Search

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]

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 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]

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]

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

Frieze patterns have been introduced by Coxeter [Acta Arith. 18 (1971), pp. 297–310] in the 1970's and have recently attracted renewed interest due to their close connection with Fomin-Zelevinsky's cluster algebras. Frieze patterns can be interpreted as assignments of values to the diagonals of a triangulated polygon satisfying certain conditions for crossing diagonals (Ptolemy relations). Weak friezes, as introduced by Çanakçı and Jørgensen [Adv. in Appl. Math. 131 (2021), Paper No. 102253], are generalizing this concept by allowing to glue dissected polygons so that the Ptolemy relations only have to be satisfied for crossings involving one of the gluing diagonals. To any frieze pattern one can associate a symmetric matrix using a triangular fundamental domain of the frieze pattern in the upper and lower half of the matrix and putting zeroes on the diagonal. Broline, Crowe and Isaacs [Geometriae Dedicata 3 (1974), pp. 171–176] have found a formula for the determinants of these matrices and their work has later been generalized in various directions by other authors. These frieze pattern determinants are the main focus of our paper. As our main result we show that this determinant behaves well with respect to gluing weak friezes: the determinant is the product of the determinants for the pieces glued, up to a scalar factor coming from the gluing diagonal. Then we give several applications of this result, showing that formulas from the literature, obtained by Broline-Crowe-Isaacs, Baur-Marsh [J. Combin. Theory Ser. A 119 (2012), pp. 1110–1122], Bessenrodt-Holm-Jørgensen [J. Combin. Theory Ser. A 123 (2014), pp. 30–42] and Maldonado [ Frieze matrices and infinite frieze patterns with coefficients , Preprint, arXiv: 2207.04120 , 2022] can all be obtained as consequences of our result. [ABSTRACT FROM AUTHOR]

In this paper, we study the following fractional Choquard equation with weight (−Δ)su=1|x|N−α∗h(x)|u|ph(x)|u|p−2uinℝN,$$ {\left(-\Delta \right)}&#x0005E;su&#x0003D;\left(\frac{1}{{\left&#x0007C;x\right&#x0007C;}&#x0005E;{N-\alpha }}\ast h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;p\right)h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{p-2}u\kern0.5em \mathrm{in}\kern0.5em {\mathrm{\mathbb{R}}}&#x0005E;N, $$where 02s,p>2,α>0$$ 02s,p>2,\alpha >0 $$ and h$$ h $$ is a positive weight function satisfying h(x)≥C|x|a$$ h(x)\ge C{\left&#x0007C;x\right&#x0007C;}&#x0005E;a $$ at infinity, for some a≥0$$ a\ge 0 $$. We establish, in this paper, a Liouville type theorem saying that if maxN−4s−2a,0<α

How do the curators of science and technology collections represent the daily realities of doing science? Through the acquisition of Professor Stephen Hawking's office by the Science Museum, this paper will explore what is involved in making major acquisitions for national collections. How do curators consider what to preserve from the eclectic range of items found in the working spaces of scientists? What do the personal artefacts of a scientist's life represent, and what do acts of curatorial choices say about the narratives that are foregrounded -- and those that are not -- in positioning that life historically? And how do those choices illuminate the considerations involved in the way science and technology is represented in our national collections? By going beyond the glass case, we consider what it takes to bring an object into a collection: the intellectual considerations of how its stories are preserved for a nation and the practical considerations required so that items can even be considered for future display. The paper illuminates the formal and informal networks around scientists' collections, and the processes and judgements that science and technology curators make every day when choosing what could be important for defining our history. Using the Stephen Hawking office as a case study the article explores the representation of scientific practice in museum collections, the relationship of some collections with celebrity and disability, and some of the challenges posed by science and technology acquisitions compared to other types of museum object. The paper explores how knowledge is generated in museum collections, through the act of acquiring a new collection. It asks fundamental questions, which are essential to the fields of museology and science and technology studies, about the contribution to knowledge made by personal scientific objects. It goes beyond the study of collections as artefacts of display in exhibitions and galleries, providing a detailed analysis of a routine but oftenneglected aspect of behind-the-scenes museum work: the acquisition of a collection. Arguing that a large and complex collection is a vital tool for understanding the complexity of science, the paper uses the 'museum as method' (Thomas, 2016) which prioritises simple curatorial questions and the use of the objects in exploration; this enables scholars and curators to respond to material evidence of scientific knowledge, and identify narratives that are prioritised, and others that are obscured, in the historic record. In doing so, it suggests that curators are uniquely placed to provide insights into the roles of human and non-human actors in the construction of scientific knowledge, demonstrating how the Hawking collection allows us to explore the nature of scientific practice, the creation of scientific celebrity, and the potential to give visibility to disability within the history of science whilst de-centring the myth of the scientific genius in museum narratives. [ABSTRACT FROM AUTHOR]

