Numerical methods for construction reachability sets of dynamical systems

The research is devoted to the problem of reachability sets construction and representation in a control problem of a dynamical system. The paper discusses two numerical methods for construction reachability sets of dynamical systems. These methods differ in the way of representations of the reachability sets. The first method is oriented on solution of the control problem on the plane and connected with a representation of sets in the form of polygons. The second one is connected with a pixel representation of sets in the m-dimensional Euclidian space and simplicial complexes. © 2012 American Institute of Physics

CONTROL SYSTEM DEPENDING ON A PARAMETER

A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given

Assessment of the Role of Regional Taxes in the Dynamics of Budget Revenues of the Irkutsk Region: Modern Realities of Subsidization

The relevance of studying the dynamics of regional tax revenues to the regional budget is conditioned by the need to analyze the budgetary and tax potentials of the Irkutsk region in the modern period, assess budgetary independence (dependence) on federal assistance, to determine the further development potential of this region. The purpose of the study is to establish the role of regional taxes in the formation of the regional budget of the Irkutsk region at the present stage of development. To achieve this goal, an analysis was made of the receipt of tax and non-tax revenues of the regional budget for the period from 2016 to 2021. Both general scientific methods (analysis, synthesis, classification) and special ones (method of economic analysis, statistical-economic method) were used. The general structure and dynamics of tax and non-tax revenues of the subject is shown; analyzed income from regional taxes for the specified period. The indicators characterizing the share of regional taxes in the total amount of regional budget revenues, as well as the volume of gratuitous receipts are given. It is conclusions are drawn that the tax on the property of organizations is the fundamental one, the share of which in the total amount of regional taxes on average for the period under study is 86%. At the same time, the share of regional taxes in the total volume of regional budget revenues is small (11.8% in the pre-crisis period from 2016 to 2018 and 8.1% in 2019–2021). The impact of the crises of 2019 and 2020 is shown on income dynamics. It was determined that in 2021, despite the positive dynamics in most indicators, the volume of regional taxes remained at the level of 2018, and the level of subsidization of the region has increased significantly over the past 3 years

Remission in schizophrenia: results of cross-sectional with 6-month follow-up period and 1-year observational therapeutic studies in an outpatient population

<p>Abstract</p> <p>Background</p> <p>A standardized definition of remission criteria in schizophrenia was proposed by the International group of NC Andreasen in 2005 (low symptom threshold for the eight core Positive and Negative Syndrome Scale (PANSS) symptoms for at least 6 consecutive months).</p> <p>Methods</p> <p>A cross-sectional study of remission rate, using a 6-month follow-up to assess symptomatic stability, was conducted in two healthcare districts (first and second) of an outpatient psychiatric service in Moscow. The key inclusion criteria were outpatients with an <it>International Classification of Diseases</it>, 10th edition (ICD-10) diagnosis of schizophrenia or schizoaffective disorder. Remission was assessed using modern criteria (severity and time criteria), PANSS and Global Assessment of Functioning (GAF). Patients who were stable but did not satisfied the symptomatic criteria were included in a further 1-year observational study, with the first group (first district) receiving risperidone (long-acting, injectable) (RLAI) and the second group (second district) continuing to receiving routine treatment. Symptoms were assessed with PANSS, social functioning with the personal and social performance scale, compliance with rating of medication influences scale, and extrapyramidal side effects with the Simpson-Angus scale.</p> <p>Results</p> <p>Only 64 (31.5%) of 203 outpatients met the criteria for symptomatic remission in the cross-sectional study, but at the end of the 6-month follow-up period, 158 (77.8%) were stable (irrespective of remission status). Among these only 53 (26.1%) patients fulfilled the remission criteria. The observational study had 42 stable patients in the RLAI group and 35 in the routine treatment group: 19.0% in the RLAI group and 5.7% in the control group met remission criteria after 12 months of therapy. Furthermore, reduction of PANSS total and subscale scores, as well as improvement in social functioning, was more significant in the first group.</p> <p>Conclusions</p> <p>Only around one-quarter of our outpatient schizophrenic population met full remission criteria. Use of RLAI gave a better remission rate than achieved in standard care with routine treatment. Criteria for remission should take into account clinical course and functioning to support clinical care.</p

An Approach Problem with an Unknown Parameter and Inaccurately Measured Motion of the System

A control system with an unknown constant parameter is considered on a finite time interval. The actual value of the parameter in this control system is unknown to the person controlling the system at the moment when the systems starts moving. Finding an unknown parameter is made by applying a trial control to the control system for a short period of time along with monitoring the corresponding change in the movement of the system. After finding the approximate determination of the unknown parameter we can construct resolving control in the usual way, but we must take into account the additional error associated with the process of approximate determination of the parameter. In this paper, we investigate the influence of the error of measuring phase variable on the accuracy of unknown parameter recovery. © 201

К оценке хаусдорфова отклонения выпуклых многоугольников в R2 от их геометрической разности с кругами

We study a problem concerning the estimation of the Hausdorff deviation of convex polygons in R2 from their geometric difference with circles of sufficiently small radius. Problems with such a subject, in which not only convex polygons but also convex compacts in the Euclidean space Rn are considered, arise in various fields of mathematics and, in particular, in the theory of differential games, control theory, convex analysis. Estimates of Hausdorff deviations of convex compact sets in Rn in their geometric difference with closed balls in Rn are presented in the works of L.S. Pontryagin, his staff and colleagues. These estimates are very important in deriving an estimate for the mismatch of the alternating Pontryagin's integral in linear differential games of pursuit and alternating sums. Similar estimates turn out to be useful in deriving an estimate for the mismatch of the attainability sets of nonlinear control systems in Rn and the sets approximating them. The paper considers a specific convex heptagon in R2. To study the geometry of this heptagon, we introduce the concept of a wedge in R2. On the basis of this notion, we obtain an upper bound for the Hausdorff deviation of a heptagon from its geometric difference with the disc in R2 of sufficiently small radius. © 2020 Udmurt State University. All rights reserved

Control Systems Depending on a Parameter

A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given.This research was supported by the Russian Science Foundation (project no. 19-11-00105)

Orbitally induced hierarchy of exchange interactions in zigzag antiferromagnetic state of honeycomb silver delafossite Ag3Co2SbO6

We report the revised crystal structure, static and dynamic magnetic properties of quasi-two dimensional honeycomb-lattice silver delafossite Ag3Co2SbO6. The magnetic susceptibility and specific heat data are consistent with the onset of antiferromagnetic long range order at low temperatures with N\'eel temperature TN ~ 21.2 K. In addition, the magnetization curves revealed a field-induced (spin-flop type) transition below TN in moderate magnetic fields. The GGA+U calculations show the importance of the orbital degrees of freedom, which maintain a hierarchy of exchange interaction in the system. The strongest antiferromagnetic exchange coupling was found in the shortest Co-Co pairs and is due to direct and superexchange interactions between the half-filled xz+yz orbitals pointing directly to each other. The other four out of six nearest neighbor exchanges within the cobalt hexagon are suppressed, since for these bonds active half-filled orbitals turned out to be parallel and do not overlap. The electron spin resonance (ESR) spectra reveal a Gaussian shape line attributed to Co2+ ion in octahedral coordination with average effective g-factor g=2.3+/-0.1 at room temperature and shows strong divergence of ESR parameters below 120 K, which imply an extended region of short-range correlations. Based on the results of magnetic and thermodynamic studies in applied fields, we propose the magnetic phase diagram for the new honeycomb-lattice delafossite