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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]

In 1987, Michael Wiegner in his seminal paper (J. Lond. Math. Soc. (2), 35 (1987) 303–313) provided an important result regarding the energy decay of Leray solutions u(·,t)$ \bm{u}(\cdot ,t)$ to the incompressible Navier–Stokes in Rn$ \mathbb {R}^{n}$: if the associated Stokes flows had their L2$L^{2}$ norms bounded by O(1+t)−α$ O(1 + t)^{-\;\!\alpha }$ for some 0<α⩽(n+2)/4$ 0 < \alpha \leqslant (n+2)/4$, then the same would be true of ∥u(·,t)∥L2(Rn)$ \Vert \hspace{0.56917pt} \bm{u}(\cdot ,t) \hspace{0.56917pt} \Vert _{L^{2}(\mathbb {R}^{n})}$. The converse also holds, as shown by Skalák (J. Math. Fluid Mech. 16 (2014) 431–446) and by our analysis below, which uses a more straightforward argument. As an application of these results, we discuss the genericity problem of algebraic decay estimates for Leray solutions of the unforced Navier–Stokes equations. In particular, we prove that Leray solutions with algebraic decay generically satisfy two‐sided bounds of the form (1+t)−α≲∥u(·,t)∥L2(Rn)≲(1+t)−α$(1+t)^{-\alpha }\lesssim \Vert \bm{u}(\cdot ,t)\Vert _{L^2(\mathbb {R}^n)} \lesssim (1+t)^{-\alpha }$. [ABSTRACT FROM AUTHOR]

This paper reports on students' conceptions of minima points. Written assignments and individual interviews uncovered salient, concept images, as well as erroneous mis-out examples that mistakenly regard examples as non-examples and mis-in examples that mistakenly grant non-examples the status of examples. We used Tall and Vinner's theoretical framework to analyze the students' errors that were rooted in mathematical and in real-life contexts. [ABSTRACT FROM AUTHOR]

In this paper, we, a group of graduate students in mathematics education, discuss some of the metacognitive benefits of the non-traditional teaching methods we observed employed by one of our professors. This professor's methods challenge the common belief that well-managed class time is key for positive learning outcomes. Instead, he orients his teaching to share the exploration and sense-making phases of doing mathematics. The goal of his teaching is to share the idea that learning mathematics is a process of "refining our mathematical thinking". We argue that this approach to teaching helps students see that mathematics is a human endeavor, appreciate the cycles of learning mathematics and the importance of struggle throughout the process, and gain some insight on what it means to be an expert in mathematics. We encourage teachers and professors to move away from obsessing about structured, well-organized class time, and to instead move towards having flexible and risk-oriented class time. [ABSTRACT FROM AUTHOR]

Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demonstrate that different solutions--hiding one biscuit, arbitrarily sharing the extra biscuit, randomizing allocation, dividing the extra biscuit into three parts, and successively dividing it into smaller and smaller parts--involve different mathematical methods and evoke different human values. We discuss the construction of quantum biscuit splitting devices and the use of machine learning to divide biscuits. We argue that the multitude of different mathematically-correct solutions to this problem (each with its own ethical justification) might influence the values held by practicing mathematicians. The example we propose here has been used in teaching to help students understand why mathematics cannot be cleanly separated from human values. [ABSTRACT FROM AUTHOR]

This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, generaleducation classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student's developing identity in mathematics and, more broadly, in STEM. The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for various classroom settings are discussed in detail. [ABSTRACT FROM AUTHOR]

This paper presents some existence and uniqueness results for a solution of a system of equations. Our results extend and generalize the well-known and celebrated results of Boyd and Wong [Proc. Amer. Math. Soc. 20 (1969)], Matkowski [Dissertations Math. (Rozprawy Mat.) 127 (1975)], Proinov [Nonlinear Anal. 64 (2006)], Ri [Indag. Math. (N. S.) 27 (2016)] and many others. We also present some illustrative examples to validate our results. [ABSTRACT FROM AUTHOR]

This paper defines a new operation through extending the idea of the 0-dimensional crossing change and Shimizu's 2-dimensional region crossing change [A. Shimizu, Region crossing change is an unknotting operation, J. Math. Soc. Jpn. 66(3) (2014) 693–708, doi:10.2969/jmsj/06630693] to a 1-dimensional version called the arc crossing change. We will also prove that the arc crossing change is an unknotting operation with the help of Gauss diagrams. [ABSTRACT FROM AUTHOR]

