Mathematical Support Research Articles

Spatial visualization and measurement of area: A case study in spatialized mathematics instruction

The purpose of this study was to explore the influence of spatial visualization skills when students solve area tasks. Spatial visualization is closely related to mathematics achievement, but little is known about how these skills link to task success. We examined middle school students’ representations and solutions to area problems (both non-metric and metric) through qualitative and quantitative task analysis. Task solutions were analyzed as a function of spatial visualization skills and links were made between student solutions on tasks with different goals (i.e., non-metric and metric). Findings suggest that strong spatial visualizers solved the tasks with relative ease, with evidence for conceptual and procedural understanding. By contrast, Low and Average Spatial students more frequently produced errors due to failure to correctly determine linear measurements or apply appropriate formula, despite adequate procedural knowledge. A novel finding was the facilitating role of spatial skills in the link between metric task representation and success in determining a solution. From a teaching and learning perspective, these results highlight the need to connect emergent spatial skills with mathematical content and support students to develop conceptual understanding in parallel with procedural competence.

Stepwise Optimization Method of Group Control Strategy Applied to Chiller Room in Cooling Season

Central air-conditioning systems account for the largest share of energy consumption in public buildings, wherein the chiller room is the main source. The current empirical strategies of chiller room group control have difficulty realizing integrity, timeliness, and equipment adjustment accuracy and lead to energy wastage. Therefore, the operation strategy optimization model is of great value for achieving energy savings. This study proposed a stepwise optimization method for central air-conditioning systems, which is divided into the chilled side (the chiller and chilled water pump) and the cooling side (the chiller, cooling water pump, and cooling tower). The optimal points of the two sides are calculated sequentially and integrated as the global optimization result. To construct the stepwise optimization model, mathematical power models of the equipment in use were established to provide mathematical support for objective functions, and a short-term load prediction model with a matching optimization step size was established for energy constraints. The TRNSYS simulation model was developed to verify the energy-saving effects of the stepwise optimization model according to the energy-saving rates of 6.41% and 13.56% attained in both cases. The stepwise optimization strategy can more effectively guide practical applications and provide another way of thinking with respect to the group control optimization of chiller rooms in public buildings.

Local Adaptiveness of Mixed Higher Order Partial Differential Equations and Its Application in Image Denoising

Background: Image denoising methods based on partial differential equations have attracted much attention due to their "infinite" local adaptation capabilities, high flexibility, and strong mathematical theoretical support. Methods: This paper proposes a mixed higher order partial differential equation denoising model for the step effect caused by the second-order denoising model and the edge blur caused by the fourth-order denoising model. The model combines the second-order and fourth-order terms based on the relationship between the variational energy minimization and the partial differential equations. The fourth-order term is used to remove noise in the uniform area of the image to avoid the step effect, and the second-order term is used at the edge to avoid boundary blur. Results: Theoretical analysis and numerical experiment results show that the proposed model has weak solutions and can effectively avoid the step effect and maintain the edge. Conclusion: The image denoising results of the model are better than those of other improved denoising models in subjective effect, and objective evaluation indicators, such as SNR, PSNR, and MSSIM.

Hybrid Condition Monitoring System for Power Transformer Fault Diagnosis

The important parts of a transformer, such as the core, windings, and insulation materials, are in the oil-filled tank. It is difficult to detect faults in these materials in a closed area. Dissolved Gas Analysis (DGA)-based fault diagnosis methods predict a fault that may occur in the transformer and take the necessary precautions before the fault grows. Although these fault diagnosis methods have an accuracy of over 95%, their validity is controversial since limited data are used in the studies. The success rates and reliability of fault diagnosis methods in transformers, one of the most important pieces of power systems equipment, should be increased. In this study, a hybrid fault diagnosis system is designed using DGA-based methods and Fuzzy Logic. A mathematical approach and support vector machines (SVMs) were used as decision-making methods in the hybrid fault diagnosis systems. The results of tests performed with 317 real fault data sets relating to transformers showed accuracy of 95.58% using a mathematical approach and 96.23% using SVMs.

