Mathematical Research Research Articles

On the Importance of Illustration for Mathematical Research

On the Importance of Illustration for Mathematical Research

Examination of High School Entrance Examination (LGS) Science Questions According to the Cognitive Process Dimension of the Revised Bloom Taxonomy and the Cognitive Domain Steps of the International Mathematics and Science Trends

Çalışmanın amacı, 2018 ve 2019 Liselere Geçiş Sistemi Fen Bilimleri sorularının Yenilenmiş Bloom Taksonomisinin bilişsel süreç boyutuna ve Uluslararası Matematik ve Fen Eğilimleri Araştırması bilişsel alan basamaklarına göre incelenmesidir. Çalışmada, incelenen Fen Bilimleri soruları, Yenilenmiş Bloom Taksonomisinin bilişsel süreç boyutuna ve Uluslararası Matematik ve Fen Eğilimleri Araştırması bilişsel alan basamaklarına göre sınıflandırılmıştır. Araştırmada doküman analizi yöntemi kullanılmıştır. Yenilenmiş Bloom Taksonomisinin bilişsel süreç boyutuna göre, Uluslararası Matematik ve Fen Eğilimleri Araştırması ve Liselere Geçiş Sistemi Fen Bilimleri sorularının, ağırlıklı olarak alt düzey bilişsel alanda yer aldığı tespit edilmiştir. Uluslararası Matematik ve Fen Eğilimleri Araştırması bilişsel alan basamaklarına göre, Liselere Geçiş Sistemi Fen Bilimleri sorularının ise bilme basamağı ağırlıklı olduğu belirlenmiştir.

Exploring the Relevance of Advanced Mathematical Knowledge for Secondary-Level Instruction

The usefulness of advanced mathematics in teaching is referred to as its relevance for secondary-level mathematics instruction. This paper is based on research that explores teachers' views on the relevancy of advanced mathematics and their expectations from advanced mathematics courses for teacher preparation programs. Ten secondary-level mathematics teachers participated in this study. semi-structured interviews with open-ended questions and focus group discussions were utilised for data collection and thematic for data analysis. The finding indicates that advanced mathematics is relevant for developing mathematical proficiency, mathematical, and logical thinking, knowledge of mathematical context mathematical activities and increased problem-solving skills and professional competencies. Along with advanced mathematical knowledge, technological and research knowledge, and skills are expected from undergraduate teacher preparation courses. Therefore, it is suggested to incorporate the expected form of knowledge in the teacher preparation program.

Optimisation of Cross-Border Project Management In Higher Education Institutions in the Context of the Impact of Global Economic Crises

In today's globalized and interconnected world, the impact of global crises poses increasing risks to the economic situation of each country in particular. The study of cross-border cooperation in the context of current crisis processes allows us to identify new risks and ways to minimize them. The purpose of the study is to analyze ways to optimize the management of cross-border projects in the context of the impact of global economic crises. Scenario planning, SWOT analysis, statistical and mathematical research methods are used in the course of the study. The article discusses the peculiarities of managing cross-border projects on the example of the Precarpathian National University in the context of the impact of global economic crises. Using the example of the university, the author analyzes the implementation of cross-border projects for the period of 2020-2022, which occurred during two crises. The first global economic crisis is caused by the COVID-19 pandemic and the second regional crisis is caused by the war in Ukraine. The risks faced by the grantee in implementing international programs are identified. The study analyzed four different cross-border projects, which made it possible to assess all the risks in more detail and identify existing problems. For a detailed analysis, the medium-sized PrePOD project was selected, which operated from 2020 to 2022 and received an average amount of funding. The strengths and weaknesses of cross-border cooperation were assessed. The study pays special attention to the role of the Precarpathian National University, emphasizing the need for financial risk management, effective communication, compliance with the law, and adaptation of national legislation to European standards. The paper formulates strategies for improving the management of cross-border projects in the context of global crises, and proposes to create research centers to improve the management of grant activities. It has been determined that flexibility and communication are the international factors that can reduce the impact of crisis processes on the implementation of international cooperation.

Exploring the Contributions of Nepalese Mathematicians in the Modern Era with a Specific Emphasis on Research Areas

This study explores the extensive realm of modern Mathematical research carried out by Nepalese Mathematicians, analyzing their substantial contributions across different Mathematical fields amid Nepal's changing socioeconomic context. Through comprehensive research, it elucidates the development of Mathematical concepts, the emergence of skilled Mathematicians, and the influence of their research on both local and international Mathematical communities. The paper aims to spotlight renowned Nepalese Mathematicians of the Modern era and their doctoral research endeavors, underscoring the pivotal role of Mathematics in shaping the country's path and progress.

