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The level of difficulty of mathematical test items is a critical aspect for evaluating test quality and educational outcomes. Accurately predicting item difficulty during test creation is thus significantly important for producing effective test papers. This study used more than ten years of content and score data from China's Henan Provincial College Entrance Examination in Mathematics as an evaluation criterion for test difficulty, and all data were obtained from the Henan Provincial Department of Education. Based on the framework established by the National Center for Education Statistics (NCES) for test item assessment methodology, this paper proposes a new framework containing eight features considering the uniqueness of mathematics. Next, this paper proposes an XGBoost-based SHAP model for analyzing the difficulty of mathematics tests. By coupling the XGBoost method with the SHAP method, the model not only evaluates the difficulty of mathematics tests but also analyzes the contribution of specific features to item difficulty, thereby increasing transparency and mitigating the "black box" nature of machine learning models. The model has a high prediction accuracy of 0.99 for the training set and 0.806 for the test set. With the model, we found that parameter-level features and reasoning-level features are significant factors influencing the difficulty of subjective items in the exam. In addition, we divided senior secondary mathematics knowledge into nine units based on Chinese curriculum standards and found significant differences in the distribution of the eight features across these different knowledge units, which can help teachers place different emphasis on different units during the teaching process. In summary, our proposed approach significantly improves the accuracy of item difficulty prediction, which is crucial for intelligent educational applications such as knowledge tracking, automatic test item generation, and intelligent paper generation. These results provide tools that are better aligned with and responsive to students' learning needs, thus effectively informing educational practice. [ABSTRACT FROM AUTHOR]

This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking. [ABSTRACT FROM AUTHOR]

With the rapid development of modern technologies, autonomous or robotic construction sites are becoming a new reality in civil engineering. Despite various potential benefits of the automation of construction sites, there is still a lack of understanding of their complex nature combining physical and cyber components in one system. A typical approach to describing complex system structures is to use tools of abstract mathematics, which provide a high level of abstraction, allowing a formal description of the entire system while omitting non-essential details. Therefore, in this paper, autonomous construction is formalised using categorical ontology logs enhanced by abstract definitions of individual components of an autonomous construction system. In this context, followed by a brief introduction to category theory and ologs, exemplary algebraic definitions are given as a basis for the olog-based conceptual modelling of autonomous construction systems. As a result, any automated construction system can be described without providing exhausting detailed definitions of the system components. Existing ologs can be extended, contracted or revised to fit the given system or situation. To illustrate the descriptive capacity of ologs, a lattice of representations is presented. The main advantage of using the conceptual modelling approach presented in this paper is that any given real-world or engineering problem could be modelled with a mathematically sound background. [ABSTRACT FROM AUTHOR]

This correction notice provides updates and corrections to a research paper on deep machine learning model-based cyber-attacks detection in smart power systems. The paper proposes a deep learning-based attack detection model that addresses system disturbances caused by natural events and cyber-attacks. It discusses the use of principal component analysis (PCA) for feature selection and the potential of deep learning-based and decision tree classifiers for detecting cyber-attacks in intelligent energy grids. The notice also includes updates to references, clarifications on the experimental data set, and feature selection based on PCA. The study evaluates the effectiveness of the proposed model using various assessment indexes and compares it to conventional methods, concluding that the proposed model is effective in detecting cyber-attacks and demonstrates good performance in detecting destructive attacks. [Extracted from the article]

This document is a correction notice for a paper titled "An Investigation on Spiking Neural Networks Based on the Izhikevich Neuronal Model: Spiking Processing and Hardware Approach." The correction addresses an error in the affiliation of one of the authors, Ehsan Nazemi. The updated affiliation should include the Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City, Vietnam. Additionally, there was an error in the Introduction section where a paragraph with unexplained references was mistakenly copied from one of the author's theses. This paragraph has been removed, and the order of references has been adjusted accordingly. The authors assure that these corrections do not affect the scientific conclusions of the paper. [Extracted from the article]

This paper introduces a novel classification method for multi-class multi-label datasets, named multi-class multi-label logistic model tree (MMLMT). Our approach supports multi-label learning to predict multiple class labels simultaneously, thereby enhancing the model's capacity to capture complex relationships within the data. The primary goal is to improve the accuracy of classification tasks involving multiple classes and labels. MMLMT integrates the logistic regression (LR) and decision tree (DT) algorithms, yielding interpretable models with high predictive performance. By combining the strengths of LR and DT, our method offers a flexible and powerful framework for handling multi-class multi-label data. Extensive experiments demonstrated the effectiveness of MMLMT across a range of well-known datasets with an average accuracy of 85.90%. Furthermore, our method achieved an average of 9.87% improvement compared to the results of state-of-the-art studies in the literature. These results highlight MMLMT's potential as a valuable approach to multi-label learning. [ABSTRACT FROM AUTHOR]