[M. Ma, The connectivity of exchanged hypercubes, Discrete Math., Algorithms Appl. 2(2) (2010) 213–220.] proved that the vertex connectivity and the edge connectivity of the exchanged hypercube are each equal to the minimum degree of the graph. This paper presents a proof of that result, which is substantially simpler and more intuitive. [ABSTRACT FROM AUTHOR]

Let $ \hat {\mathcal {S}}_{(\alpha,\beta)} $ S ^ (α , β) be the familiar class of almost spirallike functions of type β and order α in the unit disk (see Definition 1.1). In this paper, first, we prove that for a function $ f(z)=z+\sum _{n=2}^\infty a_nz^n $ f (z) = z + ∑ n = 2 ∞ a n z n in the class $ \hat {\mathcal {S}}_{(\alpha,\beta)} $ S ^ (α , β) , then $$\begin{align*} & |a_{3}-\lambda a_{2}^2|\\ & \quad \leq (1-\alpha)\cos{\beta}\max\{1,|1-4(1-\alpha)(1-\lambda)\cos{\beta}\,{\rm e}^{{\rm i}\beta}|\},\quad \lambda\in \mathbb{C}. \end{align*} $$ | a 3 − λ a 2 2 | ≤ (1 − α) cos ⁡ β max { 1 , | 1 − 4 (1 − α) (1 − λ) cos ⁡ β e i β | } , λ ∈ C. The above estimation is sharp. Second, we extend this result to the bounded starlike circular domain in $ \mathbb {C}^{n} $ C n and obtain the sharp estimates. The results presented here would provide extensions of those given by Xu et al. [The Fekete and Szegö problem on the bounded starlike circular domain in $ \mathbb {C}^n $ C n . Pure Appl Math Q. 2016;12:621–638] and Xiong [Sharp coefficients bounds for class of almost starlike mappings of order α in $ \mathbb {C}^n $ C n . J Math Inequalities. 2020;14:853–865]. Finally, a certain conjecture is also formulated. [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]

Although the educational potential of social media has been widely acknowledged, it remains unclear whether social media use might present opportunities for the development of math identity. This study drew on the socialization framework of math identity to examine the relationships between social media use for math learning, bicultural identity integration, ethnic‐math beliefs and math identity among ethnic minority high school students in China. Structural equation modelling results showed that (a) social media use was positively related to math identity; (b) high bicultural identity integration was positively associated with math identity, while biased ethnic‐math beliefs were negatively related to math identity and (c) social media use suppressed the socialization process of math identity, weakening the maladaptive roles of low bicultural identity integration and biased ethnic‐math beliefs in shaping math identity. Our findings highlight the beneficial role of social media use in student math learning. Theoretical and practical implications are discussed. Practitioner notesWhat is already known about this topicSocial media use for learning is associated with students' academic motivation, engagement and academic achievement.Social media use may have affordances for identity development, especially for ethnic minorities.The formation of ethnic minority students' math identity is intertwined with their math and ethnic socialization.What this paper addsSocial media use for math learning was directly and positively related to ethnic minorities' math identity.This study quantitatively confirmed the associations of bicultural identity integration and ethnic‐math beliefs with math identity.Social media use suppressed the relations of bicultural identity integration and ethnic‐math beliefs with math identity.Implications for practice and/or policyPromoting social media use for math learning benefits ethnic minority students' math identity.Social media use for math learning could alleviate the maladaptive role of low bicultural identity integration and biased ethnic‐math beliefs in math identity development.Ethnic minority students' math identity socialization processes merit attention. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to identify the current situation of higher education institutions in Spain regarding the introduction of the Sustainable Development Goals in the classroom, and what is the role of mathematics in this task. Design/methodology/approach: A review is made of how the concept of sustainability has evolved in higher education, its gradual introduction in the University and the way in which this subject is approached in the field of mathematics. Findings: The study concludes that higher education has a key role to play in designing strategies that lead to the global sustainability of the planet. This implies major changes in degree curricula, assessment, competences and teacher training. Cross-disciplinarity and interdisciplinarity between different subjects within the same degree is a strategy for students to analyse the Sustainable Development Goals using mathematical techniques. Social implications: The University as an institution must train socially responsible professionals who are aware of the importance of promoting a sustainable world. Changes should be made to introduce values in the classroom that promote and encourage sustainability. Training should be seen as a continuous process that leads to the preparation of professionals committed to society and nature and who develop strategies aimed at improving the planet through values. Originality/value: Through practical activities, the Sustainable Development objectives can be analysed from several subjects of the same degree, emphasising the interdisciplinary and transversal nature that should be the central axis of higher education. Each subject can develop a strategy for change in favour of sustainability that will be reinforced and increased by working together on the proposed teaching practice. In this way, the contents of the different subjects are not isolated, but rather the student can see how there is an interrelationship between them and with real life. [ABSTRACT FROM AUTHOR]

