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The paper compares the accuracy of reconstruction using different wavelets, and the authors also use fast and discrete Fourier transforms together to calculate the forward and inverse continuous wavelet transform in the frequency domain. Due to the use of calculations in the frequency domain, it becomes possible to perform decomposition, reconstruction, image filtering, and other transformations with high performance and precision. For multiscale signal analysis, a wavelet with a rectangular amplitude-frequency response has been constructed, which allows for an increase in the accuracy of decomposition and reconstruction compared to the Mallat algorithm presented in Matlab computer mathematics. At the same time, the time of multiscale analysis is reduced several times compared to the Mallat algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of small-amplitude unique solutions near the Maxwellian for the Fokker–Planck–Boltzmann equation in a finite channel with specular reflection boundary conditions. The solution space we consider is denoted as L k ̄ 1 L T ∞ L x 1 , v 2 , introduced in Duan et al. [Commun. Pure Appl. Math. 74(5), 932–1020 (2021)]. In addition, we investigate the long-time behavior of solutions for both hard and soft potentials. [ABSTRACT FROM AUTHOR]

I revisit my 1993 paper on Putnam and mathematical realism focusing on the indispensability argument and how it has fared over the years. This argument starts from the claim that mathematics is an indispensable part of science and draws the conclusion, from holistic considerations about confirmation, that the ontology of science includes abstract objects as well as the physical entities science deals with. [ABSTRACT FROM AUTHOR]

Inclusive teaching practices can be characterized as recurrent ways how teachers work with their students' diverse abilities, but how exactly are they enacted in subject matter classrooms? The paper proposes a conceptual framework to unpack inclusive practices according to the student ability to which they refer, in five typical jobs for teachers: (a) identifying the demands for the ability, (b) differentiating learning goals, (c) compensating for low abilities, (d) enhancing abilities, and (e) addressing the abilities in joint learning. The proposed job-ability framework for inclusive teaching practices is substantiated in a video study of 25 mathematics lessons on percentages with the same curriculum material. In total, rather than 50, 133 different inclusive teaching practices were identified in 3862 sequences and structured into 20 cells. They address four abilities (from most often to least often): (1) selective attention/working memory, (2) mathematical pre-knowledge, (3) language proficiency, and (4) metacognitive regulation. The large variance of enacted practices identified within and between lessons calls for professional development that elicits, leverages, and extends the repertoire of practices. While the reported frequencies are specific to the chosen teaching unit, the job-ability framework can be transferred to other subject-matter classrooms and used in professional development programs. [ABSTRACT FROM AUTHOR]

In this paper, we study 4-dimensional complete hypersurfaces with w-constant mean curvature in the unit sphere. We give a lower bound of the scalar curvature for 4-dimensional complete hypersurfaces with w-constant mean curvature. As a by-product, we give a new proof of the result of Deng-Gu-Wei [Adv. Math. 314 (2017), pp. 278–305] under the weaker topological condition. [ABSTRACT FROM AUTHOR]

Fractions are challenging for both typically achieving children and adults. Although some prior research has focused on fraction difficulties of children with mathematics difficulties (MD), persistent difficulties encountered by adults with MD remain unknown. It is possible that these adults may be able to compensate for some deficits. In this study, we administered an un-timed, paper-based fraction achievement test to French adults with and without MD to compare their knowledge of fractions. Compared with controls, adults with MD performed worse in fraction number lines, fraction concepts, fraction arithmetic, and word problems. However, no difference in performance between the two groups was observed on symbolic representations. This suggests that adults with MD might be able to perform rote procedures such as transcoding from a verbal to a symbolic representation but are severely impaired for fraction number line, fraction concept, and fraction arithmetic. Exploratory error pattern analyses for fraction number line and fraction arithmetic further revealed mistakes similar to those observed in prior studies on children with MD, indicating core deficits in fraction understanding in individuals with MD. [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]

Background: Providing students with worked out problem solutions is a beneficial instructional technique in STEM disciplines, and studying examples that have been worked out incorrectly may be especially helpful for reducing misconceptions in students with low prior content knowledge. However, past results are inconclusive and the effects of incorrect worked examples alone or in combination with correct examples remains unclear. Objectives: We aim to address whether studying incorrect examples alone or in combination with correct examples can support the reduction of students' fraction misconceptions, operationalized as errors made with high confidence. Methods: After incorrectly solving a sampling problem, 130 students in 4th through 11th grade in the U.S. were randomly assigned to a condition in an online problem set focused on fraction equivalence. Students studied either single‐type worked examples (i.e., correct or incorrect; n = 49) or combination‐type worked examples (correct and incorrect; n = 41) or engaged in a problem‐solving control (n = 50). Results: Studying a combination of correct and incorrect worked examples was as effective as the problem‐solving control with feedback at improving fraction equivalence knowledge and reducing the rate of high‐confidence errors. Students in both the combination condition and the problem‐solving with feedback condition outperformed those who studied either correct or incorrect worked examples alone. Conclusions: Results support the inclusion of a combination of correct and incorrect worked examples when teaching students with low prior content knowledge. Studying a combination of example types within an online tutor helps to reduce misconceptions about fractions, a topic students commonly struggle with. A problem‐solving task with corrective feedback worked equally well. Lay Description: What is already known about this topic: Studying worked examples of mathematical solutions improves student learning.Incorrect examples, either alone or in combination with correct examples, are particularly effective for improving learning for students with low prior knowledge in the target content.Comparing correct and incorrect examples is also effective at improving problem‐solving but this effect may be specific to those with high prior knowledge.Still unknown are the impacts of these different combinations of examples on misconceptions in particular. What this paper adds: We show that studying a combination of correct and incorrect examples reduces math misconceptions.Problem‐solving with corrective feedback within an online tutor also has this effect. Implications for practice and/or policy: Using a combination of example types will help reduce students' misconceptions about fractions. [ABSTRACT FROM AUTHOR]

