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Automatic test paper design is critical in education to reduce workloads for educators and facilitate an efficient teaching process. However, current designs fail to satisfy the realistic teaching requirements of educators, including the consideration of both test quality and efficiency. This is the main reason why teachers still manually construct tests in most teaching environments. In this paper, the quality of tests is quantitatively defined while considering multiple objectives, including a flexible coverage of knowledge points, cognitive levels, and question difficulty. Then, a model based on the technique of linear programming is delicately designed to explore the optimal results for this newly defined problem. However, this technique is not efficient enough, which cannot obtain results in polynomial time. With the consideration of both test quality and generation efficiency, this paper proposes a genetic algorithm (GA) based method, named dynamic programming guided genetic algorithm with adaptive selection (DPGA-AS). In this method, a dynamic programming method is proposed in the population initialization part to improve the efficiency of the genetic algorithm. An adaptive selection method for the GA is designed to avoid prematurely falling into the local optimal for better test quality. The question bank used in our experiments is assembled based on college-level calculus questions from well-known textbooks. The experimental results show that the proposed techniques can construct test papers with both high effectiveness and efficiency. The computation time of the test assembly problem is reduced from 3 hours to 2 seconds for a 5000-size question bank as compared to a linear programming model with similar test quality. The test quality of the proposed method is better than the other baselines.

In this work, we propose an adaptive variation on the classical Heavy-ball method for convex quadratic minimization. The adaptivity crucially relies on so-called “Polyak step-sizes”, which consists of using the knowledge of the optimal value of the optimization problem at hand instead of problem parameters such as a few eigenvalues of the Hessian of the problem. This method happens to also be equivalent to a variation of the classical conjugate gradient method, and thereby inherits many of its attractive features, including its finite-time convergence, instance optimality, and its worst-case convergence rates.The classical gradient method with Polyak step-sizes is known to behave very well in situations in which it can be used, and the question of whether incorporating momentum in this method is possible and can improve the method itself appeared to be open. We provide a definitive answer to this question for minimizing convex quadratic functions, an arguably necessary first step for developing such methods in more general setups.

We consider the problem of linearizing a pseudo-Boolean function $f : \lbrace 0,1\rbrace ^n \rightarrow \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This motivates the definition of the linearization complexity of $f$ as the minimum such $k$. Our theoretical contributions are the proof that random polynomials almost surely have a high linearization complexity and characterizations of its value in case we do or do not restrict the set of admissible Boolean functions. The practical relevance is shown by devising and evaluating integer linear programming models of two such linearizations for the low auto-correlation binary sequences problem. Still, many problems around this new concept remain open.

Background:Understanding fractions in mathematics often poses greater complexity compared to integral numbers. The primary difficulty lies in students' inadequate grasp of fractional basics, notably in comparing and sequencing fractions. Aim: This research seeks to create and evaluate a learning pathway's effect on fourth graders' comprehension of fractions, with a focus on their comparison and sequencing. Method: Employing a design research validation study approach, the research progresses through preliminary design, experimental design, and retrospective analysis. Conducted in a Palembang school involving six fourth graders recommended by their teacher, data collection encompassed essay-based pre and post-tests, Student Activity Sheets, observations, interviews, and documentations. The data analysis was retrospectively carried out, anchored on HLT as the benchmark. Result: Findings reveal a student learning trajectory encompassing three principal activities. Initially, students used folding and gluing of paper to discern fraction values. Subsequently, they engaged in coloring and illustrating folds for fraction comparison. The final activity involved drawing, coloring boxes, and fraction comparison and sequencing. Overall, students showed proficiency in understanding and determining fraction values and comparing them, yet struggled with ordering certain fractions. Conclusion: The structured learning path facilitated students' understanding of basic fraction concepts, especially in comparing them. Nevertheless, reinforcing methods or approaches for teaching fraction ordering is essential.

This study investigates the surface characteristics of printing papers using fractal geometry, focusing on surface roughness and surface friction as independent properties. The fractal dimension (FD) was analyzed using the power spectral density method, which provided a more distinct characterization of paper surfaces compared to the variogram method. Surface roughness and friction were measured using a stylus-based contact profilometer, and mean absolute deviation (MAD) parameters, such as the mean absolute deviation of surface roughness (RMAD) and friction, were calculated to capture surface variability. The results revealed that while conventional parameters, such as roughness average (Ra) and the average coefficient of friction, are highly sensitive to measurement conditions, MAD-based parameters demonstrate greater robustness and stability. For instance, the regression equation for RMAD vs. Ra showed a strong correlation, with an R² value close to 1.0. However, the slopes were significantly less than one. Furthermore, FD exhibited weak correlations with surface roughness and friction, with R² values of 0.342 and 0.016, respectively, highlighting its unique ability to characterize autocorrelation or complexity of surface. Additionally, the effects of coating on paper surfaces were evaluated, revealing reduced flocculation of surface profiles but a 5% increase in FD, indicating enhanced surface complexity. These findings underscore the complementary role of FD in providing a comprehensive understanding of surface properties, with potential applications in quality control and the design of paper products.