The Fibonacci sequence has broad applications in mathematics, where its inherent patterns and properties are utilized to solve various problems. The sequence often emerges in areas involving growth patterns, series, and recursive relationships. It is known for its connection to the golden ratio, which appears in numerous natural phenomena and mathematical constructs. In this research paper, we introduce new concepts of convergence and summability for sequences of real and complex numbers by using Fibonacci sequences, called Δ -Fibonacci statistical convergence, strong Δ -Fibonacci summability, and Δ -Fibonacci statistical summability. And, these new concepts are supported by several significant theorems, properties, and relations in the study. Furthermore, for this type of convergence, we introduce one-sided Tauberian conditions for sequences of real numbers and two-sided Tauberian conditions for sequences of complex numbers. [ABSTRACT FROM AUTHOR]

The Rubik's Cube mechanism (RCM) is a kind of reconfigurable mechanism with multiple characteristics such as multiple configurations, variable topology, strong coupling, and reconfigurability. Crossover research on the RCM with mathematics, chemistry, cryptography, and other disciplines has led to important breakthroughs and progress. It is obvious that the invention and creation of a new RCM can provide important ideological inspiration and theoretical guidance for the accelerated iterative updating of Rubik's Cube products and the expansion of their applications. This paper investigates the type synthesis method for a regular hexagonal prism (RHP) RCM (RHPRCM). Through analysis of the reconfigurable movement process of the RCM, two mechanism factors are abstracted, a type synthesis process for the RHPRCM is proposed, a symmetry layout method for the RCM's revolute axis based on the RHP space polyhedron is proposed, and an analysis method for the intersection of the revolute pair contact surfaces (RPCSs) based on the adjacency matrix is proposed. Taking a revolute axis passing through the center of an RHP and having only one RPCS for each revolute axis as an example, an RHPRCM with different topological structures is synthesized. The relevant research in this paper can provide methodological guidance for the synthesis of other spatial RCMs. [ABSTRACT FROM AUTHOR]

This paper presents a survey of advanced concepts and research perspectives, of a philosophical-mathematical approach to describe the dynamics of systems of many interacting living entities. The first part introduces the general conceptual framework. Then, a critical analysis of the existing literature is developed and referred to a multiscale view of a mathematics of living organisms. This paper attempts to understand how far the present state-of-the-art is far from the achievement of such challenging objective. The overall study leads to identify research perspectives and possible hints to deal with them. [ABSTRACT FROM AUTHOR]

Despite being a prominent and influential figure in the German and Jewish Enlightenment, Salomon Maimon's skeptical standpoint seems to veer towards radical and unsustainable assertions, denying the validity of any knowledge—including natural science—except for mathematics. This paper seeks to demonstrate that Maimon's skepticism concerning non-mathematical knowledge does not propose an incoherent skepticism nor contradict the enlightened perspective of developing natural sciences. To achieve this, I aim to show that (1) Maimon's radical claim originates from the radical nature of the question he answers, and (2) the key to understanding it lies in grasping the concept of synthesis in his philosophy, from which different meanings of knowledge follow. [ABSTRACT FROM AUTHOR]

Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on fuzzy Aumann's integral theory, the Hermite–Hadamard's type inequalities are introduced for a newly defined class of nonconvex functions, which is known as  U · D preinvex fuzzy number-valued mappings ( U · D preinvex  F · N · V · M s) on coordinates. Some Pachpatte-type inequalities are also established for the product of two  U · D preinvex  F · N · V · M s, and some Hermite–Hadamard–Fejér-type inequalities are also acquired via fuzzy Aumann's integrals. Additionally, several new generalized inequalities are also obtained for the special situations of the parameters. Additionally, some of the interesting remarks are provided to acquire the classical and new exceptional cases that can be considered as applications of the main outcomes. Lastly, a few suggested uses for these inequalities in numerical integration are made. [ABSTRACT FROM AUTHOR]

This paper presents a new and innovative examination method designed to foster creativity, problem-solving, and collaboration in mathematics education. Traditional assessment practices often focus on rote memorization and fail to engage students in the exploration of mathematical concepts and connect the content to real-world problems. In contrast, the proposed examination approach requires students to invent and solve their own mathematical tasks based on their personal interests and experiences. By actively engaging with mathematical concepts and relationships, students deepen their understanding while developing essential skills such as communication, self-assessment, and peer feedback. Anonymized peer correction is also introduced as a means of minimizing bias and promoting objectivity and a wider understanding. The study investigates student perceptions of the examination based on their experiences regarding its effects on creativity and problem-solving skills. The findings suggest that the new way of examining may not only enhance students' mathematical understanding and problem-solving abilities but also foster a collaborative learning environment that encourages communication and peer support. The paper concludes that the adoption of this new method has the potential to transform traditional assessment practices and promote more engaged, creative, and collaborative learning experiences for students in a wide range of subjects. [ABSTRACT FROM AUTHOR]

