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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]

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]

Computer-based curriculum-based measurement (CBM) is a relatively common practice, but surprisingly few studies have examined the reliability of computer-based CBM. This study sought to examine the reliability of CBM administered via paper/pencil versus the computer. Twenty-one of 25 students in two third-grade classes (N = 21) participated in two generalizability studies. The primary facet of interest, format of assessment, was examined for two measures, a fact operation (fact family measure) and a more complex operation (multidigit addition). Researchers administered four alternate forms of each measure under both computer and paper/pencil conditions. Results indicated ideal reliability of measurement within all conditions and results were consistent across assessment formats for the fact operation. However, assessment format explained a large proportion of variance for the more complex skill (multidigit addition). Results indicate a need to consider the reliability of transitioning assessment from paper/pencil to computer-based response on a measure-by-measure basis. [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]

Prospective authors are requested to submit new, unpublished manuscripts for inclusion in the upcoming event described in this call for papers. [ABSTRACT FROM AUTHOR]

If (S, ◦,≤) is an ordered hypersemigroup, an equivalence relation ρ on S is called congruence if (a, b) ∈ ρ implies (a ◦ x, b ◦ x) ∈ ρ and (x ◦ a, x ◦ b) ∈ ρ for every x ∈ S ; in the sense that for every u ∈ a ◦ x there exists v ∈ b ◦ x such that (u, v) ∈ ρ and for every u ∈ x◦a there exists v ∈ x◦b such that (u, v) ∈ ρ. It has been proved in Turk J Math 2021(5) [On the paper “A study on (strong) order-congruences in ordered semihypergroups”] that if S is an ordered hypersemigroup, then there exists a congruence ρ on S such that S/ρ is an ordered hypersemigroup. This result, is the main result for an involution ordered hypersemigroup by Xinyang Feng, Jian Tang and Yanfeng Luo in U.P.B. Sci. Bull, Series A, 2018, but its proof is wrong; the correct proof is given in the present paper. Examples illustrate the results. [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]

Giving the proper citations, it is shown that, except of Lemma 2.4 and Theorem 2.6, almost all the results of the paper in the title have been previously published for ordered hypersemigroups in Eur. J. Pure Appl. Math. and they are not new. There are also two results obtained from ordered semigroups just putting a "o" instead of "o" (that isn't a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. One of them can be obtained as corollary to a theorem in Eur. J. Pure Appl. Math. as well, and it is not new. [ABSTRACT FROM AUTHOR]

In this short note we prove that the Kurepa (K) function is different from the Smarandache-Kurepa (SK) function, therefore, these functions are not the same, as Mijajlović has unfoundedly accused the prestigious Encyclopedia of Mathematics and this author. This note is an answer to Mijajlović's paper (Žarko Mijajlović, Fifty years of Kurepa's !n hypothesis, Bulletin T.CLIV de l'Académie serbe des sciences et des arts - 2021 Classe des Sciences mathématiques et naturelles Sciences mathématiques, No. 46, 169-181 (2021). [ABSTRACT FROM AUTHOR]

This note is written to show that the definition of the LA-semihypergroup by V. Amjad, K. Hila and F. Yousafzai "Generalized hyperideals in locally associative left almost semihypergroups, New York J. Math. 2014" should be corrected and that it is not enough to replace the multiplication "·" of an LA-semigroup by the hyperoperation "ο" to pass from an LA-semigroup to an LA-semihypergroup. The two examples of the paper based on the definition of the LA-semihypergroup are wrong that is a further indication that this definition needs correction. According to the last section of the paper, the paper generalizes the results of an LA-semigroup by M. Akram, N. Yaqoob and M. Khan "On (m, n) -ideals of left almost semigroups, Appl. Math. Sci. (Ruse) 2013" while the paper duplicates, without citation, the section 4 of the paper by W. Khan, F. Yousafzai, W. Guo and M. Khan "On (m, n) -ideals of left almost semigroups, J. Semigroup Theory Appl. 2014" with the usual change of "·" to "ο". [ABSTRACT FROM AUTHOR]

Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. [ABSTRACT FROM AUTHOR]

