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COVID-19 pandemic has raised concerns for a number of strategical social interactions. From quarantines and social distancing to vaccination and geopolitics, the cooperation or even the coordination of efforts has been challenging, as governments, economic sector, institutions, and individuals, often have conflicting interests. Game theory, which is a mathematical tool extensively used in order to determine the outcomes of strategical interactions, has been applied to a number of issues arising from the pandemic. In this paper, 60 publications are analyzed to identify the key contributions of game theory to addressing COVID-19. First, 10 keywords-topic are chosen and each publication is examined to consider if it deals with these topics. Then R package "igraph" and cluster Louvain are used in order to group the papers to 3 clusters. The results indicate that there is a temporal variation in the topics examined. In the beginning the main concern has been coupling the modelling of the transmission of the virus with social distancing responses from the public and quarantining policy. Then the economic implications of the pandemic drew the attention and finally the application of the vaccination campaigns and the cooperation of the individuals with vaccination guidelines. The paper targets on bridging the gap between game theorists and epidemiologists, illustrating how modelling agents interactions can improve responses. The clusters created can help researchers identify groups of problems that can be addressed jointly, using similar approaches. The analysis indicates that game theory can reveal social aspects that can improve the responses to future emergencies. [ABSTRACT FROM AUTHOR]

COVID-19 pandemic has raised concerns for a number of strategical social interactions. From quarantines and social distancing to vaccination and geopolitics, the cooperation or even the coordination of efforts has been challenging, as governments, economic sector, institutions, and individuals, often have conflicting interests. Game theory, which is a mathematical tool extensively used in order to determine the outcomes of strategical interactions, has been applied to a number of issues arising from the pandemic. In this paper, 60 publications are analyzed to identify the key contributions of game theory to addressing COVID-19. First, 10 keywords-topic are chosen and each publication is examined to consider if it deals with these topics. Then R package "igraph" and cluster Louvain are used in order to group the papers to 3 clusters. The results indicate that there is a temporal variation in the topics examined. In the beginning the main concern has been coupling the modelling of the transmission of the virus with social distancing responses from the public and quarantining policy. Then the economic implications of the pandemic drew the attention and finally the application of the vaccination campaigns and the cooperation of the individuals with vaccination guidelines. The paper targets on bridging the gap between game theorists and epidemiologists, illustrating how modelling agents interactions can improve responses. The clusters created can help researchers identify groups of problems that can be addressed jointly, using similar approaches. The analysis indicates that game theory can reveal social aspects that can improve the responses to future emergencies. [ABSTRACT FROM AUTHOR]

Mathematics is often treated as different from other disciplines, since arguments in the field rely on deductive proof rather than empirical evidence as in the natural sciences. A mathematical paper can therefore, at least in principle, be replicated simply by reading it. While this distinction is sometimes taken as the basis to claim that the results in mathematics are therefore certain, mathematicians themselves know that the published literature contains many mistakes. Reading a proof is not easy, and checking whether an argument constitutes a proof is surprisingly difficult. This article uses peer review of submissions to mathematics journals as a site where referees are explicitly concerned with checking whether a paper is correct and therefore could be published. Drawing on 95 qualitative interviews with mathematics journal editors, as well as a collection of more than 100 referee reports and other correspondence from peer review processes, this article establishes that while mathematicians acknowledge that peer review does not guarantee correctness, they still value it. For mathematicians, peer review 'adds a bit of certainty', especially in contrast to papers only submitted to preprint servers such as arXiv. Furthermore, during peer review there can be disagreements not just regarding the importance of a result, but also whether a particular argument constitutes a proof or not (in particular, whether there are substantial gaps in the proof). Finally, the mathematical community is seen as important when it comes to accepting arguments as proofs and assigning certainty to results. Publishing an argument in a peer-reviewed journal is often only the first step in having a result accepted. Results get accepted if they stand the test of time and are used by other mathematicians. [ABSTRACT FROM AUTHOR]

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

This study employs bibliometric analysis to systematically explore the Visual Basic (VB) education research landscape, identifying significant trends, influential authors, and future research directions. Utilizing data from Scopus-indexed journals, we examined 529 papers published between 1994 and October 2023, identified through the keywords "visual basic," "visualbasic," "teaching," and "learning." These papers were analyzed using Biblioshiny to generate a bibliometric map, following four steps: data harvesting, data screening, data visualization, and data analysis. Our research reveals critical VB programming trends from 1994 to 2023, with academic output peaking in 2010 and declining since 2007. Ongoing interest is noted due to legacy system applications. Global publication reach facilitates cross-border information exchange, and top affiliations and authors underscore extensive and influential participation in this field. The research emphasizes incorporating fundamental and advanced themes in educational curricula. It suggests future research focusing on new programming paradigms, longitudinal studies, and VB relevance to technological advancements and industrial needs. Enhanced collaboration, interdisciplinary research, and attention to global trends are essential for maintaining the relevance of VB programming education, optimizing legacy systems, improving educational practices, and preparing students for modern programming environments. [ABSTRACT FROM AUTHOR]

