Mathematical Support Research Articles

FORMALIZATION OF DECISION-MAKING PROCESSES IN AVIATION MANAGEMENT

Currently, fighter aircraft is one of the most important components in the war with the russian federation. It is used to gain superiority in the air during combat, destroy means of air attack, air support of the Ground Forces, the Naval Forces, provision of aerial intelligence data to control bodies, aerial damage to enemy aviation, land and sea formations, objects of the state and military administration, rear facilities and military-economic potential, transport communications, performance of other special tasks. To ensure high efficiency of combat use, tactical (fighter) aviation brigades are equipped with automation equipment. The experience of the combat use of fighter aircraft during wars and local military conflicts of the last decade shows that ensuring high efficiency of aircraft control is achieved by automating control processes through the use of modern software and mathematical support of the automated control system, based on fundamentally new approaches, in including the use of a single formal system for presenting the knowledge of combat control officers. However, the capabilities of aviation and air defense control systems to solve logical and analytical problems are limited. In the existing complex of automation tools, the final result of the task of determining the impact on the target is evaluated qualitatively – if it is possible for the fighter to enter a given tactically advantageous position relative to the target. The existing SPMZ ASU uses mathematical models, the systems of restrictions of which do not allow to fully use the existing potential of the available composition of information sources, to form recommendations based on incomplete, inaccurate input information, which negatively affects the quality of aviation management. Thus, the need to automate decision- making processes in aviation management using the latest information technologies is urgent. One of the promising directions of formalization of decision-making processes in aviation management is the creation of models that provide for the formalization of the mental activity of decision-makers. The purpose of the article. Automation of decision-making processes in aviation management using the latest information technologies. One of the promising directions of formalization of decision-making processes in aviation management is the creation of models that provide for the formalization of the mental activity of decision-makers.

How can EdTech Personalise the Instruction for Tertiary Students Requiring Mathematics Support?

Many students enter mathematically intensive courses with deficiencies in their mathematical skills. Universities have responded to this challenge with additional support. However, existing approaches have exhibited limited success. This paper proposes research into the effectiveness of a personalised approach to mathematical remediation driven by the affordances of EdTech.

SVD-AE: An asymmetric autoencoder with SVD regularization for multivariate time series anomaly detection

Anomaly detection in multivariate time series is of critical importance in many real-world applications, such as system maintenance and Internet monitoring. In this article, we propose a novel unsupervised framework called SVD-AE to conduct anomaly detection in multivariate time series. The core idea is to fuse the strengths of both SVD and autoencoder to fully capture complex normal patterns in multivariate time series. An asymmetric autoencoder architecture is proposed, where two encoders are used to capture features in time and variable dimensions and a shared decoder is used to generate reconstructions based on latent representations from both dimensions. A new regularization based on singular value decomposition theory is designed to force each encoder to learn features in the corresponding axis with mathematical supports delivered. A specific loss component is further proposed to align Fourier coefficients of inputs and reconstructions. It can preserve details of original inputs, leading to enhanced feature learning capability of the model. Extensive experiments on three real world datasets demonstrate the proposed algorithm can achieve better performance on multivariate time series anomaly detection tasks under highly unbalanced scenarios compared with baseline algorithms.

Numeracy E-Module with Edugame As A Support For Mathematics Learning for Sixth-Grade Elementary School Students

The Covid-19 pandemic has caused learning loss, one of which is in mathematics learning. Students enjoy technology products because of online learning, but schools must encourage teachers to make their own. This research aimed at developing a numeracy E-module with edugame. This type of research was developed using the ADDIE method to produce e-modules that can support less than optimal learning due to learning loss during the COVID-19 pandemic. The methods used to collect data were questionnaires and tests. Data collection instruments were in the form of questionnaires and test questions. Data analysis techniques used descriptive qualitative, quantitative, and inferential statistical analysis. The research results showed that this e-module was very suitable for use as a support for mathematics learning in sixth-grade elementary school because it received a validation score from media experts of 90.7% and material experts of 86.7% and a user response of 100%. Apart from that, based on the t-test, it showed differences in learning outcomes after students used the numeracy module with edugame. The n-gain test result was 80.3%. It can be concluded that this e-module influences and improves student learning outcome and it is suitable for learning.

