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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]

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]

Curriculum-based measurement (CBM) tools are increasingly administered through technology-based modalities such as computers and tablets. Two studies were conducted to examine whether students perform similarly on paper-based and tablet-based math fact probes. Ten students completed 1-min addition or multiplication math probes using a single-case multielement design. Students completed the probes using traditional paper and pencil, a tablet using a stylus to write the answer, or a tablet application using a keyboard to type the answer. Visual analysis of time series graphs showed that the majority of students performed better on the paper-based probes than on either the keyboard or stylus probes. Nonoverlap of all pairs (NAP) effect size measures indicated medium to large differences between paper and stylus probes and paper and keyboard probes but weak effects between stylus and keyboard probes. Discussion focuses on the implications for educators and the use of different CBM modalities for interindividual and intraindividual comparisons. [ABSTRACT FROM AUTHOR]

We attempt to identify the 25 most-cited statistical papers, providing some brief commentary on each paper on our list. This list consists, to a great extent, of papers that are on non-parametric methods, have applications in the life sciences, or deal with the multiple comparisons problem. We also list the most-cited papers published in 1993 or later. In contrast to the overall most-cited papers, these are predominately papers on Bayesian methods and wavelets. We briefly discuss some of the issues involved in the use of citation counts. [ABSTRACT FROM AUTHOR]

Summarizes the construction of paper folding. Method for approximating rational subdivisions or arbitrary angles and line segments; Angle-folding algorithm; Approximating angles, regular polygons and star polygons; Dissection of angles into equal parts.

There have been many studies of the comparability of computer-administered and paper-administered tests. Not surprisingly (given the variety of measurement and statistical sampling issues that can affect any one study) the results of such studies have not always been consistent. Moreover, the quality of computer-based test administration systems has changed considerably over recent years, as has the computer-experience of students. This study synthesizes the results of 81 studies performed between 1997 and 2007. The estimated effect size across all studies was very small (-.01 weighted, .00 unweighted). Meta-analytic methods were used to ascertain whether grade (elementary, middle, or high school) or subject (English Language Arts, Mathematics, Reading, Science, or Social Studies) had an impact on comparability. Grade appeared to have no affect on comparability. Subject did appear to affect comparability, with computer administration appearing to provide a small advantage for English Language Arts and Social Studies test (effect sizes of .11 and .15, respectively), and paper administration appearing to provide a small advantage for Mathematics tests (effect size of -.06). [ABSTRACT FROM AUTHOR]

The article offers information on dynamical systems and irrational angle construction by paper-folding. Construction of rational angle to any desired accuracy by folding a strip of paper requires approximating method. The construction uses a periodic sequence composed of two types of folding moves, guided by number-theoretic properties of the angle's fractional representation. The number-theoretic scheme must be replaced by something new, the Folds and Switchfold prescription, in the construction of irrational angles.

The present study aimed at validating a computerized mental rotation task developed for use in functional Magnetic Resonance Imaging (fMRI) studies. Eighty-three females and 74 males completed the computerized task, two pencil-and-paper tests of mental rotation, and reported their high school grades in mathematics, English, and history. The computerized task involved the presentation of pairs of three-dimensional stimuli that differed in orientation by 0, 40, 80, 120, or 160 degrees. Results showed significant gender differences in favor of males in the three main tasks, although gender interacted with angle of rotation in the computerized task. Evidence for concurrent validity was obtained in the form of significant correlations between performance on tasks relevant to mental rotation (paper and pencil tests and mathematics grades), whereas discriminant validity was demonstrated by a lack of correlation with tasks deemed irrelevant to mental rotation (English and history grades). These findings support the use of our computerized mental rotation task as a valid measure of mental rotation abilities in fMRI studies. [ABSTRACT FROM AUTHOR]