The International Sirius Mathematics Center, located on the Black Sea coast, was founded in 2019 by the Talent and Success Foundation for organizing mathematical conferences and other events promoting the development of mathematics in Russia. In 2024, the Center has acquired its own Russian-language journal for publication of original research papers by participants of conferences held at the Center. The authors are invited to submit papers to the journal at https://ef.msp.org/submit/sirius [ABSTRACT FROM AUTHOR]

Copyright of EduAdvance: Journal of Advancements in Education (JAE) is the property of EduAdvance: Journal of Advancements in Education (JAE) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This note is devoted to developing Morrey regularity theory for the following system of Rivière \begin{equation*} -\Delta u=\Omega \cdot \nabla u+f \qquad \text {in }B^{2}, \end{equation*} under the assumption that f belongs to some Morrey space. Our results extend the L^p regularity theory of Sharp and Topping [Trans. Amer. Math. Soc. 365 (2013), pp. 2317–2339], and also generalize a Hölder continuity result of Wang [Calc. Var. Partial Differential Equations 56 (2017), Paper No. 23, 24] on harmonic mappings. Potential applications of our results are also possible in second order conformally invariant geometrical problems as that of Wang [Calc. Var. Partial Differential Equations 56 (2017), Paper No. 23, 24]. [ABSTRACT FROM AUTHOR]

In this true story, one mathematics major supports another in an unexpected way. [ABSTRACT FROM AUTHOR]

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper responds to the need for understanding trends and gaps in extant research related to adult education in mathematics and numeracy, given changing skill demands and skill gaps regarding adults, and related policy, theorizing, and practice trends. This paper presents the results of a scoping review of recent empirical research related to adult education in mathematics and numeracy, published in 22 selected journals from 2019 to 2022, including 15 journals in adult education and seven in mathematics education. The results show that only 39 relevant empirical studies were found among over 2300 research papers reviewed, and that few of those focus on practice-related of adult education in mathematics and numeracy. The results provide quantitative evidence suggesting that the field of adult numeracy education is under-researched, and help to identify gaps in empirical research involving adult numeracy, including on emerging topics such as on modeling and critical interpretation. The results also point to research opportunities that can strengthen theorizing and practice in both mathematics education and adult numeracy education. [ABSTRACT FROM AUTHOR]

This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on proof and proving in both school and university mathematics. As an organizing framework, we used Cohen et al.'s triadic conceptualization of instruction, which draws attention not only to the main actors of the didactical process (i.e., the Teacher and Students) and the Content around which the actors' work is organized (herein, content related to proof and proving), but also to the relationships among the actors and the content. Out of the 103 papers we reviewed, almost half fell in the Student-Content category, which is consistent with the existence of a substantial number of frameworks, methods, and research findings related to students' engagement with proof and proving. About a quarter of the papers fell in the Student–Teacher-Content category, which reflects an emphasis on viewing instructional practice in proof and proving in a holistic, systemic way. Only few papers fell in the categories that did not include Content in them, namely, the categories of Student, Teacher, and Student–Teacher; this suggests mathematics education research on proof and proving has a strong disciplinary identity, which potentially differentiates it from other mathematics education research strands. About a fifth of the papers were oriented towards 'breaking ground' through making an explicit theoretical and/or methodological contribution (Student–Teacher-Content and Content were the main categories where such contributions appeared), whilst the majority of the papers were focused on 'building ground' through elaborating or employing existing methodological and/or theoretical approaches. [ABSTRACT FROM AUTHOR]

ISO 15189 requires laboratories to estimate the uncertainty of their quantitative measurements and to maintain them within relevant performance specifications. Furthermore, it refers to ISO TS 20914 for instructions on how to estimate the uncertainty and what to take into consideration when communicating uncertainty of measurement with requesting clinicians. These instructions include the responsibility of laboratories to verify that bias is not larger than medically significant. If estimated to be larger than acceptable, such bias first needs to be eliminated or (temporarily) corrected for. In the latter case, the uncertainty of such correction becomes part of the estimation of the total measurement uncertainty. If small enough to be acceptable, bias becomes part of the long term within laboratory random variation. Sources of possible bias are (not limited to) changes in reagent or calibrator lot variation or calibration itself. In this paper we clarify how the rationale and mathematics from an EFLM WG ISO/A position paper on allowable between reagent lot variation can be applied to calculate whether bias can be accepted to become part of long-term imprecision. The central point of this rationale is to prevent the risk that requesting clinicians confuse changes in bias with changes in the steady state of their patients. [ABSTRACT FROM AUTHOR]

This article describes the outcomes of a faculty partnership between a math professor and a composition professor to improve the final paper in a research-focused senior capstone math course. Much attention has been paid in recent years to the importance of undergraduate research experiences and how to best create and support such endeavors. However, little space has been dedicated to helping math faculty design and scaffold writing assignments to support their students' development as scholars. We describe how our partnership took place, the changes we made to existing assignments and the creation of new ones, and an assessment of our efforts completed by an interdisciplinary group of faculty and students, which showed marked improvement in the areas of information literacy, critical thinking, and quality of writing. [ABSTRACT FROM AUTHOR]

