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Let R be a commutative ring with identity. In this paper, we study 2-prime ideals of a Dedekind domain and a Prfiufer domain. We prove that a nonzero ideal I of a Dedekind domain R is 2-prime if and only if I = P, for some maximal ideal P of R and positive integer . We give some results of ring R in which every ideal I is 2-prime. Finally, we define almost 2-prime, almost 2-primary and weakly 2-primary ideals, and investigate some properties of these ideals. [ABSTRACT FROM AUTHOR]

In this paper, an operational matrix method based on the Bell polynomials has been presented to find approximate solutions of highorder Volterra integro-difierential equations. This method uses a simple computational manner to obtain a quite acceptable approximate solution. The main characteristic behind this method lies in the fact that on the one hand, the problem will be reduced to a system of algebraic equations and on the other hand, the effciency and accuracy of the Bell polynomials for solving these equations are acceptable. The convergence analysis of this method will be shown by preparing some theorems. Moreover, we will obtain an estimation of the error bound for this algorithm. Finally, some examples are presented to illustrate the applicability, eficiency and accuracy of this scheme in comparison with some other well-known methods such as Legendre, Bernoulli, Taylor and Bessel polynomial algorithms. [ABSTRACT FROM AUTHOR]

Suppose G is a finite non-abelian group and (G) is a graph with non-central conjugacy classes of G as its vertex set. Two vertices L and K in such that ab = ba. This graph is called the commuting conjugacy class graph of G. The purpose of this paper is to compute the commuting conjugacy class graph of the finite 2 such that ab = ba. This graph is called the commuting conjugacy class graph of G. The purpose of this paper is to compute the commuting conjugacy class graph of the finite 2-group Gm(n) and G(n). [ABSTRACT FROM AUTHOR]

The main purpose of the present paper is about characterizing properties of the perfect uid space-time admits the gradient Ricci- Bourguignon soliton. This gives some results about stability of the energy momentum tensor and also under some conditions pursues that a perfect uid space-time is Ricci symmetric. As an special case, when a perfect uid space-time equipped with the Ricci-Bourguignon soliton which has Ricci biconformal vector field, we show that the metric of this space is Einstein. [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]

In this paper we consider a Parabolic systems modeling bacteria pattern formation proposed by Aotani et al.(Jap. J. Indust. Appl. Math., 27:5–22, 2010). According to Yagi’s arguments (in Abstract Parabolic Evolution equations), we reduce them to corresponding evolution equations and show the existence of time global solutions. [ABSTRACT FROM AUTHOR]

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

This article provides insight into the mathematics and designs of quilts inspired by Fibonacci and logarithmic spirals. We introduce the history and development of the Fibonacci number sequence and how to hand-draw a Fibonacci spiral. Further, we explain the relationship between the Fibonacci spiral and logarithmic spirals, the advantages of using logarithmic spirals to create designs, and how to produce digital spiral designs using Desmos, a free web-based graphing calculator. Finally, we discuss methods for designing spiral quilts or other triangle and spiral designs (such as collage or other media) and derive a formula for calculating the apex angles of the triangles. We hope to inspire the reader’s imagination to spiral out of bounds to explore, create, and discover the beauty of mathematics in what you will create. [ABSTRACT FROM AUTHOR]

Reference (Ericksen in Q. J. Mech. Appl. Math. 45:545–554, 1992), a short and dense paper by J.L. Ericksen, is taken as a primary source of terms frequently used in continuum thermodynamics, in an attempt to make their significance as precise as possible. [ABSTRACT FROM AUTHOR]

In this paper, we will focus our attention on the structure of halmost Ricci solitons on complex hyperbolic quadric. We will prove non-existence a contact real hypersurface in the complex hyperbolic quadric Qm∗,m ≥ 3, admitting the gradient almost Ricci soliton. Moreover, the gradient almost Ricci soliton function f is trivial. [ABSTRACT FROM AUTHOR]

Recently, a serious problem in communications is security. Hiding data is one of the most important security techniques. Steganography is the art and science of hiding information in a cover media. Texts are the most usual method of communication and so they are very suitable for cover objects. In this paper, we give a new technique for text steganography. There exist different models, such as RGB, HSL, HSV to determine a color. The main goal of the proposed algorithm is the fact that some different but very similar colors in RGB have the same code in HSL. We use this fact to hide data. For this purpose, first we find a color B′ in RGB, which is very similar to black in such a way that they have the same code in HSL. Then, by changing the color of each character of the text to black or B′, we conceal the information. We will show that the capacity of this method is better than some other methods of text steganography, and then we show that the invisibility of this algorithm is very high, which is the most prominent feature of the proposed technique. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a notion of Connes biprojectivity for a dual Banach algebra A with respect to its w∗-closed ideal I, say I-Connes biprojectivity. Some Lipschitz algebras Lipα(X) and some matrix algebras are studied under this new notion. Also, with some mild assumptions, the relation between IConnes biprojectivity and left ϕ-contractibility is given, where ϕ is a ω∗-continuous multiplicative linear functional on A. As an application, we characterize Connes biprojectivity of some Lipschitz algebras. [ABSTRACT FROM AUTHOR]