The Riemann hypothesis (RH) is one of the major unsolved problems in pure mathematics. In the present paper, a parameterized family of non-cooperative games is constructed with the property that, if RH is true, then any game in the family admits a unique Nash equilibrium. We argue that this result is not degenerate. Indeed, neither is the conclusion a tautology, nor is RH used to define the family of games. • The Riemann Hypothesis (RH) is a famous open problem in mathematics. • This paper constructs generalized difference-form contests related to RH. • These contests admit a unique Nash equilibrium if RH holds true. • We argue that the result is not degenerate in any obvious way. [ABSTRACT FROM AUTHOR]

A paper of Reeder–Yu [J. Amer. Math. Soc. 27 (2014), pp. 437–477] gives a construction of epipelagic supercuspidal representations of p-adic groups. The input for this construction is a pair (\lambda, \chi) where \lambda is a stable vector in a certain representation coming from a Moy–Prasad filtration, and \chi is a character of the additive group of the residue field. We say two such pairs are equivalent if the resulting supercuspidal representations are isomorphic. In this paper we describe the equivalence classes of such pairs. As an application, we give a classification of the simple supercuspidal representations for split adjoint groups. Finally, under an assumption about unramified base change, we describe properties of the Langlands parameters associated to these simple supercuspidals, showing that they have trivial L-functions and minimal Swan conductors, and showing that each of these simple supercuspidals lies in a singleton L-packet. [ABSTRACT FROM AUTHOR]

We show that if G$G$ is a finitely generated group such that its profinite completion Ĝ$\widehat{G}$ is "far from being projective" (i.e., the kernel of the universal Frattini cover of Ĝ$\widehat{G}$ is not a small profinite group), then the class of existentially closed G$G$‐actions on fields is not elementary. Since any infinite, finitely generated, virtually free, and not free group is "far from being projective," the main result of this paper corrects an error in our paper, Beyarslan and Kowalski (Proc. London Math. Soc., (2) 118 (2019), 221–256), by showing the negation of Theorem 3.26 in that paper. [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]

The document titled "Discussion of 'A general theory for anisotropic Kirchhoff-Love shells with in-plane bending of embedded fibers'" is a critique of a paper that contains misleading and incorrect statements. The objections mainly focus on two remarks made in the paper. The document argues that the symmetrization employed in a previous work is valid for all cases, contrary to what the paper suggests. It also disputes the claim that a theory fails to properly account for the energetic effect of a change in geodesic curvature. The document provides counterarguments and references to support its claims. The author of the document is David J Steigmann. [Extracted from the article]

In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in ℝ3$$ {\mathrm{\mathbb{R}}}&#x0005E;3 $$. Under suitable conditions, we prove that, for any given positive integer k$$ k $$, the problem we considered has at most one solution possessing exactly k−1$$ k-1 $$ nodes. Together with the results presented by Nagasaki [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2): 211–232, 1989] and Tanaka [Proc. Roy. Soc. Edinburgh Sect. A. 138 (6): 1331–1343, 2008], we can prove that more types of nonlinear elliptic equations have the uniqueness of nodal radial solutions. [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]

If p(z) = Xn ν=0 aνz ν is a polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1, Jain [Bull. Math. Soc. Sci. Math. Roumania Tome, 59(2016), 339-347] proved max |z|=1 |p′ (z)| ≥ nAk max |z|=1 |p(z)|, where Ak = ( |a0| + |an|k n+1/ |ao|(1 + k n+1) + |an|(k n+1 + k 2n) ) . In this paper, we initially derive a generalized form that not only encompasses but also enhances the aforementioned inequality. Additionally, we extend this formulation to a more comprehensive result, thereby producing an improved outcome for certain established inequalities as a specific instance. [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]