Separation of variables is a common method for producing an analytical based solution to partial differential equations. Despite the wide application of this method, often the physical phenomena described by the differential equations are not adequately involved in the discourse over the appropriate methods to solve a given problem, particularly in mathematics curricula. However, as mathematics is the tool to better understanding of the physical world, the meaning of the differential equation, boundary conditions, and initial conditions cannot be detached from the methods used to solve the differential equations. Failure to recognize the physical conditions being studied can lead to solution methods that are invalid or unphysical. This paper demonstrates how awareness of the physical nature of the system being investigated and its relationship to the mathematics can guide the selection of the relevant solution methods. To illustrate the importance of the comprehension of the physical meaning behind the mathematical equations and representations and the need to avoid rote application a solution technique, the logic behind the selection of the appropriate solution techniques for the one-dimensional transient heat conduction equation is considered under different imposed conditions which lead to different trends in system operation. [ABSTRACT FROM AUTHOR]

A study of the class \Delta consisting of topological \Delta-spaces was originated by Jerzy Ka̧kol and Arkady Leiderman [Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 86–99; Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 267–280]. The main purpose of this paper is to introduce and investigate new classes \Delta _2 \subset \Delta _1 properly containing \Delta. We observe that for every first-countable X the following equivalences hold: X\in \Delta _1 iff X\in \Delta _2 iff each countable subset of X is G_{\delta }. Thus, new proposed concepts provide a natural extension of the family of all \lambda-sets beyond the separable metrizable spaces. We prove that (1) A pseudocompact space X belongs to the class \Delta _1 iff countable subsets of X are scattered. (2) Every regular scattered space belongs to the class \Delta _2. We investigate whether the classes \Delta _1 and \Delta _2 are invariant under the basic topological operations. Similarly to \Delta, both classes \Delta _1 and \Delta _2 are invariant under the operation of taking countable unions of closed subspaces. In contrast to \Delta, they are not preserved by closed continuous images. Let Y be l-dominated by X, i.e. C_p(X) admits a continuous linear map onto C_p(Y). We show that Y \in \Delta _1 whenever X \in \Delta _1. Moreover, we establish that if Y is l-dominated by a compact scattered space X, then Y is a pseudocompact space such that its Stone–Čech compactification \beta Y is scattered. [ABSTRACT FROM AUTHOR]

Let S be the polynomial ring on the space of non-square generic matrices or the space of odd-sized skew-symmetric matrices, and let I be the determinantal ideal of maximal minors or Pf the ideal of sub-maximal Pfaffians, respectively. Using desingularizations and representation theory of the general linear group we expand upon work of Raicu–Weyman–Witt [Adv. Math. 250 (2014), pp. 596–610] to determine the S-module structures of Ext^j_S(S/I^t, S) and Ext^j_S(S/Pf^t, S), from which we get the degrees of generators of these Ext modules. As a consequence, via graded local duality we answer a question of Wenliang Zhang [J. Pure Appl. Algebra 225 (2021), Paper No. 106789] on the socle degrees of local cohomology modules of the form H^j_\mathfrak {m}(S/I^t). [ABSTRACT FROM AUTHOR]

This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov–Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12–26) and extends the convergence results from O (10 7) degrees of freedom (DOFs) to O (10 9) DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear scaling with respect to the wave frequency. The paper concludes with numerical results on hp -adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast. [ABSTRACT FROM AUTHOR]

This paper is theoretically driven by doctoral research data. The corresponding doctoral research involved fifteen participants who live in Brazil: immigrants and parents of immigrant students from Haiti and Venezuela and mathematics teachers in schools with immigrant students in São Paulo (Brazil). The research aims to consider socially and racially structured exclusions, to discuss perspectives and approaches, and to challenge mathematics education with immigrant students towards inclusive actions. Thinking about what inclusion and inclusive mathematics education with immigrant students could mean goes toward glimpsing the roots of what can obstruct such a process, which means taking the path towards unwrapping the processes of exclusion and violence against the immigrant population. Immigrants’ and teachers’ voices will be heard in this article to support discussions about the issues around inclusive mathematics education. I present situations that illustrate that microexclusions may accompany the inclusive context in subtle practices. Microexclusions tend to isolate people in a given environment, even if that environment is considered inclusive. This paper aims to discuss a crucial situation: the barriers to including immigrant students have to do with various levels of oppressive social structures. I identify four types of microexclusion related to immigrants having to do with exoticization, misleading identification, second-class citizen treatment, assimilation, and misprise. [ABSTRACT FROM AUTHOR]