Let G = (V,E) be a simple graph. A set D ⊆ V is a strong dominating set of G, if for every vertex x ∈ V \ D there is a vertex y ∈ D with xy ∈ E(G) and deg(x) ≤ deg(y). The strong domination number γst(G) is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on γst(G) when G is modified by operations on vertices and edges of G. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive investigation into the role of mathematics in everyday life and the pivotal function of mathematics teachers in fostering mathematical understanding and competence. Mathematics plays a crucial role in everyday life, enhancing decision-making, financial management, problem-solving, and critical thinking. The ubiquitous presence of mathematics in activities such as budgeting, cooking, shopping, and planning underscores its importance. Mathematics is essential for good governance, as it underpins data-driven decision-making, policy formulation, economic planning, and resource allocation. Recommendations for promoting mathematical proficiency include integrating real-world applications into the curriculum, offering professional development for teachers, and encouraging collaborative learning. Such measures can enhance mathematical literacy, contributing to personal development, societal progress, and effective governance. Mathematics, with its rich historical roots stretching back to ancient civilizations, has evolved into a broad discipline encompassing various branches such as arithmetic, algebra, geometry, and calculus. Each branch plays a crucial role in practical applications ranging from personal finance and cooking to navigation and health monitoring. Effective mathematics education, however, hinges on the proficiency and dedication of mathematics teachers who not only impart theoretical knowledge but also cultivate critical thinking and problem-solving skills in their students. To optimize performance in high-stakes assessments like the West African Examination Council (WAEC) Mathematics examination, it is essential to employ diverse instructional strategies, integrate technology, and provide continuous practice and assessment. It is recommended that governments should support teachers through robust remuneration, timely salary payments, and ongoing professional development to sustain motivation and high-quality instruction. Furthermore, the establishment of mathematics laboratories in schools is recommended to enhance practical learning experiences and deepen students' understanding of mathematical concepts. In the realm of governance, mathematics is indispensable for data analysis, policy formulation, and strategic planning. By addressing these areas comprehensively, we can create an educational environment that not only demystifies mathematics and reduces associated phobias but also prepares students to excel academically and apply mathematical principles effectively in their daily lives and future careers. [ABSTRACT FROM AUTHOR]

Copyright of Bulletin of Ablai Khan KazUIRandWL: Series 'Pedagogical Sciences' is the property of Kazakh Ablai Khan University of International Relations & World Languages and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

Despite being a prominent and influential figure in the German and Jewish Enlightenment, Salomon Maimon's skeptical standpoint seems to veer towards radical and unsustainable assertions, denying the validity of any knowledge—including natural science—except for mathematics. This paper seeks to demonstrate that Maimon's skepticism concerning non-mathematical knowledge does not propose an incoherent skepticism nor contradict the enlightened perspective of developing natural sciences. To achieve this, I aim to show that (1) Maimon's radical claim originates from the radical nature of the question he answers, and (2) the key to understanding it lies in grasping the concept of synthesis in his philosophy, from which different meanings of knowledge follow. [ABSTRACT FROM AUTHOR]

The paper is concerned with Lane–Emden and Brezis–Nirenberg problems involving the affine p-Laplace nonlocal operator Δ p 풜 , which has been introduced in [J. Haddad, C. H. Jiménez and M. Montenegro, From affine Poincaré inequalities to affine spectral inequalities, Adv. Math. 386 2021, Article ID 107808] driven by the affine L p energy ℰ p , Ω from convex geometry due to [E. Lutwak, D. Yang and G. Zhang, Sharp affine L p Sobolev inequalities, J. Differential Geom. 62 2002, 1, 17–38]. We are particularly interested in the existence and nonexistence of positive C 1 solutions of least energy type. Part of the main difficulties are caused by the absence of convexity of ℰ p , Ω and by the comparison ℰ p , Ω ⁢ (u) ≤ ∥ u ∥ W 0 1 , p ⁢ (Ω) generally strict. [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]

