Pub Date : 2023-01-01DOI: 10.21638/11701/spbu10.2023.211
G. Rego, R. Voronov
The article is devoted to the problem of reactive navigation of a mobile robot with limited information about the environment. An algorithm for finding a path from source to the target with a minimum number of turns is described. The idea of the algorithm is based on the bug family of algorithms for reactive navigation. The mobile robot remembers the boundaries of obstacles and calculates the angle of rotation depending on the surrounding situation. The difference from bug algorithms is that the robot does not move “along the obstacle”, but turns only in a limited number of cases. The results of testing the algorithm on simulated polygons are presented. Models of fallen trees, stumps and swamps were considered as obstacles. The performance of the algorithm is evaluated by comparing the minimum possible number of turns with the number of turns in the path obtained using the algorithm.
{"title":"Dynamic path planning algorithm for autonomous mobile robot with a minimum number of turns in unknown environment","authors":"G. Rego, R. Voronov","doi":"10.21638/11701/spbu10.2023.211","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.211","url":null,"abstract":"The article is devoted to the problem of reactive navigation of a mobile robot with limited information about the environment. An algorithm for finding a path from source to the target with a minimum number of turns is described. The idea of the algorithm is based on the bug family of algorithms for reactive navigation. The mobile robot remembers the boundaries of obstacles and calculates the angle of rotation depending on the surrounding situation. The difference from bug algorithms is that the robot does not move “along the obstacle”, but turns only in a limited number of cases. The results of testing the algorithm on simulated polygons are presented. Models of fallen trees, stumps and swamps were considered as obstacles. The performance of the algorithm is evaluated by comparing the minimum possible number of turns with the number of turns in the path obtained using the algorithm.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84241607","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.110
A. Fominyh, V. Karelin, L. Polyakova
The article considers the problem of optimal control of an object described by a system of ordinary differential equations with a continuously differentiable right-hand side and with a nonsmooth (but only a quasidifferentiable) quality functional. The problem is in the Mayer form with either free or partially fixed right end. Piecewise-continuous and bounded controls are supposed to be admissible if they lie in some parallelepiped at any moment of time. The phase coordinates and controls are also subject to mixed pointwise constraints. Phase constraints are taken into account by introducing new variables with known boundary conditions into the system. The standard discretization of the original system and the parametrization of the control are carried out, theorems are given on the convergence of the solution of the discrete system obtained to the desired solution of the continuous problem. Further, in order to study the resulting discrete system, the apparatus of quasidifferential calculus is used and the method of the quasidifferential descent is applied. Examples illustrating the operation of the algorithm are given.
{"title":"Method for solving an optimal control problem in the Mayer form with a quasidifferentiable functional in the presence of phase constraints","authors":"A. Fominyh, V. Karelin, L. Polyakova","doi":"10.21638/11701/spbu10.2023.110","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.110","url":null,"abstract":"The article considers the problem of optimal control of an object described by a system of ordinary differential equations with a continuously differentiable right-hand side and with a nonsmooth (but only a quasidifferentiable) quality functional. The problem is in the Mayer form with either free or partially fixed right end. Piecewise-continuous and bounded controls are supposed to be admissible if they lie in some parallelepiped at any moment of time. The phase coordinates and controls are also subject to mixed pointwise constraints. Phase constraints are taken into account by introducing new variables with known boundary conditions into the system. The standard discretization of the original system and the parametrization of the control are carried out, theorems are given on the convergence of the solution of the discrete system obtained to the desired solution of the continuous problem. Further, in order to study the resulting discrete system, the apparatus of quasidifferential calculus is used and the method of the quasidifferential descent is applied. Examples illustrating the operation of the algorithm are given.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76169199","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 : 2023-01-01DOI: 10.21638/11701/spbu10.2023.204
A. V. Kvasnov, Anatoliy A. Baranenko, Evgeniy Y. Butyrsky, Uliana P. Zaranik
The principle of maximum entropy (ME) has a number of advantages that allow it to be used in machine learning. The density distribution of maximum entropy (WEO) requires solving the problem of calculus of variations on the a priori distribution, where the central tendency can be used as a parameter. In Lebesgue space, the central tendency is described by the generalized Gelder average. The paper shows the evolution of the density of the ME distribution depending on the given norm of the average. The minimum Kulback — Leibler divergence between the WEO and the a prior density is achieved at the harmonic mean, which is effective in reducing the dimensionality of the training sample. At the same time, this leads to a deterioration in the function of loss in the conditions of machine learning by precedents.