In this paper, we consider sums related to the floor function. We improve previous results for some special arithmetic functions considered by O. Bordellès [On certain sums of number theory, Int. J. Number Theory, 18(9):2053– 2074, 2022], J. Stucky [The fractional sum of small arithmetic functions, J. Number Theory, 238:731–739, 2022], and J. Wu [Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski, Period. Math. Hung., 80(1):95–102, 2020]. It is worth emphasizing that we use much simpler methods to give much better results than previous. [ABSTRACT FROM AUTHOR]

This paper focuses on the vibration periodic property of Duffing oscillator with generalized initial conditions. Firstly, the undamped case is solved by Ji-Huan He’s frequency formulation; Secondly, the formulation is extended to the damped case. Numerical verification shows that the frequency formulation is mathematically simple and physically insightful and practically applicable. This paper paves a novel way for engineers to use the formulation to study nonlinear vibration system with ease and reliability. [ABSTRACT FROM AUTHOR]

Background: The substantial growth in gamification research has connected gamified learning to enhanced engagement, improved performance, and greater motivation. Similar to gamification, personalized learning analytics dashboards can enhance student engagement. Objectives: This study explores the student experiences and academic achievements using a gamified dashboard in a large, introductory STEM course. Methods: We examined two groups of students enrolled in different sections of a one‐semester‐long physical geology course with a total enrollment of 223 students. The only difference between the groups was that one had access to the dashboard. The data collection included students' assignments, overall performances, and exam scores. Students in both sections completed a Science Literacy Concept Inventory survey at the beginning and end of the term. Additionally, students completed an end‐of‐term survey containing open‐ended questions on their experience and interactions with specific elements. Results: Students shared mostly positive comments about their experience with the dashboard, and the final grade of students with access to the dashboard was 13% higher, on average, compared to their peers in the non‐dashboard section. Conclusion: With low costs and little time invested, gamified dashboards could have a significant impact on student performance in large STEM lecture courses. Lay Description: What is already known about this topic: Leaner dashboards that provide personalized feedback are linked to improved student performance in undergraduate STEM courses. However, students may be reticent to adopt dashboards, especially students in the middle range of the performance distribution, for whom the impact of the dashboard may be most significant.Prior research on gamification in STEM courses suggests that adding gameful elements like progress trackers, badges, and rewards can increase students' engagement in undergraduate coursework.The combination of personalized learning in dashboards and the motivational experience of gamification should boost student engagement, dashboard adoption, and ultimately foster academic achievement. What this paper adds: In this paper, we examine the differences in academic performance between students with and without access to a gamified learning dashboard in an undergraduate Geology course.We observe that students with access to the dashboard (the treatment group), outperform students without access (the control group). The greatest benefit is observed for students who use the dashboard more frequently.Students reported that the progress tracker, the badges, and the rewards all incentivized their use and provided useful feedback about their performance. Students who did not adopt the dashboard expressed a need for more detail about the tool and its purpose. Implications for practice and/or policy: Instructors and instructional designers for large enrollment undergraduate STEM courses should consider the affordances of gamified learner dashboards for increasing engagement and for providing synchronous feedback about learners' strategies in the course.Aligning the dashboard to the content of the curriculum—by ensuring that badges reflect key concepts‐ encouraged participation and helped students identify the utility of the tool. Dashboards should be personalized to individuals and to the course.Adding gameful elements in a low‐cost intervention for increasing adoption and engagement of dashboards in large enrollment introductory courses. [ABSTRACT FROM AUTHOR]

In [S. Yang and Y. Lin, Multilinear strongly singular integral operators with generalized kernels and applications, AIMS Math. 6 2021, 12, 13533–13551], the authors of the present paper further weaken the smoothness condition of kernel functions with multilinear strongly singular Calderón–Zygmund operators of [Y. Lin, Multilinear theory of strongly singular Calderón–Zygmund operators and applications, Nonlinear Anal. 192 2020, Article ID 111699]. They defined a new class of multilinear strongly singular integral operators, and studied its weighted L p boundedness, variable exponent L p ⁢ (⋅) boundedness and endpoint estimates. In this paper, we naturally consider the boundedness of multilinear commutators and multilinear iterated commutators, which are generated by multilinear strongly singular integral operators with generalized kernels and Lipschitz functions. Our results include the corresponding results of multilinear strongly singular Calderón–Zygmund operators and classical multilinear Calderón–Zygmund operators, respectively. [ABSTRACT FROM AUTHOR]

This paper reports a study of university lecturers' and students' experiences of teaching and learning mathematics following the abrupt requirement to switch to online teaching in 2020. A goal of the study is to share experiences that could be useful to improve the teaching and learning of mathematics in online settings. The qualitative research described is a phenomenological study and draws on interviews with ten mathematics lecturers and six undergraduate students who were enrolled in at least one university mathematical course during the lockdown in 2020. The interview data were analysed using a thematic approach. This paper reports findings regarding perceptions of lecturers and students about the challenges and benefits of online teaching and learning of mathematics, how the transition to online education has influenced assessment and sharing useful approaches for teaching and learning mathematics in online settings. [ABSTRACT FROM AUTHOR]