In this paper we extend the SuperHyperAlgebra, SuperHyperGraph, SuperHyperTopology, SuperHyperSoft Set, endowed with SuperHyperOperations, SuperHyperAxioms, and SuperHyperFunctions, to the most general form of structure, from our real world, called SuperHyperStructure in any field of knowledge. A practical application of the SuperHyperStructure is presented at the end. The prefix “Hyper” [Marty, 1934] stand for the codomain of the functions and operations to be P(H), or the powerset of the set H. While the prefix “Super” [Smarandache, 2016] stands for using the Pn (H), n ≥ 2, or the n-th PowerSet of the Set H {because the set (or system) 𝐻 (that may be a set of items, a company, institution, country, region, etc.) is organized in sub-systems, which in their turn are organized in sub-sub-systems, and so on} in the domain and/or codomain of the functions and operations.

In 1921 Mellin published a Comptes Rendu paper computing the principal solution of a polynomial using generalized hypergeometric functions of its coefficients. He used an integral transform nowadays bearing his name. Slightly over three pages, the paper is written in French in a terse style befitting the language. This article makes Mellin’s landmark result accessible to people who are not experts in hypergeometric functions and complex analysis by deriving detailed proofs that were omitted in Mellin’s paper.

This Special Issue comprises the second collection of papers submitted by both the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA) and the outstanding scholars working in the core research fields of MCA [...]

In this paper, we consider a robust combinatorial optimization problem with uncertain weights and propose an uncertainty set that generalizes interval uncertainty by imposing lower and upper bounds on deviations of subsets of items. We prove that if the number of such subsets is fixed and the family of these subsets is laminar, then the robust combinatorial optimization problem can be solved by solving a fixed number of nominal problems. This result generalizes a previous similar result for the case where the family of these subsets is a partition of the set of items.

In an era overwhelmed by academic big data, students grapple with identifying academic papers that resonate with their learning objectives and research interests, due to the sheer volume and complexity of available information. This study addresses the challenge by proposing a novel academic paper recommendation system designed to enhance personalized learning through the nuanced understanding of academic social networks. Utilizing the theory of social homogeneity, the research first constructs a sophisticated academic social network, capturing high-order social relationships, such as co-authorship and advisor–advisee connections, through hypergraph modeling and advanced network representation learning techniques. The methodology encompasses the development and integration of a hypergraph convolutional neural network and a contrastive learning framework to accurately model and recommend academic papers, focusing on aligning with students’ unique preferences and reducing reliance on sparse interaction data. The findings, validated across multiple real-world datasets, demonstrate a significant improvement in recommendation accuracy, particularly in addressing the cold-start problem and effectively mapping advisor–advisee relationships. The study concludes that leveraging complex academic social networks can substantially enhance the personalization and precision of academic paper recommendations, offering a promising avenue for addressing the challenges of academic information overload and fostering more effective personalized learning environments.

Predicting stock prices is contained in the basic approach is fundamental and technical analysis which is needed by entrepreneurs who invest their capital, this analysis is to determine the company's financial performance and must continue to be carried out, to carry out this analysis we use the help of several financial ratios where several types of ratios Return on Assets, Debt to Equity Ratio, Return on Equity, and Book Value per Share are some examples. The authors applied a quantitative descriptive approach to companies listed on the Indonesia Stock Exchange in the Pulp & Paper sector for this study. According to the Correlation and Regression tables, all of the variables ROA, ROE, DER, and BVS have an effect on stock prices, but the stock session obtained on the variables ROA, ROE, and DER has a very significant effect on stock prices but has no significant effect on stock prices on the BVS variable. So in the long term the company must implement one of two policies, namely low solvency means using less debt than own capital and a low solvency policy will not cause high interest expenses to be borne by the company so that it will affect growth.