This paper reports on the results of a study of English children's performance on a computer mathematics assessment compared with a pencil-and-paper assessment. Two matched samples of children were each assessed on one of two mathematics pencil-and-paper tests and assessed a month later on a cloned computer test. The performance scores were better on the computer tests than on the pencil-and-paper tests, although this was not statistically significant in every case. The paper goes on to discuss some of the differences between performance and approach to the question between the two media, and explores possible reasons for these differences. In conclusion, the computer tests were found to have an overall positive effect on children's performance, although not for every child and, in some instances, the computer assessment limited the way in which a question could be answered. [ABSTRACT FROM AUTHOR]

In this article we describe a method for determining the elastic constants for paper from a measured displacement field. Our model is based on the finite element method using quadrilateral elements. A method for finding the first and second order derivatives with respect to the unknown parameters plays a crucial role in the optimization process used to solve the inverse problems in this article. To reduce the influence of the noise of the input data, an efficient continuation method is used for the regularization term in the cost function. Some numerical results for synthetic data and measurement will verify the efficiency of our approach. [ABSTRACT FROM AUTHOR]

De Broglie's contribution in the Philosophical Magazine from 1924 is fascinating from many standpoints: for its moderate use of mathematics, the close connection to Einstein's special theory of relativity, and of course for the proposal of matter waves. We revisit this mostly speculative publication, which contributed crucially to the birth of quantum mechanics. [ABSTRACT FROM AUTHOR]

Discusses which shapes are possible and impossible to construct using origami. Algebraic characterization of origami; Construction process; Possibility to construct a line parallel to a given line through any given point; Construction of a cube with twice the volume of a given cube.

The application of STEM (Science, Technology, Engineering, and Math) education in solving real-world problems is challenging. To tackle this challenge, a project-based learning approach that integrates robots with cost-effective self-made toys to problem-solving was adopted to assist rural primary school students to apply STEM skills. The purpose of this study was to evaluate the effects of the project-based learning approach which includes lecturing and hands-on activities on primary school students' STEM learning outcomes and attitudes. An experiment was conducted with 25 primary school students who voluntarily participated in a STEM summer-camp programme. Students were asked to assemble a paper house equipped with an IoT control module and LED light switches, and write and edit robot scripts to produce a robot-based storytelling narrative using the paper house they made as a context. The results show that the project-based learning approach was an effective approach for cultivating primary school students' STEM knowledge and skills as evidenced from the post-written test. The relationships between the students' STEM learning outcomes and attitudes were also confirmed by a clustering analysis. Students who had higher learning attitudes also achieved higher STEM learning outcomes; the findings are also supported by the feedback from the open-ended questionnaire items. This study suggests that integrating low-cost self-made toys and robots in project-based learning activities is an effective and practical approach to enhance primary school students' learning outcomes and learning attitudes in STEM education. [ABSTRACT FROM AUTHOR]

This article introduces some efficient generalized class of factor-type exponential imputation techniques and their corresponding estimators using auxiliary information. Generalized ratio, product, and dual to ratio type exponential estimators are the special cases of our suggested imputation techniques. Biases and mean squared error expressions are derived up to the first order of large sample approximations. The proposed imputation techniques can be viewed as efficient extensions of the work of Singh and Horn [Compromised imputation in survey sampling. Metrika. 2000;51(3):267–276. doi: 10.1007/s001840000054], Singh and Deo [Imputation by power transformation. Statist Papers. 2003;44(4):555–579. doi: 10.1007/BF02926010], Toutenburg and Srivastava [Amputation versus imputation of missing values through ratio method in sample surveys. Statist Papers. 2008;49(2):237–247. doi: 10.1007/s00362-006-0009-4], Kadilar and Cingi [Estimators for the population mean in the case of missing data. Commun Stat Theory Methods. 2008;37(14):2226–2236. doi: 10.1080/03610920701855020], Singh [A new method of imputation in survey sampling. Statistics. 2009;43(5):499–511. doi: 10.1080/02331880802605114], Gira [Estimation of population mean with a new imputation methods. Appl Math Sci. 2015;9(34):1663–1672] and Singh et al. [An improved alternative method of imputation for missing data in survey sampling. J Stat Appl Probab. 2022;11(2):535–543. doi: 10.18576/jsap]. Our proposed estimators are compared with these estimators, including the mean, ratio, and regression imputation techniques. Thereafter, a numerical illustration and simulation study are conducted for a comparative study using real and simulated data sets, and the demonstration shows that our suggested estimators are the most efficient estimators. [ABSTRACT FROM AUTHOR]

