A Variational Formulation of Symplectic Noncommutative Mechanics

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [14]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.Comment: 17 pages, Latex. Accepted for publication in IJGMM

ОРГАНІЗАЦІЯ БУХГАЛТЕРСЬКОГО ОБЛІКУ ТА РИЗИК-МЕНЕДЖМЕНТ ОСВІТНЬОЇ ДІЯЛЬНОСТІ: НАПРЯМИ РОЗВИТКУ В УМОВАХ ВПРОВАДЖЕННЯ СИСТЕМИ УПРАВЛІННЯ ЯКІСТЮ

The article aims to justify the measures for organizing the formation and provision of information from the accounting system for the risk management process in order to ensure the stability and sustainability of the development of higher education institutions. The goal has been realized on the basis of the application of the methods of observation, comparison, analysis, synthesis, generalization and economic-statistical method. The made analysis allowed to determine the risks of non-fulfilment of information needs regarding the functioning of higher education institutions for each study group (applicants, students, participants, parents of students/applicants, administration, employers, customers of research projects, teachers, government, society, governing bodies), which made it possible to offer an organizational approach to the information support of risk management of educational activities. This approach covers corrective management actions (in terms of accounting functions) on each of the defined processes of the risk management system (admission process for higher education, planning the educational process, organizing the educational process, staffing educational activities), executives, responsible entities and output data. Taking into account the provisions of regulatory documents, scientists' developments and practical experience in risk management has allowed to determine the stages of risk management in educational activities of a higher education institution (risk analysis, risk assessment, direct risk management, risk monitoring, risk management reporting) indicating the role of accounting personnel in each of them. It has been substantiated that the main advantages of the proposed approach to information management of risk management of educational activities of higher educational institutions are the simplicity of use (provided with properly devised documentation), the complexity of the approach (coverage of all quality management system processes), responsiveness to identified risks; accounting structure of higher education institutions. It is proved that the proposals will contribute to the improvement of the accounting display of actions to minimize the risks of educational activities of higher educational institutions, thereby ensuring the strengthening of their competitiveness on the market of educational services.Поставлено завдання обґрунтувати заходи щодо організації формування та надання інформації, яка продукується в системі бухгалтерського обліку, для процесу управління ризиками з метою забезпечення стабільності та стійкості розвитку закладів вищої освіти. Поставлену мету реалізовано на основі застосування методів спостереження, порівняння, аналізу, синтезу, узагальнення та економіко-статистичного методу. Проведений аналіз дозволив визначити ризики невиконання інформаційних потреб щодо функціонування закладів вищої освіти для кожної досліджуваної групи (абітурієнтів, студентів, слухачів, здобувачів, батьків студентів / абітурієнтів, адміністрації, роботодавців, замовників науково-дослідних робіт, викладачів, держави, суспільства, органів управління), що дозволило запропонувати організаційний підхід до інформаційного забезпечення управління ризиками освітньої діяльності. Зазначений підхід охоплює коригувальні управлінські дії (в частині облікових функцій) на кожному з визначених процесів системи управління ризиками (процес прийому на навчання для здобуття вищої освіти; планування освітнього процесу; організація освітнього процесу, кадрове забезпечення освітньої діяльності), виконавців, відповідальних суб’єктів і вихідних даних. Урахування положень нормативних документів, напрацювань науковців і практичний досвід управління ризиками дозволив визначити етапи управління ризиками освітньої діяльності закладів вищої освіти (аналіз ризиків, оцінка ризику, безпосереднє управління ризиками, моніторинг ризику, звітування з управління ризиками) із зазначенням ролі облікового персоналу на кожному з них. Обґрунтовано, що основними перевагами запропонованого підходу до інформаційного забезпечення управління ризиками освітньої діяльності закладів вищої освіти є простота застосування (за умови належно розробленого документального забезпечення), комплексність підходу (охоплення всіх процесів системи управління якістю), оперативність реагування на виявлені ризики; урахування структури закладу вищої освіти. Доведено, що пропозиції сприятимуть удосконаленню облікового відображення дій з мінімізації ризиків освітньої діяльності закладів вищої освіти, тим самим забезпечивши посилення їхньої конкурентоспроможності на ринку освітніх послуг

Lagrange structure and quantization

A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the Lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in $d+1$ dimensions, being localized on the boundary, are proved to be equivalent to the original theory in $d$ dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily Lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.Comment: Minor corrections, format changed, 40 page