The paper is written as a reflection on the author's online teaching of a graduate elementary mathematics content and methods course through the asynchronous modality. The need for developing skills in posing problems that integrate non-technological and technological problem-solving strategies is emphasized. Such problems are considered agency of design-based mathematics education. The importance of revealing hidden mathematical ideas stemming from teacher candidates' willingness to explore self-posed problems within the forum components of the course is discussed. Using these hidden ideas, the paper demonstrates connectivity among different mathematical concepts including historical connections. Teacher candidates' reflections on the course have been included and reviewed. [ABSTRACT FROM AUTHOR]

Foundry Degassing Units (FDU) are used for refining aluminum alloys. For an ideal refining process using an FDU unit, it is necessary to select several parameters, which are linked to each other. For a rotary impeller, we searched for several parameters, such as its optimal shape, speed in the liquid alloy, and distance from the bottom of the refining ladle, where the aforementioned parameters contribute to the overall wear and life of the rotor and, consequently, of the rotor shaft. The Computational Fluid Dynamics (CFD) method can be used to determine the above-mentioned parameters. This paper describes the particular steps of preparation of rotor geometry for the subsequent setting up of the basic numerical model. [ABSTRACT FROM AUTHOR]

In this paper, I attempt to describe Mark Burgin's results in non-Diophantine mathematics, which are important for the foundation of mathematics and its application in quantum field theory. In particular, the elimination of divergences in quantum electrodynamics is described. [ABSTRACT FROM AUTHOR]

In this paper, it is noted that three apparently disparate areas of mathematics—singularity analysis, complex symmetry analysis and the distributional representation of special functions—have a basic commonality in the underlying methods used. The insights obtained from the first of these provides a much-needed explanation for the effectiveness of the latter two. The consequent explanations are provided in the form of two theorems and their corollaries. [ABSTRACT FROM AUTHOR]

Accurate sky identification is one of the most important functions of an automated telescope mount. The more accurately the robotic telescope is navigated to the investigated part of the sky, the better the observations and discoveries made. In this paper, we present mathematical methods for accurate sky identification (celestial coordinates determination). They include the automatic selection of the reference stars, preliminary and full sky identification, as well as an interaction with international databases, which are a part of the astrometric calibration. All described methods help to receive accurately calculated astrometric data and use it for the positional calibration and better navigation of the automated telescope mount. The developed methods were successfully implemented in the Collection Light Technology (CoLiTec) software. Through its use, more than 1600 small solar system objects were discovered. It has been used in more than 700,000 observations and successful sky identifications, during which, five comets were discovered. Additionally, the accuracy indicators of the processing results of the CoLiTec software are provided in the paper, which shows benefits of the CoLiTec software and lower standard deviation of the sky identification in the case of low signal-to-noise ratios. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Attitude Control of UAVs with Search Optimization and Disturbance Rejection Strategies" published in the journal Mathematics. The correction involves the removal of an author, Dr. Chunbo Luo, from the authorship list. Dr. Luo did not consider his contribution sufficient for authorship and requested to be removed. The correction does not impact the scientific conclusions of the paper. The remaining authors are Wensheng Li, Fanke Yang, Liqiang Zhong, Hao Wu, Xiangyuan Jiang, and Andrei V. Chukalin. [Extracted from the article]

Learning mathematics with understanding involves productively struggling to make connections between different mathematical ideas. Such productive struggle is associated with three primary constructs: grit, persistence, and perseverance. Each of these constructs has a distinct definition, background, and implied utility in mathematics education research. However, these constructs are often colloquially conceptualized as synonyms, leading to a misconception of what can be learned through the lens of each construct. The purpose of this paper is to carefully examine the literature on grit, persistence, and perseverance and to review and distinguish the ways in which these constructs offer insights into learning mathematics with understanding. [ABSTRACT FROM AUTHOR]