Floer theory for Lagrangian cobordisms was developed by Biran and Cornea in a series of papers [Lagrangian cobordism. I, J. Amer. Math. Soc. 26 (2013) 295–340; Lagrangian cobordism and Fukaya categories, Geom. Funct. Anal. 24 (2014) 1731–1830; Cone-decompositions of Lagrangian cobordisms in Lefschetz fibrations, Selecta Math. 23 (2017) 2635–2704] to study the triangulated structure of the derived Fukaya category of monotone symplectic manifolds. This paper explains how to use the language of stops to study Lagrangian cobordisms in Liouville manifolds and the associated exact triangles in the derived wrapped Fukaya category. Furthermore, we compute the cobordism groups of non-compact Riemann surfaces of finite type. [ABSTRACT FROM AUTHOR]

This paper concerns with the dynamical properties of a diffusive viral model with free boundaries, which describes the spread of viruses in space. Unlike the paper (Li et al. in Sci China Math 64:1971–1992, 2021), free boundaries at both ends will extend to infinity, i.e., the habitat eventually expands to the entire space. Moreover, the virus will eventually die out when the Basic Reproduction Number R 0 ≤ 1 , while the virus will stabilize in a positive equilibrium when R 0 > 1 and some further assumptions (Theorem 3.2). [ABSTRACT FROM AUTHOR]

This paper shows that K_t-minor-free (and K_{s, t}-minor-free) graphs G are subgraphs of products of a tree-like graph H (of bounded treewidth) and a complete graph K_m. Our results include optimal bounds on the treewidth of H and optimal bounds (to within a constant factor) on m in terms of the number of vertices of G and the treewidth of G. These results follow from a more general theorem whose corollaries include a strengthening of the celebrated separator theorem of Alon, Seymour, and Thomas [J. Amer. Math. Soc. 3 (1990), 801–808] and the Planar Graph Product Structure Theorem of Dujmović et al. [J. ACM 67 (2020)]. [ABSTRACT FROM AUTHOR]

This paper presents a semester-long bottle design project for an undergraduate Numerical Analysis course. Students implement numerical methods in MATLAB to design and 3D print a bottle. Employing mathematical methods to compute features of their designs enhances students' understanding of numerical techniques in design applications. Student feedback highlights the project's efficacy in demonstrating the intersection of mathematics and design, fostering creativity, and instilling a deeper appreciation for mathematical principles in real-world contexts. [ABSTRACT FROM AUTHOR]

This study is focused on investigating parental involvement in students' mathematical activities. It presents a comprehensive bibliometric analysis that examines new areas of research to discover current trends and future research opportunities related to parental involvement in their children's mathematics activities. This study intends to provide a meaningful contribution toward enhancing educational interventions in the future. The metadata of the publications included in this analysis was extracted from the Scopus and ERIC databases using the search criteria "(parent OR parent) AND (involvement OR support) AND (math or math) AND student." After the screening step, a comprehensive analysis was conducted on a total of 944 articles using the tools Harzing's Publish or Perish 8, Biblioshiny, and VOSviewer 1.6.20. The findings indicated that studies on this topic covered 42 years and accumulated a total of 17,392 citations. The most prolific year in terms of publications was 2023, with a peak of 80 studies published. The leading contributors to this body of research were Jianzhong Xu and James Reed Campbell, each authoring six papers. The keyword mapping results revealed several interesting research avenues for future investigation, such as the incorporation of psychological interventions, longitudinal studies, multidisciplinary approaches, and the utilization of technology. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a new contraction principle via altering distance and C -class functions with rational forms which extends and generalizes the existing version provided by Hasan Ranjbar et al. [H. Ranjbar, A. Niknam, A fixed point theorem in Hilbert C ∗ -modules, Korean J. Math. , 30 (2022), 297–304]. Specifically, the rational forms involved in the contraction condition we presented involve the p -th power of the displacements which can exceed the second power mentioned in Hasan Ranjbar et al.'s paper. Moreover, we also proved a fixed point theorem for this type of contraction in the Hilbert C ∗ -module. Some adequate examples were provided to support our results. As an application, we applied our result to prove the existence of a unique solution to an integral equation and a second-order (p , q) -difference equation with integral boundary value conditions. [ABSTRACT FROM AUTHOR]