Математическое и алгоритмическое обеспечение системы технического зрения гибкой производственной системы

The issue of designing a vision system based on algorithmic and mathematical support is considered. A flexible production system for the manufacture of evaporators of refrigeration units was chosen as the object of research. The analysis of existing projects of technical vision systems (TVS) for quality control of products – evaporators installed on an industrial robot. The purpose and main issues of the implementation of algorithmic and software for the functioning of the TVS and its architecture in accordance with the specifics of the object under study are set. The general scheme of functioning of subsystems of automated design of TVS for quality control of evaporators on a production stream of the flexible production system is offered. A mathematical model has been developed for identifying the evaporator blank, taking into account the corresponding coordinate system, the origin of which is the geometric center of this object, and the X-axis is formed by the largest radius of the image under consideration. The description of the TVS is given taking into account the interaction of the TVS correlator with the graphical terminal. When working with the TVS correlator, the evaporator surface that needs to be recognized is placed in one of the stable states on the working surface of the system, where the orientation coordinates of the evaporator positions are determined. The calculation of the memory volume of the storage system of the correlator TVS is carried out. The issue of forming a working scene for the TVS correlator of an industrial robot by sequentially performing operations to set graphic images of objects in a given array is considered. At the same time, its reflection coefficient (0-100%) is set for each evaporator model.

Conveyor Belt Object Identification: Mathematical, Algorithmic, and Software Support

Conveyor Belt Object Identification: Mathematical, Algorithmic, and Software Support

Causal evidence of the effect of a course specific mathematical learning and support center on economics students’ performance and affective variables

ABSTRACT The positive impact of Math Learning Support Centers (MLSCs) on student performance is well-documented in existing literature. However, we argue in this study that many of these evaluations could be improved methodologically. Using a more rigorous approach, we investigated the effect of an MLSC on students’ performance and affective variables in an economic study program. Our data, collected over six years, was analyzed using Propensity Score Matching and Difference-in-Differences methods, to control for observable and time-invariant unobservable characteristics. Contrary to a majority of the existing literature, we found no direct impact of students’ participation in the MLSC on students’ math performance. However, we identified positive effects on students’ test anxiety and other affective variables. Moreover, we found that students’ engagement in the learning process during the semester (e.g. by attending classes and solving exercise sheets) was a key driver of skill growth. These findings underscore the importance of more rigorous methodological approaches in future evaluations of MLSCs and other similar support systems.

Proceedings of the 2022 Computational Techniques and Applications Conference

CTAC 2022 Queensland University of Technology, Brisbane, Australia 29 November – 2 December, 2022 The 21st Biennial Computational Techniques and Appli- cations Conference (CTAC-2022) was hosted by the School of Mathematical Sciences and Centre for Data Science at Queensland University of Technology in Brisbane. The ANZIAM Special Interest Group in Computational Mathematics is responsible for this series of conferences, the first of which was held in 1981. The meeting provides an interactive forum for researchers interested in the de- velopment and use of computational methods applied to engineering, scientific and other problems. Participants of the conference are able to submit a short article based on their presentation for publication in this special section of the ANZIAM Journal (Electronic Supplement). The ed- itors, Tim Moroney, Qianqian Yang, Vivien Challis and Elliot Carr, thank the referees whose efforts have helped improve the quality of these conference proceedings. This Special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed conference papers. The eight keynote presentations were as follows. Chris Drovandi, Queensland University of TechnologyLikelihood-Free Bayesian Inference and Model Mis- specification Jennifer Flegg, The University of Melbourne Mathematical Modelling of Avascular Tumour Growth Frances Kuo, The University of New South Wales Lattice Meets Lattice—Application of Lattice Cuba- ture to Models in Lattice Gauge Theory Christian Lubich, University of Tuebingen Convergent evolving surface finite element algo- rithms for geometric evolution equations Marco Palombo, Cardiff University Perspectives on AI-powered brain microstructure imaging Emilie Sauret, Queensland University of TechnologyA hybrid Lattice Boltzmann approach for simulating viscoelastic instabilities and elastic turbulence Karen E Willcox, The University of Texas at Austin Predictive Digital Twins: From Aerospace Engineer- ing to Computational Oncology Andy Wilkins, CSIROThe Importance of Mathematics The presentation by Andy Wilkins was a public lecture. The conference attracted 76 registered participants, and featured a total of 54 contributed talks. CTAC2022 Organising Committee (QUT) • Tim Moroney • Qianqian Yang • Ian Turner• Vivien Challis • Elliot Carr• Sarie Gould CTAC2022 Scientific Committee • Kevin Burrage (QUT)• Vivien Challis (QUT)• Frances Kuo (UNSW)• Bishnu Lamichhane (Newcastle) • Quoc Thong Le Gia (UNSW) • Fawang Liu (QUT)• William Mclean (UNSW) • Tim Moroney (QUT)• Linda Stals (ANU)• Ian Turner (QUT)• Qianqian Yang (QUT) Acknowledgements QUT acknowledges the Turrbal and Yugara, as the First Nations owners of the lands where QUT now stands. We pay respect to their Elders, lores, customs and creation spirits. We recognise that these lands have always been places of teaching, research and learning. QUT acknowledges the important role Aborigi- nal and Torres Strait Islander people play within the QUT community. We gratefully acknowledge support from the following sponsors: School of Mathematical Sciences, QUT Centre for Data Science, QUT Modelling and Simulation Society of Australia and New Zealand Inc Mathematics of Computation and Optimization (MoCaO) special interest group of the Australian Mathematical Society The ANZIAM Student Support Scheme