This study provides a systematic literature review of research in the field of teaching and learning mathematics through Content and Language Integrated Learning (CLIL), Content-Based Instruction (CBI), and English Medium Instruction (EMI). The review aims to examine the most relevant literature with a focus on mathematics and CLIL, CBI, or EMI in Scopus and Web of Science per the Preferred Reporting Items for Systematic Reviews (PRISMA) guidelines. Based on 151 sources, 52 papers were selected according to predefined selection criteria. The papers were analysed and coded according to the following categories: (1) geographical productivity, (2) diachronic productivity growth, (3) main objectives, (4) methodology, and research design, (5) variables and measurement instruments, (6) context and sample details, and (7) main findings. The results reveal that most of the research analysed has been carried out in the Asian continent, followed by Europe. The analysis of diachronic productivity shows that the study of the application of CLIL, CBI, and EMI programs in the teaching-learning process of mathematics has notably increased in recent years, especially in the last triennium (2020–2022). Regarding the objectives of the selected corpus, the majority aimed at teaching practices and learning processes, and outcomes in mathematics and language proficiency in CLIL, CBI, and/or EMI classrooms. The corpus analysed fits within one or more of the following categories: empirical, qualitative, descriptive, correlational, and cross-sectional. The samples utilized in different studies differ significantly, both in terms of quantity –ranging from one person to 700– and in the educational level being studied, which would be primary, secondary, or tertiary education. The main variables studied in the corpus focus on mathematical competence, language proficiency, teaching practices, teacher training, science competence, and teachers' perceptions. The most widely used instruments have been objective tests, such as questionnaires, together with standardized tests to measure some aspects related to mathematical competence and language proficiency. They are followed by an analysis of documents (academic records, teaching materials, official documents...), participant or non-participant observation, interviews, and video and audio recordings. In summary, in the scientific literature analysed, a positive or neutral view predominates on the effects of the CLIL, CBI, and EMI approaches on the learning of mathematics and the L2. This can be due to methodological issues fundamentally related to the methodology, research design, sample, and measurement instruments. Thus, we must highlight that some of the results from the selected papers must be interpreted with caution. Taking this factor into consideration, further comparative studies on a wider scale are required to examine thoroughly the effects of CLIL, CBI, and EMI on the teaching and learning of mathematics in an L2. Besides, it is important to study in greater depth the different levels of language acquisition since the research analysed shows that these have not been sufficiently addressed in the mathematical field of knowledge. [ABSTRACT FROM AUTHOR]

This correction notice addresses a mistake in the original paper titled "Cyberbullying Detection on Twitter Using Deep Learning-Based Attention Mechanisms and Continuous Bag of Words Feature Extraction." The authors apologize for omitting Prince Sultan University (PSU) from the funding statement. PSU was one of the main funders for the research, which was a collaborative effort between King Saud University, Universiti Teknologi Petronas, and Prince Sultan University. The authors express their appreciation for the generous support from these universities and state that the scientific conclusions of the paper remain unaffected. The funding statement in the original publication has been updated to include PSU. [Extracted from the article]

In this paper, an optimization approach based on an arithmetic optimization algorithm (AOA) is proposed for specifying the optimal allocation of distribution generations/generators (DGs) and capacitor banks (CBs) in radial distribution systems. The AOA is a new population-based meta-heuristic algorithm that is essentially based on using basic arithmetic operators in mathematics. The proposed approach is employed to specify the optimum placement, capacity, and power factor of DGs and CBs to decrease the distribution systems' total power loss and voltage deviation. To state the performance of the proposed approach, DGs and CBs are placed in IEEE 33-bus and 69-bus systems separately or together. When only DGs are used and the parameters of location, capacity, and power factor of DGs are determined simultaneously, the total active power loss reductions in the IEEE 33-bus and 69-bus systems are achieved at 94.42% and 98.03%, respectively. When the results of other optimization algorithms are examined, it is seen that better results are obtained with AOA. [ABSTRACT FROM AUTHOR]

Summer camps can help children continue to learn beyond school, build knowledge, keep their learning skills sharp, and help them prepare for the following school year. This paper presents participants', facilitators', and researchers' experiences in a "Problem Solvers Camp" held in the Maker Lab at an Ontario University. A total of 12 junior students participated in a one-week summer camp, during which the participants developed plausible solutions for mathematical and instant problems using their creativity while learning some mathematical concepts. The creative learning spiral (CLS) model was adopted while designing the learning activities. Throughout the camp, children had the opportunity to work with virtual tech tools to design, create, and play to complete their challenges. Afterward, they shared their work for feedback and generated new ideas to promote their creative learning. The data were collected through observations, participants' work, and their portfolios to highlight the campers' experiences throughout the camp. On the last day of the camp, the researchers also ran focus group interviews. Data analysis showed that CLS might offer engaging environments that enhance children's creative and reflective thinking skills to solve real-life problems. This study enabled children to engage in all stages of the CLS during problem solving, encouraging the exchange of ideas and opinions. The implementation of the CLS model also has the potential to inspire creativity and enhance learners' fluency and elaboration skills, especially when complemented by technological or coding tools. [ABSTRACT FROM AUTHOR]