In this paper we study the behaviour of solutions for a nonlocal hyperbolic equation. We use the Pohozaev manifold combined with a new technique to explicit two invariant regions in the space of initial data. On the first one the solution blows up (in finite or infinite time) and in the second one the solution exists globally. Additionally, we prove that the ground state solution of the elliptic problem associated to the original problem is unstable. The main goal of this paper is to present a new technique which allows us to consider nonlocal problems and to extend the classical result proved by Shatah (Trans Am Math Soc 290(2):701–710, 1985). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of (F, G)-perturbed contraction in a metric space and we establish some fixed point theorems which extends the results from Branga, A. N. Olaru, I. M. Some Fixed Point Results in Spaces with Perturbed Metrics. Carpathian J. Math. 38 (2022), no. 3, 641–654 and Olaru, I. M.; Secelean, N. A. A new approach of some contractive mappings on metric spaces. Mathematics 9 (2021), 1433. Also, an application to an integral equation and some illustrative examples are given throughout the paper. [ABSTRACT FROM AUTHOR]

A. M. Mercer prove a new version of well-known Jensen inequality which is called Jensen-Mercer inequality [16]. By using Jensen-Mercer inequality, Kian andMoslehian establish a new variant of Hermite-Hadamard inequality which is called Hermite-Jensen-Mercer inequality [15]. In this paper, we extend the Hermite-Jensen-Mercer inequality for quantum integrals by utilizing Jensen-Mercer inequality. Then we investigate the connections between our results and those in earlier works. Moreover we give some examples to illustrate the main results in this paper. This is the first paper focusing on Hermite-Jensen-Mercer inequalities for quantum integrals. [ABSTRACT FROM AUTHOR]

In this paper we study the asymptotic stability problem for KdV solitons on the half-line, with zero boundary condition and absence of the drift term, represented as ux. Unlike standard KdV, these are not exact solutions to the equation. In a previous result, we showed that these solitons are orbitally stable, provided they are placed sufficiently far from the origin. In this paper, we prove their asymptotic stability in the energy space, and provide decay properties for all remaining regions, except the "small soliton region". For the proof we follow the ideas by Martel and Merle for the big soliton part, and for the linearly dominated region we follow recent results on generalized KdV decay [C. Muñoz and G. Ponce, Comm. Math. Phys., 367 (2019), pp. 581-598, A. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explain and describe the use of presuppositional interviews as means of the researcher being able to expose their own, often unknown, assumptions about the phenomena of interest. Within this, we provide a philosophical and practical account for the development and use of a presuppositional interview from an insider perspective to expose insights which influence researcher reflexivity and directly impact on the research process. Author A's hermeneutic phenomenological study seeks to gain insights into the lived experience of children learning mathematics in outdoor environments, such as forests and woodland. The paper describes how the reflexive method of presuppositional interviewing helped him to understand more about his research position and find a clearing in his 'Being in the Wood.' A template for a presupposition interview schedule is presented. [ABSTRACT FROM AUTHOR]

This special issue brings selected papers from an international conference which brought a group of approximately 30 Science Technology and Society and Popularization of Science experts from nine South Asian and Southeast Asian countries (Bangladesh, India, Indonesia, Malaysia, Nepal, Pakistan, Singapore, Sri Lanka, and Thailand), plus the United States. They discussed how best to enhance public awareness about the role of women in Science, Technology, Engineering, and Mathematics (STEM). These papers show how to develop strategies for increasing the participation of women in STEM, both as STEM professionals and as informed and engaged, lifelong participants in a STEM-rich world. [ABSTRACT FROM AUTHOR]

By tracing roughly 200 years of the formation of American school subjects, this paper complicates some of the self-evidence for calls to adapt school subjects according to complex health concerns, more recently amplified by COVID-19. To do so, the paper diagrams a counter-memory of three key amalgams of health related to the makings of school mathematics and reading-as-literacy: balancing mind–body-spirit-matter-nation networks, scientizing a hygiene of instruction for 'ethnic' minds, and reconfiguring bio-psycho-social adjustment – all pursued as problems of duration, intensity, and distance from differently dynamic and/or racializing norms. Throughout, we draw attention to how both universalizing and ethno-specific orthodoxies and their proposed alternatives have produced school subjects as self-evident strategic sites for addressing health concerns that invite underappreciated dangers today. [ABSTRACT FROM AUTHOR]

This paper is concerned with the two-species chemotaxis-competition model with degenerate diffusion, { u t = Δ u m 1 − χ 1 ∇ ⋅ (u ∇ w) + μ 1 u (1 − u − a 1 v) , x ∈ Ω , t > 0 , v t = Δ v m 2 − χ 2 ∇ ⋅ (v ∇ w) + μ 2 v (1 − a 2 u − v) , x ∈ Ω , t > 0 , 0 = Δ w + u + v − M ‾ (t) , x ∈ Ω , t > 0 , with ∫ Ω w (x , t) d x = 0 , t > 0 , where Ω : = B R (0) ⊂ R n (n ≥ 5) is a ball with some R > 0 ; m 1 , m 2 > 1 , χ 1 , χ 2 , μ 1 , μ 2 , a 1 , a 2 > 0 ; M ‾ (t) is the spatial average of u + v . In this paper, we show that if m 1 < 2 − 4 n , χ 1 > n (2 − m 1) n (2 − m 1) − 4 ⋅ max { 1 , a 1 } μ 1 and χ 2 > μ 2 a 2 or m 2 < 2 − 4 n , χ 1 > μ 1 a 1 and χ 2 > n (2 − m 2) n (2 − m 2) − 4 ⋅ max { 1 , a 2 } μ 2 , then there exist radially symmetric initial data such that the weak solution blows up in finite time in the sense that there is T ˜ max ∈ (0 , ∞) such that lim sup t ↗ T ˜ max (∥ u (t) ∥ L ∞ (Ω) + ∥ v (t) ∥ L ∞ (Ω)) = ∞. To obtain this result, we apply the method in the previous paper (Discrete Contin. Dyn. Syst., Ser. B 28(1):262–286, 2023) to derive an integral inequality for a moment-type functional, which was introduced by Winkler (Z. Angew. Math. Phys. 69(2):69, 2018). Moreover, before proving blow-up of solutions in the above model, we give a result on finite-time blow-up under the same conditions for m 1 , m 2 , χ 1 and χ 2 in the model with the terms Δ u m 1 , Δ v m 2 replaced with the nondegenerate diffusion terms Δ (u + ε) m 1 , Δ (v + ε) m 2 , where ε ∈ (0 , 1 ] . [ABSTRACT FROM AUTHOR]