Exploring Certain Generalization of Arithmetical Functions

This article introduces a few generalized arithmetical functions and focuses on a few specific instances of these arithmetic functions. This study of certain generalizations of arithmetical functions supplements our understanding of number theory and its applications. By spreading the domain, range, or definition of traditional arithmetical functions, mathematicians unexposed new insights into the structure of integers and their relationships with other mathematical objects. Moreover, the applications of these generalizations span across various fields of mathematics, highlighting their significance and relevance in modern mathematical research. Continued exploration of these generalizations promises further discoveries and advancements in the field of number theory and beyond.

ОЦЕНКА ДИФФЕРЕНЦИАЦИИ РЕГИОНОВ АРКТИЧЕСКОЙ ЗОНЫ РФ НА ОСНОВЕ ИНФОРМАЦИОННО-АНАЛИТИЧЕСКИХ ТЕХНОЛОГИЙ

The formation of a single economic space in the Arctic zone of the Russian Federation is considered as the main task, which is the basis for realizing the development goals of the regions of the Russian Arctic. One of the solutions to the problem of creating a common spatially localized territory of the Russian Arctic megaregion, taking into account the significant differentiation of regions according to socio-economic indicators, is to identify tools for smoothing regional disparities. The use of the tested by the authors IRES RAS methodology “Information and analytical technologies for complex verification of the information base of economic and mathematical modeling of spatial economic systems” is proposed as a tool for constructing data sets suitable for full-fledged mathematical research compiled on the basis of collections of the Federal State Statistics Service.

Tomographic Inverse Problems: Mathematical Challenges and Novel Applications

This workshop brought together researchers working on mathematical problems related to tomography, with a particular emphasis on novel applications and associated mathematical challenges. Examples of respective issues represented in the workshop were tomographic imaging with Compton cameras or coupled-physics imaging, resolution and aliasing, vector and tensor field tomography, diffraction tomography, magnetic particle tomography, and limited data, all of which are motivated by the many modern applications. These topics were complemented by novel algorithmic strategies in the solution of tomographic inverse problems, such as stochastic methods and machine learning techniques. Bringing together mathematical and scientific researchers working on these different mathematical problems created a fruitful interchange with novel ideas and strong impact for the future of the field.

Cognitive modeling of multi-contextual factors of youth entrepreneurship development in the region

Subject. This article examines the issue of the implementation of private business initiative and the involvement of young people in entrepreneurial activities. Objectives. The article aims to structure the factors that determine the transition from entrepreneurial intentions to entrepreneurial activity. Methods. For the study, we used mathematical research methods. Results. The article finds that the main factors influencing the entrepreneurial activity of young people are the State policy in the field of regulation and support of entrepreneurship, social norms and attitudes to entrepreneurship in society, as well as the general economic situation. Relevance. The results of the study can be used when designing programmes for the development of the labor market in the regions of Russia.

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 15, No. 6

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 15, No. 6

Promoting Interdisciplinary Research Collaboration among Mathematics and Special Education Researchers

This manuscript provides a theoretical framing of a collaborative research design effort among mathematics education and special education researchers. To gain insight into the current state of research on mathematics learning, we drew on how researchers in mathematics education and special education have defined and operationalized the term ‘mathematical concept’ related to the learning of fractions. Using this information, we designed a future study that focuses on and connects prior research in mathematics and special education. We conclude by discussing the implications of such collaborative research efforts.

Risk-Based Assessment of the Performance of Territorial Bodies of the Federal Treasury of the Russian Federation

This paper presents the authors’ methodology of a risk-oriented approach to assessing the performance of territorial bodies of the Federal Treasury of the Russian Federation. The proposed methodology consists in the application of adjustment coefficients, which account for the quality of the execution of budgetary powers and the growth rate of the gross regional product of the corresponding territory. The goal of the study is to develop a risk-oriented methodology for assessing the contribution of the territorial bodies of the Federal Treasury to the United Nations sustainable development goals and national goals. The current study employs systemic, process based, risk-oriented approaches, statistical data analysis, and mathematical research methods. The gross regional product for the subjects of the Russian Federation is calculated for 2018–2019. Based on an analysis of Russian and foreign research on modern controlling systems and in accordance with the current concept of controlling, an attempt is made to develop a methodology for assessing the performance of the Federal Treasury and its territorial bodies. The main conclusion of the study is that the most expedient approach to assessing the efficiency of territorial bodies of the Federal Treasury is through the balanced scorecard system built in accordance with the strategic goals of the Federal Treasury, the national goals of the Russian Federation, and the UN SDGs.