Short‐time wind speed prediction based on Legendre multi‐wavelet neural network

AbstractAs one of the most widespread renewable energy sources, wind energy is now an important part of the power system. Accurate and appropriate wind speed forecasting has an essential impact on wind energy utilisation. However, due to the stochastic and uncertain nature of wind energy, more accurate forecasting is necessary for its more stable and safer utilisation. This paper proposes a Legendre multiwavelet‐based neural network model for non‐linear wind speed prediction. It combines the excellent properties of Legendre multi‐wavelets with the self‐learning capability of neural networks, which has rigorous mathematical theory support. It learns input‐output data pairs and shares weights within divided subintervals, which can greatly reduce computing costs. We explore the effectiveness of Legendre multi‐wavelets as an activation function. Meanwhile, it is successfully being applied to wind speed prediction. In addition, the application of Legendre multi‐wavelet neural networks in a hybrid model in decomposition‐reconstruction mode to wind speed prediction problems is also discussed. Numerical results on real data sets show that the proposed model is able to achieve optimal performance and high prediction accuracy. In particular, the model shows a more stable performance in multi‐step prediction, illustrating its superiority.

Mathematical, algorithmic and software support of synphase detection of radio signals in electronic communication networks with noises

Mathematical (radio signal model as a periodically correlated stochastic process and synphase method of its processing) and algorithmic support for synphase detection of stochastic-periodic radio signals in electronic communication networks with noise by calculating new detection indicators in the form of correlation components, which ensure effective making a decision regarding the presence or the absence of a useful radio signal in obstacles of different power. For a more detailed assessment of the calculated indicators of radio signal detection in the form of correlation components, were used averaged estimates. Software for synphase detection of radio signals in electronic communication networks with a graphical user interface is implemented in the Matlab environment. The process of synphase detection of radio signals in electronic communication networks with noise was investigated and the effectiveness of the application of new detection indicators was ascertained.

Mathematical support and software systems for spare parts management of grain harvesting machinery

Agricultural production is characterized by the seasonality of technological operations, the ability to carry out which in a strictly set time depends on many factors of the external environment and the reliability of agricultural machinery. The harvest of grain and other crops by combines occupies a special place among field works. Operative carrying out of these works without down time of the grain-harvesting techniques provides the minimum losses of the agricultural production. It is possible to minimize downtime of harvesters due to technical reasons if the enterprise has at its warehouse a seasonal reserve of spare parts that are in great demand during harvesting works. The methods of reserve calculation should consider not only the reliability of some harvester parts, but the cost damage of harvester downtime and extra costs of spare parts purchase and storage. With such a large number of external factors, traditional methods are difficult to calculate. With the development of computer technology, the methods of evolutionary calculations have been widely used, in particular, genetic algorithms that allow creating self-adjusting models capable of analysing the examined indicators for the past years, reacting to the changes of current external conditions, and making short-term forecasts of the values of optimised variables. The purpose of this research was to develop a genetic algorithm and software that will enable us to meet the seasonal demand for spare parts from combine harvesters. The software allowed us to identify 66 of the most in-demand items out of 2800 warehouse items that should be reserved for the season of harvesting crops. The efficiency of the proposed solutions is proved by the reduction of the downtime of combines due to technical reasons by 37% and the increase of their shift productivity by 11.4%; at the same time, the combine reliability index, the operational readiness factor, increases by 4.38%.

Применение методов планирования эксперимента в экспертных процедурах для машинного обучения модели распределения ресурсов при ликвидации пожара

