Reflection principle characterizing groups in which unconditionally closed sets are algebraic

We give a necessary and sufficient condition, in terms of a certain reflection principle, for every unconditionally closed subset of a group G to be algebraic. As a corollary, we prove that this is always the case when G is a direct product of an Abelian group with a direct product (sometimes also called a direct sum) of a family of countable groups. This is the widest class of groups known to date where the answer to the 63 years old problem of Markov turns out to be positive. We also prove that whether every unconditionally closed subset of G is algebraic or not is completely determined by countable subgroups of G.Comment: 14 page

Formalization of OLAP-cubes and relational databases with the algebra of sets

Mathematical formalization of OLAP-cubes is developed. Dimensions of cube and Cartesian products are supplied with an algebra of sets and measure. These sets are involved in queries. Operations projection and cross section are consistent with the algebra of dimension. Relational connections between dimensions realized with the help of index maps on the works of these dimensions. We introduce three types of index maps to the dimension corresponding to the three types of relational ties. It is shown that the relational database is an OLAP-cube with the corresponding index maps, and can be written by one formula. As an example the analytical processing of the questionnairesПредлагается математическая формализация OLAP-кубов, в которой размерности куба и их декартовые произведения снабжаются алгеброй подмножеств и мерой. Эти множества участвуют в запросах. Операции проекции и сечения согласуются с алгебрами размерностей. Реляционные связи между размерностями реализуются с помощью индексных отображений на произведениях этих размерностей. Вводятся три типа индексных отображений на размерности, соответствующие трем типам реляционных связей. Показано, что реляционная база данных является OLAP-кубом с соответствующими индексными отображениями и может быть записана одной формулой. В качестве примера рассматривается аналитическая обработка анкет

The LHC Post Mortem Analysis Framework

The LHC with its unprecedented complexity and criticality of beam operation will need thorough analysis of data taken from systems such as power converters, interlocks and beam instrumentation during events like magnet quenches and beam loss. The causes of beam aborts or in the worst case equipment damage have to be revealed to improve operational procedures and protection systems. The correct functioning of the protection systems with their required redundancy has to be verified after each such event. Post mortem analysis software for the control room has been prepared with automated analysis packages in view of the large number of systems and data volume. This paper recalls the requirements for the LHC Beam Post Mortem System (PM) and the necessity for highly reliable data collection. It describes in detail the redundant architecture for data collection as well as the chosen implementation of a multi-level analysis framework, allowing for automated analysis and qualification of a beam dump event based on expert provided analysis modules. It concludes with an example of the data taken during first beam tests in September 2008 with a first version of the system

Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies

3D numerical studies have shown that the vertical voltage above the Baikal deep-water fault is detectable and that respective transfer functions, Ez-responses, are sensitive to the electrical resistivity changes of the fault, i.e. these functions appear actually informative with respect to the resistivity «breath» of the fault. It means that if the fault resistivity changed, conventional electromagnetic instruments would be able to detect this fact by measurement of the vertical electric field, Ez, or the vertical electric voltage just above the fault as well as horizontal magnetic field on the shore. Other electromagnetic field components (Ex, Ey, Hz) do not seem to be sensitive to the resistivity changes in such a thin fault (as wide as 500 m). On the other hand, such changes are thought to be able to indicate a change of a stress state in the earthquake preparation zone. Besides, the vertical profile at the bottom of Lake Baikal is suitable for electromagnetic monitoring of the fault electrical resistivity changes. Altogether, the vertical voltage above the deep-water fault might be one of earthquake precursors

Molecular-genetic aspects of the endometrium state on the day of the tentative implantation window in women with recurrent miscarriage in the programs of assisted reproductive technologies