A tour of general Hanoi graphs

The Tower of Hanoi puzzle has fascinated researchers in mathematics and theoretical computer science for over a hundred years. Many variants of the classical puzzle have been posed, such as allowing more than 3 pegs, and adding restrictions on the possible moves between the pegs. It is natural to view the pegs and allowed moves by means of a graph. The pegs are represented by the vertices of the graph, and the allowed moves by the edges. For each n, this graph yields a graph on the set of all legal configurations of n disks. Thus, the questions about the original puzzle may be reformulated as questions about connectivity and shortest paths in the graph of all configurations. Moreover, it was shown that classical Hanoi graphs are related to several interesting and useful structures such as the Sierpiński gasket and Gray codes, and thus several properties of these graphs were studied, including Hamiltonicity and planarity. In this paper we study these properties, and several others – chromatic number, clique number, and girth – for general Hanoi graphs.

Co matematyka ma do zaoferowania humaniście? Słów kilka o matematyce i jej nauczaniu

The article is concerned with mathematics. Numerous examples from its history prove that certain aspects of mathematical research can also be an inspiration for the humanities and literature. The main purpose is to look for these inspirations closer and show their usefulness in mathematical education.

Unrealistic Expectations and Compromised Observations in School Mathematics Research

It is not often acknowledged that educational research increasingly places unrealistic expectations on teachers, especially teachers of mathematics. This paper explores issues relating to idealism within educational research, especially in terms of how it manifests as potentially unrealistic expectations academics may have of, and place on, classroom teachers. The paper draws on reflections from observing an international panel of mathematics education researchers observing classroom teachers at work. It outlines some of the philosophical complications of observations, especially its theory-laden nature, and outlines some potential implications such idealism can have for teachers, and how this may be linked to mathematics culture.

О некоторых проблемах использования отдельных постулатов «экономической теории преступлений и наказаний» в целях «оптимизации» уровня преступности

The problem of optimizing the level of crime is one of the urgent problems facing domestic and foreign criminology. The relevance of this problem is due to the fact that crime is a phenomenon that causes enormous damage to society, which, on the one hand, reduces the income of the population, and on the other hand, requires certain expenses for the maintenance of the law enforcement system to prevent it, which leads to an increase in the social costs of society.
 The purpose of the study is to determine to what extent certain postulates of the "economic theory of crimes and punishments" proposed by scientists - economists can be used in order to optimize the level of crime.
 The subject of research in this article are the features and patterns of criminal and law enforcement activities, the knowledge of which allows us to conclude that there are or are no problems when using certain postulates of the "economic theory of crimes and punishments" to optimize the level of crime
 Methodology and methods. In the course of the study, an analysis was made of the possibilities of using certain postulates of the "economic theory of crimes and punishments" in order to optimize the level of crime. The implementation of this kind of analysis involves the use of a number of research methods, which include: the method of modeling the behavior of a criminal; a method of testing models of economic postulates of the economic theory of crimes and punishments in specific situations, followed by the formulation of conclusions about the validity or inconsistency of these models, including the use of mathematical and statistical research methods. At the same time, mathematical and statistical research methods were used to determine the level of detection of crimes, as well as to analyze the dependence of the costs of law enforcement and the actual level of crime.
 Research results and their scientific novelty. The study found that in a number of cases the postulates of the economic theory of crimes and punishments do not adequately reflect the existing socio-legal reality. The reason for this is the presence of dubious postulates underlying this or that model of criminal and law enforcement activities. Among such dubious postulates are the following postulates: the postulate that the behavior of the criminal is rational In reality, the behavior of the criminal is not always rational; 2 the postulate that the level of crime is inversely proportional to the magnitude of the costs of law enforcement (in other words, the higher the costs of law enforcement, the lower the level of crime, in reality, in some cases this is far from an obvious fact; 3 the damage from organized crime is always lower than the damage from unorganized crime, since the level of organized crime is allegedly lower than the level of unorganized crime, which is also far from obvious. Based on the analysis of individual postulates of the economic theory of crimes and punishments, it was concluded that the use of these postulates does not always lead to optimization the level of crime, because these postulates do not always adequately reflect the legal reality.

