Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.110
A. Goncharova, E. Kolpak, Maria Yu. Vil’, Alina Abramova, E. Busko
The article explores modeling the development of ovarian cancer, the treatment of this oncologicaldisease in women, the assessment of the time to achieve remission, and the assessment of the time of the onset of relapse. The relevance of the study is that ovarian cancer is one of the most common cancers in women and has the highest mortality rate among all gynecological diseases. Modeling the process of the development of the disease makes it possible to better understand the mechanism of the development of the disease, as well as the time frame of the onset of each stage, as well as the assessment of the survival time. The aim of the work is to develop a model of an ovarian tumor. It is based on a model of competition between two types of cells: epithelial cells (normal cells) and tumor cells (dividing cells). The mathematical interpretation of the competition model is the Cauchy problem for a system of ordinary differential equations. Treatment is seen as the direct destruction of tumor cells by drugs. The behavior of solutions in the vicinity of stationary points is investigated by the eigenvalues of the Jacobi matrix of the right side of the equations. On the basis of this model, the distribution of conditional patients by four stages of the disease is proposed. Biochemical processes that stimulate the accelerated growth of the tumor cell population are modeled by a factor that allows tumor cells to gain an advantage in a competitive relationship with epithelial cells. The spatio-temporal dynamics of an ovarian tumor leads to a modification of the competition model due to the introduction of additional factors into it, taking into account the presence of increased nutrition of ovarian tumors, the exit of the tumor from the plane of the ovary, as well as the effect of treatment on tumor cells. The new model describes the interaction conditions with a system of second-order partial differential equations. The results of computer modeling demonstrate an assessment of the distribution of conditional patients by stages of the disease, the time of onset of relapse, the duration of remission, the obtained theoretical results of modeling are compared with the real data.
{"title":"Mathematical modeling of malignant ovarian tumors","authors":"A. Goncharova, E. Kolpak, Maria Yu. Vil’, Alina Abramova, E. Busko","doi":"10.21638/11701/spbu10.2022.110","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.110","url":null,"abstract":"The article explores modeling the development of ovarian cancer, the treatment of this oncologicaldisease in women, the assessment of the time to achieve remission, and the assessment of the time of the onset of relapse. The relevance of the study is that ovarian cancer is one of the most common cancers in women and has the highest mortality rate among all gynecological diseases. Modeling the process of the development of the disease makes it possible to better understand the mechanism of the development of the disease, as well as the time frame of the onset of each stage, as well as the assessment of the survival time. The aim of the work is to develop a model of an ovarian tumor. It is based on a model of competition between two types of cells: epithelial cells (normal cells) and tumor cells (dividing cells). The mathematical interpretation of the competition model is the Cauchy problem for a system of ordinary differential equations. Treatment is seen as the direct destruction of tumor cells by drugs. The behavior of solutions in the vicinity of stationary points is investigated by the eigenvalues of the Jacobi matrix of the right side of the equations. On the basis of this model, the distribution of conditional patients by four stages of the disease is proposed. Biochemical processes that stimulate the accelerated growth of the tumor cell population are modeled by a factor that allows tumor cells to gain an advantage in a competitive relationship with epithelial cells. The spatio-temporal dynamics of an ovarian tumor leads to a modification of the competition model due to the introduction of additional factors into it, taking into account the presence of increased nutrition of ovarian tumors, the exit of the tumor from the plane of the ovary, as well as the effect of treatment on tumor cells. The new model describes the interaction conditions with a system of second-order partial differential equations. The results of computer modeling demonstrate an assessment of the distribution of conditional patients by stages of the disease, the time of onset of relapse, the duration of remission, the obtained theoretical results of modeling are compared with the real data.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75906814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.104
D. Kuranov, T. Andreeva, M. Bedrina
A mathematical model is proposed for calculating the ionization potentials of molecules on the surface of dielectrics in order to quantify changes in the electronic characteristics of materials on a substrate. The semiconductor and photoelectronic properties of nanosystems based on phthalocyanine derivatives are determined by the electronic structure of molecules. Based on the zinc phthalocyaninate molecule ZnC32N8H16, model structures are constructed that increase this molecule by attaching benzene rings ZnC48N8H24, ZnC64N8H32 and a model simulating the film structure of Zn4C120N32 H48. Graphene was considered as a nanostructure modeling a fragment of a monomer lm. The ionization potentials of these compounds on the surface of magnesium oxide, sodium chloride and silicon are calculated. In the presence of a substrate, the ionization potentials of all nanostructures decrease, while the values of the surface ionization potentials remain fundamentally dierent in their magnitude for all compounds. The compound ZnC64N8H32 sprayed onto the surface exhibits the best photoelectronic properties, its surface ionization potential is comparable to graphene.