This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition's truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowledge that can be satisfied by putative proofs (and proof sketches), as well as by non-deductive arguments in science, but not by non-deductive arguments from mathematical evidence. The necessary condition concerns whether we can justly expect that if the mathematical proposition is actually false, despite the evidence for its truth, then this fact has an explanation. [ABSTRACT FROM AUTHOR]

In the paper 'Composition operators on weighted Bergman spaces of Dirichlet series. J Math Anal Appl. 2015;426:340–363', Bailleul completely characterized the boundedness of composition operators on weighted Bergman spaces of Dirichlet series for the case of symbols with $ c_0\ge 1 $ c 0 ≥ 1. But the sufficient conditions for the other case $ c_0=0 $ c 0 = 0 were unsolved. In this paper, we follow this line and study the boundedness of composition operators on weighted Bergman spaces of Dirichlet series for the case $ c_0=0 $ c 0 = 0. Moreover, we also obtain the compact characterizations of composition operators with $ c_0\geq 1 $ c 0 ≥ 1. [ABSTRACT FROM AUTHOR]

Provides a mathematical explanation on paperfolding. Some observations from paperfolding experiments; Theorems that explain the observations.

In order to learn the concept of statistical techniques one needs to run real experiments that generate reliable data. In practice, the data from some well-defined process or system is very costly and time consuming. It is difficult to run real experiments during the teaching period in the university. To overcome these difficulties, statisticians developed simple and very economical experiments, which can be performed in the class by the students. Stone studied the variation, bias, stability and statistical quality control through the Blind Paper Cutting (BPC) experiment. In this article, the Blind Paper Cutting experiment is demonstrated on the basis of basic principles of experiment design. A BPC experiment is performed considering different factors, and important factors to optimise the response are identified through complete factorial design. The appropriate response model using important factors has been constructed. [ABSTRACT FROM AUTHOR]

Integrating socioscientific issues (SSI) into education is gaining widespread adoption in classrooms due to its positive impact on student's critical thinking, environmental awareness, holistic knowledge and/or the idea of combining science and mathematics. This paper explores the idea of using comics as appropriate media for elementary school students to engage with SSI content. Because of the difficulties in integrating SSI into classrooms, SSI-based learning is more commonly applied in high school and higher education settings, with limited implementation in earlier education. To answer this gap, we developed comics that have SSI content for elementary schools. Comics are chosen as reliable tools for visualising and simplifying complex concepts and making SSI content more accessible and engaging. This paper describes our comics on earthquake-related issues in Indonesia and the principles that guided its design. SSI inherently involves multiple perspectives, so the integration brings together science, and mathematics within the one comic. In integrating different disciplines of comic content, we utilised the rule-of-five framework, widely employed to merge five representational models (experiential, verbal, numerical, visual, and symbolic) commonly used in developing content combining two or more different academic disciplines. [ABSTRACT FROM AUTHOR]

In this paper, we explore the roles of gender social norms in explaining the gender gap in maths test scores across the entire distribution. Applying generalized quantile regression models, we show that gender-equal cultural norms eliminate the gender gap in maths scores at the top of the distribution. Moreover, this effect is concentrated among students in the higher grade level. An investigation of the underlying mechanisms shows that girls from more gender-equal regions are less likely to hold maths-specific stereotypes and are likely to receive more attention from maths teachers. Additionally, girls from more gender-equal regions tend to perceive that parents have higher educational aspirations for them and are more confident about their future. Our paper provides compelling evidence that policy initiatives aiming at fostering egalitarian gender norms could serve as powerful tools to alleviate the gender gap in maths at the top of the distribution. [ABSTRACT FROM AUTHOR]