{"title":"On the influence of the cental trend on the nature of the density distribution of maximum entropy in machine learning","authors":"A. V. Kvasnov, Anatoliy A. Baranenko, Evgeniy Y. Butyrsky, Uliana P. Zaranik","doi":"10.21638/11701/spbu10.2023.204","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.204","url":null,"abstract":"The principle of maximum entropy (ME) has a number of advantages that allow it to be used in machine learning. The density distribution of maximum entropy (WEO) requires solving the problem of calculus of variations on the a priori distribution, where the central tendency can be used as a parameter. In Lebesgue space, the central tendency is described by the generalized Gelder average. The paper shows the evolution of the density of the ME distribution depending on the given norm of the average. The minimum Kulback — Leibler divergence between the WEO and the a prior density is achieved at the harmonic mean, which is effective in reducing the dimensionality of the training sample. At the same time, this leads to a deterioration in the function of loss in the conditions of machine learning by precedents.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"16 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81902209","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 : 2022-06-22DOI: 10.21638/11701/spbu10.2023.205
Almaz Mustafin, Aliya Kantarbayeva
Clearing functions (CFs), which express a mathematical relationship between the expected throughput of a production facility in a planning period and its workload (or work-inprogress, WIP) in that period have shown considerable promise for modeling WIP-dependent cycle times in production planning. While steady-state queueing models are commonly used to derive analytic expressions for CFs, the finite length of planning periods calls their validity into question. We apply a different approach to propose a mechanistic model for one-resource, one-product factory shop based on the analogy between the operation of machine and enzyme molecule. The model is reduced to a singularly perturbed system of two differential equations for slow (WIP) and fast (busy machines) variables, respectively. The analysis of this slow-fast system finds that CF is nothing but a result of the asymptotic expansion of the slow invariant manifold. The validity of CF is ultimately determined by how small is the parameter multiplying the derivative of the fast variable. It is shown that sufficiently small characteristic ratio ’working machines: WIP’ guarantees the applicability of CF approximation in unsteady-state operation.
{"title":"Clearing function in the context of the invariant manifold method","authors":"Almaz Mustafin, Aliya Kantarbayeva","doi":"10.21638/11701/spbu10.2023.205","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2023.205","url":null,"abstract":"Clearing functions (CFs), which express a mathematical relationship between the expected throughput of a production facility in a planning period and its workload (or work-inprogress, WIP) in that period have shown considerable promise for modeling WIP-dependent cycle times in production planning. While steady-state queueing models are commonly used to derive analytic expressions for CFs, the finite length of planning periods calls their validity into question. We apply a different approach to propose a mechanistic model for one-resource, one-product factory shop based on the analogy between the operation of machine and enzyme molecule. The model is reduced to a singularly perturbed system of two differential equations for slow (WIP) and fast (busy machines) variables, respectively. The analysis of this slow-fast system finds that CF is nothing but a result of the asymptotic expansion of the slow invariant manifold. The validity of CF is ultimately determined by how small is the parameter multiplying the derivative of the fast variable. It is shown that sufficiently small characteristic ratio ’working machines: WIP’ guarantees the applicability of CF approximation in unsteady-state operation.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"12 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87497215","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/spbu10.2022.414
E. Lezhnina, Gennady M. Khitrov, Elizaveta A. Kalinina, Ivan A. Kononov
In modern management, one of the most popular and effective approaches to organizing activities is the creation of temporary working groups. An important indicator is the effectiveness of such groups, which strongly depends on the internal structure of the working group and the relationship between team members. For the effective functioning of the group, it is necessary that the group consists of a leader and subordinates. The artificial appointment of a team leader often proves ineffective. The article solves the problem of dividing the team into working groups, taking into account the relationship between individual personalities. Two algorithms are proposed: the first one divides the team into separate groups of possible leaders and subordinates, the second one makes effective working groups. The effectiveness of the group is calculated based on the ee efficiency function, which takes into account interpersonal relationships. Practical and numerical experiments were carried out to verify the adequacy of the model.