Within the context of Indian religions, Jainism has long been recognized for its extensive use of permutations and combinations. However, the application of these principles within Buddhist scriptures has received relatively little scholarly attention. This paper introduces a new example of the specific application of permutations and combinations in Buddhist scriptures. In this paper, we focus on the first saṅghādisesa rule in the Theravāda-vinaya, which lists a series of element sets and arranges these elements according to a certain pattern known as "ten-roots" (mūla), and we discover that these arrangements form a regular numerical sequence, called "oblong numbers". Moreover, similar patterns with different quantities are also found in the fourth Pārājika and the fifth saṅghādisesa rules. This indicates that the compilers of the Theravāda-vinaya did not use this mathematical knowledge without basis. Interestingly, we also found the use of this sequence in the Bakhshālī manuscript. Therefore, in this article, after summarizing and verifying the arrangement rules of the Theravāda-vinaya, we discuss whether the oblong numbers were influenced by Greek mathematics. [ABSTRACT FROM AUTHOR]

The question of when a vertex algebra is a quantization of the arc space of its associated scheme has recently received a lot of attention in both the mathematics and physics literature. This property was first studied by Tomoyuki Arakawa and Anne Moreau (see their paper in the references), and was given the name \lq\lq classical freeness" by Jethro van Ekeren and Reimundo Heluani [Comm. Math. Phys. 386 (2021), no. 1, pp. 495-550] in their work on chiral homology. Later, it was extended to vertex superalgebras by Hao Li [Eur. J. Math. 7 (2021), pp. 1689–1728]. In this note, we prove the classical freeness of the simple affine vertex superalgebra L_n(\mathfrak {o}\mathfrak {s}\mathfrak {p}_{m|2r}) for all positive integers m,n,r satisfying -\frac {m}{2} + r +n+1 > 0. In particular, it holds for the rational vertex superalgebras L_n(\mathfrak {o}\mathfrak {s}\mathfrak {p}_{1|2r}) for all positive integers r,n. [ABSTRACT FROM AUTHOR]

Tablet‐based technology has become a conduit for the administration of curriculum‐based measurement (CBM) tools. Using tablets to administer CBM probes has many advantages; however, little is known about how students perform on CBMs when administered via a tablet. The current investigation compared digits correct per minute obtained from 44 third‐grade students on CBM addition fluency probes administered via three different modalities. Students completed the probes using traditional paper and pencil, a tablet using their fingers to write the answer, or a tablet application using a keyboard to type the answer. A within‐subjects group design showed students performed significantly better on the tablet when using their finger to write the answer, even though most students (58%) indicated this was their least preferred modality. The discussion focuses on the implications for educators and the use of different CBM modalities for interindividual and intraindividual comparisons. Practitioner points: Third‐grade students responded to math facts faster when writing with their fingers on an iPad, even compared to paper and pencil.The results are inconsistent with other studies that found students were faster when using paper and pencil.Finally, most third‐grade students preferred answering addition facts with a pencil on paper. [ABSTRACT FROM AUTHOR]

Very recently, P. Saha et al. [A global optimality result in probabilistic spaces using control function. Optimization. 2021;70:2387–2400] studied the existence of best proximity points for Banach type ϕ-proximal contractions in the framework of Menger probabilistic metric spaces. In this paper, we present a simple proof of their main existence result which is based on a fixed point theorem for ϕ-contractive self-mappings in complete Menger PM-spaces due to B.S. Choudhury and K. Das [A new contraction principle in Menger spaces. Acta Math Sin. 2008;24:13791386]. [ABSTRACT FROM AUTHOR]

The interrogation of often unintended practices of marginalisation has gained focus in research on mathematics teaching and mathematics teacher education throughout the last decades. In this introductory survey paper, work against marginalisation in these contexts of mathematics education is viewed in terms of work towards equity, diversity and inclusion. Based on this interpretation, we present a framework on awareness and practice of equity, diversity and inclusion in mathematics teaching and mathematics teacher education research. We then use this framework and a survey method of mapping review to identify and comment on a selection of studies. As a result, we illustrate three research moves towards equity, diversity and inclusion, in the form of interconnected themes: (1) Widening the understanding of the mathematics and the mathematics education curricula (2) Improving the practice and discussion of mathematics teaching (3) Unpacking ideologies in mathematics teaching and mathematics teacher education. We finally examine the themes and the special issue papers together to foreground commonalities regarding awareness of discriminatory discourses and practices of creating and distributing opportunities for all groups, including those historically and currently marginalised. Despite the important increase of equity-driven principles of awareness, we conclude that mathematics education research on teaching and on teacher education needs more examples of practices whose development has been proved to challenge marginalisation. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with the identity 1R, and let R* be the multiplicative group of units in R. An element a ∈ R* is called an exceptional unit if there exists a b ∈ R* such that a + b = 1R. We set R** to be the set of all exceptional units in R. In this paper, we consider the residue-class ring Zn. For any positive integers n, s, and c ∈ Zn, let Ns(n, c) :=#{(x1, ..., xs) ∈ (Z** n ) s : x1 + ... + xs(n, c). Later on, Yang and Zhao (Monatsh. Math. 182 (2017)) extended Sander’s theorem to finite terms by using exponential sum theory. In this paper, using matrix theory, we present an explicit formula for N2(n, c). Later on, Yang and Zhao (Monatsh. Math. 182 (2017)) extended Sander’s theorem to finite terms by using exponential sum theory. In this paper, using matrix theory, we present an explicit formula for Ns(n, c). This extends and improves earlier results. [ABSTRACT FROM AUTHOR]