{"title":"Calculation of the ionization potential of zinc and graphene phthalocyaninates on the surface of dielectrics","authors":"D. Kuranov, T. Andreeva, M. Bedrina","doi":"10.21638/11701/spbu10.2022.104","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.104","url":null,"abstract":"A mathematical model is proposed for calculating the ionization potentials of molecules on the surface of dielectrics in order to quantify changes in the electronic characteristics of materials on a substrate. The semiconductor and photoelectronic properties of nanosystems based on phthalocyanine derivatives are determined by the electronic structure of molecules. Based on the zinc phthalocyaninate molecule ZnC32N8H16, model structures are constructed that increase this molecule by attaching benzene rings ZnC48N8H24, ZnC64N8H32 and a model simulating the film structure of Zn4C120N32 H48. Graphene was considered as a nanostructure modeling a fragment of a monomer lm. The ionization potentials of these compounds on the surface of magnesium oxide, sodium chloride and silicon are calculated. In the presence of a substrate, the ionization potentials of all nanostructures decrease, while the values of the surface ionization potentials remain fundamentally dierent in their magnitude for all compounds. The compound ZnC64N8H32 sprayed onto the surface exhibits the best photoelectronic properties, its surface ionization potential is comparable to graphene.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79092016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.311
A. P. Zhabko, V. Provotorov, S. Sergeev
This work is a natural continuation of the authors’ research on flow phenomena in the direction of increasing the dimensionality of the network-like domain of change of the space variable. The possibility of practical use of the analysis of the stability of operator-difference schemes to solve the issue of stability (stabilization) of wave phenomena in the engineering of the process of transferring continuous media through network-like carriers (water pipelines, gas and oil pipelines, industrial carriers of petroleum products) is shown. Namely, if the scheme is stable, then sufficiently small changes in the initial data of the mathematical model of the process imply small changes of the solution of the difference problem, i. e. in practice do not lead to undesirable aftereffects. If the schema is unstable, then small changes to the initial data can lead to arbitrarily large changes of the solution. In the process of exploitation of industrial constructions of network-like carriers, wave phenomena inevitably arise, the consequence of which are various kinds of instabilities that entail destruction of one nature or another. It is possible to avoid or essentially reduce such undesirable oscillations using the analysis of the stability properties of the mathematical model of the wave process. The obtained results are used in the algorithmically and digitalization of modern technological processes of the movement of fluid media and gases.
{"title":"Stability of operator-difference schemes with weights for the hyperbolic equation in the space of summable functions with carriers in the network-like domain","authors":"A. P. Zhabko, V. Provotorov, S. Sergeev","doi":"10.21638/11701/spbu10.2022.311","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.311","url":null,"abstract":"This work is a natural continuation of the authors’ research on flow phenomena in the direction of increasing the dimensionality of the network-like domain of change of the space variable. The possibility of practical use of the analysis of the stability of operator-difference schemes to solve the issue of stability (stabilization) of wave phenomena in the engineering of the process of transferring continuous media through network-like carriers (water pipelines, gas and oil pipelines, industrial carriers of petroleum products) is shown. Namely, if the scheme is stable, then sufficiently small changes in the initial data of the mathematical model of the process imply small changes of the solution of the difference problem, i. e. in practice do not lead to undesirable aftereffects. If the schema is unstable, then small changes to the initial data can lead to arbitrarily large changes of the solution. In the process of exploitation of industrial constructions of network-like carriers, wave phenomena inevitably arise, the consequence of which are various kinds of instabilities that entail destruction of one nature or another. It is possible to avoid or essentially reduce such undesirable oscillations using the analysis of the stability properties of the mathematical model of the wave process. The obtained results are used in the algorithmically and digitalization of modern technological processes of the movement of fluid media and gases.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84456952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.103
T. Kosovskaya, N. N. Kosovskii
The paper describes an approach to the formation of ontology based on descriptions of objects in terms of the predicate calculus language. With this approach, an object is represented as a set of its elements, on which a set of predicates is defined that defines the properties of these elements and the relationship between them. A description of an object is a conjunction of literals that are true on elements of an object. In the present work, ontology is understood as an oriented graph with descriptions of subsets as nodes and such that the elements of a set at the end of an oriented edge have the properties of the elements of the set at the beginning of this edge. Three settings of an ontology construction problem are considered: 1) all predicates are binary and subsets of the original set of objects are given; 2) all predicates are binary and it is required to find subsets of the original set; 3) among the predicates there are many-valued ones and subsets of the original set of objects are given. The main tool for construction such a description is to extract an elementary conjunction of literals of predicate formulas that is isomorphic to subformulas of some formulas. The definition of an isomorphism of elementary conjunctions of atomic predicate formulas is given. The method of ontology construction is formulated. An illustrative example is provided.
