Meandering of trajectories of polynomial vector fields in the affine n-space

We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in Rn and an affine hyperplane. The problem turns out to be closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives. This exposition constitutes an extended abstract of a forthcoming paper: only the basic steps are outlined here, with all technical details being either completely omitted or at best indicated

Hopf Term for a Two-Dimensional Electron Gas

In this Comment on the paper by W. Apel and Yu. A. Bychkov, cond-mat/9610040 and Phys. Rev. Lett. 78, 2188 (1997), we draw attention to our prior microscopic derivations of the Hopf term for various systems and to shortcomings of the Apel-Bychkov derivation. We explain how the value of the Hopt term prefactor $\Theta$ is expressed in terms of a topological invariant in the momentum space and the quantized Hall conductivity of the system. (See also related paper cond-mat/9703195)Comment: RevTeX, 1 page, no figure

Interacting two helical edge modes in quantum spin Hall systems

We study theoretically the two interacting one-dimensional helical modes at the edges of the quantum spin Hall systems. A new type of inter-edge correlated liquid (IECL) without the spin gap is found. This liquid shows the diverging density wave (DW) and superconductivity (SC) correlations much stronger than those of the spinfull electrons. Possible experimental observations are also discussed

Using the HACCP method in quality risk management in the production of oromucosal gel

Introduction. With the adoption in the EU of the regulatory document of the European Medicines Agency (European Medicines Agency) EMA / INS / GMP / 79766/2011 “Quality Risk Management (ICH Q9)”separate guidance was issued in Ukraine in 2011 - Instruction ST-N MOH 42-4.2: 2011 “Medicines. Quality Risk Management (ICH Q9)”. Pharmaceutical industry and regulatory bodies professionals can assess and manage risk using recognized risk management tools and / or internal techniques (e.g., standard working methods).Application of general principles and approaches of the Guideline “Medicines. Quality Risk Management (ICH Q9)”at the stage of pharmaceutical development, using appropriate risk management tools both in general to the manufacture of medicines and to individual processes is an effective measure of quality assurance for the developed medicinal product. The technology of the combined dental gel was developed taking into account its properties as a dispersed system, as well as the properties of the active and auxiliary substances that are part of it. In order to manage quality risks effectively, it is necessary to have data about the sustainability of the process. Critical process parameters that need to be managed or monitored to ensure the required quality of the drug should be identified and specified. Materials and methods of the research. The subject of the study was the technology and technological scheme of the production of a combined gel for the treatment of infectious diseases of the mucous membrane of the mouth and gums. Hazard Analysis and Critical Control Points (HACCP) were used to evaluate and manage risks in the manufacture of the new drug. The HACCP tool, the “Decision tree”, was used to establish critical control points. Results of the research and discussion. An expert group of experts conducted an analysis and evaluation of the danger of individual stages of the technological process and determination of the criticality of the controlled parameters. The group consisted of qualified specialists from the pharmaceutical development department, thefactoryworkshop for the production of soft medicines, the quality control department. Analysis of the technological scheme of production of combined dental, showed that almost all stages of the dental gel manufacturing process are critical and marked in grey. Using the tool “Decision tree”, we identified the critical control points of the technological process of gel production, and set the eligibility criteria. Risk factors were evaluated on the basis of two indicators: the likelihood of a hazard factor and the degree of risk created by that factor. The likelihood of a risk factor was as follows: unlikely, quitelikely, probably, very likely. The degree of risk was assessed on a ten-point scale. During the processing of the gel technology, certain critical control points were monitored with the aim of developing preventive and corrective actions in case of their fall outside the eligibility criteria. in the process of gel production, risk (physical factor) at the stages of metronidazole suspension preparation, preparation of gel base and gel directly is “Quite likely”. “Unlikely” occurrence of a dangerous factor at such stages as the weighing of active and auxiliary substances, the preparation of solutions and during the input control of raw materials. The risk level of each factor, ranging from 2 to 7 points, was determined and corrective and preventive actions were developed for all critical control points to prevent risks to the quality of the medicinal product. Conclusions. Based on the data obtained in the development of dental gel technology and using scientific knowledge and methodology of risk assessment by the method of HACCP, an analysis of technological scheme of its production was carried out. Process risks have been identified, critical control points have been identified and their allowed limits. For each control parameter, the probability of occurrence and the degree of risk were determined, and measures were proposed to prevent or eliminate the effects of the risk.DOI: 10.5281/zenodo.3885070

Oscillation of linear ordinary differential equations: on a theorem by A. Grigoriev

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients.Comment: 16 page

Дослідження напружено-деформованого стану циліндра з мікроструктурними перетвореннями за умов імпульсного навантаження

Axisymmetric dynamic problem of thermomechanical loading of a steel cylinder is considered. Volume strain caused by the microstructural transformations of the martensitic type under cooling solids as well as into consideration and dependence inelastic characteristics of material for multiphase state are taken. The thermomechanical nonlinear behavior of an isotropic material is described by unified flow model generalized for the case of multiphase material state. The problem is solved numerically by the implicit step-by-step time integration method, by the iterative method and by the finite element method. The investigation of the stress-strain state of an inelastic material with regard for the dependence of parameters of the flow model on the phase composition of a material is carried out by using of numerical simulation. We established that microstructural transformations significantly reduce residual inelastic strain and promote the appearance of compressive stresses. The results obtained in the work can be used in calculations of parameters of surface hardening technologies. Pages of the article in the issue: 176 - 179 Language of the article: UkrainianРозглядається осесиметрична задача про імпульсне термомеханічне навантаження сталевого циліндра. Враховуються об’ємні деформації, які супроводжують мікроструктурні перетворення мартенситного типу при охолодженні тіл, а також залежність непружних характеристик матеріалу від фазового складу. Термомеханічна поведінка ізотропного матеріалу описується моделлю течії Боднера-Партома. Задача розв’язується чисельно методом покрокового неявного інтегрування за часом, ітераційним методом та методом скінченних елементів. За допомогою чисельного моделювання проводиться дослідження напружено-деформованого стану за умов врахування залежності параметрів моделі від мікроструктури матеріалу. Встановлено, що мікроструктурні перетворення суттєво зменшують залишкові деформації та сприяють появі стискальних напружень. Отримані результати можуть бути використані в інженерних розрахунках на міцність елементів конструкцій, а також параметрів технологій поверхневого зміцнення