P. S. Das [Sivaramakrishna Das, P. Fuzzy groups and level subgroups. J. Math. Anal. Appl. 84 (1981), no. 1, 264-269.] proved that the level subgroups of any fuzzy subgroup of a finite group form a chain. In this paper we extend it to modules and showed that the level submodules of a fuzzy module also form a chain. With the help of these results we introduced fuzzy noetherian module for noetherian modules. Some results are proved for level submodules of any fuzzy module of modules with composition series. [ABSTRACT FROM AUTHOR]

In this paper we derive a two dimensional spray model with gyroscopic effects as the mean-field limit of a system modeling the interaction between an incompressible fluid and a finite number of solid particles. This spray model has been studied by Moussa and Sueur (Asymptotic Anal., 2013), in particular the mean-field limit was established in the case of W1,∞ interactions. First we prove the local in time existence and uniqueness of strong solutions of a monokinetic version of the model with a fixed point method. Then we adapt the proof of Duerinckx and Serfaty (Duke Math. J., 2020) to establish the mean-field limit to the spray model in the monokinetic regime in the case of Coulomb interactions. [ABSTRACT FROM AUTHOR]

We are concerned with the following fractional Kirchhoff variational inequality: .... In this paper, by applying penalization techniques from Bensoussan and Lions (1978) combined with mountain pass theorem, we show the existence and concentration behavior of positive solution to the cited variational inequality. This result extend some results established by Alves, Barros and Torres [J. Math. Anal. Appl. 494 (2021)] to the fractional case. [ABSTRACT FROM AUTHOR]

In this paper, we study the non‐Hermitian Yang–Mills (NHYM) bundles over compact Kähler manifolds. We show that the existence of harmonic metrics is equivalent to the semisimplicity of NHYM bundles, which confirms the Conjecture 8.7 in Kaledin and Verbitsky (Selecta Math. (N.S.) 4 (1998) 279–320). [ABSTRACT FROM AUTHOR]

In 1989 Mason and Newman (Commun. Math. Phys. 121 659–68) proved that there is a 1-1-correspondence between self-dual metrics satisfying Einstein vacuum equation (in complex case or in neutral signature) and pairs of commuting parameter depending vector fields X 1 (λ) , X 2 (λ) which are divergence free with respect to some volume form. Earlier Plebański (1975 J. Math. Phys. 16 2395–402) showed instances of such vector fields depending of one function of four variables satisfying the so-called I or II Plebański heavenly PDEs. Other PDEs leading to Mason–Newman vector fields are also known in the literature: Park (1992 Int. J. Mod. Phys. A 7 1415), Husain (1994 Phys. Rev. Lett. 72 800), Grant (1993 Phys. Rev. D 48 2606–12), Schief (Phys. Lett. A 223 55–62). In this paper we discuss these matters in the context of the web theory, i.e. theory of collections of foliations on a manifold, understood from the point of view of Nijenhuis operators. In particular we show how to apply this theory for constructing new 'heavenly' PDEs based on different normal forms of Nijenhuis operators in 4D, which are integrable similarly to their predecessors. Relation with the Hirota dispersionless systems of PDEs and the corresponding Veronese webs, which was recently observed by Konopelchenko–Schief–Szereszewski, is established in all the cases. We also discuss some higher dimensional generalizations of the 'heavenly' PDEs and the existence of related vacuum Einstein metrics in 4D-case. [ABSTRACT FROM AUTHOR]

The paper proposes EXPLODE, a new model of exploratory learning environment for teaching and learning neural networks. The EXPLODE model is about pedagogically instrumenting a software development environment to transform it into an exploratory learning environment for neural networks. Such an environment is particularly aimed for students who are skilled in programming and meets typical challenges in teaching and learning neural networks, related to the lack of prerequisite knowledge in mathematics. By providing such students with a familiar learning environment and allowing them to programmatically experiment with neural networks, the EXPLODE model aims at improving the students' learning outcomes and learning experience. The effectiveness of the model was evaluated in an experimental study with 77 final-year IT students. The results have shown that the students from the experimental group, that is, those who were exposed to the EXPLODE model, scored higher on the knowledge test. Furthermore, the perceived learning experience of the experimental group was better than that of the control group. The results have also suggested that the proposed model helps students better understand learning topics that require practical experience and facilitates a deeper understanding of the internal operations of neural networks. [ABSTRACT FROM AUTHOR]