A closer look at teacher support and achievement emotions in Chinese mathematics classrooms: mediating roles of academic control and intrinsic/extrinsic value

This cross-sectional study looks into how students’ perceived teacher support is linked to achievement emotions in mathematics via academic control and value. The data was gathered from 602 secondary students (13-16-year-olds) in 16 mathematics classrooms from three public schools in Jiangsu province, China. Participants were asked to respond to the paper-pencil questionnaire assessing students’ perceived teacher support, cognitive appraisals, and achievement emotions in mathematics. Findings showed that cognitive appraisals played complete mediation roles in teacher support and achievement emotions. Intrinsic value and mathematics self-concept were shown to serve a positive role in teacher support and achievement emotions, whereas extrinsic value was found to play a negative one. Besides, teacher support showed the greatest indirect effect on achievement emotions through mathematics self-concept. Lastly, findings indicated the great relevance of teacher support to students’ anger, boredom, enjoyment and relaxation in mathematics classrooms.

On the decision-making on the choice of GTM - assessment of the current status and development perspective

This article analyzes the current state of problems associated with the choice of well interventions based on the analysis of accumulated scientific and practical experience for various fields. Let us note the fact that recently there has been a development and improvement of analytical methods for forecasting indicators, followed by the adoption of an informed decision, the implementation of which allows improving the quality of conducted geological and technical measures. The accumulated experience of research work makes it possible to solve the problems of creating a methodology on an integrated basis with its mathematical, software and information support in order to optimize the planning process of geological and technical operations, to develop the structure of automated systems and algorithms for their functioning, it was possible to build linear and multiplicative algorithms based on the transformation of reservoir characteristics into the form relevant factors, the purpose of which is to express the dependence of the effectiveness of measures taken on the characteristics formed.

Shooting Simulator «Inhibitor»: Mathematical Support of Target Layout Animation

A mathematical support of target layout animation on the image of the shooting range with shielding by nearby objects and without flickering for the optical-electronic shooting simulator'Inhibitor' developed at Institute of mechanics UdmFRC UB RAS and at Computer facilities department of Kalashnikov ISTU jointly with JSC «Kalashnikov» Concern» is described. The tactical and technical task for the implementation of realistic target layout animation is given: support for all exercises from the Shooting Course with emerging-disappearing and moving targets on the surface of the shooting range with local objects that shield them, as well as folds of the area and other targets. Movements should be realistic in speed and angular dimensions of targets, smooth without jerking and correspond to the exercise scenario from the Firing Course: targets up to 2 m/s, armored vehicles up to 4 m/s at an angle of 15-20 from maximum ranges to minimum ones. The animation frequency should be maintained at least 25 frames/s, with the priority of the target layout (at least up to 32 at the same time) over special effects and local objects. The conducted studies of the animated target positioning accuracy with strong reduction in their size at longer ranges to ensure the realism of aiming at such images confirmed compliance with the requirements of TDP (significantly less than 0.3 thousandth range or 1.5 mm). Based on the prospects for further research and development of electronic shooting simulators and thanks to the improvement of computing tools and the development of software graphic libraries, it is necessary to expand the functional capabilities of simulators and reduce the cost, so as to increase competitiveness, for example, due to the realism of the animation of the target environment.

Development of mathematical decision-making support tools for effective response to emergencies during the transportation of dangerous substances by road transport

Every year, the world sees an increase in the volume of hazardous goods transported by road. However, emergencies may arise related to the depressurization of containers (tanks, containers, cylinders, etc.) during the transportation of dangerous goods under various circumstances (traffic accidents, natural disasters, acts of terrorism, etc.). Furthermore, it can cause the ingress of hazardous chemicals into the environment and create significant risks for the population of the surrounding areas and habitat. The existing methods for assessing chemical accident consequences need to be revised. Therefore, they are not practical tools for solving problems of prompt response to emergencies associated with accidents while transporting dangerous substances by road transport. Unlike the existing ones, the authors developed new mathematical tools that consider all the main factors. They allow for determining the area of the affected zone, forecasting changes in its scale, and assessing risks to public health due to such emergencies. Comparison of the simulation results with the field measurements data showed high accuracy of the developed mathematical support.

