Mathematical Research Research Articles

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

Introduction to INFER special issue on “new aspects of economic and financial integration”

AbstractThis Special Issue (SI) gathers 13 papers presented at the 23rd INFER Annual Conference which took place in Lisbon, 8–10 September 2021, at ISEG – Lisbon School of Economics and Management. The conference was organised by INFER (International Network for Economic Research), UECE (Research Unit on Complexity and Economics), and REM (Research in Economics and Mathematics). The papers of the SI focus on key topics in international macroeconomics, revisit the fiscal policy conduct within a globalised world, investigate how uncertainty and risk affect macroeconomic policies, and analyse the links between labor market outcomes, automation, and economic integration.

Global Research Output Human Immunodeficiency Virus From 1954-2022: Literature Review

HIV (human immunodeficiency virus) have two primary HIV strains are HIV-1 and HIV-2. Both can lead to AIDS and our work is explained to easily find out the data about HIV. We conducted the research work of HIV between the years of 1954-2022. We classified the models by their mathematical structure and research question. The amount of information that researchers are analyzing from etiology, pathogenesis, in-vivo, in-vitro, and human trials grows daily. As compared data for the HIV research and review work the research will perform moderately with the review work. The In-vivo and the In-vitro work are performed little lower than the other work. This is the useful research review source for the HIV research work. We created a segregation of desirable features of models, reviewed and classified the articles to inform our conclusions.

Numerical Analysis on the Flow Depth Behaviour in Dividing Open-Channel for Trapezoidal and Rectangular Cross-Sectional Channel

Open-channel with dividing flow refers to any side water withdrawals from streams, rivers or main channel. It has become an important issue, especially when measuring the flow rate and depth of water as part of environmental management schemes and many practical projects such as the system of irrigation and drainage, water and wastewater treatment plants and other water resources projects. Although the behaviour of water flow has been studied by the previous researchers, most studies have only been carried out in simulation and lab experiment for a straight prismatic main channel. The mathematical research has not yet been fully understood, particularly in relation to the behaviour of water flow. Therefore, in this study, the modified general equations of dividing open-channel flow for rectangular and trapezoidal in the form of non-linear polynomial equations are proposed to determine the upstream flow depth in rectangular and trapezoidal cross-sectional channel. The computations of water flow depth influenced by Froude number and discharge ratio are performed with Newton-Raphson procedure in Maple software. The numerical solution shows the good agreement with the experimental data as reported in the literature. When the discharge ratio is low, the flow depth in trapezoidal and rectangular channels exhibits similarity. However, as the discharge ratio increases, the flow depth in the rectangular channel surpasses that in the trapezoidal channel. Furthermore, as the Froude number increases, the rectangular channel experiences a greater flow depth in comparison to the trapezoidal channel.

The Sufficiency of Solutions for Non-smooth Minimax Fractional Semi-Infinite Programming with (BK,ρ)−Invexity

Minimax fractional semi-infinite programming is an important research direction for semi-infinite programming, and has a wide range of applications, such as military allocation problems, economic theory, cooperative games, and other fields. Convexity theory plays a key role in many aspects of mathematical programming and is the foundation of mathematical programming research. The relevant theories of semi-infinite programming based on different types of convex functions have their own applicable scope and limitations. It is of great value to study semi-infinite programming on the basis of more generalized convex functions and obtain more general results. In this paper, we defined a new type of generalized convex function, based on the concept of the K−directional derivative, that is, uniform (BK,ρ)−invex, strictly uniform (BK,ρ)−invex, uniform (BK,ρ)−pseudoinvex, strictly uniform (BK,ρ)−pseudoinvex, uniform (BK,ρ)−quasiinvex and weakly uniform (BK,ρ)−quasiinvex function. Then, we studied a class of non-smooth minimax fractional semi-infinite programming problems involving this generalized convexity and obtained sufficient optimality conditions.

Management Mathematics: The Audacity of BOPE

Abstract Accepted by: Aris Syntetos Can mathematical research from a business school professor that is published in academic journals also substantially improve actual industrial practice in global supply chains? Yes. Can mathematics and operations management help improve fairness in access to organ transplants? Yes, again. Can mathematics developed for business applications facilitate the development of new types of quantum hardware? Also, yes. I have three main messages in this invited essay: (1) free yourself from self-imposed constraints and explore a wider range of new problems and arcane mathematics; (2) be bold and imaginative in developing novel solutions and (3) implement your ideas in practice, scaling them with a channel partner.

A Proof That the Set of NP-problems is Bigger Than the Set of P-problems by Using a Logical Consideration

The field of informatics is the domain that emerged by applying the mathematical logic on electronic devices called computers in order to simplify many tasks for humans. The application of informatics in all economic and scientific areas is the most important factor that made our civilization reach our current phase of development. Nowadays, the experts and even the beginners of informatics are eager to use quantum computers. However, there is still an unsolved problem of classical theoretical informatics in ordinary electronic computers. It is the famous philosophical problem of the “Millenium Prize” of the Clay Mathematics Institute concerning the complexity of problems that has been treated by many other researchers but without acceptable sufficient answers. A solution to this problem can make all the fields based on informatics make huge progress. And thus, thanks to my short studies about informatics, I present to you this mathematical proof that deals with the sets of P problems, NP-Complete problems and NP-Hard problems in the field of classical electronic computers in order to prove new formulas about the cardinals of each group of complexity problems and about the intersections of each one of these sets. The aim is to contribute to an acceptable solution for this Millenium Problem and the methodology is purely logical and mathematical. The readers won’t need any complicated notions from the background of previous informatics or mathematics research in order to understand the demonstrations of this article since the proof is based only on notions of sets by starting with easy logical considerations. Furthermore, you will find in this work a proof of an interesting theorem about the complexity of problems that allows us to identify NP-problems even if their algorithms have infinite time of execution. This paper ends by proving that the set of NP-Problems is definitely bigger than the set of PProblems. Hence, all the readers are invited to understand and develop this work by inspecting the applied logical considerations in order to succeed in finding a sufficient solution to the interesting Millenium Problem of complexity.

THE IMPORTANCE OF MATHEMATICS IN THE PROSPERITY OF SOCIETY

This research article illustrates the importance of learning mathematics and the significance of understanding mathematical principles and concepts in the modern global environment through thinking critically. The article talks about the great encyclopedist-scientists Muhammad al-Khwarizmi and Abu Rayhan Biruni, and their great discoveries and valuable contributions in the field of mathematics. Moreover, it includes some quotes from Shakuntala Devi, popularly known as the Human Computer, a Mathematician and author who became popular for her incredible and almost supernatural calculation skills. Additionally, this paper provides information on “dyscalculia” as well as its impact on humans’ overall well-being and mathematical research to come up with a cure in the period of COVID-19