{"title":"Extraction of common properties of objects for creation of a logic ontology","authors":"T. Kosovskaya, N. N. Kosovskii","doi":"10.21638/11701/spbu10.2022.103","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.103","url":null,"abstract":"The paper describes an approach to the formation of ontology based on descriptions of objects in terms of the predicate calculus language. With this approach, an object is represented as a set of its elements, on which a set of predicates is defined that defines the properties of these elements and the relationship between them. A description of an object is a conjunction of literals that are true on elements of an object. In the present work, ontology is understood as an oriented graph with descriptions of subsets as nodes and such that the elements of a set at the end of an oriented edge have the properties of the elements of the set at the beginning of this edge. Three settings of an ontology construction problem are considered: 1) all predicates are binary and subsets of the original set of objects are given; 2) all predicates are binary and it is required to find subsets of the original set; 3) among the predicates there are many-valued ones and subsets of the original set of objects are given. The main tool for construction such a description is to extract an elementary conjunction of literals of predicate formulas that is isomorphic to subformulas of some formulas. The definition of an isomorphism of elementary conjunctions of atomic predicate formulas is given. The method of ontology construction is formulated. An illustrative example is provided.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85205352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.205
G. Kurbatova, E. Vinogradova, V. A. Klemeshev
An approach to a simplified calculation of the characteristics of a steady gas flow through a pipeline is proposed. In this approach, the pressure is calculated using an isothermal model; the temperature analysis is reduced to a cubic equation solving. A simple analytical gas leak point coordinate dependence on the pressure and gas flow values is obtained at outlet from the pipeline. The result of comparison of calculations for the general and simplified models of gas flow in pipelines is presented. A criterion has been determined for the fulfillment of which it is permissible to use a simplified approach to calculating the gas characteristics and the leak point coordinates. Using an example of practical interest, the high accuracy of the calculation according to the proposed approach of both pressure and temperature in the flow and the gas leak coordinate in the pipeline is demonstrated.
{"title":"ANALYSIS OF SIMPLIFIED GAS TRANSPORTATION MODELS. CALCULATION OF THE GAS LEAK LOCATION IN A PIPELINE","authors":"G. Kurbatova, E. Vinogradova, V. A. Klemeshev","doi":"10.21638/11701/spbu10.2022.205","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.205","url":null,"abstract":"An approach to a simplified calculation of the characteristics of a steady gas flow through a pipeline is proposed. In this approach, the pressure is calculated using an isothermal model; the temperature analysis is reduced to a cubic equation solving. A simple analytical gas leak point coordinate dependence on the pressure and gas flow values is obtained at outlet from the pipeline. The result of comparison of calculations for the general and simplified models of gas flow in pipelines is presented. A criterion has been determined for the fulfillment of which it is permissible to use a simplified approach to calculating the gas characteristics and the leak point coordinates. Using an example of practical interest, the high accuracy of the calculation according to the proposed approach of both pressure and temperature in the flow and the gas leak coordinate in the pipeline is demonstrated.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85148131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.301
K. Batenkov
Оne of the methods of analysis and synthesis of communication network structures is considered, based on the simplest approach to calculating the probability of connectivity - the method of iterating over the states of the network edges. Despite its significant drawback, which consists in the considerable complexity of the calculations carried out, it turns out to be quite in demand both at the stage of debugging new analysis methods and when performing the procedure of sequential synthesis of network structures. The proposed method of sequential synthesis can be presented in the form of stages, at each of which one or more edges (network elements) are added. An increase in the number of edges used leads to an increase in the number of variations of the connectivity functions of a graph with an added edge, and hence to an increase in the complexity of operations for calculating conditional probabilities. At the same time, such a complication makes it possible to more accurately solve the synthesis problem, since not in all situations the sequential addition of edges is equivalent to sorting through all possible alternatives. Both the described method of analyzing the structures of communication networks based on the enumeration of states and the synthesis method differ in the essential simplicity of the implementation of the processes of the calculations carried out. It is this circumstance that allows us to use these methods as reference. The accuracy of the calculations depends solely on the capabilities of hardware and software systems and is in no way limited directly by the method of sorting states. As a result, the calculation of the probability of connectivity with precision accuracy, which is typical for situations of comparative analysis of communication networks with the availability and survivability coefficients of individual network elements close to the threshold values, also turns out to be feasible on the basis of the methods considered.