Semidefinite programming (SDP) problems typically utilize a constraint of the form X ⪰ x x T to obtain a convex relaxation of the condition X = x x T , where x ∈ R n . In this paper, we consider a new hyperplane branching method for SDP based on using an eigenvector of X - x x T . This branching technique is related to previous work of Saxeena et al. (Math Prog Ser B 124:383–411, 2010, https://doi.org/10.1007/s10107-010-0371-9) who used such an eigenvector to derive a disjunctive cut. We obtain excellent computational results applying the new branching technique to difficult instances of the two-trust-region subproblem. [ABSTRACT FROM AUTHOR]

Let 퐺 be a finite reductive group such that the derived subgroup of the underlying algebraic group is a product of quasi-simple groups of type 햠. In this paper, we give an explicit description of the action of automorphisms of 퐺 on the set of its irreducible complex characters. This generalizes a recent result of M. Cabanes and B. Späth [Equivariant character correspondences and inductive McKay condition for type 햠, J. Reine Angew. Math.728 (2017), 153–194] and provides a useful tool for investigating the local sides of the local-global conjectures as one usually needs to deal with Levi subgroups. As an application we obtain a generalization of the stabilizer condition in the so-called inductive McKay condition [B. Späth, Inductive McKay condition in defining characteristic, Bull. Lond. Math. Soc.44 (2012), 3, 426–438; Theorem 2.12] for irreducible characters of 퐺. Moreover, a criterion is given to explicitly determine whether an irreducible character is a constituent of a given generalized Gelfand–Graev character of 퐺. [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]

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]

A subalgebra A of a C*-algebra M is logmodular (resp. has factorization) if the set {a*a; a ∈M is invertible with a, a--1 ∈ A} is dense in (resp. equal to) the set of all positive and invertible elements of M. In this paper, we show that the lattice of projections in a (separable) von Neumann algebra M whose ranges are invariant under a logmodular algebra in M, is a commutative subspace lattice. Further, if M is a factor then this lattice is a nest. As a special case, it follows that all reflexive (in particular, completely distributive CSL) logmodular subalgebras of type I factors are nest algebras, thus answering in the affirmative a question by Paulsen and Raghupathi (Trans. Amer. Math. Soc. 363 (2011) 2627-2640). We also give a complete characterization of logmodular subalgebras in finite-dimensional von Neumann algebras. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of optimal pairs for optimal control problems with their states constrained pointwise to Riemannian manifolds. For this purpose, by means of the Riemannian geometric tool, we introduce a crucial Cesari-type property, which is an extension of the classical Cesari property (see Definition 3.3, p. 51 in [L. D. Berkovitz, Optimal Control Theory, Appl. Math. Sci. 12, Springer-Verlag, New York, Heidelberg, 1974]) from the setting of Euclidean spaces to that of Riemannian manifolds. Moreover, we show the efficiency of our result by a concrete example. [ABSTRACT FROM AUTHOR]

Let R be a commutative Noetherian ring and I be an ideal of R with cd(I, R) = t ≥ 1. In this paper, we consider the Lynch's conjecture and we obtain a partial answer for this conjecture. More precisely, we show that if M is an R-module such that 0 ̸= Ht I (M) is I-cofinite, then AnnRHt I (R) ⊆ p for some minimal prime ideal p of R. [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 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]

Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on fuzzy Aumann's integral theory, the Hermite–Hadamard's type inequalities are introduced for a newly defined class of nonconvex functions, which is known as  U · D preinvex fuzzy number-valued mappings ( U · D preinvex  F · N · V · M s) on coordinates. Some Pachpatte-type inequalities are also established for the product of two  U · D preinvex  F · N · V · M s, and some Hermite–Hadamard–Fejér-type inequalities are also acquired via fuzzy Aumann's integrals. Additionally, several new generalized inequalities are also obtained for the special situations of the parameters. Additionally, some of the interesting remarks are provided to acquire the classical and new exceptional cases that can be considered as applications of the main outcomes. Lastly, a few suggested uses for these inequalities in numerical integration are made. [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]

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]