Understanding the Influence of Teacher-Student Relationship on Mathematics Achievement: Evidence From Korean Students

Learning does not occur through one-way lecturing. Rather, it occurs through reciprocal interactions. This means that a student’s response to a teacher’s guidance is critical in their learning. Moreover, it has been known that student learning can be influenced by school mean SES (socioeconomic status) insofar as it impacts the shared learning environment. In the present study, we examine (1) the relationship between math teacher support and student motivation on student mathematics achievement; and (2) whether student motivation interacts with teacher support in learning mathematics and how those interactions affect student mathematics achievement across various school mean SES (low, medium, high). The Programme for International Student Assessment 2012 survey data for 5,033 South Korean students was used in this research. In this study, the results show that (1) the effects of math teacher support and student motivation differ by school mean SES; and (2) there is no interaction between student motivation and math teacher support. Therefore, the findings of this study indicate that school SES impacts the shared learning environment and has a strong influence on student response to math teacher support and the relationship between student motivation and math achievement. Based on these results, implications for teacher education to improve teacher support are suggested.

Methods of automation and interpretation of the quality educational tests in distributed virtual learning systems

The subject matter of the article is the development of mathematical and algorithmic support for intellectual tools, which allows you to conduct continuous control of the knowledge of students (subjects of study) objectively and comprehensively. The goal of the work is to create methods for assessing the quality of educational tests and automating such processes. The following tasks were solved in the article: formation of a testing model in a distributed virtual learning environment and a validity assessment model based on the content of sets of test tasks. The following methods used are – algebra of finite predicates and operations, methods of mathematical statistics and methods of intellectual data analysis. The following results were obtained – the principles of intellectual analysis of the value of reliability coefficients, validity coefficients, discriminability coefficient, the difficulty index of the task of assessing the knowledge of subjects of training are formulated. Conclusions: the application of methods of formalization of test evaluation, analysis of software requirements, software development confirm the need to introduce quantitative methods of assessing students' knowledge into educational practice. The introduction of quantitative methods involves the correct setting of control goals, the selection of the measurement object and the selection of measurement tools. The use of pedagogical tests contributes to the effective implementation of all control functions and corresponds to its main principles for solving the problem of assessing the quality of tests, based on distributed virtual learning models and analysis methods. A test example of calculations was developed, with the help of which the efficiency of the proposed methods was researched.

ADMINISTRATION OF MEASURES FOR THE RESTORATION OF SOILS TRANSFORMED AS A RESULT OF MILITARY OPERATIONS

The Earth is a wealth of society. Its role in addressing the food problem cannot be overstated. It is known that the population's demand for staple food products doubles on average every thirty years. Therefore, in order to provide enough food for all the people living in the years 2010-2020, the productivity of agriculture needs to be doubled. The solution to this incredibly complex task primarily depends on the efficiency of land utilization. Observations are conducted using ground-based methods, primarily field-based techniques, and remote sensing tools. The establishment of correlation relationships between ground-based and remote sensing methods is carried out on dedicated test sites. The purpose of the article is to provide proposals for implementing measures for the restoration of lands transformed as a result of military actions. The methodology should include modern mathematical support, including principles of database creation, automated data processing and retrieval systems, and methods for real-time and long-term forecasting. For an accurate assessment of such transformations and the implementation of targeted regulation of soil processes, there is a need to organize systematic monitoring services to observe them. The absence of such monitoring can lead to irreversible degradation of the soil cover, which would later require enormous costs and time for restoration. It is clear that from both economic and socio-environmental perspectives, it is more practical and advantageous to prevent adverse changes rather than trying to remedy them later. By processing such information, it is possible to identify optimal natural conditions for various activities, predict both positive and negative factors for agricultural operations, and take measures to reduce the impact of negative factors on human life and activities. It is known that for a long time, observations were only conducted on changes in the state of the natural environment caused by natural factors. Indeed, the state of the biosphere changes under the influence of both natural and anthropogenic factors. However, there is a significant difference in the outcomes of these influences: the state of the biosphere, which constantly changes due to natural causes, usually returns to its previous state. Large balanced ecological systems, geosystems, change extremely slowly under the influence of natural processes. These gradual evolutionary changes occur only over time measured by historical epochs. The deteriorating ecological situation in Ukraine, including the agroecological state of the soil cover, emphasizes the need for the State Agrochemical Service to transition from soil agrochemical surveys to comprehensive soil-agrochemical monitoring of agricultural lands. Such monitoring belongs to the ecological monitoring type and consists of three main components: soil surveys (including laboratory analysis), assessment of their agro-ecological condition, prediction of changes in relevant indicators, and soil fertility management, which refers to the specific properties of soils that distinguish them qualitatively from their parent geological formations.