The aim of this study was to examine if--and to what extent--a sensory modality's conceptual congruency influences learning in digital environments. Building on previous work in multimedia and embodied learning, the study used custom software to systematically vary the conceptual congruency of two sensory modalities (aural and bodilykinesthetic). One hundred seventy-nine (N = 179) elementary students with prior knowledge of addition used the software as an introduction to multiplication. Results found that the participants who experienced more conceptual congruency in the aural and bodily-kinesthetic modalities demonstrated greater understanding of the target concept as measured by paper-based tests. In addition, the findings revealed the two modalities worked in a combinatorial fashion, suggesting a more-isbetter impact on participant understanding. The study concludes with a discussion of the findings, along with an exploration of the theoretical and practical implications for designing sensory experiences that influence learning. [ABSTRACT FROM AUTHOR]

Let X be an abelian metric group with an invariant metric, Y be a real normed space and K be a convex cone in Y. We prove that a K-subadditive (K-superadditive) compact- and convex-valued map F : X → C C (Y) , for which the functionals f y ∗ (x) = inf y ∗ (F (x)) are lower (upper, resp.) semicontinuous for any real continuous and non-negative on K functional y ∗ , has to be locally K-bounded on X. Our results refer to the papers Banakh and Jabłońska (Israel J Math 230:361–386, 2019), Jabłońska and Nikodem (Math Inequal Appl 22:1081–1089, 2019) and Nikodem (Aequationes Math 62:175–183, 2001). [ABSTRACT FROM AUTHOR]

In this paper the author looks at the letters of two renowned women mathematicians and scientists of the Victorian period, Mary Somerville and Ada Lovelace, while also considering the imperceptibility of Sophie Germain, an important French mathematician and philosopher in their epistolary exchanges and philosophical writings. Drawing on the importance of mathematical correspondences and epistolary education in the creation, circulation and dissemination of knowledge, as well as in processes of formal and informal learning, the author argues that Lovelace’s and Somerville’s letters leave traces of a remarkable genealogical line of women’s mentorship and personal relations in the nineteenth century world of British mathematics in the backdrop of contradictory discourses around gender, mathematics, and science education. [ABSTRACT FROM AUTHOR]

Given a collection of hypergraphs H=(H1,...,Hm)${{\bf H}}=(H_1, \ldots , H_m)$ with the same vertex set, an m$m$‐edge graph F⊂∪i∈[m]Hi$F\subset \cup _{i\in [m]}H_i$ is a transversal if there is a bijection ϕ:E(F)→[m]$\phi :E(F)\rightarrow [m]$ such that e∈E(Hϕ(e))$e\in E(H_{\phi (e)})$ for each e∈E(F)$e\in E(F)$. How large does the minimum degree of each Hi$H_i$ need to be so that H${{\bf H}}$ necessarily contains a copy of F$F$ that is a transversal? Each Hi$H_i$ in the collection could be the same hypergraph, hence the minimum degree of each Hi$H_i$ needs to be large enough to ensure that F⊆Hi$F\subseteq H_i$. Since its general introduction by Joos and Kim (Bull. Lond. Math. Soc. 52 (2020) 498–504), a growing body of work has shown that in many cases this lower bound is tight. In this paper, we give a unified approach to this problem by providing a widely applicable sufficient condition for this lower bound to be asymptotically tight. This is general enough to recover many previous results in the area and obtain novel transversal variants of several classical Dirac‐type results for (powers of) Hamilton cycles. For example, we derive that any collection of rn$rn$ graphs on an n$n$‐vertex set, each with minimum degree at least (r/(r+1)+o(1))n$(r/(r+1)+o(1))n$, contains a transversal copy of the r$r$th power of a Hamilton cycle. This can be viewed as a rainbow version of the Pósa–Seymour conjecture. [ABSTRACT FROM AUTHOR]

While there is increased attention to power, privilege, and access in mathematics education, conversations around race and disability are often left out of the conversation. Disability in mathematics continues to be studied with a lens that focuses on behavior, rather than attending to the situated and sociopolitical context in which teaching and learning takes place. This paper specifically calls on the importance of an intersectional analysis of ability and the need for explicit conversation on the interwoven nature of race and disability to uncover exclusionary practices of hyper‐labeling, hyper‐surveilling, and hyper‐punishing for those outside notions of normalcy. Drawing on sociopolitical perspectives informed by Disability Critical Race Theory (DisCrit) and DisCrit Classroom Ecology, I share a framework of DisCrit noticing to consider the interwoven nature of racism and ableism in mathematics classrooms, provide a context to develop preservice teacher DisCrit noticing during mathematics methods, and a case example to highlight implications and transformative possibilities for (re)organizing classrooms through the DisCrit noticing framework. [ABSTRACT FROM AUTHOR]