The goal of this paper is to establish new Maximum Principles for parabolic equations in the framework of mixed local/nonlocal operators. In particular, these results apply to the case of mixed local/nonlocal Neumann boundary conditions, as introduced by Dipierro, Proietti Lippi, and Valdinoci [Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), pp. 1093–1166]. Moreover, they play an important role in the analysis of population dynamics involving the so-called Allee effect, which is performed by Dipierro, Proietti Lippi, and Valdinoci [J. Math. Biol. 89 (2024), Paper No. 19]. This is particularly relevant when studying biological populations, since the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction. [ABSTRACT FROM AUTHOR]

This paper describes a Lesson Study in which in-service mathematics secondary-school teachers, collaborating with researchers, involve grade 10 students in tessellation problems. The data are collected by an experiment carried out in the context of the "Liceo Matematico" project, with three volunteer teachers. The experiment goal was to craft a collaborative design of the research lesson between teachers and researchers. The research aim of the paper is to examine the use of Lesson Study in the institutional and cultural context of Italian secondary school with the use of Cultural Transposition as a theoretical framework. The research is qualitative with idiographic aims, based on video research. The educational aim of the research is to provide a solid basis for a revamped in-service teacher education first in the context of the project, then in curricular context. Semiotic mediation is used to provide, within Lesson Study, the conceptual framework for teachers and researchers collaborative design of the research lesson. The results show that Lesson Study, as a foreign practice, is an opportunity for teachers to confront their teaching practices, to enrich their professional development, resulting in more awareness on their didactical action in and outside the classroom. [ABSTRACT FROM AUTHOR]

In this paper, we define rational type Geraghty tower contraction mapping and prove the existence of such finite and infinite rational Geraghty tower theorem(s) in complete metric spaces. The results we establish in this paper extend, improve, generalise and unify some existing results in the literature. [ABSTRACT FROM AUTHOR]

This paper deals with a new stochastic method to solve Lotka's Law with higher degree of Newton-Cotes Quadrature Rule as an alternate method to existing solution of the value determination of the constant part of the power law; so far, M.L. Pao gave a solution with an equation to determine the area under the curve with numerical integration rule with degree=1 which is also known as Trapezoidal Rule. Here, next higher degree 2, popularly known as Simpson's 1/3 rule at closed interval [x 1,] has been used to establish a deterministic equation form to solve authors' productivity realized through Lotka's Law. Re-estimating the value of C with higher degree quadrature rule is very crucial as the probability of inclusion of more area and exclusion of unnecessary area under the curve is more precise. Another area of investigation is the determination of p value (Pao determined p=20), i.e. whether p=20 can be altered? Or equation derived through Simpson's 1/3 rule, whether it can give a minimal residual error beyond p=20. This paper is dedicated to build up a mathematical equation to solve the constant value(C) of the Lotka's law equation as well as enlighten all these investigating points. [ABSTRACT FROM AUTHOR]

Fourier transform is one of the oldest and well-known technique in the field of mathematics and engineering mathematical works. As the concept of uncertainty has been introduced in the mathematics, most of the works gravitate towards the use Neutrosophic set. So, it is also important to study the Fourier transform in the sense of Neutrosophic set. In this paper we have applied the Neutrosophic Fourier transform in solving heat equation, and integral equation. Where detailed examples are given to clarify each case. [ABSTRACT FROM AUTHOR]

In this paper, we study the scattering theory for the cubic inhomogeneous Schrödinger equations with inverse square potential i u t + Δ u - a | x | 2 u = λ | x | - b | u | 2 u with a > - 1 4 and 0 < b < 1 in dimension three. In the defocusing case (i.e. λ = 1 ), we establish the global well-posedness and scattering for any initial data in the energy space H a 1 (R 3) . While for the focusing case(i.e. λ = - 1 ), we obtain the scattering for the initial data below the threshold of the ground state, by making use of the virial/Morawetz argument as in Dodson and Murphy (Proc Am Math Soc 145:4859–4867, 2017) and Campos and Cardoso (Proc Am Math Soc 150:2007–2021, 2022) that avoids the use of interaction Morawetz estimate. We also address the existence and the non-existence of normalized solutions of the above Schrödinger equation in dimension N for the focusing and defocusing cases. [ABSTRACT FROM AUTHOR]

Several notions of topological entropy for non necesarily continuous semiflows were introduced because the classical notion of topological entropy does not work cause the discontinuity of these systems. In particular, in Jaque and San Martin (J Differ Equ 266:3580–3600, 2019) was studied the definition of topological entropy by using separated and spanned sets, respectively, associated to a certain pseudosemimetric. Besides, it was proved that for regular impulsive semiflows the notion obtained by using separated sets can be computed trough a suitable conjugacy with a continuous system. In this paper, we will show that the same result holds for the entropy defined by spanning sets by adding a mild condition on the semiflow. This result extends, for this kind of semiflows, those obtained by Bowen (Trans Am Math Soc 153:401–414, 1971) and Dinaburg (Dokl Akad Nauk SSSR 190:19–22, 1970) respectively for the continuous case. [ABSTRACT FROM AUTHOR]