Golovatyuk K. P., Nosenko O. M., Makshayeva E. T., Trofimov D. Yu., Donnikov A. E., Kolin V. V. Molecular-genetic aspects of the endometrium state on the day of the tentative implantation window in women with recurrent miscarriage in the programs of assisted reproductive technologies. Journal of Education, Health and Sport. 2017;7(9):621-626. eISSN 2391-8306. DOI http://dx.doi.org/10.5281/zenodo.1068361 http://ojs.ukw.edu.pl/index.php/johs/article/view/5076 The journal has had 7 points in Ministry of Science and Higher Education parametric evaluation. Part B item 1223 (26.01.2017). 1223 Journal of Education, Health and Sport eISSN 2391-8306 7 © The Authors 2017; This article is published with open access at Licensee Open Journal Systems of Kazimierz Wielki University in Bydgoszcz, Poland Open Access. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. This is an open access article licensed under the terms of the Creative Commons Attribution Non Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted, non commercial use, distribution and reproduction in any medium, provided the work is properly cited. This is an open access article licensed under the terms of the Creative Commons Attribution Non Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted, non commercial use, distribution and reproduction in any medium, provided the work is properly cited. The authors declare that there is no conflict of interests regarding the publication of this paper. Received: 15.08.2017. Revised: 20.09.2017. Accepted: 29.09.2017. MOLECULAR-GENETIC ASPECTS OF THE ENDOMETRIUM STATE ON THE DAY OF THE tentative IMPLANTATION WINDOW IN WOMEN WITH recurrent miscarriage IN THE PROGRAMS OF ASSISTED REPRODUCTIVE TECHNOLOGIES 1K. P. Golovatyuk, 2O. M. Nosenko, 1E. T. Makshayeva, 3D. Yu. Trofimov, 4A. E. Donnikov, 3V. V. Kolin 1Limited Liability Company Medical Center for Reproductive Health "Gameta", Odessa, Ukraine; 2Odessa National Medical University, Ukraine; 3Limited Liability Company "NPF DNA-Technology", Moscow, Russia; 4FGBU Scientific Center for Obstetrics, Gynecology and Perinatology. named after acad. V.I. Kulakov Ministry of Health care and Social Development of Russia, Moscow, Russia; e-mail: [email protected] Abstract More than 50% of pregnant women after the programs of assisted reproductive technologies (ART) face the problem of recurrent miscarriage (RMC), especially in the first trimester. Significant role in the development of RMC has infectious factor and chronic inflammation in the endometrium. The aim: to reveal the peculiarities of immune response mRNA genes of the inflammatory component expression in the period of the tentative implantation window (TIW) in women with RMC in ART programs. Material and methods. The main group consisted of 240 patients with RMC in ART programs; the control group included 100 conditionally healthy fertile women. On the ground of PCR reverse transcription, the mRNA of the IL-1β, IL-2, IL-10, Foxp3, TLR9, IL-2Rα cytokine genes was examined in endometrial samples obtained with the help of biopsy on the TIW day. Results. Analysis of the transcriptional profile of the immune response genes in the endometrium on TIW day revealed that the relative level of mRNA expression of the IL-1β, IL-2, Foxp3, TLR9, IL-2Rα genes did not differ significantly in the main and control groups. Statistically significant decrease in mRNA expression of IL-10 gene was observed in women with RPL. Conclusions. A feature of mRNA expression of the inflammatory component of the immune response in TIW period in women with RMC in ART programs is a decrease in the expression level of the IL-10 gene mRNA, which may be one of the reasons for the unfavorable outcomes of the onset pregnancy. Key words: recurrent miscarriage, assisted reproductive technologies, immune response, reverse transcription-polymerase chain reaction, tentative implantation window

Economic-geographical aspects of competitiveness and positioninng of countries and regions

© 2015, Mediterranean Center of Social and Educational Research. All rights reserved. At present, the increased competition between countries and regions made the problem of study of competitiveness and positioning of regions in the system of the world and national economy relevant. This problem becomes even more important in conditions of the development of globalization and transition of countries to the post-industrial stage of development. All this led to the necessity to find ways to assess the competitiveness and the necessity for deeper analysis of the concept of competitiveness. Competitiveness of countries, regions and other territorial entities should be considered in mutual balance of all the principles of socio-economic development by a range of indicators of the following subsystems: population, economy, infrastructure, environment