Abstract Basic numerical skills provide an important foundation for the learning of mathematics. Thus, it is critical that researchers and educators have access to valid and reliable ways of assessing young children's numerical skills. The purpose of this study was to evaluate the concurrent, predictive, and incremental validity of a two-minute paper-and-pencil measure of children's symbolic (Arabic numerals) and non-symbolic (dot arrays) comparison skills. A sample of kindergarten children (M age = 5.86, N = 439) were assessed on the measure along with a number line estimation task, a measure of arithmetic, and several control measures. Results indicated that performance on the symbolic comparison task explained unique variance in children's arithmetic performance in kindergarten. Longitudinal analyses demonstrated that both symbolic comparison and number line estimation in kindergarten were independent predictors of 1st grade mathematics achievement. However, only symbolic comparison remained a unique predictor once language skills and processing speed were taken into account. These results suggest that a two-minute paper-and-pencil measure of children's symbolic number comparison is a reliable predictor of children's early mathematics performance. Highlights • We tested the validity and reliability of a recently developed Numeracy Screener. • Performance on the symbolic comparison task predicted kindergarten children's arithmetic performance. • Performance on the symbolic comparison task in kindergarten predicted school mathematics achievement one year later. • The Numeracy Screener may be a useful tool for early mathematics researchers and educators alike. [ABSTRACT FROM AUTHOR]

Developing mathematical connections for pupils continues to be at the forefront of educational policies worldwide. One strategy suggested to support the connections pupils make is the idea of developing "coherence". Research regarding coherence has increased within mathematics education, however, the term is used widely. It therefore becomes necessary for coherence to be further conceptualised. In this systematic scoping review, five databases were searched for literature on the topic of coherence in school-based mathematics education. A total of 11,587 pieces of literature were extracted. Following further screening, 35 papers were reviewed. The findings suggest that there is limited consensus regarding the conceptualisation of coherence, leading to fragmented perceptions across the literature. This paper presents a framework for coherence based on the TIMSS curriculum model to support international comparisons of coherence and provide clarity for mathematics education researchers and school colleagues when considering which aspect of coherence they are addressing. [ABSTRACT FROM AUTHOR]

This paper studies the inhomogeneous defocusing coupled Schrödinger system i ⁢ u ˙ j + Δ ⁢ u j = | x | - ρ ⁢ (∑ 1 ≤ k ≤ m a j ⁢ k ⁢ | u k | p ) ⁢ | u j | p - 2 ⁢ u j , ρ > 0 , j ∈ [ 1 , m ] . The goal of this work is to prove the scattering of energy global solutions in the conformal space made up of f ∈ H 1 ⁢ (ℝ N) such that x ⁢ f ∈ L 2 ⁢ (ℝ N) . The present paper is a complement of the previous work by the first author and Ghanmi [T. Saanouni and R. Ghanmi, Inhomogeneous coupled non-linear Schrödinger systems, J. Math. Phys. 62 2021, 10, Paper No. 101508]. Indeed, the supplementary assumption x ⁢ u 0 ∈ L 2 enables us to get the scattering in the mass-sub-critical regime p 0 < p ≤ 2 - ρ N + 1 , where p 0 is the Strauss exponent. The proof is based on the decay of global solutions coupled with some non-linear estimates of the source term in Strichartz norms and some standard conformal transformations. Precisely, one gets | t | α ⁢ ∥ u ⁢ (t) ∥ L r ⁢ (ℝ N) ≲ 1 for some α > 0 and a range of Lebesgue norms. The decay rate in the mass super-critical regime is the same one as of e i ⋅ Δ ⁢ u 0 . This rate is different in the mass sub-critical regime, which requires some extra assumptions. The novelty here is the scattering of global solutions in the weighted conformal space for the class of source terms p 0 < p < 2 - ρ N - 2 + 1 . This helps to better understand the asymptotic behavior of the energy solutions. Indeed, the source term has a negligible effect for large time and the above non-linear Schrödinger problem behaves like the associated linear one. In order to avoid a singular source term, one assumes that p ≥ 2 , which restricts the space dimensions to N ≤ 3 . In a paper in progress, the authors treat the same problem in the complementary case ρ < 0 . [ABSTRACT FROM AUTHOR]

In this paper, we employ the techniques in [C. Cavaterra, S. Dipierro, Z. Gao and E. Valdinoci, Global gradient estimates for a general type of nonlinear parabolic equations, J. Geom. Anal. 32 2022, 2, Paper No. 65] and the approach in [H. T. Dung and N. T. Dung, Sharp gradient estimates for a heat equation in Riemannian manifolds, Proc. Amer. Math. Soc. 147 2019, 12, 5329–5338] to derive sharp gradient estimates for a positive solution to the heat equation u t = Δ ⁢ u + a ⁢ u ⁢ log ⁡ u in a complete noncompact Riemannian manifold (where a is a real constant). This is an extension of the gradient estimates of Dung and Dung. [ABSTRACT FROM AUTHOR]

Background: Evidence‐based practice is the principle governing a range of healthcare practices and beyond. However, it has suffered from a lack of philosophical rigour. This paper sets out to analyse the epistemological basis of evidence‐based practice. Method: The paper uses a conceptual analysis. First, it describes the implicit epistemology at work in evidence‐based practice. Second, it evaluates the implicit epistemological basis. Results: The analysis indicates that evidence‐based practice lacks an explicit epistemological basis. It shows, moreover, that the implicit epistemological basis is untenable. Conclusion: There is a need to re‐think the epistemological basis for evidence‐based practice. Evidence‐based practice is out of touch with developments within philosophy of science. [ABSTRACT FROM AUTHOR]