Although socioeconomic disadvantage is linked with academic underachievement, many children from low-income backgrounds perform well in school. Which modifiable factors predict this academic resilience? We examine between- and within-person predictors of one important academic metric - mathematics performance - across adolescence in 1715 (796 male, 919 female) youth living in poverty in Ireland, using data from three waves (9, 13, and 17/18 years) of the Growing Up in Ireland study. Using linear mixed models, math performance was worse when adolescents had more socioemotional and behavioural difficulties, more child-parent relationship conflict, parents had lower expectations of the adolescent's educational achievement, and when primary caregivers had less education. Adolescents who had better intellectual self-concept and attended a non-disadvantaged school had greater math performance. This research adds to the growing body of work suggesting academic resilience is dynamic and multisystemic; it provides potential targets at multiple levels to promote such resilience., (© 2024 The Author(s). British Journal of Developmental Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.)

Frank and Wolfe’s celebrated conditional gradient method is a well-known tool for solving smooth optimization problems for which minimizing a linear function over the feasible set is computationally cheap. However, when the objective function is nonsmooth, the method may fail to compute a stationary point. In this work, we show that the Frank–Wolfe algorithm can be employed to compute Clarke-stationary points for nonconvex and nonsmooth optimization problems consisting of minimizing upper-$C^{1,\alpha }$ functions over convex and compact sets. Furthermore, under more restrictive assumptions, we propose a new algorithm variant with stronger stationarity guarantees, namely directional stationarity and even local optimality.

We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as the analogue of the helicoidal Karcher-Scherk surfaces.

Global education in China, particularly in the rural regions, has not been extensively investigated. This paper discussed Chinese schoolteachers' perceptions of and approaches to global education to address a gap in the Western discourses. A total of 12 in-service schoolteachers were identified by the snowball sampling method. All participants were interviewed in two-round semi-structured in-depth interviews. Data then were analysed based on an open coding system and phenomenological approach. Results show that rural schoolteachers held an integrated definition framework and systematic approach towards global education. Their perceptions of global education encompassed broad arrays of cultural awareness, competencies, environmental issues, and humanistic values in national and international contexts. Factors contributing to this conceptual framework included teachers' personal teaching experience, the students' social-economic status, and national and international policies. Additionally, sampled rural schools adopted a whole-school approach to conducting global education, i.e., embedding into formal curricula, using interdisciplinary and integrated studies, involving various school programs, and being part of the schools' philosophy. It further discussed the gap between teachers' conceptual framework and their concrete implementation of global education. Overall, this paper provided a distinctive perspective of global education from the rural schoolteachers to reveal global education remains marginalized in China.

Standards are a set of guidelines or criteria used to ensure consistency, quality, safety, and compatibility in products, services, and processes [...]

Abstract Very recently Jain et al. (J. Inequal. Appl. 2022:73, 2022) introduced the concept of multivalued F-contraction with altering distance function and investigated the existence of best proximity points for this class of mappings. In this article we prove that the existence of best proximity points for multivalued F-contraction non-self mappings can be obtained from the corresponding fixed point result for multivalued F-contraction self mappings, and so the main conclusion due to Jain et al. is not a real generalization of fixed point theory.

A scheme for the integration of $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type fractional differential equations (FDEs) is presented in this paper. The approach is based on the expansion of solutions to FDEs via fractional power series. It is proven that $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type FDEs can be transformed into equivalent $ \left(\, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)}\right)^n $-type FDEs via operator calculus techniques. The efficacy of the scheme is demonstrated by integrating the fractional Riccati differential equation.

From time to time, we hear in the news about a breach or attack on some well-known companies as just news, but it is a serious problem because it is the privacy of citizens, their money in trade and managing their businesses and projects. In this paper, we offer a review of the honey encryption planner. Honey Encryption is the encryption system that ensures flexibility versus the brute-force attack through the provision of plain reasonable text, but false for each key is invalid utilized by a trespasser to decrypt a message, two key areas are open it is difficult to create a compelling message trap that's perfect enough to deceive the striker even when he believes that he has the message in its original form. The next problem, the typo issue, where a valid phony plain text seem to a lawful user when he accidentally enters the wrong key. Our goal is to have more satisfaction disguised tricks that are perfect enough to prevent a trespasser from getting the original message, We also need new security methods because the attackers are looking for new ways to attack the systems, so we proposed a new way to protect messages and passwords well and difficult to break and take all the possibilities of attack, including the brute-force, and then the data is hidden in an image with a public secret key.