This paper describes an Online Teaching Lab model that incorporates elements of lesson study and studio model for teacher learning. We focus on changes in design and facilitation decisions of two specific Online Teaching Labs and study differences in teachers' verbal and written responses to better understand how the process supports teacher learning. Middle grades mathematics teachers took part in the Online Teaching Labs. Data included video recordings of professional development team meetings, lesson implementation, Online Teaching Labsi and teachers' written work on 'Capture Sheets.' Data were analysed based on observable behaviours we intended participating teachers would enact. We found a relationship between the intentional changes facilitators made from the first to second Online Teaching Lab and teacher responses. Facilitators made more explicit mention of the learning goals, increased opportunities for teacher discussion, and included varied video clips. As compared to teachers in the first iteration, teachers in the second Online Teaching Lab more frequently identified teacher discourse moves related to engagement and cognitive demand of tasks and identified connections between teacher pedagogy, student strategies, and mathematical goals. The design, implementation, and outcomes are novel because the model includes features of lesson study and studio model through an online medium. [ABSTRACT FROM AUTHOR]

Motivation: This research investigates the transformative impact of integrating AI into mathematics education, aiming to enhance students' conceptual understanding and self‐efficacy. It addresses the crucial need for innovative teaching methods in response to contemporary challenges in education and aims to fill gaps in understanding the potential drawbacks and benefits of AI implementation. Objectives: The primary goal of this study is to investigate the effects of AI tools, such as GeoGebra and ChatGPT, on students' conceptual understanding and self‐efficacy in a mathematics classroom setting, with a focus on collaborative learning, teacher‐led discussions, and problem‐solving. Methods: Employing a mixed‐methods approach, the research involves pre‐ and post‐implementation surveys, supplemented by qualitative data from interviews, focus groups, and classroom observations. The study emphasises the utilisation of AI in collaborative learning environments and explores the challenges and opportunities associated with its integration. Results and Conclusions: The study reveals a noteworthy enhancement in students' conceptual understanding and self‐efficacy belief when AI tools are incorporated into mathematics education. However, it highlights concerns such as technological challenges, potential teacher replacement fears, biases in AI systems, and difficulties related to pacing and social interaction. To optimise the use of AI, the paper suggests strategies like adaptive learning platforms, real‐world simulations, intelligent tutoring systems, and data‐driven instruction, positioning AI as a complement rather than a substitute for traditional teaching methods. The study recommends addressing challenges through additional support resources and transparent communication, emphasising the need for a thoughtful integration of AI in education. Lay Description: What is currently known about the subject matter?: AI is increasingly being integrated into educational settings.AI offers potential for personalised learning experiences.Concerns exist regarding AI replacing human educators and ethical issues such as data privacy and bias.Effectiveness of AI in improving student performance varies depending on the implementation and context. What this paper adds?: Provides empirical evidence on how GeoGebra and ChatGPT enhance students' conceptual understanding and confidence in mathematics.Identifies specific challenges and concerns from students and teachers regarding AI use.Demonstrates how integrating GeoGebra and ChatGPT boosts student engagement and motivation, leading to improved understanding of mathematical concepts.Offers insights into student engagement levels and interaction patterns with AI tools. Implications of the findings for practitioners: Emphasise the need for careful selection and validation of AI to ensure they meet educational objectives.Address ethical concerns and ensure data privacy when implementing AI in education.Encourage ongoing evaluation and refinement of practices related to the use of AI, ensuring that they meet ethical standards and address data privacy concerns.Advocate for the establishment of acceptable criteria and conventions for AI use in education, improving their effectiveness and usability based on student and educator feedback. [ABSTRACT FROM AUTHOR]

This paper provides a brief overview of findings in mathematical cognition and how a human-like AI in mathematics may look like. Then, it provides six reasons in favor of a human-like AI for mathematics: (1) human cognition, with all its limits, creates mathematics; (2) human mathematics is insightful, not merely deductive steps; (3) human cognition detects structure in the real world; (4) human cognition can tackle and detect complex problems; (5) human cognition is creative; (6) human cognition considers ethical issues. The paper provides a tentative frame to the question whether human mathematical cognition is relevant for designing an artificial intelligence that works on and creates mathematics. [ABSTRACT FROM AUTHOR]