This paper set out to contribute to mathematics education research by elaborating on a methodology developed during a study, trying to understand, view and follow shifts in prospective teachers' discursive patterns. The methodology aims to illustrate and describe how prospective teachers adapt to the context of teaching through a flexible process. This flexible process is then described in the result as a narrative. It is argued that the methodology can be used in relation to different theoretical directions, such as research about beliefs, knowledge, or identity. Another contribution is that the methodology presented gives insights into bridging the gap between different analytical levels, micro and macro. With a theoretical foundation in 'Cultural Worlds' [Holland, D., Skinner, D., Lachicotte, W., & Cain, C. (1998). Identity and agency in cultural worlds. Harvard University Press.] the Social Semiotic approach of Systemic Functional Linguistics, SFL [Halliday, M., & Hasan, R. (1989). Language, context, and text: Aspects of language in a social-semiotic perspective (2nd ed.). Oxford University Press] is used as a methodological tool. SFL offers a toolkit that allows the analysis of meaning at the clause level to uncover how and why a speaker produces a particular wording rather than any other in a specific social practice. The paper aims to illustrate and describe how to go beyond findings in the micro-analysis and then present the result as a narrative case. [ABSTRACT FROM AUTHOR]

Background: A strong knowledge of mathematics, beginning at the elementary level, is critical for participation in today's complex world. The home may be one way to facilitate individualized mathematics instruction, given that children spend more time at home than in an academic institution. Therefore, researchers are interested to see whether the home numeracy environment (HNE) can provide a solid foundation for children's mathematics understanding. Further, children's digital mathematics exploration at home is increasingly common (e.g., using math apps). Objectives: The present study evaluates the digital home numeracy practice (DHNP) model and explores its effect on children's mathematics knowledge across five domains (numeration, number operation, pattern recognition, spatial sense, and applied problem‐solving). Methods: To conduct this study, 117 Canadian parents and their children from Grade 1 through 5 completed a DHNP survey and a range of in‐person mathematics measures. Results and Conclusions: The results identified significant relations between parents and children's implicit mathematics factors (e.g., math anxiety, motivation). Children's mathematics anxiety and parents' academic estimations and expectations for their children positively predicted children's mathematics knowledge. In terms of DHNP components, parental involvement in DHNP predicted children's numeration and applied problem‐solving knowledge. Implications: Taken together, the results detail the contribution of parental and child factors to children's mathematics knowledge and suggest that parents adjust their role in DHNP according to their children's mathematics ability. Lay Description: What is (not) known about the subject matter?: Research is less developed on the impact of home technology in the mathematics learning processExisting research did not use a multi‐measure approach to assess the relationships between a variety of home numeracy factors and fundamental mathematics concepts and processes What is the contribution of this paper?: The paper highlights the importance of considering different home related factors to understand the role of home numeracy practices in children's mathematics developmentIt provides a holistic view of digital home numeracy practice (DHNP) by examining several implicit and explicit components of home numeracy environmentChildren's mathematics anxiety predicts their mathematics knowledgeParental estimation and expectation about their children's mathematics performance predicts their mathematics knowledge across several domains whereas parental role on DHNP impacts children's numeration only What are the implications of the findings?: The findings provide an understanding of the significant value of including digital mathematics practices in the study of the home mathematics environmentThe outcome of the study provides guidance for educators and researchers to better understand and leverage DHNP, and its impact on children's mathematics educationFuture research should investigate to what extent digital features should be included in the DHNP model. This will provide insights into the impact of using well‐designed apps on children's mathematics learning [ABSTRACT FROM AUTHOR]

The authors replies to the comment made by Yang and Zhou (2024 J. Phys. A: Math. Theor.) on his 2015 paper entitled 'Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras' (Jacobsen 2015 J. Phys. A: Math. Theor. 48 454003). [ABSTRACT FROM AUTHOR]

The article provide a range of conceptual approaches to the development of fraction-based understanding including paper folding, the use of number lines and using multiple fraction representations to build a foundation of success in mathematics. Topics include earliest experiences students have when learning fractions are hands-on activities involving paper folding and the coloring of 2D shapes; and useful to work with the length model first and then transition students to the number line.