Introduction. Intellectualization of control systems, including decision support systems, is an urgent need in the field of fire management. There are various types of support for decision makers. The paper focuses on mathematical and referential support, which makes it possible, on the basis of machine-learned optimization models, to prepare for the decision maker a set of suboptimal solutions consistent with his system of preferences. As a basis for the distribution of limited resources of fire and rescue units with simultaneous calls, a transport model is used, the parameters of the payoff function of which are trained on a sample of retrospective data formed with the participation of an experienced decision maker. To select solutions, expert procedures are used that are optimized by experiment planning methods, which can significantly reduce the time to prepare a decision without losing its quality, which makes the study relevant. Purpose of research. The purpose of the article is to construct and illustrate algorithms for applying the principles of optimal design of an experiment in the procedures for expert evaluation of options for distributing homogeneous resources of fire and rescue units over simultaneous calls. Methods. Methods of optimization, expert evaluation, machine learning of optimization models, simulation modeling, experiment planning were used. Results and discussion. The proposed technology for accelerating expert procedures for choosing the optimal distribution of homogeneous resources of fire and rescue units for simultaneous calls based on the principles of optimal planning of the experiment is illustrated by the example of two fire and rescue units and three calls. This example shows the effect of reducing the number of necessary assessments performed by decision makers by more than 70 %. In the case of distribution of different types of resources for each of them, a separate procedure should be built, similar to that described in this article. Conclusion. The results of a study of the application of the principles of optimal design of an experiment to speed up expert procedures for choosing by a decision maker the best option for distributing limited resources of fire and rescue units between simultaneous calls are presented. The proposed algorithm seems appropriate to be included in the expert system for supporting the management of fires. Keywords: fire and rescue unit; simultaneous calls; resources; transportation task; expert assessments; experiment planning; decision maker.

Evaluation of the Allocation of Public Resources Destined to the Fight against COVID-19 in the Brazilian Regions Using Data Envelopment Analysis (DEA)

This work presents an exploratory analysis concerning the understand of which Brazilian states have proven efficient in combating the Covid-19 pandemic, based on the treasury provided to them by the federal government, along with the understand of the association between input and output variables. As mathematical modeling support, the Data Envelopment Analysis (DEA) methodology is used as aid in the exploratory analysis. In this scenario, the states were analyzing based on the data of the treasury provided in the portal transparency of the federal government as well as the data of contamination and deaths available in the site informing health also of the government. The results show that with the CCR model, seven states are efficient while eleven are exposed in the BCC model. After the reduction in the number of inputs and outputs, the BCC model showed a decrease in the number of efficient states, being seven the new number to demonstrate an increase in inefficiency aspects.

СПЕКТРАЛЬНЫЙ АНАЛИЗ ИНФОРМАЦИОННОЙ СИСТЕМЫ

To monitor physical processes in real time, a fast Fourier transform (FFT) algorithm is widely used, which allows spectral analysis of data. The article discusses the FFT algorithm, with which you can estimate the information parameters of the harmonic signal. The data is extracted using a recursive filter satisfying the Riccati equation. The algorithm is implemented in the Wolfram Mathematica software environment. Using this algorithm reduces the amount of calculations while maintaining the required accuracy. The article also presents the results of monitoring students of technical areas, during the training of which information technologies were used. The professional skills gained during the training allow graduates of technical areas to solve applied engineering problems, to develop mathematical support for projects.

STRUCTURE OF THE COMPUTER COMPLEX FOR CALCULATING THE STRENGTH OF PRISMATIC BODIES BASED ON THE SEMI-ANALYTIC METHOD OF FINITE ELEMENTS

One of the main and responsible stages of creating an apparatus for numerical analysis of structures using the finite element method is its implementation in the form of a set of programs. The principles of complex construction should take into account modern requirements for strength calculation software in modern calculation complexes. Among them, first of all, automation of the main stages of the computing process, rational use of the resources of the operating and external memory of storage devices, non-closedness in relation to the classes of problems to be solved, algorithms for the task of input data, the method of discretization and solution of systems of equations and etc. In addition, the structure of the programs should take into account the specifics of the semi-analytical method of finite elements, for which such a large experience of creating developed systems of mathematical support for the search of spatial structures has not yet been accumulated, as when using the traditional version of FEM. Considerable experience in solving finite element mechanics problems, accumulated over the past decades, has been reflected in a number of industrial commercial software complexes of domestic (LIRA, SCAD) and foreign (ANSYS, Nastran, ABAQUS) production. The developed finite element base of these software complexes allows you to obtain solutions to a wide range of problems of the mechanics of a deformable rigid body for objects of different dimensions, including for massive spatial bodies, and convenient means of input-output of information and processing of the obtained results make them very accessible to a wide circles of users and allow to display the obtained results with the maximum degree of visibility. There are also object-oriented complexes created at manufacturing enterprises and research institutes, for example at the Institute of Strength Problems of the National Academy of Sciences of Ukraine, at the Dnipropetrovsk National University. The conducted research will determine the most optimal ways of solving the listed problems from the point of view of computing costs and complexity of implementation, as well as outline the circle of unsolved issues.