{"title":"Аnalysis and synthesis of communication network structures by state enumeration method","authors":"K. Batenkov","doi":"10.21638/11701/spbu10.2022.301","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.301","url":null,"abstract":"Оne of the methods of analysis and synthesis of communication network structures is considered, based on the simplest approach to calculating the probability of connectivity - the method of iterating over the states of the network edges. Despite its significant drawback, which consists in the considerable complexity of the calculations carried out, it turns out to be quite in demand both at the stage of debugging new analysis methods and when performing the procedure of sequential synthesis of network structures. The proposed method of sequential synthesis can be presented in the form of stages, at each of which one or more edges (network elements) are added. An increase in the number of edges used leads to an increase in the number of variations of the connectivity functions of a graph with an added edge, and hence to an increase in the complexity of operations for calculating conditional probabilities. At the same time, such a complication makes it possible to more accurately solve the synthesis problem, since not in all situations the sequential addition of edges is equivalent to sorting through all possible alternatives. Both the described method of analyzing the structures of communication networks based on the enumeration of states and the synthesis method differ in the essential simplicity of the implementation of the processes of the calculations carried out. It is this circumstance that allows us to use these methods as reference. The accuracy of the calculations depends solely on the capabilities of hardware and software systems and is in no way limited directly by the method of sorting states. As a result, the calculation of the probability of connectivity with precision accuracy, which is typical for situations of comparative analysis of communication networks with the availability and survivability coefficients of individual network elements close to the threshold values, also turns out to be feasible on the basis of the methods considered.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82795033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.106
Sergey A. Strekopytov, M. Strekopytova
The convergence problem for non-autonomous systems of differential equations with a quasiperiodic right-hand side in an independent argument is considered. It is proposed to replace the consideration of the set of solutions of the system of differential equations under consideration by considering the movements of a dynamic quasi-periodic system generated by these differential equations. Necessary and sufficient conditions are obtained when a dynamic quasi-periodic system has the convergence property, and a proof is given.
{"title":"On the convergence of dynamic quasiperiodic systems","authors":"Sergey A. Strekopytov, M. Strekopytova","doi":"10.21638/11701/spbu10.2022.106","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.106","url":null,"abstract":"The convergence problem for non-autonomous systems of differential equations with a quasiperiodic right-hand side in an independent argument is considered. It is proposed to replace the consideration of the set of solutions of the system of differential equations under consideration by considering the movements of a dynamic quasi-periodic system generated by these differential equations. Necessary and sufficient conditions are obtained when a dynamic quasi-periodic system has the convergence property, and a proof is given.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77521474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.202
N. Moldovyan, A. Moldovyan
Structure of a 4-dimensional algebra and generating parameters of the hidden discrete logarithm problem the field GF'(p) is studied in connection with using it as algebraic support of the hidden discrete logarithm problem that is an attractive primitive of post-quantum signature schemes. It is shown that each invertible 4-dimensional vector that is not a scalar vector is included in a unique commutative group representing a subset of algebraic elements. Three types of commutative groups are contained in the algebra and formulas for computing the order and the number of groups are derived for each type. The obtained results are used to develop algorithms for generating parameters of digital signature schemes based on computational difficulty of the hidden logarithm problem.