Background: Mindfulness practices enhance executive function skills and academic achievement, spurring interest in integrating mindfulness interventions into education. Embedding mindfulness practice into a digital math game may provide a low‐cost, scalable way to induce mindfulness and boost game‐based learning, yet this approach remains unexplored. Objectives: We investigated the learning benefits of integrating mindfulness exercises in a digital math learning game and examined how students' trait mindfulness might moderate the outcomes. Methods: Two classroom studies were conducted with 404 5th and 6th grade students from six public schools in the U.S. (nStudy 1 = 227, nStudy 2 = 177). The two randomized controlled experiments assigned students to one of the three conditions: passive control (playing the digital learning game Decimal Point), story‐enriched active control, or mindfulness‐enriched condition. Trait mindfulness, learning gains, and in‐game problem‐solving (including problem‐solving duration, error count and correctness after reminder) were assessed. Study 2 included a manipulation check to better understand the effects of the mindfulness intervention. Results: Findings showed no significant differences in learning gains, problem‐solving duration or error count among the conditions. Students' trait mindfulness did not moderate these outcomes. Mindfulness reminders in the mindfulness‐enriched game led to more correct answers after errors than jokes in the story‐enriched game. Study 2 revealed that we failed to induce higher state mindfulness through the mindfulness inductions. Conclusions: Mindfulness prompts could be especially beneficial for students experiencing frustration during gameplay, warranting more exploration for digital game‐based instruction. We highlight barriers and future directions for fostering mindfulness through computer‐based instruction in classrooms. Lay Description: What is currently known about this topic?: Researchers focus on digital games as productive learning environments for math, with potential for higher learning gains compared with traditional methods. However, results are mixed, and not all games lead to improved math outcomes.Executive function (EF) skills are crucial for math learning, and mindfulness‐based interventions show promise in enhancing EF skills in school‐aged students.Embedding mindfulness practice into a digital math game may provide a low‐cost, scalable way to induce mindfulness and, in turn, boost EF skills and game‐based learning, yet this approach remains unexplored What does this paper add?: This paper presents the results of two randomized control trials investigating the feasibility and benefits of incorporating mindfulness exercises into a digital math game designed for middle school students. Benefits are compared to those of a story‐enriched and regular version of the same digital math learning game.The paper also explores variations in the effects of the mindfulness‐enriched game based on students' initial trait mindfulness levels.We observe that listening to mindfulness inductions at the beginning of game sessions do not induce mindfulness, and therefore does not benefit math learning.We find that mindfulness prompts received after recurrent errors can be beneficial for students' problem solving. Implications of study findings for practitioners: Our study provides important information on how digital learning game designers should attempt to induce mindfulness in a digital game to promote learning.Digital learning game designers should consider incorporating mindfulness exercises into their games strategically. Presenting mindfulness inductions in audio format at the beginning of game sessions may not induce mindfulness or benefit math learning. Instead, designers should focus on integrating mindfulness prompts at moments when students encounter frustration within the learning game.Beyond embedding audio mindfulness exercises in the game, learning designers should also consider alternative technological and game features to induce mindfulness within a learning game. [ABSTRACT FROM AUTHOR]

Background: With the growing integration of technology in education, the adoption of blended learning (b‐learning) has gained attention. B‐learning combines traditional classroom teaching with online components, holding potential to enhance student outcomes and educational efficiency. Yet, current research predominantly concentrates on higher education institutions in urban areas, creating a void in understanding its impact on K‐12 education, particularly in rural settings. Objectives: This qualitative study aims to propose recommendations for successful implementation of blended learning in rural K‐12 areas by addressing the key stakeholders influencing its adoption and identifying the main factors affecting its success. Methods: We performed a content analysis of grey literature documents detailing the implementation of b‐learning in K‐12 education. Additionally, interviews with crucial stakeholders such as teachers, principals, and experts in rural schools in South America provide insights into the challenges and prospects of b‐learning adoption in these contexts. Results and Conclusions: The study identifies pivotal stakeholders for effective b‐learning implementation, outlining their roles and addressing challenges inherent in rural settings. Recommendations for enhancing b‐learning's implementation in developing countries are also proposed. The research underscores the significance of involving diverse stakeholders such as governmental bodies, school leaders, educators, students, and families to ensure a holistic and efficient approach to blended learning. Lay Description: What is currently known about this topic: Blended Learning Definition and Benefits: Blended learning combines face‐to‐face and online instruction, enhancing student engagement and personalization by providing diverse learning pathways.Growth in K‐12 Implementation: Blended learning gained traction in K‐12 education, boosting academic outcomes, driven by recognition of learner diversity and potential in meeting students' needs.Contextual Challenges: Implementation challenges arise in low‐income households and rural areas, including limited access to technology and internet connectivity, impacting student engagement and success. What does this paper add: Focusing on Rural Dynamics: This study helps to fill a gap by investigating blended learning in rural K‐12 settings, spotlighting key players and success drivers in these unique contexts.Recommendations from Various Sources: By combining interviews and grey literature, this research generates comprehensive, practical recommendations grounded in both empirical insights and real‐world perspectives.Insights into Rural Hurdles: This paper extends the discussion on blended learning by addressing specific rural barriers, proposing family involvement, private sector partnerships for training, and tailored pedagogical strategies. Implications for practice or policy: Leadership and Collaboration: Effective school leadership and collaboration with local governments are pivotal for fruitful blended learning implementation, ensuring defined roles, responsibility, and accountability.Adaptable Curriculum Design: An adaptable, centralized curriculum aligns with recommendations, fostering efficient tracking of student progress and enabling customized learning.Engagement‐Centric Pedagogies: Recommendations spotlight interactive, student‐centered teaching methods, tailored to diverse student needs, nurturing active participation and elevated learning outcomes. [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]