Аналіз моделей процесів позаагрегатного оброблення чавуну

The aim of this paper is to perform a generalized analysis of studies on modeling the processes of out-of-furnace treatment of cast iron. Mathematical models are classified according to the basic principles of modeling. A description of different models based on different principles is given, depending on their type and the differences between them. A more detailed analysis of some of the fundamental models and expressions obtained in their construction is carried out. An example of models built on experimental data is given. Neural network models consist of artificial neurons that are connected to each other by means of connecting weights, i.e., model parameters, in the form of layers. Neurons are a set of mathematical functions that modify the input data to obtain an estimate of the desired result. A large number of network parameters makes training a neural network a cumbersome computational process. The large number of network connection weights that need to be optimized when training such models usually requires a large amount of input data. The paper presents domestic achievements in the construction of mathematical models of the out-of-furnace iron treatment process. The principles of creating an integrated database that summarizes information on the parameters of various technologies for desulphurization of cast iron, including the developed system unit of the information retrieval system, are described; the concept of an expert system for making decisions on process control and selection of a rational technology for out-of-furnace desulphurization of cast iron is developed; the variant of the developed information and mathematical support of the expert system with the module for out-of-furnace treatment of cast iron with granular magnesium and coinjection of magnesium and lime is described; the results of the study are presented. The paper describes the models devoted to numerical and physical modeling of the phenomena that occur in the ladle during injection, as well as to the study of the regularities of the gas-powder flow.

МАТЕМАТИЧНА МОДЕЛЬ ВЗАЄМОВІДНОСИН СИСТЕМИ КЕРУВАННЯ ІНФОРМАЦІЙНОЮ БЕЗПЕКОЮ

An effective solution to the problems of analysis and synthesis of information security management systems can not be provided by simple ways of simply describing their behavior in different conditions - systems engineering solves problems that require quantitative evaluation of characteristics. Such data, obtained experimentally or by mathematical modeling, should reveal the properties of information security management systems. The main one is efficiency, which means the degree of compliance of the results of information protection to the goal. The latter, depending on the resources available, the knowledge of developers and other factors, can be achieved to one degree or another, and there are alternative ways to implement it. In a number of publications the authors propose the basics of the categorical apparatus of set theory, which allows to explain the relationship between sets of threats and sets of information protection system, which allows to build different mathematical models to analyze information exchange systems in critical application systems. At present, the creation of information security management systems is not possible without research and generalization of world experience in building information systems and their constituent subsystems, one of the key of which are information protection and intrusion prevention systems. Components of the process of attacking the mechanisms of protection and blocking or destruction of cyber threats themselves are components of the mathematical support of such systems. The basis of such models is the mathematical apparatus, which should ensure the adequacy of modeling of information security processes for any conditions of cyber threats. When defining the mathematical apparatus, it is necessary to clearly understand how certain sets of cyber threats are built, and how the sets of cyber threat sets, sets of security system elements and sets of cyber attack detection systems, which should control the correctness of the information security process. The article analyzes various options for building models of information security management system and creates a mathematical model that takes into account the internal relationships of different subsets of components of the information security system under the influence of cyber threats.