The well-known notion of an extending module is closely linked to that of a Baer module. A right R -module M is called extending if every submodule of M is essential in a direct summand. On the other hand, a right R -module M is called Baer if for all N ≤ M , l S (N) ≤ ⊕ S S where S = End R (M). In 2004, Rizvi and Roman generalized a result of [A. W. Chatters and S. M. Khuri, Endomorphism rings of modules over nonsingular CS rings, J. London Math. Soc.  21(2) (1980) 434–444.] in terms of modules and showed the connections between Baer and extending modules via the result: "a module M is -nonsingular extending if and only if M is -cononsingular Baer". M R is called -nonsingular if ∀ φ ∈ S such that Ker φ ≤ e M , φ = 0. Moreover, M R is called -cononsingular if for any N ≤ M with φ N ≠ 0 for all 0 ≠ φ ∈ S , implies N ≤ e M. In view of this result, every Baer module which happens to be -cononsingular will automatically become an extending module. In this paper, our main focus is the study of -cononsingularity of modules. Our investigations are also motivated by the fact that very little is known about the notion of -cononsingularity while sufficient knowledge exists about the other three remaining notions in the preceding result. Moreover, we introduce the notion of special extending (or sp-extending, for short) of a module and show that the class of -cononsingular modules properly contains the class of extending modules and the class of special extending modules. Among other results, we obtain a new analogous version for the Rizvi–Roman's result which illustrates the close connections between Baer and extending modules. Examples illustrating the notions and delimiting our results are provided. [ABSTRACT FROM AUTHOR]

This paper proposes a framework for constructing high-order linearly implicit exponential integrators that conserve a quadratic invariant. This is then applied to the scalar auxiliary variable (SAV) approach. Quadratic invariants are significant objects that are present in various physical equations and also in computationally efficient conservative schemes for general invariants. For instance, the SAV approach converts the invariant into a quadratic form by introducing scalar auxiliary variables, which have been intensively studied in recent years. In this vein, Sato et al. (Appl. Numer. Math. 187, 71-88 2023) proposed high-order linearly implicit schemes that conserve a quadratic invariant. In this study, it is shown that their method can be effectively merged with the Lawson transformation, a technique commonly utilized in the construction of exponential integrators. It is also demonstrated that combining the constructed exponential integrators and the SAV approach yields schemes that are computationally less expensive. Specifically, the main part of the computational cost is the product of several matrix exponentials and vectors, which are parallelizable. Moreover, we conduct some mathematical analyses on the proposed schemes. [ABSTRACT FROM AUTHOR]

Telescopers for a function are linear differential (resp. difference) operators annihilating the definite integral (resp. definite sum) of this function. They play a key role in Wilf–Zeilberger theory and algorithms for computing them have been extensively studied in the past 30 years. In this paper, we introduce the notion of telescopers for differential forms with D-finite function coefficients. These telescopers appear in several areas of mathematics, for instance parametrized differential Galois theory and mirror symmetry. We give a sufficient and necessary condition for the existence of telescopers for a differential form and describe a method to compute them if they exist. Algorithms for verifying this condition are also given. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of the volume preserving mean curvature flow of closed hypersurfaces in the hyperbolic space. We prove that an L 2 -almost umbilical hypersurface will be deformed to a totally umbilical hypersurface along the flow. Our result removes the assumption on the mean curvature in the theorems of Huang-Lin-Zhang [Peking J. Math. (2023)] and Leng-Xu-Zhao [Int. J. Math. (2014)]. [ABSTRACT FROM AUTHOR]

Between 1873 and 1876, Felix Klein published a series of papers that he later placed under the rubric anschauliche Geometrie in the second volume of his collected works (1922). The present study attempts not only to follow the course of this work, but also to place it in a larger historical context. Methodologically, Klein's approach had roots in Poncelet's principle of continuity, though the more immediate influences on him came from his teachers, Plücker and Clebsch. In the 1860s, Clebsch reworked some of the central ideas in Riemann's theory of Abelian functions to obtain complicated results for systems of algebraic curves, most published earlier by Hesse and Steiner. These findings played a major role in enumerative geometry, whereas Plücker's work had a strongly qualitative character that imbued Klein's early studies. A leitmotif in these works can be seen in the interplay between real curves and surfaces as reflected by their transformational properties. During the early 1870s, Klein and Zeuthen began to explore the possibility of deriving all possible forms for real cubic surfaces as well as quartic curves. They did so using continuity methods reminiscent of Poncelet's earlier approach. Both authors also relied on visual arguments, which Klein would later advance under the banner of intuitive geometry (anschauliche Geometrie). [ABSTRACT FROM AUTHOR]