In this paper, the recognition of fidgety speech emotion is studied, and real-world speech emotions are collected to enhance emotion recognition in practical scenarios, especially for cognitive tasks. We first focused on eliciting fidgety emotions and data acquisition for general math learning. Students practice mathematics by performing operations, solving problems, and orally responding to questions, all of which are recorded as audio data. Subsequently, the teacher evaluates the accuracy of these mathematical exercises by scoring, which reflects the cognitive outcomes of the students. Secondly, we propose an end-to-end speech emotion model based on a multi-scale one-dimensional (1-D) residual convolutional neural network. Finally, we conducted an experiment to recognize fidgety speech emotions by testing various classifiers, including SVM, LSTM, 1-D CNN, and the proposed multi-scale 1-D CNN. The experimental results show that the classifier we constructed can identify fidgety emotion well. After conducting a thorough analysis of fidgety emotions and their influence on the learning process, a clear relationship between the two was apparent. The automatic recognition of fidgety emotions is valuable for assisting on-line math teaching. [ABSTRACT FROM AUTHOR]

The study of symmetry is a fascinating and unifying subject that connects various areas of mathematics in the twenty-first century. Algebraic structures offer a framework for comprehending the symmetries of geometric objects in pure mathematics. This paper introduces new concepts in algebraic structures, concentrating on semimodules over semirings and analysing the neutrosophic structure in this context. We explore the properties of neutrosophic subsemimodules and neutrosophic ideals after defining them. We discuss, utilizing neutrosophic products, the representations of neutrosophic ideals and subsemimodules, as well as the relationship between neutrosophic products and intersections. Finally, we derive equivalent criteria in terms of neutrosophic structures for a semiring to be fully idempotent. [ABSTRACT FROM AUTHOR]

The present paper investigates the following inhomogeneous generalized Hartree equation i u ˙ + Δ u = ± | u | p − 2 | x | b (I α ∗ | u | p | · | b) u , where the wave function is u : = u (t , x) : R × R N → C , with N ≥ 2 . In addition, the exponent b > 0 gives an unbounded inhomogeneous term | x | b and I α ≈ | · | − (N − α) denotes the Riesz-potential for certain 0 < α < N . In this work, our aim is to establish the local existence of solutions in some radial Sobolev spaces, as well as the global existence for small data and the decay of energy sub-critical defocusing global solutions. Our results complement the recent work (Sharp threshold of global well-posedness versus finite time blow-up for a class of inhomogeneous Choquard equations, J. Math. Phys. 60 (2019), 081514). The main challenge in this work is to overcome the singularity of the unbounded inhomogeneous term | x | b for certain b > 0 . [ABSTRACT FROM AUTHOR]

This article explores the accessibility of symbolic computations, such as using the Wolfram Mathematica environment, in promoting the shift from informal experimentation to formal mathematical justifications. We investigate the accuracy of computational results from mathematical software in the context of a certain summation in trigonometry. In particular, the key issue addressed here is the calculated sum ∑ n = 0 44 tan ⁡ 1 + 4 n ° . This paper utilizes Wolfram Mathematica to handle the irrational numbers in the sum more accurately, which it achieves by representing them symbolically rather than using numerical approximations. Can we rely on the calculated result from Wolfram, especially if almost all the addends are irrational, or must the students eventually prove it mathematically? It is clear that the problem can be solved using software; however, the nature of the result raises questions about its correctness, and this inherent informality can encourage a few students to seek viable mathematical proofs. In this way, a balance is reached between formal and informal mathematics. [ABSTRACT FROM AUTHOR]

Nowadays, ICT play a fundamental role in education, as they are essential in all areas of knowledge at any educational stage. Specifically, in the area of mathematics, within the Primary Education stage, they are also very valid resources. This is demonstrated by the latest scientific studies. In recent times, the scientific literature has provided evidence of all this through different research studies. The aim of this paper is to analyze all those publications that deal with the teaching–learning processes of mathematics through ICT in primary education. The aim is to show the current state of the scientific literature and what elements and aspects to highlight are common to the documents analyzed. By means of the systematic literature review method, we analyzed 11 articles indexed in Scopus and the Web of Science, with the result that the use of ICT in this area is still scarce, as the volume of publications in this respect is very low. This could also indicate a prevalence of traditional methodologies associated with the teaching of mathematics that could hinder students' acquisition of mathematical competence. However, those studies that show the use of ICT demonstrate that its use leads to an improvement in performance, motivation, and problem solving. [ABSTRACT FROM AUTHOR]

The paper under discussion has some shortcomings in regard to mathematical formulation of the problem related to acoustics, its justification, some references analyses and the text, and we feel that this study has not been finished to its full extent. From the point of view of acoustic jet formation, the mathematical model used by the authors has a number of significant limitations which are not taken into account. Moreover, the formal analogy between the parameters of electromagnetic waves and acoustic waves should be used with caution in the conditions of localized beams (acoustic jet), and the limits of their application should be justified. [ABSTRACT FROM AUTHOR]