This paper focuses on the Southern African Association for Research in Mathematics, Science and Technology Education's (SAARMSTE's) role as a platform supporting research dissemination and connecting researchers in early grades mathematics (EGM) in the Southern African region. A review of the Long Papers in SAARMSTE over the last 20 years supports the finding of the other review papers in this Special Issue: that there has been substantial growth of attention to EGM since 2013. However, two distinctions are marked when looking at conference papers rather than journal papers. Firstly, there is a particularly large expansion of work in the last 5 years, with a broadening base of participation in this work. Second, looking across all the formats of conference presentations indicates SAARMSTE's role in supporting and building EGM as a key focus of research attention, and bringing together regional and international groups with interests in this area. Given that conference proceedings usually offer a broader picture of emerging interests than journal papers, we reflect on the range of foci of attention within EGM in the SAARMSTE Proceedings, and trends within this. These trends also help us to point to areas that are likely to be of key interest in the next decade. [ABSTRACT FROM AUTHOR]

Recently, the systems of e-learning are improved technologically and the led to the emergence of e-learning systems that reached the level of adaptation to students. Through which, it changed the entire education system during the Internet era. Nonetheless, the use of rule-based, assumption-based, and network-based method have some vital methodologies used to implement learner models across adaptive learning systems. The so common way to structure the learner models approaches rely on the personalization and user modelling. However, personalization and user modeling found out to be the best approaches-not only in developing students' talents but also in allowing students to take their own learning direction and making sure that they are using their potential to the fullest. The mismatching in viewpoints and perceptions between teachers and technicians along with a lack of appropriate technical knowledge have been identified as some of the major challenges affecting the learner model development. the main objective of this article is to show the use of different approaches through the recent scholars’ in implementing learner models within adaptive e-learning systems. Moreover, approaches and challenges in implementing learner models are also described

Background: Past studies clarified the relationship between dimensions of teaching and achievement emotions. However, more information is needed about the underlying process behind this relationship among students with different mathematical abilities., Aims: This study examined the association between students' perceived teaching quality and achievement emotions in Chinese mathematics classrooms, focusing on students with different mathematics achievements., Samples: There are 1045 secondary school students (49.1% girls; M age  = 13.90, SD = .84) from Chinese mathematics classrooms in the present study., Methods: A multi-group structural equation model was adopted to test the relationship between teaching quality and achievement emotions between low- and high-achieving students., Results: Control-value appraisals mediated in teacher support and achievement emotions in both student groups. At the same time, control-value appraisals failed to mediate cognitive activation and achievement emotions in low-achieving students, while the mediating effect of control-value appraisals was identified in high-achieving students. Besides, classroom management was related to achievement emotions via academic value only in low-achieving students. In contrast, it was related to achievement emotions via control-value appraisals in high-achieving students., Conclusions: The results clarified the mediation roles of control-value appraisals in teaching quality and achievement emotions in students with low- and high-achieving achievements. Similarities and differences were also identified between the two student groups. Teacher support was beneficial to students' positive emotions while classroom management helped to lessen students' negative emotions. High-achieving students benefited more from activating teaching compared with low-achieving students., (© 2024 British Psychological Society.)

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pretest and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students' results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students' disorientation is one of the purposes of history in mathematics education.

While proof has been studied from different perspectives in the mathematics education literature for decades, students continue to struggle to build proof comprehension. Complicating this, the manner in which proof comprehension is assessed largely remains to be the definition-theorem-proof format in which students are asked to reproduce proofs or similar proofs that are presented in class. This approach can encourage students to memorize proofs rather than develop tools for syllogistic reasoning. This paper reports on a seven-year collaboration among research mathematicians and mathematics educators. Following a model for proof comprehension, they implemented a cycle of planning assessments, implementing them and evaluating student responses in several courses each semester for three years at two universities. The model-based assessments were designed with probing questions about proofs or subproofs to point student attention to the relationships among definitions, statements and their relationships, as well as the logic used to help students to both develop proof knowledge and demonstrate their mathematical thinking. Discrepancies between the intention of assessments and student responses led to refinements as the team reviewed the results to inform its practice. Collaboration, experience and empirical data informed the development of the new "Promoting Reasoning in Undergraduate Mathematics (PRIUM) Qualitative Framework for Proof Comprehension." The paper discusses three main results: the Framework and how to use it, the Framework's utility at the individual, course and program levels of departmental evaluation, and a collaborative research process that may be utilized between research mathematics educators and mathematicians.

This paper presents research that examined teacher talk about moderation of English, mathematics and science assessment across Years 4, 6 and 8 as part of a broader inquiry into the use of scaled exemplars to support consistency of teacher judgement. The paper draws on Dorothy E Smith's sociological work, including the process of mapping textual connections to research everyday practices. We illustrate how moderation activities were shaped by systemic policy and related documents. We further illustrate how teachers used artefacts that they were created as part of the research project to leverage the value of moderation discussions. In the project, teachers generated artefacts that were written commentaries or texts explicating their judgement decisions (cognitive commentaries). Our analysis demonstrates how teachers then took these cognitive commentaries and independently embedded them into their everyday work. Teachers described how they used the artefacts in their moderation discussions as a means of improving their own practice, as well as their students' learning. We argue that when teachers are provided with the time and space to share their assessment and pedagogic knowledge and practice with school colleagues, including via cognitive commentaries, they are able to expand their field of professional impact and build their professional knowledge and practice.