This paper revisits Wittgenstein’s heavily criticized claims about the admissibility of inconsistencies in mathematics. It argues from the perspective of mathematics as a tool and combines material from the history and practice of engineering that makes Wittgenstein’s claims about contradiction and inconsistency look much more plausible. Against this background, the paper interprets passages from Wittgenstein, including his exchange with Alan Turing where he highlights that basic laws of thought are at issue and that reflecting on them would be “the most important thing” he has talked about. [ABSTRACT FROM AUTHOR]

Recent rank-based attacks have reduced the security of Rainbow, which is one of the multi-layer UOV signatures, below the NIST security requirements by speeding up iterative kernel-finding operations using classical mathematics techniques. If quantum algorithms are applied to perform these iterative operations, the rank-based attacks may be more threatening to multi-layer UOV, including Rainbow. In this paper, we propose a quantum rectangular MinRank attack called the Q-rMinRank attack, the first quantum approach to key recovery attacks on multi-layer UOV signatures. Our attack is a general model applicable to multi-layer UOV signature schemes, and in this paper, we provide examples of its application to Rainbow and the Korean TTA standard, HiMQ. We design two quantum oracle circuits to find the kernel in consideration of the depth-width trade-off of quantum circuits. One is to reduce the width of the quantum circuits using qubits as a minimum, and the other is to reduce the depth using parallelization instead of using a lot of qubits. By designing quantum circuits to find kernels with fewer quantum resources and complexity by adding mathematical techniques, we achieve quadratic speedup for the MinRank attack to recover the private keys of multi-layer UOV signatures. We also estimate quantum resources for the designed quantum circuits and analyze quantum complexity based on them. The width-optimized circuit recovers the private keys of Rainbow parameter set V with only 1089 logical qubits. The depth-optimized circuit recovers the private keys of Rainbow parameter set V with a quantum complexity of 2 174 , which is lower than the complexity of 2 221 recovering the secret key of AES-192, which provides the same security level as parameter set III. [ABSTRACT FROM AUTHOR]

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

We access most of our most cherished beliefs via testimony. Philosophy is no exception. We treat spoken and written philosophical testimony as evidence for philosophical claims. Nonetheless, this paper argues that philosophical testimony is unable to justify philosophical beliefs. If testimony is the only evidence we have to justify philosophical beliefs, this entails skepticism about philosophy. Call this the testimony challenge. First, the paper argues that philosophical testimony does not meet the conditions under which evidence can justify our beliefs. Second, it shows that philosophical testimony cannot provide preemptive epistemic reasons as science and mathematics do. Finally, it answers the self‐defeat objection and a set of objections aiming to block the thesis that philosophical testimony does not justify philosophical beliefs. The paper aims to rethink the role of philosophical testimony in philosophy and reinforce the skeptical worries raised by methodological and disagreement challenges. [ABSTRACT FROM AUTHOR]

The paper dwells on the contributions of APOS theory to the development of teaching and learning of mathematics in school. APOS is an acronym for action, process, object, and schema. The theory emerges as an extension to constructivism but with a more focused and robust learner-centered approach to the teaching and learning of mathematics. Proponents of the theory believed that learning occurs initially as an action or activity in learners' cognitive settings, independent of learners' environment, triggered by cognitive coherence, then it is transformed to process, where learner now waits for internalization of the earlier activity, preparatory to the occurrence of learning. At object level, learner now considers what has been learnt earlier to have been fully internalized into mathematical object(s). Lastly, at schema level, the object learnt is assumed to have been embedded in the learners' schema-a cognitive structure formed as a result of accumulated learning experience, and a complete mental image of what has been learnt is said to have been formed. Against the backdrop of this, the paper looks at how this theory had changed the narrative about teaching and learning of mathematics vis-à-vis the bearing of the theory to other cognitive abilities of the learner such as intelligence and creativity. In the end, the paper suggests the application of APOS theory in teaching and learning mathematics at all levels of learning in Nigeria and beyond. [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]