Curiosity has long been touted as important for the ability to learn and has been linked with innovation and entrepreneurship. It is also important that employers know how to identify curious potential employees in cost-effective ways during recruitment processes. This paper explores the association between curiosity and cognitive ability. Recruitment processes rely heavily on educational attainment, especially when recruiting young people with low labour market experience. This paper explores the association between curiosity and maths, science, and reading ability in youth. Using six waves of data from the 2003, 2006, and 2009 cohorts of the Longitudinal Surveys of Australian Youth, we examine the extent to which the curiosity of young adults is associated with their school-age cognition level. We find that curious individuals are more likely to have had higher levels of science and reading ability in school, yet curiosity is negatively associated with school-age mathematics ability. These findings provide clear strategies for employers wanting to recruit curious employees without access to expensive profiling techniques. [ABSTRACT FROM AUTHOR]

The connections between critical pedagogy, living theory and participatory action research (PAR) are discussed to explore their combined strength for empowering students, positively impacting on their attitudes towards their mathematics learning and creating social change in their primary-secondary mathematics transitions. This transition is recognised as creating social inequalities which existing transition research has failed to resolve. The interpretation of critical pedagogy, living theory and PAR are described before a summary of their application in a small scale, two-year study in a British curriculum school in Muscat, Oman. Critical pedagogy combined with living theory and PAR provides the theoretical and methodological framework to empower the students epistemologically. This paper gives an example of how PAR with students was conducted within the framework of critical pedagogy theory and living theory methodology. This account provides a valuable reference for participatory action researchers. The paper concludes that the combination of critical pedagogy, living theory and PAR can empower students to create social change. [ABSTRACT FROM AUTHOR]

In this paper, we present the analysis of the students' achievements in learning calculus in a dynamic software environment during the Covid19 crisis. Two groups of students, the experimental and the control one, were monitored. Blended learning was applied to the students in the experimental group, with the help of Microsoft Teams and dynamic software GeoGebra, in autumn 2020. All students in the control group learned in the classroom without using GeoGebra in 2019. The comparison between these two groups of first-year students, regarding their calculus test results, is described in this paper. It is interesting that the results of the experimental group were significantly better than the results of students in the control group, despite the fact that the students from the experimental group learned during the Covid19 crisis. [ABSTRACT FROM AUTHOR]

Emerging digital technologies offer a transformative potential to redefine learning tasks and many examples of this potential are now available. The scaling of the innovative pedagogies emerging from the research into widespread and sustainable practice, however, remains problematic. This paper addresses the issue of scaling by using Design Based Research (DBR), also known as Educational Design Research, within teacher professional development to reposition teachers' thinking about the place of digital tools in their teaching. Using a project seeking to support the use of new digital technologies to develop children's spatial reasoning as a 'worked example', this paper highlights how the bringing together of the knowledge of educational research and knowledge of teaching practice in DBR can provide a catalyst for epistemic change. The paper will argue that DBR positions the knowledge and practice objects of both research and teaching as 'epistemic' or 'not yet known' objects and, therefore, the legitimate focus of experimentation and reflection. [ABSTRACT FROM AUTHOR]

Research Findings: Children are increasingly using touchscreen technologies at home, which has become a recurring feature within their classroom too. Research has investigated the potential effect of using computer-based tests to assess pupils' performance rather than traditional paper tests. An agreement has still not been formed about the impact of the mode of assessment on pupils' mathematical test scores. A mixed methods design was employed to explore the impact of the testing on young children's mathematical test scores. Thirty-seven children 4-7-years old were recruited from a primary school in England with their parents. A mathematical test on paper and an iPad was administered to each participant which was accompanied by an interview. Data regarding the use of touchscreens at home were explored with an on-line parental questionnaire. The results showed that gender and test type impact mathematical test scores, with females performing the best on the iPad test. The findings also suggested that as tablet usage increased at home, iPad mathematical test scores decreased. The interviews revealed that children rely on different strategies when resolving mathematical problems. Practice or Policy: Digital testing may enable a better investigation of mathematical skills in the first years of schooling and of differences between males and females' responses to solving mathematical questions, which then could be used to tailor the curriculum. [ABSTRACT FROM AUTHOR]