This correction notice addresses an omission in a previously published paper titled "Ricci Vector Fields Revisited." The authors apologize for not including acknowledgements in the original paper and express their gratitude for the support received from King Saud University in Riyadh, Saudi Arabia. The authors assure readers that this correction does not impact the scientific conclusions of the paper. The correction has been approved by the Academic Editor and the original publication has been updated. The authors of the paper are Hanan Alohali, Sharief Deshmukh, and Gabriel-Eduard Vîlcu. [Extracted from the article]

Simple Summary: Cancer is basically a tough condition on a patient's body where cell grows uncontrollably. Normal cells are affected, which destroys the health of the patient. The main problem in cancer is spreading from one part to another. Therefore, the mathematical modeling of cancerous tumors integrates to check overall stability. A novel approach is introduced such as Bernstein polynomial with combination of genetic algorithm, sliding mode controller, and synergetic control. The proposed solution has easily eliminated cancerous cells within five days using synergetic control. In addition, five cases are incorporated to evaluate error function. In addition, a brief comparative study is added to contrast the simulation results with theoretical modeling. Cancerous tumor cells divide uncontrollably, which results in either tumor or harm to the immune system of the body. Due to the destructive effects of chemotherapy, optimal medications are needed. Therefore, possible treatment methods should be controlled to maintain the constant/continuous dose for affecting the spreading of cancerous tumor cells. Rapid growth of cells is classified into primary and secondary types. In giving a proper response, the immune system plays an important role. This is considered a natural process while fighting against tumors. In recent days, achieving a better method to treat tumors is the prime focus of researchers. Mathematical modeling of tumors uses combined immune, vaccine, and chemotherapies to check performance stability. In this research paper, mathematical modeling is utilized with reference to cancerous tumor growth, the immune system, and normal cells, which are directly affected by the process of chemotherapy. This paper presents novel techniques, which include Bernstein polynomial (BSP) with genetic algorithm (GA), sliding mode controller (SMC), and synergetic control (SC), for giving a possible solution to the cancerous tumor cells (CCs) model. Through GA, random population is generated to evaluate fitness. SMC is used for the continuous exponential dose of chemotherapy to reduce CCs in about forty-five days. In addition, error function consists of five cases that include normal cells (NCs), immune cells (ICs), CCs, and chemotherapy. Furthermore, the drug control process is explained in all the cases. In simulation results, utilizing SC has completely eliminated CCs in nearly five days. The proposed approach reduces CCs as early as possible. [ABSTRACT FROM AUTHOR]

It is well-known that the weighted averages of two competing forecasts may reduce mean squared prediction errors (MSPE) and may also introduce certain inefficiencies. In this paper, we take an in-depth view of one particular type of inefficiency stemming from simple combination schemes: Mincer and Zarnowitz inefficiency or auto-inefficiency for short. Under mild assumptions, we show that linear convex forecast combinations are almost always auto-inefficient, and, therefore, greater reductions in MSPE are almost always possible. In particular, we show that the process of taking averages of forecasts may induce inefficiencies in the combination, even when individual forecasts are efficient. Furthermore, we show that the so-called "optimal weighted average" traditionally presented in the literature may indeed be inefficient as well. Finally, we illustrate our findings with simulations and an empirical application in the context of the combination of headline inflation forecasts for eight European economies. Overall, our results indicate that in situations in which a number of different forecasts are available, the combination of all of them should not be the last step taken in the search of forecast accuracy. Attempts to take advantage of potential inefficiencies stemming from the combination process should also be considered. [ABSTRACT FROM AUTHOR]

The allocation of seats in a legislative body to groups based on their size is a crucial issue in legal and political studies. However, recent findings suggest that an optimal allocation of seats may not be proportional to the size of the groups. For instance, the European Parliament (EP) utilizes a subproportional system known as degressive proportionality. Unfortunately, current apportionment methods for the EP lack a rigorous axiomatic analysis and fail to adequately address equality. Building upon recent research on equality in subproportional settings, this paper proposed a novel generalization of existing axioms and divisor methods for proportionality to encompass subproportionality with relative equality. Specifically, we consider a function f (p) = a + b p γ on the standard number of seats for a group of size p, where a, b and γ are given non-negative constants, and a is an integer. This theory is exemplified through an empirical study focused on the EP. [ABSTRACT FROM AUTHOR]