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]

We study locally maximal attractors of expanding dynamical systems. Our main result is a representation of these attractors with the help of topological Markov chains corresponding to the Markov partitions of these attractors, which allows us to describe the dynamics of system on them. Ya. G. Sinai was the first who constructed and used Markov partitions for Anosov's diffeomorphisms [Funk. Anal. Prilozh., 2, No 1, 64; No 3, 70 (1968); English translation:Funct. Anal. Appl., 2, No 1, 61; No 3, 245 (1968)]. Expanding endomorphisms regarded as the simplest representatives of endomorphisms were first studied by M. Shub [Amer. J. Math., 91, No 1, 175 (1969)]. To construct Markov partitions for expanding endomorphisms, we update Sinai's approach in the proper way. A more detailed historical overview can be found in the work by O. M. Sharkovsky [Ukr. Mat. Zh., 74, No. 12, 1709 (2023); English translation:Ukr. Math. J., 74, No. 12, 1950 (2023)]. In this work, Sharkovsky indicated that the methods used to prove the main results presented in [Dokl. Akad. Nauk SSSR, 170, No. 6, 1276 (1966); English translation:Sov. Math. Dokl., 7, No. 5, 1384 (1966)] were, in fact, published in the collection of papers "Dynamical systems and the problems of stability of solutions of differential equations" (1973) issued by the Institute of Mathematics of the Academy of Sciences of Ukraine. This collection is difficultly accessible and was never translated into English. Note that, in the indicated paper, these methods were applied to somewhat different objects. To the best of our knowledge, there is no information about publications of similar results. In view of the outlined history and importance of the described approach (based on Markov partitions and topological Markov chains) for the description of construction of the attractors, it seems reasonable to publish these results anew. [ABSTRACT FROM AUTHOR]

Encryption and decryption are the two processes in the cryptosystem that ensure the safe transfer of data or sensitive information. Apart from classical mathematics, graph theory techniques are employed nowadays to construct a strong cryptosystem. This paper uses graph techniques such as decomposition and labelling to encrypt and decrypt an alphanumeric string of length 8. The novelty of this paper is the introduction of (S9,C3)-multi-decomposition and a new labelling technique - anti-magic decomposed labelling, which is applied in the cryptosystem. [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 considers a specific autonomous Schwarzian differential equation given by Sf=c(f−σ1)(f−σ2)/[(f−τ1)(f−τ2)]$$\begin{equation*} \hspace*{35pt} S_f=c(f-\sigma _1)(f-\sigma _2)/[(f-\tau _1)(f-\tau _2)] \end{equation*}$$and presents a complete characterization of its transcendental meromorphic solutions, thus confirming a conjecture posed by Liao and Wu recently. By combining our results with those obtained in a previous paper (Math. Z. 2 (2022), 1657–1672), we are able to explicitly construct all transcendental meromorphic solutions of the autonomous Schwarzian differential equations. Additionally, we identify all nonconstant rational solutions of the autonomous Schwarzian differential equations, with the exception of one special case. [ABSTRACT FROM AUTHOR]

The chord log-Minkowski problem asks for necessary and sufficient conditions for a finite Borel measure on the unit sphere so that it is the cone-chord measure of a convex body. The chord log-Minkowski problem has been extensively studied by Guo, Xi, and Zhao [Math. Ann. (2023), DOI 10.1007/s00208-023-02721-8]; Lutwak, Xi, Yang, and Zhang [Commun. Pure Appl. Math. (2023), DOI 10.1002/cpa.22190]; Qin [Adv. Math. 427 (2023), Paper No. 109132]. In this paper, we solve the chord log-Minkowski problem when q\in (0,1), without symmetry assumptions. [ABSTRACT FROM AUTHOR]