The majority of children in mainstream (no fee, poorly resourced, African language dominant) public schools in South Africa fall significantly behind curricular norms in mathematics by Grade 3; the early learning gap grows across time. The provision of quality instructional materials is a well-recognised component of effective strategies to improve early grade mathematics in low- and middle-income contexts. However, there has been little explication of what constitutes quality instructional materials, nor long-term design work to contribute theory to this instructional design challenge. Across 15 years, the author has been working in an education design hub with teacher educators and teachers in the rural Eastern Cape, with the goal of improving early grade mathematics. The gains in mathematics performance have been among the most significant reported in research literature. This paper presents the design principles emerging from the work. Engaging the theoretical layers discussed by diSessa and Cobb, the paper contributes to design theory by emphasising the relationship between explicit instructional assumptions and design principles, integrating four ontological categories (motive, pedagogy, language use and mathematical meaning-making). Since 2011, the Department of Basic Education has provided learner workbooks to support teaching and learning in foundation phase mathematics at system scale. It is hoped that this paper will contribute to the ongoing development of this vital national resource. The paper makes explicit instructional assumptions and design principles (available for critique, adaptation, and refinement), and provides a more nuanced framework through which to assess and improve materials across time. [ABSTRACT FROM AUTHOR]

The article presents an appendix note on a statistical question raised in the preceding paper.

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

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

This paper employs two scalar parameters to extend auxiliary function-based integral inequality into a new formulations, say a parametrised auxiliary function-based integral inequality. Using these formulations, the constituent signals are utilised more efficiently by exploiting the interaction between them to reduce conservatism. Numerical example for stability analysis of linear systems with time-varying delay shows the improved performance of the proposed new formulations in terms of maximum delay bounds and decision variables. [ABSTRACT FROM AUTHOR]

For a simple graph G on n vertices the Seidel Estrada index of G, denoted by $ SEE(G) $ SEE (G) , is defined as $ SEE(G)=\sum _{i=1}^ne^{\theta _i} $ SEE (G) = ∑ i = 1 n e θ i , where $ \theta _1,\ldots,\theta _n $ θ 1 , ... , θ n are the Seidel eigenvalues (the eigenvalues of the Seidel matrix) of G. In this paper, we find the maximum and minimum values of the Seidel Estrada index among all graphs with the fixed number of vertices. Our results confirm some conjectures on Seidel Estrada index of graphs that have been posed in [M. Hakimi-Nezhaad, M. Ghorbani, On the Estrada Index of Seidel Matrix, Mathematics Interdisciplinary Research5 (2020) 43–54]. [ABSTRACT FROM AUTHOR]

The study described in this paper investigated a unique collaboration among a special education and two general educators that sought to prepare students for success in the general education mathematics curriculum and that consisted of coordinated, reform-based instructional design across classroom and pull-out services provided by the special educator including preteaching. During preteaching, the special educator delivered instruction on key mathematics and collaboration skills that special education students would need a few days before they would receive instruction on the same content in their general education classrooms. Their collaboration produced high levels of teacher satisfaction, substantive teacher change, and increases in student engagement, self-efficacy, and achievement. [ABSTRACT FROM AUTHOR]

In this paper, we consider a singular Adams' inequality with logarithmic weights in the unit ball of $ \mathbb {R}^4 $ R 4 . Our results extend the results of Zhu and Wang [Adams' inequality with logarithmic weights in $ \mathbb {R}^4 $ R 4 . Proc Amer Math Soc. 2021;149(8):3463–3472] on Adams' inequality with logarithmic weights to singular case. Then, we study the existence of solutions for some weighted mean field equations, relying on variational methods and the singular Adams' inequality with logarithmic weights we previously established. [ABSTRACT FROM AUTHOR]