We have interviewed becoming mathematics teachers, in the last semester of their education, asking how they experience their time as teacher students with the focus on inclusive teaching. In their forthcoming daily work, they will be responsible for arranging for inclusive teaching that addresses all the learners' needs in mathematics. We believe the voices of future teachers are important to include in conversations about how programs prepare future mathematics teachers for the work of teaching in today's schools and classrooms. We used storylines as a theoretical construct to discuss the socio-political aspects of mathematics teacher education through the lens of two research questions: What storylines emerged in interviews with becoming mathematics teachers in their last semester of teacher education when they talked about teaching in diverse classrooms? What implications might these storylines have on mathematics teacher education? Our analysis made us aware of three important storylines: (1) storylines about the importance of language in mathematics education; (2) storylines about the importance of accepting diverse methods when doing mathematics; and (3) storylines about issues of invisibility at play in mathematics classrooms. In this paper, we discuss the importance of creating space for discussions in teacher education about issues that may challenge inclusive practices in mathematics classrooms. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of symmetric difference operators in terms of overlap and grouping functions, for which the associativity property is not strongly required. These symmetric difference operators are weaker than symmetric difference operators in terms of positive and continuous t-norms and t-conorms. Therefore, in the sense of the characters of mathematics, these operators do not necessarily satisfy certain properties, such as associativity and the neutrality principle. We analyze several related important properties based on two models of symmetric differences. [ABSTRACT FROM AUTHOR]

Currently, a large amount of information is presented graphically. However, visually impaired individuals do not have access to visual information. Instead, they depend on tactile illustrations—raised lines, textures, and elevated graphics that are felt through touch—to perceive geometric and various other objects in textbooks. Tactile graphics are considered an important factor for students in the science, technology, engineering, and mathematics fields seeking a quality education because teaching materials in these fields are frequently conveyed with diagrams and geometric figures. In this paper, we conducted a systematic literature review to identify the current state of research in the field of automatic tactile graphics generation. Over 250 original research papers were screened and the most appropriate studies on automatic tactile graphic generation over the last six years were classified. The reviewed studies explained numerous current solutions in static and dynamic tactile graphics generation using conventional computer vision and artificial intelligence algorithms, such as refreshable tactile displays for education and machine learning models for tactile graphics classification. However, the price of refreshable tactile displays is still prohibitively expensive for low- and middle-income users, and the lack of training datasets for the machine learning model remains a problem. [ABSTRACT FROM AUTHOR]

The Victorian Curriculum and Assessment Authority (VCAA) introduced the use of Computer Algebra System (CAS) technology (calculator and software) into the senior secondary mathematics curriculum and examination assessment in three phases, starting with a research-based pilot from 2000, followed by parallel implementation of CAS and non-CAS subjects from 2006 and culminating in transition to CAS-assumed subjects in 2010. This paper reports reflections on these developments over two decades from the perspectives of a researcher and the state mathematics manager (the authors) in consultation with four implementing teachers (the consultants). The authors critically examined the strategic design decisions that were made for the initiative over time. Then, with contributions from the four consultants, technical design issues relating to assessment and to teaching and the changes over a decade were investigated. A range of modifications have been made over the two decades, driven by changes in device capability and progressively increasing teaching expertise. The place of CAS in senior mathematics is now widely accepted, partly because an examination component not allowing any technology has been implemented. Examination questions have become more general, which may have added difficulty, but more questions involve setting up a real situation mathematically. [ABSTRACT FROM AUTHOR]

This paper presents a simplified model of the population migration problem, addressed to first-year engineering students in order to show them the use of linear algebra tools. The study consists of predicting the census in the city centre and in the suburbs, determining the city population equilibrium point, and making a sociological interpretation of population flows. This practical problem is part of the seminar "Applications of Linear Algebra in Engineering", which is being held at the Universitat Politècnica de Catalunya-BarcelonaTech (UPC). This seminar consists in the learning of linear algebra by the implementation of real applications where mathematical tools are required to resolve them. This paper presents an application of linear algebra to the population migration problem and analyses students' appreciation through anonymous surveys and personal interviews. The surveys assessed students' motivation towards the subject of linear algebra and their learning of mathematical concepts. Personal interviews were conducted for students in order to let them express in detail their opinion about the seminar. The results confirm that the introduction of real applications in the learning of mathematics increases students' motivation and involvement, which implies an improvement in students' performance in the first courses of STEM degrees. [ABSTRACT FROM AUTHOR]