This paper concerns a distinction between circumstantial truths that hold because of the circumstances and acircumstantial truths that hold regardless of, or transcend, the circumstances. Previous discussions of the distinction tended to focus on its applications, such as to modality, logical truth, and essence. This paper focuses on developing the distinction largely, but not entirely, in abstraction from its potential applications. As such, the paper's main contribution is to further clarify the distinction itself. An indirect contribution is to help guide its future applications. [ABSTRACT FROM AUTHOR]

This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an early and integral part in the undergraduate mathematics curriculum. By computation we mean the ability to rapidly and easily program exploratory calculations, and as well display the results with a versatile suite of graphics capabilities. The problems used here, and the philosophy behind them, derive from a MATLAB-based course in computation, programming, and mathematical applications that the author has taught for over 10 years. [ABSTRACT FROM AUTHOR]

The "Maker" movement is a cultural as well as educational phenomenon that has the potential to offer significant opportunities to students in conditions of social, economic and cultural disadvantage. The research reported in this paper, however, suggests that the simple provision of "Maker Spaces" for such activity is simplistic and not sufficient to realise this potential. The research involved a mixed methods study of a cohort of year 7 students (n = 26) in an Australian school located in a socio-economically disadvantaged outer-metropolitan region. The cohort undertook a range of Maker activities at a new "creativity centre" built at the school. Results indicate that the activities had positive impact on student attitudes towards science, technology, engineering and mathematics (STEM) overall, but that the impact was highly specific across attitudinal constructs. A strong ranging effect was also evident, suggesting that the impact of the experience was highly dependent on students' initial attitudes. Reflecting on these results, the paper also offers a reference framework that may help keep equity in mind when designing different kinds of Maker experience. [ABSTRACT FROM AUTHOR]

In this paper we consider finding a second-order stationary point (SOSP) of nonconvex equality constrained optimization when a nearly feasible point is known. In particular, we first propose a new Newton-conjugate gradient (Newton-CG) method for finding an approximate SOSP of unconstrained optimization and show that it enjoys a substantially better complexity than the Newton-CG method in [C. W. Royer, M. O'Neill, and S. J. Wright, Math. Program., 180 (2020), pp. 451-488]. We then propose a Newton-CG based augmented Lagrangian (AL) method for finding an approximate SOSP of nonconvex equality constrained optimization, in which the proposed Newton-CG method is used as a subproblem solver. We show that under a generalized linear independence constraint qualification (GLICQ), our AL method enjoys a total inner iteration complexity of O(ε7/peration complexity of O(ε7/2 min\{ n, ε3/4\}) for finding an (ε, ε)-SOSP of nonconvex equality constrained optimization with high probability, which are significantly better than the ones achieved by the proximal AL method in [Y. Xie and S. J. Wright, J. Sci. Comput., 86 (2021), pp. 1-30]. In addition, we show that it has a total inner iteration complexity of O(ε11/2) and an operation complexity of O(ε11/2 min\{ n, ε5/4\}) when the GLICQ does not hold. To the best of our knowledge, all the complexity results obtained in this paper are new for finding an approximate SOSP of nonconvex equality constrained optimization with high probability. Preliminary numerical results also demonstrate the superiority of our proposed methods over the other competing algorithms. [ABSTRACT FROM AUTHOR]

Background: People with aphasia (PWA) can experience functional numeracy difficulties, that is, problems understanding or using numbers in everyday life, which can have numerous negative impacts on their daily lives. There is growing interest in designing functional numeracy interventions for PWA; however, there are limited suitable assessments available to monitor the impact of these interventions. Existing functional numeracy assessments lack breadth and are not designed to be accessible for PWA, potentially confounding their performance. Additionally, they do not include real‐life demands, such as time pressure, which may affect their ecological validity. Thus, there is a crucial need for a new assessment to facilitate further research of PWA's functional numeracy. Aims: To develop, validate and pilot a wide‐ranging, aphasia‐friendly functional numeracy assessment to investigate how functional numeracy is impacted by aphasia severity and time pressure demands, and to explore predictors of PWA's functional numeracy. Methods & Procedures: To develop the Functional Numeracy Assessment (FNA), 38 items inspired by the General Health Numeracy Test (GHNT) and Excellence Gateway were adapted for suitability for PWA and entered in a computerized psychometric‐style test. The final 23 items (FNA23) were selected based on 213 neurotypical controls' performance, and controlled for difficulty, response modality and required numeracy skills. Aphasia‐friendly adaptations of the GHNT and Subjective Numeracy Scale were used to examine the FNA23's concurrent validity. Internal consistency reliability and interrater reliability (for spoken responses) were also examined. A novel Time Pressure Task was created by slight adaptation of seven FNA23 questions to explore the effects of time pressure on functional numeracy performance. A total of 20 PWA and 102 controls completed all measures on an online testing platform. Outcomes & Results: The FNA23 demonstrated acceptable internal consistency reliability (KR‐20 = 0.81) and perfect interrater reliability (for spoken responses). FNA23 and GHNT scores were positively associated, suggesting satisfactory concurrent validity. PWA demonstrated poorer functional numeracy than controls and took longer to complete assessments, indicating that aphasia impacts functional numeracy. Time pressure did not significantly impact performance. PWA demonstrated a wide range of functional numeracy abilities, with some performing similarly to controls. Conclusions & Implications: The FNA23 is a wide‐ranging, valid and reliable assessment which, with further development, will be a useful tool to identify and monitor PWA's functional numeracy difficulties in research and clinical practice. Considering PWA's widespread functional numeracy difficulties evidenced by this study, all PWA would likely benefit from routine evaluation for functional numeracy difficulties as part of their neurorehabilitation journeys. WHAT THIS PAPER ADDS: What is already known on this subject: Few studies have investigated functional numeracy difficulties in PWA. No published functional numeracy assessments exist that have been specifically designed to be accessible for PWA. What this paper adds to existing knowledge: The newly developed FNA23 is a valid and reliable tool to extensively assess PWA's functional numeracy. This study confirmed previous findings of widespread functional numeracy difficulties in PWA that are related to their aphasia severity. What are the potential or actual clinical implications of this work?: The FNA23 can be used to assess PWA's functional numeracy to inform areas of strengths and difficulties to target in intervention, and to monitor progress towards achieving intervention objectives. All PWA should be routinely evaluated for functional numeracy difficulties. [ABSTRACT FROM AUTHOR]