This document is our reply to the Comment by Lei Li, Jiuyang Liang, and Zhenli Xu on our recent work (Onegin et al 2024 J. Phys. A: Math. Theor. 57 205002), where we investigated the pressure of classical Coulomb systems using the Ewald summation technique. The Comment raised concerns about our treatment of one- and two-component plasma systems, especially regarding the correctness of the derivation of formula (4.13) in Liang et al (2022 J. Chem. Phys. 157 144102), the contribution of the compensating background and calculations performed with LAMMPS. In this reply, we address each of these points in detail, demonstrating that our original findings remain valid. [ABSTRACT FROM AUTHOR]

The human capability to react or adapt to upcoming changes strongly relies on the ability to forecast them [...]

This project explored what constitutes "ethical practice of mathematics". Thematic analysis of ethical practice standards from mathematics-adjacent disciplines (statistics and computing), were combined with two organizational codes of conduct and community input resulting in over 100 items. These analyses identified 29 of the 52 items in the 2018 American Statistical Association Ethical Guidelines for Statistical Practice, and 15 of the 24 additional (unique) items from the 2018 Association of Computing Machinery Code of Ethics for inclusion. Three of the 29 items synthesized from the 2019 American Mathematical Society Code of Ethics, and zero of the Mathematical Association of America Code of Ethics, were identified as reflective of "ethical mathematical practice" beyond items already identified from the other two codes. The community contributed six unique items. Item stems were standardized to, "The ethical mathematics practitioner…". Invitations to complete the 30-min online survey were shared nationally (US) via Mathematics organization listservs and other widespread emails and announcements. We received 142 individual responses to the national survey, 75% of whom endorsed 41/52 items, with 90-100% endorsing 20/52 items on the survey. Items from different sources were endorsed at both high and low rates. A final thematic analysis yielded 44 items, grouped into "General" (12 items), "Profession" (10 items) and "Scholarship" (11 items). Moreover, for the practitioner in a leader/mentor/supervisor/instructor role, there are an additional 11 items (4 General/7 Professional). These results suggest that the community perceives a much wider range of behaviors by mathematicians to be subject to ethical practice standards than had been previously included in professional organization codes. The results provide evidence against the argument that mathematics practitioners engaged in "pure" or "theoretical" work have minimal, small, or no ethical obligations., (© 2024. The Author(s).)

Perception is an individual's ability to respond, interpret, and distinguish a view of any information to a stimulus. So the aims of this study was to find out: (1) students' perceptions of the use of an equation editor in writing mathematical notation as assignments for calculus class I papers, (2) students' perceptions of writing calculus I paper assignments using the manual method (handwriting). The research subjects consisted of 16 students majoring in Extension Informatics Engineering (afternoon class) Semester I. The type of research was descriptive qualitative. Data collection techniques are interviews. The analysis stage is to analyze the results of the interviews. The results of the study concluded that: (1) 11 (eleven) students agreed to use the equation editor in writing calculus I paper assignments,the rest were still confused about the use of the equation editor; and (2) all students do not agree if the paper is written using the manual method (handwriting) because the results are not neat and take a long time.

Peer review has never been a uniform practice but is now more diverse than ever. Despite a vast literature, little is known of how different disciplines organize peer review. This paper draws on ninety-five qualitative interviews with editors and publishers and several hundred written reports to analyze the organization of peer review in pure mathematics. This article focuses on the practice of "quick opinions" at top journals in mathematics: asking (senior) experts about a paper's importance, and only after positive evaluation sending the paper for a full review (which most importantly means checking the paper's correctness). Quick opinions constitute a form of "importance only" peer review and are thus the opposite of the "soundness only" approach at mega-journals such as PLOS ONE. Quick opinions emerged in response to increasing submissions and the fact that checking correctness in mathematics is particularly time-consuming. Quick opinions are informal and are often only addressed to editors. They trade on, indeed reinforce, a journal hierarchy, where journal names are often used as a "members' measurement system" to characterize importance. Finally, quick opinions highlight that a key function of the peer-reviewed journal today, apart from validation and filtration, is "designation"—giving authors items on their CV. [ABSTRACT FROM AUTHOR]

This Special Issue comprises the first collection of papers submitted by the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA), as well as outstanding scholars working in the core research fields of MCA [...]