Review of biorthogonal coupled cluster representations for electronic excitation

Single reference coupled-cluster (CC) methods for electronic excitation are based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in terms of excited CC states, also referred to as correlated excited (CE) states, and an associated set of states biorthogonal to the CE states, the latter being essentially configuration interaction (CI) configurations. The bCC representation generates a non-hermitian secular matrix, the eigenvalues representing excitation energies, while the corresponding spectral intensities are to be derived from both the left and right eigenvectors. Using the perspective of the bCC representation, a systematic and comprehensive analysis of the excited-state CC methods is given, extending and generalizing previous such studies. Here, the essential topics are the truncation error characteristics and the separability properties, the latter being crucial for designing size-consistent approximation schemes. Based on the general order relations for the bCC secular matrix and the (left and right) eigenvector matrices, formulas for the perturbation-theoretical (PT) order of the truncation errors (TEO) are derived for energies, transition moments, and property matrix elements of arbitrary excitation classes and truncation levels. In the analysis of the separability properties of the transition moments, the decisive role of the so-called dual ground state is revealed. Due to the use of CE states the bCC approach can be compared to so-called intermediate state representation (ISR) methods based exclusively on suitably orthonormalized CE states. As the present analysis shows, the bCC approach has decisive advantages over the conventional CI treatment, but also distinctly weaker TEO and separability properties in comparison with a full (and hermitian) ISR method

The study of the negative pion production in neutron-proton collisions at beam momenta below 1.8 GeV/c

A detailed investigation of the reaction np -> pp\pi^{-} has been carried out using the data obtained with the continuous neutron beam produced by charge exchange scattering of protons off a deuterium target. A partial wave event-by-event based maximum likelihood analysis was applied to determine contributions of different partial waves to the pion production process. The combined analysis of the np -> pp\pi^{-} and pp -> pp\pi^{0} data measured in the same energy region allows us to determine the contribution of isoscalar partial waves (I=0) in the momentum range from 1.1 up to 1.8 GeV/c. The decay of isoscalar partial waves into (^1S_0)_{pp}\pi$ channel provides a good tool for a determination of the pp S-wave scalar scattering length in the final state which was found to be a_{pp}=-7.5\pm 0.3 fm.Comment: 6 pages, 6 figure

Singularities, Lax degeneracies and Maslov indices of the periodic Toda chain

The n-particle periodic Toda chain is a well known example of an integrable but nonseparable Hamiltonian system in R^{2n}. We show that Sigma_k, the k-fold singularities of the Toda chain, ie points where there exist k independent linear relations amongst the gradients of the integrals of motion, coincide with points where there are k (doubly) degenerate eigenvalues of representatives L and Lbar of the two inequivalent classes of Lax matrices (corresponding to degenerate periodic or antiperiodic solutions of the associated second-order difference equation). The singularities are shown to be nondegenerate, so that Sigma_k is a codimension-2k symplectic submanifold. Sigma_k is shown to be of elliptic type, and the frequencies of transverse oscillations under Hamiltonians which fix Sigma_k are computed in terms of spectral data of the Lax matrices. If mu(C) is the (even) Maslov index of a closed curve C in the regular component of R^{2n}, then (-1)^{\mu(C)/2} is given by the product of the holonomies (equal to +/- 1) of the even- (or odd-) indexed eigenvector bundles of L and Lmat.Comment: 25 pages; published versio

Natural chain-breaking antioxidants and their synthetic analogs as modulators of oxidative stress

Oxidative stress is associated with the increased production of reactive oxygen species or with a significant decrease in the effectiveness of antioxidant enzymes and nonenzymatic defense. The penetration of oxygen and free radicals in the hydrophobic interior of biological membranes initiates radical disintegration of the hydrocarbon “tails” of the lipids. This process is known as “lipid peroxidation”, and the accumulation of the oxidation products as peroxides and the alde-hydes and acids derived from them are often used as a measure of oxidative stress levels. In total, 40 phenolic antioxidants were selected for a comparative study and analysis of their chain-breaking antioxidant activity, and thus as modulators of oxidative stress. This included natural and natural-like ortho-methoxy and ortho-hydroxy phenols, nine of them newly synthesized. Applied experimental and theoretical methods (bulk lipid autoxidation, chemiluminescence, in silico methods such as density functional theory (DFT) and quantitative structure–activity relationship ((Q)SAR) modeling) were used to clarify their structure–activity relationship. Kinetics of non-inhibited and inhibited lipid oxidation in close connection with inhibitor transformation under oxidative stress is considered. Special attention has been paid to chemical reactions resulting in the initiation of free radicals, a key stage of oxidative stress. Effects of substituents in the side chains and in the phenolic ring of hydroxylated phenols and biphenols, and the concentration were discussed