In this paper, we explore Norwegian teachers’ perspectives on inclusive teaching practices in the mathematics classroom, defined as practices which maximise every pupil’s potential regardless of prior attainment. As previous research suggests, both mathematics teachers’ perspectives in general and the conceptualisation of inclusion, inclusive education, and inclusive practices are culturally situated, varying significantly across countries and educational systems. We draw on data from a large project in Norway focusing on the use of grouping by attainment and its relation to policy and pedagogical practices around inclusion in mathematics. Participants were 13 primary and lower-secondary mathematics teachers from six schools in the Oslo area. Analysis of semi-structured interviews focusing on strategies for inclusion of all pupils in mathematics classrooms reveals the cultural particularities of mathematics teachers’ perspectives on inclusive practices, highlighting the value of similar investigations in other cultural contexts. [ABSTRACT FROM AUTHOR]

Teaching music often focuses on developing musical concepts, through comparisons and discriminations. This paper contributes to the discussion on concept development in music through recognition of common elements in a situation and a shift from a local to a general level, considering theoretical approaches to mathematical generalisation. It sets to explore preschool children's understanding of tempo and its use in new musical situations. The research involved a musical intervention in six preschool classrooms. Critical incidences from focus group discussions and non-participant observation recorded children's understanding of tempo from their musical actions, drawings, responses and reflection to teacher questions. The findings highlight that children could go beyond the specific content of the activities and focus on the basic characteristics of tempo, integrating them into their song creations. A teaching approach oriented to generalisation through concept development can assist teachers to elaborate musical content and realise students' level of understanding. [ABSTRACT FROM AUTHOR]

In this paper, we study the centralizer of a separating continuous flow without fixed points. We show that if M is a compact metric space and $ \phi _t:M\to M $ ϕ t : M → M is a separating flow without fixed points, then $ \phi _t $ ϕ t has a quasi-trivial centralizer, that is, if a continuous flow $ \psi _t $ ψ t commutes with $ \phi _t $ ϕ t , then there exists a continuous function $ A: M\to \mathbb {R} $ A : M → R which is invariant along the orbit of $ \phi _t $ ϕ t such that $ \psi _t(x)=\phi _{A(x)t}(x) $ ψ t (x) = ϕ A (x) t (x) holds for all $ x\in M $ x ∈ M. We also show that if M is a compact Riemannian manifold without boundary and $ \Phi _u $ Φ u is a homogenous separating $ C^1 $ C 1 $ \mathbb {R}^m $ R m -action on M, then $ \Phi _u $ Φ u has a quasi-trivial centralizer, that is, if $ \Psi _u $ Ψ u is a $ \mathbb {R}^{ m} $ R m -action on M commuting with $ \Phi _u $ Φ u , then there is a continuous map $ A: M\to \mathcal {M}_{m\times m}(\mathbb {R}) $ A : M → M m × m (R) which is invariant along orbit of $ \Phi _u $ Φ u such that $ \Psi _{u}(x)=\Phi _{A(x)u}(x) $ Ψ u (x) = Φ A (x) u (x) for all $ x\in M $ x ∈ M. These improve Theorem 1 of [M. Oka, Expansive flows and their centralizers, Nagoya Math. J. 64 (1976), pp. 1–15.] and Theorem 2 of [W. Bonomo, J. Rocha, and P. Varandas, The centralizer of Komuro-expansive flows and expansive $ \mathbb {R}^d $ R d -actions, Math. Z. 289(3–4) (2018), pp. 1059–1088.] respectively. [ABSTRACT FROM AUTHOR]

Numerous studies affirm the importance of students' attitudes for mathematical education. This study uses mathematical autobiographical essays to examine the mathematical experiences and attitudes of undergraduate students enrolled in mathematics classes at a Midwestern University in the United States. The essays of 41 students (20 men, 21 women) out of 170 enrolled in College Algebra, Precalculus, and Calculus were analyzed using the categories of (1) confidence in mathematics ability, (2) value of mathematics, and (3) liking of mathematics. This paper provides context and theoretical depth to student reports of their attitudes in these categories. Statements at the intersections of both confidence and liking, and value and liking provide additional insights. First, students who perceive mathematics as valuable are more likely to like it. Second, the vast majority of students talk about confidence and liking together, and with a positive correlation. Further, these students tend to talk about liking or not liking mathematics because of their perceived ability in mathematics. Our study suggests the importance of proactive teaching strategies to improve students' perceptions of the value, liking of, and their confidence in, mathematics, and also suggests self-efficacy as a potential theoretical basis for this work. [ABSTRACT FROM AUTHOR]