This paper details a literature review of mathematics vocabulary intervention studies for students with mathematics difficulty. The primary aim was to identify instructional practices that support mathematics vocabulary development. We conducted a database search to identify mathematics intervention studies either focused exclusively on vocabulary or with an embedded vocabulary component. Ultimately, 13 studies with participants from kindergarten to Grade 8 were included in the review. The majority of included studies had dual foci on vocabulary and other mathematics content, including whole number computation, word problem solving, fractions, algebra, or geometry. All studies that measured mathematics vocabulary performance indicated positive student outcomes. In addition, multiple studies indicated positive effects on measures of other mathematics content beyond mathematics vocabulary knowledge. We noted six instructional practices across studies that bolstered the mathematics vocabulary performance of students with mathematics difficulty. From most to least common, these practices included formal vocabulary use, explicit instruction, use of representations, repeated exposures, pre‐teaching, and graphic organizers. Implications are addressed for both researchers and practitioners. [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]

In this paper, we construct center stable manifolds of unstable line solitary waves for the Zakharov–Kuznetsov equation on R × T L and show the orbital stability of the unstable line solitary waves on the center stable manifolds, which yields the asymptotic stability of unstable solitary waves on the center stable manifolds near by stable line solitary waves. The construction is based on the graph transform approach by Nakanishi and Schlag (SIAM J Math Anal 44:1175–1210, 2012). Applying the bilinear estimate on Fourier restriction spaces by Molinet and Pilod (Ann Inst H Poincaré Anal Non Lineaire 32:347–371, 2015) and modifying the mobile distance in Nakanishi and Schlag (2012), we construct a contraction map on the graph space. [ABSTRACT FROM AUTHOR]

In [D. Feng and W. Huang, J. Math. Pures Appl. 106, 411–452 (2016)], the authors studied weighted topological pressure and established a variational principle for it. In this paper, we introduce the notion of local weighted topological pressure and generalize Feng and Huang's main results to localized version. [ABSTRACT FROM AUTHOR]

This paper extends some results of Mattila (J. Fractal Geom. 66 (2021) 389–401 and Ann. Acad. Sci. Fenn. A Math. 42 (2017) 611–620), in particular, removing assumptions of positive lower density. We give conditions on a general family Pλ:Rn→Rm,λ∈Λ$P_{\lambda }:\mathbb {R}^n\rightarrow \mathbb {R}^m, \lambda \in \Lambda$, of orthogonal projections which guarantee that the Hausdorff dimension formula dimA∩Pλ−1{u}=s−m$\dim A\cap P_{\lambda }^{-1}\lbrace u\rbrace =s-m$ holds generically for measurable sets A⊂Rn$A\subset \mathbb {R}^{n}$ with positive and finite s$s$‐dimensional Hausdorff measure, s>m$s>m$. As an application we prove for Borel sets A,B⊂Rn$A,B\subset \mathbb {R}^{n}$ with positive s$s$‐ and t-dimensional$t{\text{-dimensional}}$ measures that if s+(n−1)t/n>n$s + (n-1)t/n > n$, then dimA∩(g(B)+z)⩾s+t−n$\dim A\cap (g(B)+z) \geqslant s+t - n$ for almost all rotations g$g$ and for positively many z∈Rn$z\in \mathbb {R}^{n}$. We shall also give an application to the estimates of the dimension of the set of exceptional rotations. [ABSTRACT FROM AUTHOR]

We establish higher dimensional versions of a recent theorem by Chen and Haynes [Int. J. Number Theory 19 (2023), 1405–1413] on the expected value of the smallest denominator of rational points in a randomly shifted interval of small length, and of the closely related 1977 Kruyswijk–Meijer conjecture recently proved by Balazard and Martin [Bull. Sci. Math. 187 (2023), Paper No. 103305]. We express the distribution of smallest denominators in terms of the void statistics of multidimensional Farey fractions and prove convergence of the distribution function and certain finite moments. The latter was previously unknown even in the one‐dimensional setting. We furthermore obtain a higher dimensional extension of Kargaev and Zhigljavsky's work on moments of the distance function for the Farey sequence [J. Number Theory 65 (1997), 130–149] as well as new results on pigeonhole statistics. [ABSTRACT FROM AUTHOR]