In a series of work by Wormleighton [Selecta Math. (N.S.) 28 (2022), p 9], Wormleighton [J. Symplectic Geom. 19 (2021), pp. 475–506], and Chaidez and Wormleighton [ECH embedding obstructions for rational surfaces, arXiv: 2008.10125 , 2020], algebraic capacities were introduced in an algebraic manner for polarized algebraic surfaces and applied to the symplectic embedding problems. In this paper, we give a reformulation of algebraic capacities in terms of only a tamed pair of symplectic form and almost complex structure. We show that they actually only depend on the cohomology class of the symplectic form for a rational manifold. Since it is not known that any symplectic form on a rational manifold is Kähler, this novel formulation potentially is more general on a rational manifold. Additionally, for manifolds with b_2^+=1, we derive asymptotic results that are parallel to the context of ECH (Embedded Contact Homology) and algebraic settings. When assuming c_1\cdot [\omega ]>0 on rational manifolds, we further introduce a sequence of tropical polynomials which will succinctly describe those capacities viewed as functions over the domain parametrizing such symplectic forms. As an application, we give a purely symplectic proof of the correspondence between algebraic capacities and ECH capacities for smooth toric surfaces. [ABSTRACT FROM AUTHOR]

In Kim et al. (Nagoya Math J 178: 37-53, 2005), Lee and Lee (J Geometry Phys 56(10): 2011-2023, 2006), the authors developed a nice formula to compute the Nielsen number of a self-map on an infra-nilmanifold. For the case of nilmanifolds this formula was extended to n-valued maps in Deconinck and Dekimpe (J Fixed Point Theory Appl 25(4): Paper No. 84, 29, 2023). In this paper, we extend these results further and establish the averaging formula to compute the Nielsen number of any n-valued affine map on an infra-nilmanifold. [ABSTRACT FROM AUTHOR]

In a celebrated paper of Marcus and Ree [M. Marcus, R. Ree. Diagonals of doubly stochastic matrices. Quart J Math Oxford Ser. 1959; 10(1):296–302], it was shown that if $ A=[a_{ij}] $ A = [ a ij ] is an $ n \times n $ n × n doubly stochastic matrix, then there is a permutation $ \sigma \in S_n $ σ ∈ S n such that $ \sum _{i,j=1}^{n} a_{i,j}^{2} \leq \sum _{i=1}^{n} a_{i,\sigma (i)} $ ∑ i , j = 1 n a i , j 2 ≤ ∑ i = 1 n a i , σ (i) . Erdős asked for which doubly stochastic matrices the inequality is saturated. Although Marcus and Ree provided some insight for the set of solutions, the question appears to have fallen into oblivion. Our goal is to provide a complete answer in the particular, yet non-trivial, case when n = 3. [ABSTRACT FROM AUTHOR]

This paper focuses on the possible usage of qualitative mathematics in psychology. Qualitative mathematics is understood to be equivalent to pure mathematics. First, it is explained that mathematics is a discipline studying patterns in reproducible mental objects. Qualitative mathematics is presented as an alternative to measurement, potentially offering the same level of exactness, clarity, and rigor. This perspective might lead psychologists to explore connections between a phenomenon and any kind of mathematical structure, regardless of whether the structure is quantitative. Usage of (any) mathematical structures might require scholars who are familiar with them. Consequently, changes in mathematics education may also be needed. Introducing non-numerical structures into mathematics education—thereby partially revisiting the New Math Movement—could train individuals more prepared for a creative approach to the use of structures and less inclined to view everything as quantitative. [ABSTRACT FROM AUTHOR]

This paper aims to investigate new coincidence point theorems for self‐maps under an extended rational contraction. Our approach uses the p‐adic distance in partially ordered ultrametric spaces. Furthermore, to illustrate our major discoveries, we give a comprehensive numerical analysis. This study expands on prior research in partially ordered ultrametric spaces to provide a more comprehensive understanding of such spaces using rational contraction. [ABSTRACT FROM AUTHOR]

As part of the demands of a globalized and interconnected world, studying second languages has become a major priority. Bilingual programs implemented in recent decades have motivated an educational strategy in which content area courses are taught through L2. The potential costs of this strategy in academic performance are debated, especially in challenging areas such as mathematics. The present work systematically reviewed 71 papers based on experiments measuring mathematics performance in bilinguals in order to establish if bilinguals show a (dis)advantage in mathematics compared to monolinguals. The results of a total of 305,136 participants (57,703 bilinguals and 247,503 monolinguals) show that bilingualism does not seem to affect mathematical performance, but this is dependent on whether subjects are highly proficient bilinguals. This type of bilingual may only be affected by lower reaction times depending on the testing language. On the other hand, low language proficiency negatively impacts mathematical performance. Lastly, bilingualism enhances mathematical encoding and processes in non-language-related tasks. [ABSTRACT FROM AUTHOR]

Graph theory is a crucial branch of mathematics in fields like network analysis, molecular chemistry, and computer science, where it models complex relationships and structures. Many indices are used to capture the specific nuances in these structures. In this paper, we propose a new index, the weighted asymmetry index, a graph-theoretic metric quantifying the asymmetry in a network using the distances of the vertices connected by an edge. This index measures how uneven the distances from each vertex to the rest of the graph are when considering the contribution of each edge. We show how the index can capture the intrinsic asymmetries in diverse networks and is an important tool for applications in network analysis, optimization problems, social networks, chemical graph theory, and modeling complex systems. We first identify its extreme values and describe the corresponding extremal trees. We also give explicit formulas for the weighted asymmetry index for path, star, complete bipartite, complete tripartite, generalized star, and wheel graphs. At the end, we propose some open problems. [ABSTRACT FROM AUTHOR]