{"title":"STRUCTURE OF A 4-DIMENSIONAL ALGEBRA AND GENERATING PARAMETERS OF THE HIDDEN DISCRETE LOGARITHM PROBLEM","authors":"N. Moldovyan, A. Moldovyan","doi":"10.21638/11701/spbu10.2022.202","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.202","url":null,"abstract":"Structure of a 4-dimensional algebra and generating parameters of the hidden discrete logarithm problem the field GF'(p) is studied in connection with using it as algebraic support of the hidden discrete logarithm problem that is an attractive primitive of post-quantum signature schemes. It is shown that each invertible 4-dimensional vector that is not a scalar vector is included in a unique commutative group representing a subset of algebraic elements. Three types of commutative groups are contained in the algebra and formulas for computing the order and the number of groups are derived for each type. The obtained results are used to develop algorithms for generating parameters of digital signature schemes based on computational difficulty of the hidden logarithm problem.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76456208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.116
D. Qi, V. Bure
This study is devoted to the application of methods of applied statistics to the study of investment attractiveness of regions of China. Methods of applied statistics are widely used in various engineering research, medicine, economics, sociology, astronomy, ecology, physics, information technology, etc. statistical tools is an integral part of the study. Data taken from the World Bank website and the China Statistical Yearbook. The main topic of this research is: What factors are most strongly associated with investment attractiveness in the economy of modern China? Such a study can only be carried out based on the analysis of economic data, especially in the conditions of the modern digital economy. Consequently, the problem under consideration belongs to the field of applied mathematics. First of all, need to choose a mathematical model and research method. This paper uses the method of regression analysis - one of the most important methods for analyzing economic data. Regression models are mathematical models built from empirical data. Observations (empirical data) are the numerical data on the level of investment in the regions of China, as well as the numerical values of various factors. For each year, a multiple regression model is built using the least squares method, its statistical significance is checked, statistically significant factors are selected (statistically significant coefficients for the factors correspond to them). Calculations are carried out in Excel and SPSS, using subroutines and. Mathematical functions, but at the same time, an algorithm for analyzing the initial data based on a stepwise regression algorithm has been developed, in which only one factor with the least significant coefficient (maximum p-value (t)) is discarded at each step and then an algorithm for choosing the most important factors for investment attractiveness was developed, the essence of this algorithm is that the regression models are compared for each year and how many times each factor was included in the model is calculated algorithms can be attributed to the application of methods informatics in this work. The choice of the most important factors that determine the level of investment attractiveness is made to solve the problem of managing the economy. Attracting investments is important for the effective development of every region, every city, every district. With the receipt of significant investments, it is possible to solve the problems of economic and social development. Determination of the most important factors will make it possible to most effectively solve the problem of managing the economic development of each region, each city, each district.
{"title":"Statistical analysis of investment attractiveness of China’s regions","authors":"D. Qi, V. Bure","doi":"10.21638/11701/spbu10.2022.116","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.116","url":null,"abstract":"This study is devoted to the application of methods of applied statistics to the study of investment attractiveness of regions of China. Methods of applied statistics are widely used in various engineering research, medicine, economics, sociology, astronomy, ecology, physics, information technology, etc. statistical tools is an integral part of the study. Data taken from the World Bank website and the China Statistical Yearbook. The main topic of this research is: What factors are most strongly associated with investment attractiveness in the economy of modern China? Such a study can only be carried out based on the analysis of economic data, especially in the conditions of the modern digital economy. Consequently, the problem under consideration belongs to the field of applied mathematics. First of all, need to choose a mathematical model and research method. This paper uses the method of regression analysis - one of the most important methods for analyzing economic data. Regression models are mathematical models built from empirical data. Observations (empirical data) are the numerical data on the level of investment in the regions of China, as well as the numerical values of various factors. For each year, a multiple regression model is built using the least squares method, its statistical significance is checked, statistically significant factors are selected (statistically significant coefficients for the factors correspond to them). Calculations are carried out in Excel and SPSS, using subroutines and. Mathematical functions, but at the same time, an algorithm for analyzing the initial data based on a stepwise regression algorithm has been developed, in which only one factor with the least significant coefficient (maximum p-value (t)) is discarded at each step and then an algorithm for choosing the most important factors for investment attractiveness was developed, the essence of this algorithm is that the regression models are compared for each year and how many times each factor was included in the model is calculated algorithms can be attributed to the application of methods informatics in this work. The choice of the most important factors that determine the level of investment attractiveness is made to solve the problem of managing the economy. Attracting investments is important for the effective development of every region, every city, every district. With the receipt of significant investments, it is possible to solve the problems of economic and social development. Determination of the most important factors will make it possible to most effectively solve the problem of managing the economic development of each region, each city, each district.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86093350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.21638/11701/spbu10.2022.201
S. Kuptsova, S. Y. Kuptsov
The nonlinear time-delay systems are considered and the limiting Behavior of their solutions is investigated. The case in which the solutions have a trivial equilibrium that may not be an invariant set of the system is studied. The junction of Lyapunov - Krasovskii and Razumikhin approaches is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.
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