The role of mutation, which is an error process in gene evolution, in systems of cyclically competing species has been studied from various perspectives, and it is regarded as one of the key factors for promoting coexistence of all species. In addition to naturally occurring mutations, many experiments in genetic engineering have involved targeted mutation techniques such as recombination between DNA and somatic cell sequences and have studied genetic modifications through loss or augmentation of cell functions. In this paper, we investigate nonlinear dynamics with targeted mutation in cyclically competing species. In different ways to classic approaches of mutation in cyclic games, we assume that mutation may occur in targeted individuals who have been removed from intraspecific competition. By investigating each scenario depending on the number of objects for targeted mutation analytically and numerically, we found that targeted mutation can lead to persistent coexistence of all species. In addition, under the specific condition of targeted mutation, we found that targeted mutation can lead to emergences of bistable states for species survival. Through the linear stability analysis of rate equations, we found that those phenomena are accompanied by Hopf bifurcation which is supercritical. Our findings may provide more global perspectives on understanding underlying mechanisms to control biodiversity in ecological/biological sciences, and evidences with mathematical foundations to resolve social dilemmas such as a turnover of group members by resigning with intragroup conflicts in social sciences. [ABSTRACT FROM AUTHOR]

Prahalad Chunnilal Vaidya was an eminent general relativist, gravitation theorist, physicist, mathematician, educationist and a follower of Gandhian philosophy in post-independence India. Apart from his scientific career, Vaidya is renowned for his Vaidya metric. Though he has contributed significantly to the scientific community, very few people are aware about him or his contributions. As 23 May 2019 was the 101st birth anniversary of Vaidya, here we present his contributions and their impact through a bibliometric study. This study presents an analysis of published research works of Vaidya. During his active career, he had contributed 102 publications, including 90 journal articles, 5 conference papers, 4 book chapters, 2 review articles and 1 report. His publications have received 2004 citations, h-index of 18 and i10-index of 29 from 1979 to 2018. We analysed Vaidya's publications by type, country, journals, publishers, citations, year-wise growth, collaborated authors, top cited papers, etc. This bibliometric study is an effort to draw the attention of the younger generation of scientists to Vaidya and his contributions. [ABSTRACT FROM AUTHOR]

Cooperation among kin is common in animal societies. Kin groups may form by individuals directly discriminating relatives based on kin recognition cues, or form passively through natal philopatry and limited dispersal. We describe the genetic landscape for a primitively eusocial wasp, Polistes dominula, and ask whether individuals choose cooperative partners that are nearby and/or that are genetic relatives. Firstly, we genotyped an entire sub-population of 1361 wasps and found genetic structuring on an extremely fine scale: the probability of finding genetic relatives decreases exponentially within just a few meters of an individual’s nest. At the same time, however, we found a lack of genetic structuring between natural nest aggregations within the population. Secondly, in a separate dataset where ~2000 wasps were genotyped, we show that wasps forced experimentally to make a new nest choice tended to choose new nests near to their original nests, and that these nests tended to contain some full sisters. However, a significant fraction of wasps chose nests that did not contain sisters, despite sisters being present in nearby nests. Although we cannot rule out a role for direct kin recognition or natal nest-mate recognition, our data suggest that kin groups may form via a philopatric rule-of-thumb, whereby wasps simply select groups and nesting sites that are nearby. The result is that most subordinate helpers obtain indirect fitness benefits by breeding cooperatively. [ABSTRACT FROM AUTHOR]

The Semantic Link Network is a general semantic model for modeling the structure and the evolution of complex systems. Various semantic links play different roles in rendering the semantics of complex system. One of the basic semantic links represents cause-effect relation, which plays an important role in representation and understanding. This paper verifies the role of the Semantic Link Network in representing the core of text by investigating the contribution of cause-effect link to representing the core of scientific papers. Research carries out with the following steps: (1) Two propositions on the contribution of cause-effect link in rendering the core of paper are proposed and verified through a statistical survey, which shows that the sentences on cause-effect links cover about 65% of key words within each paper on average. (2) An algorithm based on syntactic patterns is designed for automatically extracting cause-effect link from scientific papers, which recalls about 70% of manually annotated cause-effect links on average, indicating that the result adapts to the scale of data sets. (3) The effects of cause-effect link on four schemes of incorporating cause-effect link into the existing instances of the Semantic Link Network for enhancing the summarization of scientific papers are investigated. The experiments show that the quality of the summaries is significantly improved, which verifies the role of semantic links. The significance of this research lies in two aspects: (1) it verifies that the Semantic Link Network connects the important concepts to render the core of text; and, (2) it provides an evidence for realizing content services such as summarization, recommendation and question answering based on the Semantic Link Network, and it can inspire relevant research on content computing. [ABSTRACT FROM AUTHOR]

In this study, we address the question whether (and to what extent, respectively) altmetrics are related to the scientific quality of papers (as measured by peer assessments). Only a few studies have previously investigated the relationship between altmetrics and assessments by peers. In the first step, we analyse the underlying dimensions of measurement for traditional metrics (citation counts) and altmetrics–by using principal component analysis (PCA) and factor analysis (FA). In the second step, we test the relationship between the dimensions and quality of papers (as measured by the post-publication peer-review system of F1000Prime assessments)–using regression analysis. The results of the PCA and FA show that altmetrics operate along different dimensions, whereas Mendeley counts are related to citation counts, and tweets form a separate dimension. The results of the regression analysis indicate that citation-based metrics and readership counts are significantly more related to quality, than tweets. This result on the one hand questions the use of Twitter counts for research evaluation purposes and on the other hand indicates potential use of Mendeley reader counts. [ABSTRACT FROM AUTHOR]