{"title":"Working groups: Creation and management","authors":"E. Lezhnina, Gennady M. Khitrov, Elizaveta A. Kalinina, Ivan A. Kononov","doi":"10.21638/11701/spbu10.2022.414","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.414","url":null,"abstract":"In modern management, one of the most popular and effective approaches to organizing activities is the creation of temporary working groups. An important indicator is the effectiveness of such groups, which strongly depends on the internal structure of the working group and the relationship between team members. For the effective functioning of the group, it is necessary that the group consists of a leader and subordinates. The artificial appointment of a team leader often proves ineffective. The article solves the problem of dividing the team into working groups, taking into account the relationship between individual personalities. Two algorithms are proposed: the first one divides the team into separate groups of possible leaders and subordinates, the second one makes effective working groups. The effectiveness of the group is calculated based on the ee efficiency function, which takes into account interpersonal relationships. Practical and numerical experiments were carried out to verify the adequacy of the model.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"8 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89693249","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/spbu10.2022.304
A. Tur, O. Petrosian
In the paper we consider a class of the differential games with continuous updating with random information horizon. It is assumed that at each time instant, players have information about the game (motion equations and payoff functions) for a time interval with the length theta and as the time evolves information about the game updates. We first considered this type of games in 2019. Here we additionally assume that theta is a random variable. The subject of the current paper is definition of Nash equilibrium based solution concept and solution technique based on Hamilton—Jacobi—Bellman equations.
{"title":"Random information horizon for a class of differential games with continuous updating","authors":"A. Tur, O. Petrosian","doi":"10.21638/11701/spbu10.2022.304","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.304","url":null,"abstract":"In the paper we consider a class of the differential games with continuous updating with random information horizon. It is assumed that at each time instant, players have information about the game (motion equations and payoff functions) for a time interval with the length theta and as the time evolves information about the game updates. We first considered this type of games in 2019. Here we additionally assume that theta is a random variable. The subject of the current paper is definition of Nash equilibrium based solution concept and solution technique based on Hamilton—Jacobi—Bellman equations.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84940372","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/spbu10.2022.206
O. Mitrofanova, Eugenii P. Mitrofanov, Nataliya A. Bure
Thanks to the development of information technologies and computing resources, it became possible to obtain and process big data, including geospatial data. Most research in the field of precision farming is interdisciplinary in nature, with experimental field data used by disparate scientific groups. In this connection, it became necessary to develop a unified web-based system for storing, organizing, and exchanging experimental information between researchers. The first step in achieving this goal was to create a geospatial database. Since the system being developed in the future may require extensions, modifications, adjustments, integration into other projects, it seems appropriate to use the ontology to form the database structure. The most popular tools were used as the main tools: the ontology language OWL (Ontology Web Language), the Protege 5.5 development environment. The main initial information obtained in the course of experimental studies carried out at the biopolygon: weather data, agrochemical indicators (sampling of soil and plants with georeferencing), agrophysical parameters (humidity, electrical conductivity), remote sensing data. Based on the results of the analysis of the current state of research in the field of storage and systematization of experimental information in crop production, as well as a survey of ARI employees, a prototype of the database structure was formed based on the ontological approach. Nine parent classes were defined as the foundation: Field, Crop rotation - experience, Agrotechnology, Yield, Meteo, Ground samples, Orthophoto, Calendar, and Dictionary - units of measurement.