In this paper, we offer a descriptive theory of analogical reasoning in mathematics, stating general conditions under which an analogy may provide genuine inductive support to a mathematical conjecture (over and above fulfilling the merely heuristic role of 'suggesting' a conjecture in the psychological sense). The proposed conditions generalize the criteria of Hesse in her influential work on analogical reasoning in the empirical sciences. By reference to several case studies, we argue that the account proposed in this paper does a better job in vindicating the use of analogical inference in mathematics than the prominent alternative defended by Bartha. [ABSTRACT FROM AUTHOR]

There is no single canonical polynomial-time version of the Axiom of Choice (AC); several statements of AC that are equivalent in Zermelo-Fraenkel (ZF) set theory are already inequivalent from a constructive point of view, and are similarly inequivalent from a complexity-theoretic point of view. In this paper we show that many classical formulations of AC, when restricted to polynomial time in natural ways, are equivalent to standard complexity-theoretic hypotheses, including several that were of interest to Selman. This provides a unified view of these hypotheses, and we hope provides additional motivation for studying some of the lesser-known hypotheses that appear here. Additionally, because several classical forms of AC are formulated in terms of cardinals, we develop a theory of polynomial-time cardinality. Nerode & Remmel (Contemp. Math. 106, 1990 and Springer Lec. Notes Math. 1432, 1990) developed a related theory, but restricted to unary sets. Downey (Math. Reviews MR1071525) suggested that such a theory over larger alphabets could have interesting connections to more standard complexity questions, and we illustrate some of those connections here. The connections between AC, cardinality, and complexity questions also allow us to highlight some of Selman's work. We hope this paper is more of a beginning than an end, introducing new concepts and raising many new questions, ripe for further research. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish convergence and stability of Jungck -modified three-step iterations for three nonself mappings in a Banach space. The results obtained in this paper extend and improve the recent ones announced by Khan et al., Olatinwo, Hussain et al. and many papers. [ABSTRACT FROM AUTHOR]

Background: Teachers often rely on the use of open‐ended questions to assess students' conceptual understanding of assigned content. Particularly in the context of mathematics; teachers use these types of questions to gain insight into the processes and strategies adopted by students in solving mathematical problems beyond what is possible through more close‐ended problem types. While these types of problems are valuable to teachers, the variation in student responses to these questions makes it difficult, and time‐consuming, to evaluate and provide directed feedback. It is a well‐studied concept that feedback, both in terms of a numeric score but more importantly in the form of teacher‐authored comments, can help guide students as to how to improve, leading to increased learning. It is for this reason that teachers need better support not only for assessing students' work but also in providing meaningful and directed feedback to students. Objectives: In this paper, we seek to develop, evaluate, and examine machine learning models that support automated open response assessment and feedback. Methods: We build upon the prior research in the automatic assessment of student responses to open‐ended problems and introduce a novel approach that leverages student log data combined with machine learning and natural language processing methods. Utilizing sentence‐level semantic representations of student responses to open‐ended questions, we propose a collaborative filtering‐based approach to both predict student scores as well as recommend appropriate feedback messages for teachers to send to their students. Results and Conclusion: We find that our method outperforms previously published benchmarks across three different metrics for the task of predicting student performance. Through an error analysis, we identify several areas where future works may be able to improve upon our approach. Lay Description: What is already known about this topic: Open‐ended questions are used by teachers in the domain of mathematics to assess their students understanding but automated support for these types of questions are limited in online learning platforms. Recent advancements in areas of machine learning and natural language processing have led to promising results in a range of domains and applications. What this paper adds: Emulating how teachers identify similar student answers can be used to build tools that support teachers in assessing and providing feedback to student open‐ended work. Implications for practice: Developing better automated supports can increase the amount of direct feedback students receive to guide their learning. [ABSTRACT FROM AUTHOR]

In this paper, we establish a relation-theoretic set-valued version of the fixed point result of Ćirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143–147, 2007) on metric spaces endowed with an arbitrary binary relation. The results of this paper, generalize and unify the fixed point results of Ćirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143–147, 2007), Shukla and López (Quaest. Math. 45(3):1–16, 2019), and Shukla and Radenović (An. Ştiinţ. Univ. 'Al.I. Cuza' Iaşi, Mat. 63(2):339–350, 2017) in product spaces. Some examples are provided that justify and establish the importance of our results. As applications of our main result, we have established the existence of solutions to differential inclusion problems and the weak asymptotical stability and a global attractivity of the equilibrium point of a difference inclusion problem. The use of arbitrary binary relations in our results permits us to apply the results to the differential inclusion problems and difference inclusion problems with weaker assumptions than those used in the papers mentioned above. [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]