The need to complete multiple tasks concurrently is a common occurrence both daily life and in occupational activities, which can often include simultaneous cognitive and physical demands. As one example, there is increasing availability of head-worn display technologies that can be employed when a user is mobile (e.g., while walking). This new method of information presentation may, however, introduce risks of adverse outcomes such as a decrement to gait performance. The goal of this study was thus to quantify the effects of a head-worn display (i.e., smart glasses) on motor variability during gait and to compare these effects with those of other common information displays (i.e., smartphone and paper-based system). Twenty participants completed four walking conditions, as a single task and in three dual-task conditions (three information displays). In the dual-task conditions, the information display was used to present several cognitive tasks. Three different measures were used to quantify variability in gait parameters for each walking condition (using the cycle-to-cycle standard deviation, sample entropy, and the “goal-equivalent manifold” approach). Our results indicated that participants used less adaptable gait strategies in dual-task walking using the paper-based system and smartphone conditions compared with single-task walking. Gait performance, however, was less affected during dual-task walking with the smart glasses. We conclude that the risk of an adverse gait event (e.g., a fall) in head-down walking conditions (i.e., the paper-based system and smartphone conditions) were higher than in single-task walking, and that head-worn displays might help reduce the risk of such events during dual-task gait conditions. [ABSTRACT FROM AUTHOR]

Quantifying the impact of a scholarly paper is of great significance, yet the effect of geographical distance of cited papers has not been explored. In this paper, we examine 30,596 papers published in Physical Review C, and identify the relationship between citations and geographical distances between author affiliations. Subsequently, a relative citation weight is applied to assess the impact of a scholarly paper. A higher-order weighted quantum PageRank algorithm is also developed to address the behavior of multiple step citation flow. Capturing the citation dynamics with higher-order dependencies reveals the actual impact of papers, including necessary self-citations that are sometimes excluded in prior studies. Quantum PageRank is utilized in this paper to help differentiating nodes whose PageRank values are identical. [ABSTRACT FROM AUTHOR]

Background: There is widespread evidence that statistical methods play an important role in original research articles, especially in medical research. The evaluation of statistical methods and reporting in journals suffers from a lack of standardized methods for assessing the use of statistics. The objective of this study was to develop and evaluate an instrument to assess the statistical intensity in research articles in a standardized way. Methods: A checklist-type measure scale was developed by selecting and refining items from previous reports about the statistical contents of medical journal articles and from published guidelines for statistical reporting. A total of 840 original medical research articles that were published between 2007–2015 in 16 journals were evaluated to test the scoring instrument. The total sum of all items was used to assess the intensity between sub-fields and journals. Inter-rater agreement was examined using a random sample of 40 articles. Four raters read and evaluated the selected articles using the developed instrument. Results: The scale consisted of 66 items. The total summary score adequately discriminated between research articles according to their study design characteristics. The new instrument could also discriminate between journals according to their statistical intensity. The inter-observer agreement measured by the ICC was 0.88 between all four raters. Individual item analysis showed very high agreement between the rater pairs, the percentage agreement ranged from 91.7% to 95.2%. Conclusions: A reliable and applicable instrument for evaluating the statistical intensity in research papers was developed. It is a helpful tool for comparing the statistical intensity between sub-fields and journals. The novel instrument may be applied in manuscript peer review to identify papers in need of additional statistical review. [ABSTRACT FROM AUTHOR]

Research paper recommenders emerged over the last decade to ease finding publications relating to researchers’ area of interest. The challenge was not just to provide researchers with very rich publications at any time, any place and in any form but to also offer the right publication to the right researcher in the right way. Several approaches exist in handling paper recommender systems. However, these approaches assumed the availability of the whole contents of the recommending papers to be freely accessible, which is not always true due to factors such as copyright restrictions. This paper presents a collaborative approach for research paper recommender system. By leveraging the advantages of collaborative filtering approach, we utilize the publicly available contextual metadata to infer the hidden associations that exist between research papers in order to personalize recommendations. The novelty of our proposed approach is that it provides personalized recommendations regardless of the research field and regardless of the user’s expertise. Using a publicly available dataset, our proposed approach has recorded a significant improvement over other baseline methods in measuring both the overall performance and the ability to return relevant and useful publications at the top of the recommendation list. [ABSTRACT FROM AUTHOR]

In this note we point out and correct a mistake in our paper "GlobalLpestimates for degenerate Ornstein–Uhlenbeck operators with variable coefficients", published in Math. Nachr. 286 (2013), no. 11–12, 1087–1101. [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]