Prediction and feature importance analysis for wordle strategy based on machine learning models

The word guessing game, Wordle, has attracted considerable attention from researchers in computer studies and mathematics due to its significant relevance. Many studies have been taken on Wordle to explore its potential in simulating human behaviors during gameplay and devising optimal strategies for players. In this paper, strategies based on mathematics theories or machine learning technologies are compared by their feature importance in order to explore whether there is a loss of feature meaning in machine learning methods. In the whole study, the effect of features and their relations to the expectations of tries of game Wordle are also explored. More specifically, this paper introduces machine learning models such as linear, random forest, bagging as well as gradient boosting decision trees to visually provide a relation between words features (such as repeat frequency, vowels, consonants) and the expectation of attempts in a game. After establishing machine learning models, the feature importance is derived by feature engineering techniques. The importance is then compared with spearman statistical correlations based on the dataset to hence draw the conclusion of the change of feature meaning in machine learning methods. Study results indicate that there is loss of meaning and effect of features in the better fitted prediction models (gradient boosting decision trees, random forest) compared to the statistic approaches.

A Multi-Modal Retrieval Model for Mathematical Expressions Based on ConvNeXt and Hesitant Fuzzy Set

Mathematical expression retrieval is an essential component of mathematical information retrieval. Current mathematical expression retrieval research primarily targets single modalities, particularly text, which can lead to the loss of structural information. On the other hand, multimodal research has demonstrated promising outcomes across different domains, and mathematical expressions in image format are adept at preserving their structural characteristics. So we propose a multi-modal retrieval model for mathematical expressions based on ConvNeXt and HFS to address the limitations of single-modal retrieval. For the image modal, mathematical expression retrieval is based on the similarity of image features and symbol-level features of the expression, where image features of the expression image are extracted by ConvNeXt, while symbol-level features are obtained by the Symbol Level Features Extraction (SLFE) module. For the text modal, the Formula Description Structure (FDS) is employed to analyze expressions and extract their attributes. Additionally, the application of the Hesitant Fuzzy Set (HFS) theory facilitates the computation of hesitant fuzzy similarity between mathematical queries and candidate expressions. Finally, Reciprocal Rank Fusion (RRF) is employed to integrate rankings from image modal and text modal retrieval, yielding the ultimate retrieval list. The experiment was conducted on the publicly accessible ArXiv dataset (containing 592,345 mathematical expressions) and the NTCIR-mair-wikipedia-corpus (NTCIR) dataset.The MAP@10 values for the multimodal RRF fusion approach are recorded as 0.774. These substantiate the efficacy of the multi-modal mathematical expression retrieval approach based on ConvNeXt and HFS.

The rationale for the choice of preventive intraoperative anesthesia for uterine curettage in patients with individual intolerance to amide anesthetics

Background. Uterine curettage (UC) is widely used in global clinical practice owing to its great diagnostic and therapeutic value. At the same time, UC leads to a damage to the integrity of soft tissues, causing development of postoperative pain syndrome. Some patients have an individual intolerance to amide anesthetics, which limits their use in this cohort. Purpose: to improve the quality of providing anesthetic care in the early postoperative period after UC to women who have a history of individual intolerance to amide anesthetics through selection of a comprehensive method of preventive intraoperative anesthesia for this category of patients. Materials and methods. Ninety females took part in the study. Clinical, laboratory, and mathematical and statistical research methods were used to study the preventive analgesic effectiveness of the compared methods of anesthesia. Five samples of biological material, called the control points, were taken: before surgery, immediately after it, then 1, 3 and 6 hours after intervention. In this way, an idea was got about the initial level of the studied indicators and their changes during the postoperative stay in the hospital. Properties of various combinations of propofol, ketamine, fentanyl, and dexketoprofen were studied. Results. It was revealed that a combination of propofol (2 mg/kg), fentanyl (0.1 µg/kg), ketamine (0.1 mg/kg), as well as additional intravenous administration of dexketoprofen (50 mg) at the stage of premedication has the advantages in terms of preventive intraoperative analgesia. Effectiveness of the proposed method of anesthesia was proved by significantly better indicators of vital functions (heart rate, mean arterial pressure) and serum levels of some laboratory markers of stress (glucose, cortisol, insulin, cortisol-insulin index). Differences in the studied parameters were recorded both when comparing them between the groups at the same control time points and conside-ring the development and regression of the postoperative pain syndrome severity within the groups. Conclusions. The proposed method of anesthesia has a reliable advantage in terms of preventive reduction of the postoperative pain syndrome of UC in patients who cannot have application anesthesia due to individual intolerance to amide drugs. The specified method has a positive effect on vital functions and serum levels of some laboratory markers of stress, and the fastest recovery of patients is caused by a lower suppressive action of the anesthetic drugs used.

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 15, No. 5

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 15, No. 5