IMPLEMENTATION OF STRENGTH CALCULATION SOFTWARE BASED ON THE SEMI-ANALYTICAL METHOD OF FINITE ELEMENTS

One of the main and responsible stages of creating an apparatus for numerical analysis of structures using the finite element method is its implementation in the form of a set of programs. The principles of complex construction should take into account modern requirements for strength calculation software in modern calculation complexes. Among them, first of all, automation of the main stages of the computing process, rational use of the resources of the operating and external memory of storage devices, non-closedness in relation to the classes of problems to be solved, algorithms for the task of input data, the method of discretization and solution of systems of equations and etc. In addition, the structure of the programs should take into account the specifics of the semi-analytical method of finite elements, for which such a large experience of creating developed systems of mathematical support for the search of spatial structures has not yet been accumulated, as when using the traditional version of FEM. Considerable experience in solving finite element mechanics problems, accumulated over the past decades, has been reflected in a number of industrial commercial software complexes of domestic (LIRA, SCAD) and foreign (ANSYS, Nastran, ABAQUS) production. The developed finite element base of these software complexes allows you to obtain solutions to a wide range of problems of the mechanics of a deformable rigid body for objects of different dimensions, including for massive spatial bodies, and convenient means of input-output of information and processing of the obtained results make them very accessible to a wide circles of users and allow to display the obtained results with the maximum degree of visibility. There are also object-oriented complexes created at manufacturing enterprises and research institutes, for example at the Institute of Strength Problems of the National Academy of Sciences of Ukraine, at the Dnipropetrovsk National University.
 The conducted research will determine the most optimal ways of solving the listed problems from the point of view of computing costs and complexity of implementation, as well as outline the circle of unsolved issues.

КОНЦЕПЦИЯ МЕДИЦИНСКОЙ ИНФОРМАЦИОННОЙ СИСТЕМЫ ДЛЯ РЕШЕНИЯ ЗАДАЧ ДИАГНОСТИКИ ЗАБОЛЕВАНИЙ НА ОСНОВЕ ВЕРИФИКАЦИИ ФРАГМЕНТОВ МЕДИЦИНСКИХ БИОЛОГИЧЕСКИХ ОБЪЕКТОВ

This article offers one of the variants of the concept of developing and implementing the synthesisof MIS from the perspective of a systematic approach, which is designed to solve the problems of diagnosingdiseases through the application and development of a methodology for verifying the state offragments of biological objects using computed tomographic images and using statistical parameters forthis (expectation, variance, histogram, coefficient of variation, autocorrelation matrix, correlation coefficient) for quantitative assessment of the conditions of the frontal or maxillary sinus inotolaryngological diseases, chest organs in bronchopulmonary diseases, bone tissues and their identificationin accordance with the class of pathologies in the diagnosis of the patient in automatic mode byradiographic (tomographic) images. A variant of the implementation of MIS for the diagnosis and evaluationof the results of medical research is proposed, built on a modular principle based on the technologiesof Intranet and Internet networks using standard data transmission protocols, audio-video information,graphic information of a medical nature and including a subsystem of technical support, a subsystemof mathematical support, a subsystem of software, a subsystem of information support, a subsystemof organizational support, information security subsystem, subsystem of methodological supportand support. It is pointed out the current state of development of medical diagnostic equipment, theequipment of which medical institutions of the country and its non-operational accessibility to the populationcontributed to and led to the emergence and active development of new directions in the field ofradiation diagnostics, which include: digital and film radiography, computed tomography, magneticresonance imaging. A brief analysis of the implementation of mathematical models of diagnostic methodsimplemented by software for the functioning of the decision support subsystem of the medicalautomated information system is given. Examples of practical implementation of software and informationsupport for verification methods of medical objects in the form of screen forms for workingwith fragments of the object under study and the results of the analysis of radiographic images areshown. This makes it possible to increase the efficiency, accuracy of verification of the state of medicalbiological objects, the reliability of the disease diagnosis process. The scientific novelty, the resultsof the approbation of the material presented in the article at international, All-Russian conferences,scientific journals are shown.

Identifying and Negotiating Productive Instructional Improvement Goals in One-on-One Mathematics Coaching

A major affordance of one-on-one mathematics coaching is its potential to provide individualized, contextualized support for mathematics teachers’ learning. Coaches can adjust their work to individual teachers by focusing on instructional improvement goals that take account of teachers’ current knowledge, practice, and classroom contexts. It is, however, essential that coaches and teachers work to attain productive instructional improvement goals that are both feasible for teachers to attain and likely to result in immediate improvements in students’ learning, if attained. In this article, we describe how coaches can identify productive goals for individual teachers and then, on that basis, negotiate goals successfully with teachers, thereby supporting teachers in seeing productive goals as worthwhile. By describing these two processes, we further clarify the forms of coaching-specific expertise central to effective one-on-one mathematics coaching.