Abstract This comment concerns the doubtful new auxiliary equation method (Khater method) included in the above paper. We prove by simple calculation that this method is wrong. The exact solutions of the proposed nonlinear equation obtained in the above paper are all wrong. Highlights • The new auxiliary equation method is called Khater method. • We prove by simple calculation that Khater method is wrong. • We show that the exact solutions obtained in the above paper are all wrong. [ABSTRACT FROM AUTHOR]

Convex in x domain, eigenfunction, level sets, local rearrangement Erratum to the paper "Convexity in x of the level sets of the first Dirichlet eigenfunction": (Published in Math. Nachr. Keywords: convex in x domain; eigenfunction; level sets; local rearrangement EN convex in x domain eigenfunction level sets local rearrangement 1025 1025 1 03/21/23 20230301 NES 230301 Lemma 3.2 is incorrect. [Extracted from the article]

The level of difficulty of mathematical test items is a critical aspect for evaluating test quality and educational outcomes. Accurately predicting item difficulty during test creation is thus significantly important for producing effective test papers. This study used more than ten years of content and score data from China's Henan Provincial College Entrance Examination in Mathematics as an evaluation criterion for test difficulty, and all data were obtained from the Henan Provincial Department of Education. Based on the framework established by the National Center for Education Statistics (NCES) for test item assessment methodology, this paper proposes a new framework containing eight features considering the uniqueness of mathematics. Next, this paper proposes an XGBoost-based SHAP model for analyzing the difficulty of mathematics tests. By coupling the XGBoost method with the SHAP method, the model not only evaluates the difficulty of mathematics tests but also analyzes the contribution of specific features to item difficulty, thereby increasing transparency and mitigating the "black box" nature of machine learning models. The model has a high prediction accuracy of 0.99 for the training set and 0.806 for the test set. With the model, we found that parameter-level features and reasoning-level features are significant factors influencing the difficulty of subjective items in the exam. In addition, we divided senior secondary mathematics knowledge into nine units based on Chinese curriculum standards and found significant differences in the distribution of the eight features across these different knowledge units, which can help teachers place different emphasis on different units during the teaching process. In summary, our proposed approach significantly improves the accuracy of item difficulty prediction, which is crucial for intelligent educational applications such as knowledge tracking, automatic test item generation, and intelligent paper generation. These results provide tools that are better aligned with and responsive to students' learning needs, thus effectively informing educational practice. [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]

In the first part of the paper, we propose a different viewpoint on the theory of higher Airy structures (or Airy ideals), which may shed light on its origin. We define Airy ideals in the ħ -adic completion of the Rees Weyl algebra and show that Airy ideals are defined exactly such that they are always related to the canonical left ideal generated by derivatives by automorphisms of the Rees Weyl algebra of a simple type, which we call transvections. The standard existence and uniqueness result in the theory of Airy structures then follow immediately. In the second part of the paper, we construct Airy ideals generated by the nonnegative modes of the strong generators of the principal W -algebra of sp 2 N at level - N - 1 / 2 , following the approach developed in Borot et al. (Mem Am Math Soc, 2021). This provides an example of an Airy ideal in the Heisenberg algebra that requires realizing the zero modes as derivatives instead of variables, which leads to an interesting interpretation for the resulting partition function. [ABSTRACT FROM AUTHOR]

D'Arcy Thompson (1860–1948) is most remembered for his influential book On Growth and Form (1917), which looked to maths to explain why biological creatures take the shapes that they take. In January 1917, a few months before this book was released, Thompson had a letter to the editor published in Nature titled 'Stability in Flight'. Using this paper, and the response to it, as a basis, this article will investigate Thompson's relationship with mathematics, uncovering his ideas on an ideological hierarchy of subjects, where mathematics informs biology, but the reverse case is not true. It will also explore the ideas of flight Thompson discusses in the article, from the aeronautical physics paper which inspired Thompson, to the ideas on modern ornithology which agree with his work. [ABSTRACT FROM AUTHOR]

This correction notice provides updates and corrections to a research paper on deep machine learning model-based cyber-attacks detection in smart power systems. The paper proposes a deep learning-based attack detection model that addresses system disturbances caused by natural events and cyber-attacks. It discusses the use of principal component analysis (PCA) for feature selection and the potential of deep learning-based and decision tree classifiers for detecting cyber-attacks in intelligent energy grids. The notice also includes updates to references, clarifications on the experimental data set, and feature selection based on PCA. The study evaluates the effectiveness of the proposed model using various assessment indexes and compares it to conventional methods, concluding that the proposed model is effective in detecting cyber-attacks and demonstrates good performance in detecting destructive attacks. [Extracted from the article]