations are Lagrangian. The corresponding probability amplitude $\Psi$ of a field $\phi$ is defined by the same equation $\hat\Omega \Psi (\phi) = 0$ although in another representation. When the classical dynamics are Lagrangian, the solution for $\Psi (\phi)$ is reduced to the Feynman amplitude $e^{\frac{i}{\hbar}S}$, while in the non-Lagrangian case this amplitude can be a more general distribution.Comment: 33 page

General solution of classical master equation for reducible gauge theories

We give the general solution to the classical master equation (S,S)=0 for reducible gauge theories. To this aim, we construct a new coordinate system in the extended configuration space and transform the equation by changing variables. Then it can be solved by an iterative method.Comment: 15 pages; v3: refs. added, section 4 substantially improved, a section added; v4: reference and example adde

On Generalized Gauge-Fixing in the Field-Antifield Formalism

We consider the problem of covariant gauge-fixing in the most general setting of the field-antifield formalism, where the action W and the gauge-fixing part X enter symmetrically and both satisfy the Quantum Master Equation. Analogous to the gauge-generating algebra of the action W, we analyze the possibility of having a reducible gauge-fixing algebra of X. We treat a reducible gauge-fixing algebra of the so-called first-stage in full detail and generalize to arbitrary stages. The associated "square root" measure contributions are worked out from first principles, with or without the presence of antisymplectic second-class constraints. Finally, we consider an W-X alternating multi-level generalization.Comment: 49 pages, LaTeX. v2: Minor changes + 1 more reference. v3,v4,v5: Corrected typos. v5: Version published in Nuclear Physics B. v6,v7: Correction to the published version added next to the Acknowledgemen

Gauge dependence of effective action and renormalization group functions in effective gauge theories

The Caswell-Wilczek analysis on the gauge dependence of the effective action and the renormalization group functions in Yang-Mills theories is generalized to generic, possibly power counting non renormalizable gauge theories. It is shown that the physical coupling constants of the classical theory can be redefined by gauge parameter dependent contributions of higher orders in $\hbar$ in such a way that the effective action depends trivially on the gauge parameters, while suitably defined physical beta functions do not depend on those parameters.Comment: 13 pages Latex file, additional comments in section

BFV-complex and higher homotopy structures

We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the so-called strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter structure can be derived from the BFV-complex by means of homotopy transfer along contractions. Consequently the BFV-complex and the strong homotopy Lie algebroid structure are $L_{\infty}$ quasi-isomorphic and control the same formal deformation problem. However there is a gap between the non-formal information encoded in the BFV-complex and in the strong homotopy Lie algebroid respectively. We prove that there is a one-to-one correspondence between coisotropic submanifolds given by graphs of sections and equivalence classes of normalized Maurer-Cartan elemens of the BFV-complex. This does not hold if one uses the strong homotopy Lie algebroid instead.Comment: 50 pages, 6 figures; version 4 is heavily revised and extende