This paper describes the implementation of a STEM scholarship program which utilized a holistic approach to providing a multi-dimensional student support system. The program has been successful in encouraging and supporting women in Applied Mathematics and Computer Science by offering a diverse suite of extracurricular opportunities, actively engaging them in organized events, research projects, and participation in STEM communities, and helping them achieve higher GPAs and shorter times to graduation. The supported women also benefitted from close mentoring relationships with the faculty mentors. The program emphasized the development of empowering settings for women's engagement and achievement, which act to sustain and expand interest in mathematics and computing, and thereby help them to see themselves as future professionals in the field. [ABSTRACT FROM AUTHOR]

The Mathematical Sciences Department at Shenandoah University focused on increasing the participation of women in the mathematics program by fostering a welcoming learning community and promoting double majors. Data from the past decade is presented. During this time, the program saw an increase in women undergraduate mathematics majors from 11% to as high as 71%. This paper describes the initiatives taken to make these changes. [ABSTRACT FROM AUTHOR]

The University of Minnesota Talented Youth Mathematics Program (UMTYMP) is a selective, five-year accelerated mathematics program for students in grades 6–12. During the program, students take college mathematics courses on University of Minnesota campuses, starting with algebra and continuing through logic and proofs, linear algebra, and multivariable calculus. The majority of UMTYMP students come from two demographic groups: White and Asian/Asian American. In 2020, we surveyed UMTYMP students to understand the impact of model minority stereotypes (MMS) on Asian/Asian American students, particularly girls, who are labeled as "gifted" and/or "talented." In this paper, we reveal the preliminary results of this study, discuss their implications, and provide recommendations for addressing the MMS in mathematics programs. [ABSTRACT FROM AUTHOR]

We classify two of Bertrand Russell's theories of events within the point-free ontology. The first of such approaches was presented informally by Russell in 'The World of Physics and the World of Sense' (Lecture IV in Our Knowledge of the External World of 1914). Based on this theory, Russell sketched ways to construct instants as collections of events. This paper formalizes Russell's approach from 1914. We will also show that in such a reconstructed theory, we obtain all axioms of Russell's second theory from 1936 and all axioms of Thomason's theory of events from 1989. Russell's work certainly influenced the works of Stanisław Leśniewski, his student Alfred Tarski, and Czesław Lejewski – prominent members of the Lvov-Warsaw School (LWS). We see our work in the tradition of the research of Leśniewski and Tarski. Building on the technical tools developed in this environment and in the spirit of the traditional research of the LWS, we engage here, in particular, with two classic works by Russell on fundamental ontology. [ABSTRACT FROM AUTHOR]

The problem of precise characterisation of traditional forms of reasoning applied in mathematics was independently investigated and successfully resolved by Jaśkowski and Gentzen in 1934. However, there are traces of earlier interests in this field exhibited by the members of the Lvov-Warsaw School. We focus on the results obtained by Jaśkowski and Leśniewski. Jaśkowski provided the first formal system of natural deduction in 1926. Leśniewski also demonstrated in some of his papers how to construct proofs in accordance with intuitively correct principles. [ABSTRACT FROM AUTHOR]