Software and mathematical support for the calculation of production plans of a shipbuilding enterprise

Software and mathematical support for the calculation of production plans of a shipbuilding enterprise

SOFTWARE AND HARDWARE STAND AS A MODERN TOOL FOR TEACHING STUDENTS TO CONFIGURE WIRELESS NETWORKS

Goal. Theoretical justification and development of a software and hardware stand in order to train future information security specialists in setting up modern wireless networks.
 Work methodology or method. The study is based on scientific regulations of the practice-oriented learning organization. The competence-based approach was used as its methodological base, theoretical (comparison, analysis, generalization, concretization, modeling) methods were used. The development and implementation of a software and hardware stand in the educational process was carried out at Tyumen State University in 2021-2022 with the involvement of students from the “Computer Security” direction of training.
 Results. The authors have developed and applied in the educational process a software and hardware laboratory stand that combines virtualization tools for software and hardware components of a computer network.
 The stand is used to study the modern infrastructure of a computer network which is used in enterprises and companies by students of the “Computer Security” specialization. It can also be used while teaching modern wireless networks configuration for students of the directions: “Mathematical support and administration of information systems”, “Computer science and computer technology”, “Software engineering”.
 On the basis of the stand a cycle of laboratory works was developed for senior students of the “Computer security” specialization as part of the study of the “Wireless computer networks security” discipline.
 Scope of results. The results of the study can be applied in the field of training future IT-specialists in the higher education system.

DATA CLUSTERING BASED ON INDUCTIVE LEARNING OF NEURO-FUZZY NETWORK WITH DISTANCE HASHING

Context. Cluster analysis is widely used to analyze data of various nature and dimensions. However, the known methods of cluster analysis are characterized by low speed and are demanding on computer memory resources due to the need to calculate pairwise distances between instances in a multidimensional feature space. In addition, the results of known methods of cluster analysis are difficult for human perception and analysis with a large number of features.
 Objective. The purpose of the work is to increase the speed of cluster analysis, the interpretability of the resulting partition into clusters, as well as to reduce the requirements of cluster analysis to computer memory.
 Method. A method for cluster analysis of multidimensional data is proposed, which for each instance calculates its hash based on the distance to the conditional center of coordinates, uses a one-dimensional coordinate along the hash axis to determine the distances between instances, considers the resulting hash as a pseudo-output feature, breaking it into intervals, which matches the labels pseudo-classes – clusters, having received a rough crisp partition of the feature space and sample instances, automatically generates a partition of input features into fuzzy terms, determines the rules for referring instances to clusters and, as a result, forms a fuzzy inference system of the Mamdani-Zadeh classifier type, which is further trained in the form of a neuro-fuzzy network to ensure acceptable values of the clustering quality functional. This makes it possible to reduce the number of terms and features used, to evaluate their contribution to making decisions about assigning instances to clusters, to increase the speed of data cluster analysis, and to increase the interpretability of the resulting data splitting into clusters.
 Results. The mathematical support for solving the problem of cluster data analysis in conditions of large data dimensions has been developed. The experiments confirmed the operability of the developed mathematical support have been carried out.
 Conclusions. . The developed method and its software implementation can be recommended for use in practice in the problems of analyzing data of various nature and dimensions.

An accident diagnosis method of pressurized water reactor based on BI-LSTM neural network

Due to the lack of accident data, previous researchers used accident data obtained from system code simulation to train and verify the machine learning models. In this study, a long short-term memory (LSTM) neural network was used to construct a pressurized water reactor (PWR) accident diagnosis model. The model was trained and tested using simulation data of a PWR based on the deterministic analysis method and uncertainty analysis method. The accuracy of the LSTM model based on deterministic analysis and uncertainty analysis are 96.67% and 98.77%, respectively. The LSTM model developed in the present study is superior to traditional mathematical statistics and support vector machine (SVM) models in accident diagnosis, especially for diagnoses with uncertain data. The results of this study show that the LSTM model has practical value in reactor accident diagnosis.