This note provides a counterexample to a theorem announced in the last part of the paper (Vicente and Custódio Math Program 133:299–325, 2012). The counterexample involves an objective function f : R → R which satisfies all the assumptions required by the theorem but contradicts some of its conclusions. A corollary of this theorem is also affected by this counterexample. The main flaw revealed by the counterexample is the possibility that a directional direct search method (dDSM) generates a sequence of trial points (x k) k ∈ N converging to a point x ∗ where f is discontinuous, lower semicontinuous and whose objective function value f (x ∗) is strictly less than lim k → ∞ f (x k) . Moreover the dDSM generates trial points in only one of the continuity sets of f near x ∗ . This note also investigates the proof of the theorem to highlight the inexact statements in the original paper. Finally this work introduces a modification of the dDSM that allows, in usual cases, to recover the properties broken by the counterexample. [ABSTRACT FROM AUTHOR]

The focus of this study is to use the mixture item response theory (MixIRT) model while implementing the no-U-turn sampler as a technique for investigating the presence of latent classes (i.e., subpopulations) among eighth-grade students who were administered TIMSS 2019 mathematics subtest in paper format from the gulf cooperation council (GCC) countries. One-, two-, and constrained three-parameter logistic MixIRT models with one to four classes were used to fit to the data, where the model data fit was assessed using Bayesian fit indices. The results indicate that multiple latent classes or subpopulations can better reflect the mathematical proficiency of eighth graders from the four GCC countries, and specifically the two-class constrained three-parameter MixIRT model provides a relatively better fit to the data. The results also indicate that when a mixture of several latent classes present, the conventional unidimensional IRT model is limited in providing information for multiple latent classes and shall be avoided. In addition to adding to the existing literature on MixIRT models for international large-scale assessments such as TIMSS on its heterogenous subpopulations from a fully Bayesian approach, this study sheds light on the limitation of conventional unidimensional IRT models and subsequently directs attention to the use of the more complex MixIRT model for such assessments. [ABSTRACT FROM AUTHOR]

This paper studies a question of Bourin on noncommutative $ L^p $ L p spaces. Some inequalities due to Hayajneh et al. [Norm inequalities for positive semidefinite matrices and a question of Bourin II. Int J Math. 2021;32:2150043] and Hayajneh et al. [Norm inequalities for positive semidefinite matrices and a question of Bourin III. Positivity. 2022;26:23] are extended to the case of operators in noncommutative $ L^p $ L p spaces associated with a semifinite von Neumann algebra. We give a partial answer to a question of Bourin on noncommutative $ L^p $ L p spaces. Some related submajorization inequalities are also given. [ABSTRACT FROM AUTHOR]

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This paper focuses on the possible usage of qualitative mathematics in psychology. Qualitative mathematics is understood to be equivalent to pure mathematics. First, it is explained that mathematics is a discipline studying patterns in reproducible mental objects. Qualitative mathematics is presented as an alternative to measurement, potentially offering the same level of exactness, clarity, and rigor. This perspective might lead psychologists to explore connections between a phenomenon and any kind of mathematical structure, regardless of whether the structure is quantitative. Usage of (any) mathematical structures might require scholars who are familiar with them. Consequently, changes in mathematics education may also be needed. Introducing non-numerical structures into mathematics education--thereby partially revisiting the New Math Movement--could train individuals more prepared for a creative approach to the use of structures and less inclined to view everything as quantitative. [ABSTRACT FROM AUTHOR]

Building on previous work in fractional calculus, this paper introduces new definitions for the (ρ, k, φ)‐proportional integral and (ρ, k, φ)‐proportional H fractional derivative. This new approach retains the semigroup properties of traditional fractional integrals. A significant advantage of this fractional calculus is its compatibility with the majority of existing studies on fractional differential equations. Furthermore, we delve into the properties of the generalized fractional integrals and derivatives. We discuss, for instance, the mapping properties of the (ρ, k, φ)‐proportional integral. To elucidate these concepts, we introduce a set of new weighted spaces. Additionally, we explore the generalized Laplace transform of both the (ρ, k, φ)‐proportional integrals and (ρ, k, φ)‐proportional H fractional derivatives. Also, examples concerning the linear (ρ, k, φ)‐proportional H fractional equations are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

Hypergroups represent a generalization of groups, introduced by Marty, that are rich in applications in several sectors of mathematics and in other fields. An important class of hypergroups called join spaces is presented in this paper, along with some connections to lattice theory, in particular, to modular and to distributive lattices. In particular, we study join spaces associated with chains through functions and we analyze when such join spaces are isomorphic. Moreover, a combinatorial problem is presented for a finite context, focusing on calculating the number of isomorphisms classes of join spaces. [ABSTRACT FROM AUTHOR]