Nowadays, typing is considered as one of the highly important aspects of accessibility that the visually impaired and blinds struggle with the most as existing virtual keyboards are complex and slow. This paper proposes a new text entry method named SwingBoard for visually impaired and blind smartphone users to solve their accessibility problem. It supports a–z, 0–9, 7 punctuations, 12 symbols, and eight keyboard functionalities that are arranged in 8 zones (specific range of angles), four segments, two modes, and different gestures. The proposed keyboard is suitable for the either single-handed or both-handed operation that tracks swipe angle and length to trigger any of the 66 key events. The key triggering process is based on only swiping the finger at different angles with different lengths. Typing speed of SwingBoard is increased by including some effective features such as the quick alphabet and number mode shifting, haptic feedback feature, talkback on swipe to learn the map quickly, and customizable swipe length feature. At the end of 150 one-minute tests, seven blind participants reached an average of 19.89 words per minute (WPM) with an 88% accuracy rate which is one of the fastest-ever recorded average typing speeds for the blind. Almost all users found SwingBoard effective, easy to learn and want to keep using it. SwingBoard is a handy virtual keyboard for visually impaired people with amazing typing speed and accuracy. Rehabilitation would be easier for a visually impaired/disabled person who can adapt the current technology-oriented world and use communication tools easily. As visually impaired and blind people faced a lot of problems in their regular life because of their inability to see things, coping with the evolving world's demands from a person to do a certain task using smart devices would be easier for them with the proposed virtual keyboard topology. As the number of visually impaired and blind users of smartphones rises, faster typing becomes a vital aspect of the smartphone experience. Deaf-blind communities are expanding but solutions for them are not increasing at the same pace because of the limitation of implication. Research on a virtual keyboard with the proposed eyes-free swipe-based typing operation and ears-free reliability on haptic feedback would enable others to create new solutions. [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]

We exploit the existence and non-existence of positive solutions to the eigenvalue problem driven by the nonhomogeneous fractional $ p\& q $ p &q Laplacian operator with indefinite weights \[ \left(-\Delta_p\right)^{\alpha}u + \left(-\Delta_q\right)^{\beta}u = \lambda\left[a \left|u\right|^{p-2}u + b \left|u\right|^{q-2}u \right]\quad{\rm in}\ \Omega, \] (− Δ p) α u + (− Δ q) β u = λ [ a | u | p − 2 u + b | u | q − 2 u ] in Ω , where $ \Omega \subseteq \mathbb {R}^N $ Ω ⊆ R N is a smooth bounded domain that has been extended by zero. We further show the existence of a continuous family of eigenvalues in the case $ \Omega =\mathbb {R}^N $ Ω = R N and $ b\equiv 0 $ b ≡ 0 a.e. Our approach relies strongly on variational Analysis, in which the Mountain pass theorem plays the key role. Due to the lack of spatial compactness and the embedding $ \mathcal {W}^{\alpha, p}\left (\mathbb {R}^N\right) \hookrightarrow \mathcal {W}^{\beta, q}\left (\mathbb {R}^N\right) $ W α , p (R N) ↪ W β , q (R N) in $ \mathbb {R}^N $ R N , we employ the concentration-compactness principle of P.L. Lions [The concentration-compactness principle in the calculus of variations. The limit case. II, Rev Mat Iberoamericana. 1985;1(2):45–121]. to overcome the difficulty. Our paper can be considered as a counterpart to the important works [Alves et al. Existence, multiplicity and concentration for a class of fractional $ p\& q $ p &q Laplacian problems in $ \Bbb R^N $ R N , Commun Pure Appl Anal, 2019;18(4):2009–2045], [Benci et al. An eigenvalue problem for a quasilinear elliptic field equation. J Differ Equ, 2002;184(2):299–320], [Bobkov et al. On positive solutions for $ (p,q) $ (p , q) -Laplace equations with two parameters, Calc Var Partial Differ Equ, 2015;54(3):3277–3301], [Colasuonno and Squassina. Eigenvalues for double phase variational integrals, Ann Mat Pura Appl (4), 2016;195(6):1917–1956], [Papageorgiou et al. Positive solutions for nonlinear Neumann problems with singular terms and convection, J Math Pures Appl (9), 2020;136:1–21], [Papageorgiou et al. Ground state and nodal solutions for a class of double phase problems, Z Angew Math Phys, 2020;71:1–15], and may have further applications to deal with other problems. [ABSTRACT FROM AUTHOR]