Deformation quantization of linear dissipative systems

A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding Poisson tensor is allowed to explicitly depend on time. Starting from this pseudo-Hamiltonian formulation we develop a consistent deformation quantization procedure involving a non-stationary star-product $*_t$ and an ``extended'' operator of time derivative $D_t=\partial_t+...$, differentiating the $\ast_t$-product. As in the usual case, the $\ast_t$-algebra of physical observables is shown to admit an essentially unique (time dependent) trace functional $\mathrm{Tr}_t$. Using these ingredients we construct a complete and fully consistent quantum-mechanical description for any linear dynamical system with or without dissipation. The general quantization method is exemplified by the models of damped oscillator and radiating point charge.Comment: 14 pages, typos correcte

Poisson sigma model on the sphere

We evaluate the path integral of the Poisson sigma model on sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kahler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.Comment: 38 page

Chiral and axial anomalies in the framework of generalized Hamiltonian BFV-quantization

The regularization scheme is proposed for the constrained Hamiltonian formulation of the gauge fields coupled to the chiral or axial fermions. The Schwinger terms in the regularized operator first-class constraint algebra are shown to be consistent with the covariant divergence anomaly of the corresponding current. Regularized quantum master equations are studied, and the Schwinger terms are found out to break down both nilpotency of the BRST-charge and its conservation law. Wess-Zumino consistency conditions are studied for the BRST anomaly and they are shown to contradict to the covariant Schwinger terms in the BRST algebra.Comment: LaTeX, 24p

N=1, D=3 Superanyons, osp(2|2) and the Deformed Heisenberg Algebra

We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model introduced possesses hidden invariance under N=2 Poincar\'e supergroup with a central charge saturating the BPS bound. At the classical level the model admits a Hamiltonian formulation with two first class constraints on the phase space $T^*(R^{1,2})\times {\cal L}^{1|1}$, where the K\"ahler supermanifold ${\cal L}^{1|1}\cong OSp(2|2)/U(1|1)$ is a minimal superextension of the Lobachevsky plane. The model is quantized by combining the geometric quantization on ${\cal L}^{1|1}$ and the Dirac quantization with respect to the first class constraints. The constructed quantum theory describes a supersymmetric doublet of fractional spin particles. The space of quantum superparticle states with a fixed momentum is embedded into the Fock space of a deformed harmonic oscillator.Comment: 23 pages, Late

A minimal BV action for Vasiliev's four-dimensional higher spin gravity

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle.Comment: 39 pages, 1 figure. Additional comments in the conclusion

Radiation reaction for multipole moments

We propose a Poincare-invariant description for the effective dynamics of systems of charged particles by means of intrinsic multipole moments. To achieve this goal we study the effective dynamics of such systems within two frameworks -- the particle itself and hydrodynamical one. We give a relativistic-invariant definition for the intrinsic multipole moments both pointlike and extended relativistic objects. Within the hydrodynamical framework we suggest a covariant action functional for a perfect fluid with pressure. In the case of a relativistic charged dust we prove the equivalence of the particle approach to the hydrodynamical one to the problem of radiation reaction for multipoles. As the particular example of a general procedure we obtain the effective model for a neutral system of charged particles with dipole moment.Comment: 12 pages, 1 figure, RevTeX 4; references updated, minor textual correction

Bcr/Abl Interferes with the Fanconi Anemia/BRCA Pathway: Implications in the Chromosomal Instability of Chronic Myeloid Leukemia Cells

Chronic myeloid leukemia (CML) is a malignant clonal disorder of the hematopoietic system caused by the expression of the BCR/ABL fusion oncogene. Although it is well known that CML cells are genetically unstable, the mechanisms accounting for this genomic instability are still poorly understood. Because the Fanconi anemia (FA) pathway is believed to control several mechanisms of DNA repair, we investigated whether this pathway was disrupted in CML cells. Our data show that CML cells have a defective capacity to generate FANCD2 nuclear foci, either in dividing cells or after DNA damage. Similarly, human cord blood CD34+ cells transduced with BCR/ABL retroviral vectors showed impaired FANCD2 foci formation, whereas FANCD2 monoubiquitination in these cells was unaffected. Soon after the transduction of CD34+ cells with BCR/ABL retroviral vectors a high proportion of cells with supernumerary centrosomes was observed. Similarly, BCR/ABL induced a high proportion of chromosomal abnormalities, while mediated a cell survival advantage after exposure to DNA cross-linking agents. Significantly, both the impaired formation of FANCD2 nuclear foci, and also the predisposition of BCR/ABL cells to develop centrosomal and chromosomal aberrations were reverted by the ectopic expression of BRCA1. Taken together, our data show for the first time a disruption of the FA/BRCA pathway in BCR/ABL cells, suggesting that this defective pathway should play an important role in the genomic instability of CML by the co-occurrence of centrosomal amplification and DNA repair deficiencies