由于信息技术和计算资源的发展，获取和处理包括地理空间数据在内的大数据成为可能。精准农业领域的大多数研究本质上是跨学科的，不同的科学团体使用了实验现场的数据。在这方面，有必要开发一个统一的基于web的系统来存储、组织和交换研究人员之间的实验信息。实现这一目标的第一步是创建地理空间数据库。由于将来开发的系统可能需要扩展、修改、调整、集成到其他项目中，因此使用本体来形成数据库结构似乎是合适的。使用最流行的工具作为主要工具:本体语言OWL (ontology Web language)、Protege 5.5开发环境。在生物多边形进行的实验研究过程中获得的主要初步信息:天气数据、农业化学指标(土壤和植物的地理参照取样)、农业物理参数(湿度、电导率)、遥感数据。在分析作物生产实验信息存储与系统化研究现状的基础上，通过对ARI员工的调查，建立了基于本体论方法的数据库结构原型。9个父类被定义为基础:田地，作物轮作-经验，农业技术，产量，气象，地面样本，正射影像，日历和字典-测量单位。
{"title":"ONTOLOGICAL APPROACH APPLICATION TO THE DESIGN OF A GEOSPATIAL EXPERIMENTAL DATABASE FOR INFORMATION SUPPORT OF RESEARCH IN PRECISION AGRICULTURE","authors":"O. Mitrofanova, Eugenii P. Mitrofanov, Nataliya A. Bure","doi":"10.21638/11701/spbu10.2022.206","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.206","url":null,"abstract":"Thanks to the development of information technologies and computing resources, it became possible to obtain and process big data, including geospatial data. Most research in the field of precision farming is interdisciplinary in nature, with experimental field data used by disparate scientific groups. In this connection, it became necessary to develop a unified web-based system for storing, organizing, and exchanging experimental information between researchers. The first step in achieving this goal was to create a geospatial database. Since the system being developed in the future may require extensions, modifications, adjustments, integration into other projects, it seems appropriate to use the ontology to form the database structure. The most popular tools were used as the main tools: the ontology language OWL (Ontology Web Language), the Protege 5.5 development environment. The main initial information obtained in the course of experimental studies carried out at the biopolygon: weather data, agrochemical indicators (sampling of soil and plants with georeferencing), agrophysical parameters (humidity, electrical conductivity), remote sensing data. Based on the results of the analysis of the current state of research in the field of storage and systematization of experimental information in crop production, as well as a survey of ARI employees, a prototype of the database structure was formed based on the ontological approach. Nine parent classes were defined as the foundation: Field, Crop rotation - experience, Agrotechnology, Yield, Meteo, Ground samples, Orthophoto, Calendar, and Dictionary - units of measurement.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88302607","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/spbu10.2022.408
L. Polyakova
For an arbitrary convex function, using the infimal convolution operation, a family of continuously differentiable convex functions approximating it is constructed. The constructed approximating family of smooth convex functions Kuratowski converges to the function under consideration. If the domain of the considered function is compact, then such smooth convex approximations are uniform in the Chebyshev metric. The approximation of a convex set by a family of smooth convex sets is also considered.
{"title":"Smooth approximations of nonsmooth convex functions","authors":"L. Polyakova","doi":"10.21638/11701/spbu10.2022.408","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2022.408","url":null,"abstract":"For an arbitrary convex function, using the infimal convolution operation, a family of continuously differentiable convex functions approximating it is constructed. The constructed approximating family of smooth convex functions Kuratowski converges to the function under consideration. If the domain of the considered function is compact, then such smooth convex approximations are uniform in the Chebyshev metric. The approximation of a convex set by a family of smooth convex sets is also considered.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89517350","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":"41 1","pages":""},"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/spbu10.2022.104
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":"8 1","pages":""},"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}
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