The higher-order guaranteed lower eigenvalue bounds of the Laplacian in the recent work by Carstensen et al. (Numer Math 149(2):273–304, 2021) require a parameter C st , 1 that is found not robust as the polynomial degree p increases. This is related to the H 1 stability bound of the L 2 projection onto polynomials of degree at most p and its growth C st, 1 ∝ (p + 1) 1 / 2 as p → ∞ . A similar estimate for the Galerkin projection holds with a p-robust constant C st , 2 and C st , 2 ≤ 2 for right-isosceles triangles. This paper utilizes the new inequality with the constant C st , 2 to design a modified hybrid high-order eigensolver that directly computes guaranteed lower eigenvalue bounds under the idealized hypothesis of exact solve of the generalized algebraic eigenvalue problem and a mild explicit condition on the maximal mesh-size in the simplicial mesh. A key advance is a p-robust parameter selection. The analysis of the new method with a different fine-tuned volume stabilization allows for a priori quasi-best approximation and improved L 2 error estimates as well as a stabilization-free reliable and efficient a posteriori error control. The associated adaptive mesh-refining algorithm performs superior in computer benchmarks with striking numerical evidence for optimal higher empirical convergence rates. [ABSTRACT FROM AUTHOR]

The architectonic is key for situating Kant's understanding of science in the coming century. For Kant the faculty of reason turns to ideas to form a complete system. The coherence of the system rests on these ideas. In contrast to technical unity which can be abstracted a posteriori, architectonic ideas are the source of a priori unity for the system of reason because they connect our reasonable pursuit to essential human ends. Given Kant's focus on mathematics, in the architectonic and his critical philosophy more generally, we must have some sense of the architectonic idea of mathematics. In this paper, I argue for the key principles of the architectonic idea of mathematics: 1) because mathematics is grounded in a priori intuition, it is a peculiarly human activity; 2) the method of mathematics is one of a priori construction, a method only mathematics can employ and: 3) the objects of mathematics are extensive magnitudes. Given these principles, we can use the architectonic idea to have some clarity about how mathematics has dealt with historical development. [ABSTRACT FROM AUTHOR]

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

It is well-known that the famous Selberg integral is equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a generalization of the q-Morris constant term identity[J. Combin. Theory Ser. A 81 (1998), pp. 69–87]. This conjecture was proved and extended by Károlyi, Nagy, Petrov, and Volkov (KNPV) in 2015 [Adv. Math. 277 (2015), pp. 252–282]. In this paper, we obtain two symmetric function generalizations of the q-Baker–Forrester ex-conjecture. These include: (i) a q-Baker–Forrester type constant term identity for a product of a complete symmetric function and a Macdonald polynomial; (ii) a complete symmetric function generalization of KNPV's result. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the links between prospective elementary teachers' (PTs') ability to notice student mathematical thinking, their mathematical knowledge for teaching (MKT) and their ability to decompose learning goals into component conceptual parts (Morris et al., 2009). Previously, researchers have proposed theoretical connections between MKT and teachers' professional noticing, but empirical support for these relationships has been limited. Results of this mixed-methods study indicate that PTs who scored higher on an MKT assessment outperformed their peers in terms of attending to student thinking but had similar performance in terms of interpreting that thinking. However, PTs who were able to conceptually unpack a learning goal into subconstructs performed higher-quality interpretations of student thinking. We hypothesize that the skill of decomposing learning goals may allow PTs to apply their mathematics knowledge to successfully interpret student work. These results have implications for understanding how noticing and MKT may develop in relation with each other. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the Lie algebra bundles defined by Jordan algebra bundles of finite type over an arbitrary topological space and observe that such Lie algebra bundles are also of finite type. Also, we examine some ideal bundles of Lie algebra bundles defined by semisimple Jordan algebra bundles of finite type. [ABSTRACT FROM AUTHOR]

The paper focuses on finding the relationships between the frequency of experiencing positive and negative emotional states, students' subjective evaluation of the subjects of mathematics, Slovak language and literature, English language, civics and physical education in terms of their popularity, difficulty and importance, and school achievement in these subjects. The research population consisted of 168 (100%) pupils second and third-year pupils of a secondary vocational school in Žilina. The research included: the Subjective Emotional Habitual Well-being Questionnaire (Džuka, Dalbert, 2002) and the Attitudes to Learning Subjects Questionnaire for Pupils (Hrabal, Pavelková, 2010). The most important results of the research revealed that the teaching subject of mathematics was rated the worst in all the surveyed items. Pupils perceived mathematics as the least favourite subject, the most challenging, the least important. They had the worst average school achievement in it, experienced the most negative and least frequently positive emotional state of all the subjects studied. English was the most significant teaching subject. Physical education was the most popular subject taught to the students. Pupils' attitudes towards the subjects taught did not change much over time, being stable and unambiguous. Only the subject of mathematics, which current pupils perceived to be less popular and less important than in the past, showed a change. We found a high correlation between the frequency of experiencing a positive state of mind and the popularity of the assessed teaching subjects in mathematics and physical education. [ABSTRACT FROM AUTHOR]

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

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

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

In 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]

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]