Algorithmic and Software Program for Determining the Labor Intensity of One-Season Maintenance of Tractors

The paper describes a program for calculating the total specific labor intensity of tractor maintenance during their one-season use. The mathematical support of the program is represented by models that allow, based on data on the seasonal operation of tractors, to calculate the total specific labor intensity of maintenance. In the algorithmic support, the main stages of calculating the indicator under study are formulated. The user interface of the program is created in the form of a form using the Visual Basic for Applications programming language. In addition to the labor intensity itself, the program calculates statistical parameters, upper limits of seasonal operating time and probabilities of intervals. The proposed program can be used to calculate the total specific labor intensity of maintenance not only for tractors, but also for other machines used in agricultural production.

Mathematical Modeling Support for Lung Cancer Therapy-A Short Review.

The paper presents a review of models that can be used to describe dynamics of lung cancer growth and its response to treatment at both cell population and intracellular processes levels. To address the latter, models of signaling pathways associated with cellular responses to treatment are overviewed. First, treatment options for lung cancer are discussed, and main signaling pathways and regulatory networks are briefly reviewed. Then, approaches used to model specific therapies are discussed. Following that, models of intracellular processes that are crucial in responses to therapies are presented. The paper is concluded with a discussion of the applicability of the presented approaches in the context of lung cancer.

Teacher support and student engagement in mathematics: The chain mediating role of academic self-efficacy and achievement goal orientation

This explored how teacher support impacted student engagement in mathematics. A total of 632 students in Grades 7 to 9 from junior middle schools in China were participants (females = 54.27%, mean age = 13.97, SD = 0.88). They completed surveys on teacher support, academic self-efficacy, achievement goal orientation, and student engagement. Data analysis was conducted using SPSS 20.0 and Amos 24.0. Results showed that academic self-efficacy mediated the relationship between perceived teacher support and student engagement. Mastery-approach and performance-approach goal orientation respectively mediated the relationship between perceived teacher support and student engagement in mathematics. Academic self-efficacy and mastery-approach had a chain mediation effect on the relationship between perceived teacher support and student engagement and academic self-efficacy. Performance-approach also had a chain mediation effect between the two. The chain mediation effect of academic self-efficacy and performance-approach was stronger than the single performance-approach effect. These findings shed light on the motivational processes through which students perceive the impact of teacher support on their engagement in mathematics.

Characterizing Secondary Teachers’ Structural Reasoning

The Common Core State Standards for Mathematical Practice asks students to look for and make use of structure. Hence, mathematics teacher educators need to prepare teachers to support students’ structural reasoning. In this article, we present tasks and rubrics designed and validated to characterize teachers’ structural reasoning for the purposes of professional development. Initially, tasks were designed and improved using interviews and small pilot studies. Next, we gave written structure tasks to over 600 teachers in two countries and developed and validated rubrics to categorize responses. Our work contributes to the preparation and support of mathematics teachers as they develop their own structural reasoning and their ability to help students develop structural reasoning.

Diverse mathematical knowledge among indigenous Amazonians

We investigate number and arithmetic learning among a Bolivian indigenous people, the Tsimane', for whom formal schooling is comparatively recent in history and variable in both extent and consistency. We first present a large-scale meta-analysis on child number development involving over 800 Tsimane' children. The results emphasize the impact of formal schooling: Children are only found to be full counters when they have attended school, suggesting the importance of cultural support for early mathematics. We then test especially remote Tsimane' communities and document the development of specialized arithmetical knowledge in the absence of direct formal education. Specifically, we describe individuals who succeed on arithmetic problems involving the number five-which has a distinct role in the local economy-even though they do not succeed on some lower numbers. Some of these participants can perform multiplication with fives at greater accuracy than addition by one. These results highlight the importance of cultural factors in early mathematics and suggest that psychological theories of number where quantities are derived from lower numbers via repeated addition (e.g., a successor function) are unlikely to explain the diversity of human mathematical ability.