Conversations of educational equity in mathematics necessitate a more deliberate, nuanced look at the mathematical processes of learning for students of color from historically marginalized communities. This paper describes the theoretical work of a research collaborative that seeks to develop understanding of the experiences around mathematical identity of Latinas labeled with Learning Disabilities in mathematics classrooms. Expanding the theory of Complex Embodiment from Disability Studies, we explore new interdisciplinary theoretical and methodological tools to analyze the emotional, embodied experience of learning mathematics in the social worlds of mathematics classrooms, using emotional discourse. We take up theoretical and methodological practices around intersectionality through analysis of how power and positioning operate in mathematics identity development. We find that the young woman whose narratives we explore in this paper is positioned through deficit discourses around disability and multilingual learners, yet she understands herself through a positive mathematical affinity she shares with her mother. Over time, we see her narratives shift emotionally away from mathematics, as well as away from this connection with her mother. Her narratives help us develop a theoretical perspective that understands emotion in mathematics learning as both embodied and socially constructed. [ABSTRACT FROM AUTHOR]

Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order (FO) dynamics. It begins by studying the practical stability of a general class of tempered fractional-order (TFO) nonlinear systems, with broad applicability and potential for expanding its applications. Afterward, a polynomial controller is designed to guarantee the practical stability of the PS, encompassing the standard constant controller as a specific instance. The design conditions for this controller are resolved using the sum of squares (SOS) approach, a powerful technique for guaranteeing stability and control design. To showcase the practical value of the analytical findings, simulations of the PS are conducted utilizing SOSTOOLS. [ABSTRACT FROM AUTHOR]

Nowadays, graph theory is one of the most exciting fields of mathematics due to the tremendous developments in modern technology, where it is used in many important applications. The orthogonal double cover (O D C) is a branch of graph theory and is considered as a special class of graph decomposition. In this paper, we decompose the complete bipartite graphs K x , x by caterpillar graphs using the method of O D C s. The article also deals with constructing the O D C s of K x , x by general symmetric starter vectors of caterpillar graphs such as stars–caterpillar, the disjoint copies of cycles–caterpillars, complete bipartite caterpillar graphs, and the disjoint copies of caterpillar paths. We decompose the complete bipartite graph by the complete bipartite subgraphs and by the disjoint copies of complete bipartite subgraphs using general symmetric starter vectors. The advantage of some of these new results is that they enable us to decompose the giant networks into large groups of small networks with the comprehensive coverage of all parts of the giant network by using the disjoint copies of symmetric starter subgraphs. The use case of applying the described theory for various applications is considered. [ABSTRACT FROM AUTHOR]

In recent years, the theory of convexity has influenced every field of mathematics due to its unique characteristics. Numerous generalizations, extensions, and refinements of convexity have been introduced, and one of them is set-valued convexity. Interval-valued convex mappings are a special type of set-valued maps. These have a close relationship with symmetry analysis. One of the important aspects of the relationship between convex and symmetric analysis is the ability to work on one field and apply its principles to another. In this paper, we introduce a novel class of interval-valued (I.V.) functions called CR - γ -convex functions based on a non-negative mapping γ and center-radius ordering relation. Due to its generic property, a set of new and known forms of convexity can be obtained. First, we derive new generalized discrete and integral forms of Jensen's inequalities using CR - γ -convex I.V. functions. We employ this definition and Riemann-Liouville fractional operators to develop new fractional versions of Hermite-Hadamard's, Hermite-Hadamard-Fejer, and Pachpatte's type integral inequalities. We examine various key properties of this class of functions by considering them as special cases. Finally, we support our findings with interesting examples and graphical representations. [ABSTRACT FROM AUTHOR]

Ramsey theory constitutes the dynamics of mechanical systems, which may be described as abstract complete graphs. We address a mechanical system which is completely interconnected by two kinds of ideal Hookean springs. The suggested system mechanically corresponds to cyclic molecules, in which functional groups are interconnected by two kinds of chemical bonds, represented mechanically with two springs k 1 and k 2 . In this paper, we consider a cyclic system (molecule) built of six equal masses m and two kinds of springs. We pose the following question: what is the minimal number of masses in such a system in which three masses are constrained to be connected cyclically with spring k 1 or three masses are constrained to be connected cyclically with spring k 2 ? The answer to this question is supplied by the Ramsey theory, formally stated as follows: what is the minimal number   R (3 , 3) ? The result emerging from the Ramsey theory is R (3 , 3) = 6 . Thus, in the aforementioned interconnected mechanical system at least one triangle, built of masses and springs, must be present. This prediction constitutes the vibrational spectrum of the system. Thus, the Ramsey theory and symmetry considerations supply the selection rules for the vibrational spectra of the cyclic molecules. A symmetrical system built of six vibrating entities is addressed. The Ramsey approach works for 2D and 3D molecules, which may be described as abstract complete graphs. The extension of the proposed Ramsey approach to the systems, partially connected by ideal springs, viscoelastic systems and systems in which elasticity is of an entropic nature is discussed. "Multi-color systems" built of three kinds of ideal springs are addressed. The notion of the inverse Ramsey network is introduced and analyzed. [ABSTRACT FROM AUTHOR]