In this paper, using the method of blow-up analysis, we establish a trace Trudinger-Moser inequality involving L^p-norm and obtain the corresponding extremal on a compact Riemann surface with a smooth boundary. The result generalizes those of Li-Liu [Math. Z. 250 (2005), pp. 363–686] and Zhang [Commun. Pure Appl. Anal. 20 (2021), pp. 1721–1735]. [ABSTRACT FROM AUTHOR]

In this study, measurement invariance and differential item functioning (DIF) studies of the TIMSS 2019 4th and 8thgrade mathematics and science achievement tests were conducted for the country groups participating in both TIMSS and eTIMSS. The study sample consisted of 9560 responders of the first booklet of the 2019 cycle. Multiple Group Confirmatory Factor Analysis (MGCFA) was utilized to test measurement invariance, and Mantel-Haenszel (MH), Logistic Regression (LR), and SIBTEST were used for the DIF analyses. The measurement invariance results indicated strict invariance between groups for all tests which included 111 items in total. In the DIF analyses, for the 4th and 8th-grade mathematics tests, only three items showed moderate DIF with MH, and four items showed DIF with SIBTEST. For the 4th-grade science test, one item showed moderate DIF with both MH and SIBTEST. However, in the 8th-grade science test, no items showed DIF with MH and LR methods, while four items showed moderate DIF with SIBTEST. Overall, MH and SIBTEST techniques were in agreement, whereas LR method produced inconsistent results and showed disagreement with these two methods. The results of the measurement invariance analysis and the LR method were consistent and indicated equivalency of TIMSS and e-TIMSS scores. [ABSTRACT FROM AUTHOR]

Research in psychology and education indicates that corrective feedback can be a powerful learning tool. We provide a developmental perspective to focus specifically on how corrective feedback influences learning in childhood (∼ages 3–11). Based on a systematic search, we review 44 empirical papers published between 1990 and 2022 examining the effects of corrective feedback on children's performance in the domains of literacy (n = 18), mathematics (n = 14), and problem solving (n = 12). Across these domains, we synthesize research on how children respond to lessons and practice with, versus without, corrective feedback to provide theoretical and practical insights into (1) the effectiveness of corrective feedback in early childhood, (2) the features of effective feedback messages at different ages, and (3) the role of individual learner differences. We make several novel recommendations with some focused on future research questions and others focused on ways teachers can provide effective feedback to children. [ABSTRACT FROM AUTHOR]

Authoring of help content within educational technologies is labor intensive, requiring many iterations of content creation, refining, and proofreading. In this paper, we conduct an efficacy evaluation of ChatGPT-generated help using a 3 x 4 study design (N = 274) to compare the learning gains of ChatGPT to human tutor-authored help across four mathematics problem subject areas. Participants are randomly assigned to one of three hint conditions (control, human tutor, or ChatGPT) paired with one of four randomly assigned subject areas (Elementary Algebra, Intermediate Algebra, College Algebra, or Statistics). We find that only the ChatGPT condition produces statistically significant learning gains compared to a no-help control, with no statistically significant differences in gains or time-on-task observed between learners receiving ChatGPT vs human tutor help. Notably, ChatGPT-generated help failed quality checks on 32% of problems. This was, however, reducible to nearly 0% for algebra problems and 13% for statistics problems after applying self-consistency, a "hallucination" mitigation technique for Large Language Models. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in finding sufficient conditions, which ensure the existence of solutions to a weak (pessimistic) bilevel optimization problem (S) in a topological sequential setting. To this aim, we consider an approach of (S) by means of a family of regularized perturbed bilevel optimization problems (Sn) of (S). Unlike (S), such problems (Sn) have the privilege to admit solutions under mild assumptions. Using the notion of variational convergence, after establishing stability results, we prove the existence of solutions to problem (S). [ABSTRACT FROM AUTHOR]

This survey describes the structure of the field of research on curriculum resources in mathematics education in the period from 2018 till 2023. Based on the procedures of a systematic review relevant literature was identified using Web of Science as a database. The included literature was analyzed and categorized according to the type of curriculum resource and the area of study. Seven areas of studies were identified: studies on the role of curriculum resources, content analysis, user studies, studies on the effects of curriculum resources, studies on curriculum resource design, curriculum resources as data, and reviews. The areas were further subdivided into different subcategories based on the research questions of the included papers. The findings show that research on mathematics textbooks is still predominant in the field. The most popular areas of research are content analysis, user studies, studies on design, and studies on effects. Emerging areas are research on students' use of curriculum resources and the employment of user data from digital curriculum resources as data basis in mathematics education research. [ABSTRACT FROM AUTHOR]