This note corrects an error in our paper Anosov flows, growth rates on covers and group extensions of subshifts, Invent. Math. 223:445–483, 2021. This leaves our main results, Theorem 1.1, Corollary 1.2, Theorem 1.3 and Theorem 5.1, unchanged. We also fill a gap in the arguments presented in Sect. 9; this requires a small modification to the results in this section. [ABSTRACT FROM AUTHOR]

Based on the expectancy-value perspective on identity and identity formation, this paper explores the relationship between math identity (MI) and the dimensions of motivation (i.e. intrinsic value, attainment value, utility value and perceived competence) and math achievement in primary school. An additional aim of our research was to explore these relationships in different cultural contexts and investigate potential gender and grade differences concerning MI. The participants were 11,782 primary school students from Norway, Sweden, Estonia, Finland, Portugal and Serbia. All predictors from the motivation spectrum were significant for students' MI across the examined countries and had a stronger association with MI than math achievement. Among the motivational dimensions, intrinsic value had the strongest association with students' MI. Boys had significantly more positive math identities than girls in Estonia, Finland, Norway and Portugal. The results showed that the grade 4 students perceived themselves less as "math persons" than their grade 3 peers in all countries. [ABSTRACT FROM AUTHOR]

Parity is an important and easy to recognise property for meromorphic functions. On the parity of meromorphic functions, Liu, Liu and Korhonen [J Math Anal Appl 512(2022):126129] obtained some meaningful results. In this paper, we investigate the parity of a meromorphic function y(z) under the hypothesis that y(z)2n-2y(z)n is even. In addition, we discuss the relationship on the parity of a meromorphic function with its q-difference polynomials and differential expressions. For instance, we consider the parity of a meromorphic function y(z) under the assumption that y'(z)/ y(z)n and y(qz)/y(z)n are odd or even functions, where n is a positive integer. [ABSTRACT FROM AUTHOR]

In this paper, extending the results in Fok (Proc Am Math Soc 145:2799–2813, 2017), we compute Adams operations on the twisted K-theory of connected, simply-connected and simple compact Lie groups G, in both equivariant and nonequivariant settings. [ABSTRACT FROM AUTHOR]

In the classical bargaining problem, we propose a very mild axiom of individual rationality, which we call possibility of utility gain. This requires that for at least one bargaining problem, there exists at least one player who reaches a higher utility level than their disagreement utility. This paper shows that the Nash solution (Nash in Econometrica 18(2):155–162, 1950) is characterized by possibility of utility gain and continuity with respect to feasible sets together with Nash's axioms except weak Pareto optimality. We also show that in Nash's theorem, weak Pareto optimality can be replaced by conflict-freeness (introduced by Rachmilevitch in Math Soc Sci 76(C):107–109, 2015). This demands that when the agreement most preferred by all players is feasible, this should be chosen. Furthermore, we provide alternative and unified proofs for other efficiency-free characterizations of the Nash solution. This clarifies the role of each axiom in the related results. [ABSTRACT FROM AUTHOR]

This note remedies an error in our paper tilted Conormal Spaces and Whitney Stratifications (Found. Comput. Math., 2022). [ABSTRACT FROM AUTHOR]

In this paper, we propose a mechanical model for a game of tug of war (rope pulling). We focus on a game opposing two players, modelling each player's body as a structure composed of straight rods that can be actuated in three different ways to generate a pulling force. We first examine the static problem of two opponents being in a deadlock configuration of mechanical equilibrium; here we show that this situation is essentially governed by the ratio of masses of the players, with the heavier player having a strong advantage. We then turn to the dynamic problem and model the response of the system to an abrupt change in activation by one of the players. In this case, the system exhibits a nontrivial response; in particular, we compare a sudden pulling and a sudden "letting up," and demonstrate the existence of regimes in which the lighter player can momentarily take the advantage. [ABSTRACT FROM AUTHOR]