On Deformations of n-Lie algebras

The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and quantization of $n$-Lie algebras.Comment: Proceeding of the conference Dakar's Workshop in honor of Pr Amin Kaidi. arXiv admin note: text overlap with arXiv:hep-th/9602016 by other author

Inclusive pion double charge exchange on Oxygen(16) at 0.6-1.1 GeV

The inclusive pion double charge exchange (DCX) on oxygen nuclei has been measured in the region where additional pion production is kinematically forbidden. The experiment was performed at ITEP PS at incident pi- kinetic energies T_0= 0.59, 0.75 and 1.1 GeV. The integrated forward differential cross section was found to decrease with energy slowly. At 1.1 GeV it exceeds the theoretical prediction within the conventional sequential single charge exchange mechanism with a neutral pion in the intermediate state (Glauber elastic rescattering) by about half an order of magnitude. The sequential mechanism with two pions in the intermediate state (Glauber inelastic rescatterings), which was proposed recently, seems to be able to explain the observed slow energy dependence and allows to predict the DCX cross section for higher energies.Comment: 27 pages, 13 figures. Minor corrections, one figure added. Accepted in NP

Small-angle fragmentation of carbon ions at 0.6 GeV/n: a comparison with models of ion-ion interactions

Momentum distributions of hydrogen and helium isotopes from 12C fragmentation at 3.5° were measured at 0.6 GeV/nucleon in the FRAGM experiment at ITEP TWA heavy ion accelerator. The fragments were selected by correlated time of flight and dE/dx measurements with a magnetic spectrometer with scintillation counters. The main attention was drawn to the high momentum region where the fragment velocity exceeds the velocity of the projectile nucleus. The momentum spectra of fragments span the region of the fragmentation peak as well as the cumulative region. The differential cross sections cover six orders of magnitude. The distributions measured are compared to the predictions of three ion-ion interaction models: BC, QMD and LAQGSM03.03. The kinetic energy spectra of fragments in the projectile rest frame have an exponential shape with two temperatures, being defined by their slope parameters

Estimation of smooth vector fields on manifolds by optimization on Stiefel group

Real data are usually characterized by high dimensionality. However, real data obtained from real sources, due to the presence of various dependencies between data points and limitations on their possible values, form, as a rule, form a small part of the high-dimensional space of observations. The most common model is based on the hypothesis that data lie on or near a manifold of a smaller dimension. This assumption is called the manifold hypothesis, and inference and calculations under it are called manifold learning. Grassmann & Stiefel eigenmaps is a manifold learning algorithm. One of its subproblems has been considered in the paper: estimation of smooth vector fields by optimization on the Stiefel group. A two-step algorithm has been introduced to solve the problem. Numerical experiments with artificial data have been performed

Alignment of vector fields on manifolds via contraction mappings

According to the manifold hypothesis, high-dimensional data can be viewed and meaningfully represented as a lower-dimensional manifold embedded in a higher dimensional feature space. Manifold learning is a part of machine learning where an intrinsic data representation is uncovered based on the manifold hypothesis. Many manifold learning algorithms were developed. The one called Grassmann & Stiefel eigenmaps (GSE) has been considered in the paper. One of the GSE subproblems is tangent space alignment. The original solution to this problem has been formulated as a generalized eigenvalue problem. In this formulation, it is plagued with numerical instability, resulting in suboptimal solutions to the subproblem and manifold reconstruction problem in general. We have proposed an iterative algorithm to directly solve the tangent spaces alignment problem. As a result, we have obtained a significant gain in algorithm efficiency and time complexity. We have compared the performance of our method on various model data sets to show that our solution is on par with the approach to vector fields alignment formulated as an optimization on the Stiefel group

Dynamic characteristics of a semi-conductor sensitive element of helicoid type of the gas fire detector

На основе экспериментальных и теоретических исследований определены такие динамические характеристики полупроводникового чувствительного элемента спиралевидного типа (ППЧЭ СТ) газового пожарного извещателя (ГПИ) как передаточная функция (ПФ) и единичная переходная функция (ЕПФ). Это позволяет моделировать работу ППЧЭ СТ ГПИ без проведения дополнительных экспериментальных исследований.Отримані динамічні характеристики напівпровідникового чутливого елемента спіралевидного типу (передаточна функція й одинична перехідна функція), що дозволяють оцінити значення технічних характеристик останнього в будьякий момент часу без проведення додаткових експериментальних досліджень.Dynamic characteristics of a semi-conductor sensitive element of helicoid type are received (transfer function and individual transitive function), allowing to estimate value of characteristics of the last at any moment without carrying out of additional experimental researches

Results of investigations of the Neva Bay technosphere at RSHU

The article summarizes the results of the long-term complex observations of formation and development of the technosphere in the coastal zone of the Neva Bay and its impact on coastal hydro-biological communities by RSHU scientists. Natural and administrative borders of the Neva Bay are described and discussed. Evolution of the Neva Bay from «natural geosystem» to the «natural-and technical system» is monitored and analyzed. Peculiarities of coastal biological communities are presented. Anthropogenic stress-factors connected with hydrotechnical construction and dredging with high level of negative influence on coastal ecosystems are revealed. The program of original complex research of the functioning of the coastal «natural-and technical system» is proposed. Areas of hydrotechnical and dredging projects and parallel environmental monitoring in the Neva Bay are mapped. Artificially reclaimed coastal territories are recognized as core elements (knots) of the coastal technosphere of the Neva Bay. Anthropogenic macro-objects constructed on these areas, such as ports, business centers, elements of logistic structure, and recreational areas are observed from the «sustainable development» point of view. The effects of technosphere on abiotic and biotic components of coastal ecosystems are shown. To study the spatial and temporal variability of the state of the Neva Bay and its coastal zone under the influence of sedimentation processes and man-made impacts, high- and medium-resolution satellite data have been used. Some results from satellite observations are compared and discussed. Based on the research results, a map of the integral ecological vulnerability of the Neva Bay in relation to hydrotechnical works and dredging has been constructed. Information about the established levels of environmental vulnerability of various sections of the Neva Bay water area can be used for the benefit of marine spatial planning. Methods and technologies of compensatory measurements are compared and discussed in order to find optimal actions. Organizing of nature protection areas is recommended as a complex method for the support of the coastal zone sustainable development</jats:p