We consider quasilinear elliptic equations Δ p u + f (u) = 0 in the quarter-plane Ω, with zero Dirichlet data. For some general nonlinearities f, we prove the existence of a positive solution with a prescribed limiting profile. The question is motivated by the result in (Adv. Nonlinear Stud.13(1) (2013) 115–136), where the authors establish that for solutions u (x 1 , x 2) of the preceding Dirichlet problem, lim x 1 → ∞ u (x 1 , x 2) = V (x 2) , where V is a solution of the corresponding one-dimensional problem with V (+ ∞) = z and z is a root of f. Starting with such a profile V and a carefully selected z, the authors of this paper apply Perron's method in order to prove the existence of a solution u with limiting profile V. The work in this paper is similar in spirit to that in (Math. Methods Appl. Sci.39(14) (2016) 4129–4138), where the authors compare the sub and the super solutions by using arguments based on the strong maximum principle for semilinear equations. However, for the quasilinear case, such a maximum principle is lacking. This difficulty is overcome by employing a less classical weak sweeping principle that requires a careful boundary analysis. [ABSTRACT FROM AUTHOR]

First of all, we indicate a severe error in the analysis of the main results of both Chakraborty [Ukr. Math. J., 72, No. 11, 1794–1806 (2021)] and Chakraborty–Chakraborty [Ukr. Math. J., 72, No. 7, 1164–1174 (2020)] to show that both these papers cease to be true. Further, pertinent to the results of these two papers, we consider the unique range set of a meromorphic function over a non-Archimedean field with the smallest possible weights 0 and 1 under the aegis of its most general form to improve the existing result. [ABSTRACT FROM AUTHOR]

The number of non-negative integer matrices with given row and column sums features in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations. In this paper, we describe a new such approximation, motivated by consideration of the statistics of matrices with non-integer numbers of columns. This estimate can be evaluated in time linear in the size of the matrix and returns results of accuracy as good as or better than existing linear-time approximations across a wide range of settings. We show that the estimate is asymptotically exact in the regime of sparse tables, while empirically performing at least as well as other linear-time estimates in the regime of dense tables. We also use the new estimate as the starting point for an improved numerical method for either counting or sampling matrices with given margins using sequential importance sampling. Code implementing our methods is available. [ABSTRACT FROM AUTHOR]

Anemia is a global public health problem, especially common among children in developing countries, which affects their physical and mental health development. However, there is currently a lack of research on the relationship between anemia and academic performance. The objective of this study was to explore the association between anemia and academic performance, and the possible factors mediating this association among Chinese children. The data for this study came from the baseline survey of the Chinese Education Panel Survey Elementary School Cohort. The cohort was conducted from September 2018 to June 2019 in 160 elementary schools, covering 20 provinces and 40 counties/districts throughout China. Paper-based questionnaires were used, completed by 4th grade students, parents, head teachers, main teachers, and principals. The data used included questionnaire responses, physical measurements, and academic performance of 17,695 students. Based on students' hemoglobin levels and school altitude data, we grouped them into anemia and nonanemia categories using WHO criteria. The anemia group had 1,154 individuals, while the nonanemia group had 16,541 individuals. An ordinary least squares regression and mediation effect analysis were conducted. Our findings found the prevalence of anemia was 6.52% among Chinese Grade 4 students. Students without anemia had a higher average test score for three academic subjects than students with anemia (P < 0.001); their test scores for Chinese, Mathematics, and English were also higher (P < 0.05). Multivariate regression analysis showed a negative association between anemia and average test scores as well as individual test scores for the three subjects. Mediation analysis found that anemia affected academic performance directly (P < 0.05), and indirectly by decreasing the cognition score (P < 0.05). The indirect effect was 19.9% of the total effect. Findings highlighted anemia affected academic performance both directly and indirectly. Nutrition-related interventions should be implemented to prevent a decrease in academic performance among students with anemia. [ABSTRACT FROM AUTHOR]

In this paper, we describe an activity that involves economics and mathematics. It is included in the planning of orientation paths towards university studies within the Mathematical High School Project and is dedicated to students in the last years of high school. In particular, this research will deal with the issue of solving an economic problem using not only real analysis instruments but also geometrical topics concerning Euclidean geometry and topology. Mathematics becomes a language to understand and explain a real life problem, such as determining the optimal position of an airport, a nuclear reactor and so on. Some activities made use of dynamic geometry software and computer simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the noncommutative analog of the normal subgroup theorem for certain groups. Inspired by Kalantar and Panagopoulos (arXiv:2108.02928, 2021, 16), we show that all Γ$\Gamma$‐invariant subalgebras of LΓ$L\Gamma$ and Cr∗(Γ)$C^*_r(\Gamma)$ are (Γ$\Gamma$‐)coamenable. The groups we work with satisfy a singularity phenomenon described by Bader et al. (Invent. Math. 229 (2022), 929–985). The setup of singularity allows us to obtain a description of Γ$\Gamma$‐invariant intermediate von Neumann subalgebras L∞(X,ξ)⊂M⊂L∞(X,ξ)⋊Γ$L^{\infty }(X,\xi)\subset \mathcal {M}\subset L^{\infty }(X,\xi)\rtimes \Gamma$ in terms of the normal subgroups of Γ$\Gamma$. [ABSTRACT FROM AUTHOR]