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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]

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]

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]

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]

Students’ development of reasoning through algebraic symbols is a crucial component of most mathematics courses. This paper reports the journey of one second-semester calculus student, Cedric, as he attempted to reason about and create algebraic representations for arbitrary partial sums and infinite series through two exploratory teaching interviews. We report Cedric’s symbolizing activity in terms of Eckman's (2023) expression framework, focusing on Cedric’s development and attribution of meaning to a personal expression template for denoting partial sums and series. Specifically, we describe how Cedric leveraged his initial meanings for partial sums to create personal expressions to reason about infinite series. We then describe Cedric's construction of a general personal expression template for partial sums and series, including cognitive and physical modifications he made to his personal expression template as he symbolized various series. Our results show potentially profitable task sequences and lines of questioning that instructors might utilize to help students be more successful in constructing productive meanings for algebraic symbols. [ABSTRACT FROM AUTHOR]

The embedding of a torus into an inner form of PGL2 defines an adelic toric period. A general version of Duke's theorem states that this period equidistributes as the discriminant of the splitting field tends to infinity. In this paper we consider a torus embedded diagonally into two distinct inner forms of PGL2. Assuming the Generalized Riemann Hypothesis (and some additional technical assumptions), we show simultaneous equidistribution as the discriminant tends to infinity, with an effective logarithmic rate. Our proof is based on a probabilistic approach to estimating fractional moments of L-functions twisted by extended class group characters. [ABSTRACT FROM AUTHOR]

In the present paper, we have obtained common best proximity point theorems of nonself maps in Hausdorff topological space. Further, our results extend the results due to Gerald F. Jungck, thereby proving a generalized version of Kirk's theorem (J. London Math. 1(1):107–111, 1969). [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]

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]

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]

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]

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 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]

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]

In this paper, I follow trails of the auto/biographical turn in the field of gender and science, particularly focusing on women mathematicians' epistolary narratives. The paper emerges from a wider Leverhulme funded project of writing a feminist genealogy of «automathographies», tracing women mathematicians' historical emergence as subjects of scientific knowledge, as well as creators of philosophy and culture. What I argue is that letters are important auto/biographical documents in illuminating women's epistemological and intellectual involvement in the making of scientific knowledge, which included the development of mathematical sciences, but was also expanded in the wider cultural formations of the European modernity. In doing so, I deploy the notion of «epistolary sensibility» as a methodological and epistemological approach to archival research with women mathematicians' letters. [ABSTRACT FROM AUTHOR]

Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both courses culminated in a final project in which students created and investigated solutions to their own modeling tasks. In this paper, we describe how our courses (1) centered justice as pedagogy, (2) were environments for student agency and exploration, and (3) explicitly demonstrated how mathematics and social justice are intertwined. Drawing on frameworks of mathematical modeling for social justice, we present and analyze student-created tasks to showcase how they utilized mathematics as a tool to question and critique the world around them. [ABSTRACT FROM AUTHOR]

Axiomatic Fredholm theory in unital C*-algebras was established in [D. Kečkić, Z. Lazović, Acta Sci. Math., 83(3-4):629-655, 2017]. Following the pure algebraic approach by Keckic and Lazovic, in the author’s paper [S. Ivkovic, Banach J. Math. Anal., 17:51, 2023] we extended further this theory to axiomatic semi-Fredholm and semi-Weyl theory in unital C*- algebras. However, recently, in [S. Ivković, arXiv:2306.01133] we developed another approach to axiomatic Fredholm theory in unital C*-algebras which is based on the theory of Hilbert modules and is equivalent to the algebraic approach by Kečkić and Lazović. In this paper, we extend further that new Hilbert-module approach from Fredholm theory to semi-Fredholm and semiWeyl theory in unital C*-algebras. Hence, we provide new proofs to the results in [S. Ivkovic, Banach J. Math. Anal., 17:51, 2023]. [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 examine q-Bernstein-Bézier surfaces in Minkowski space- R13 with q as the shape parameter. These surfaces, a generalization of Bézier surfaces, have applications in mathematics, computer-aided geometric design, and computer graphics for the surface formation and modeling. We analyze the timelike and spacelike cases of q-Bernstein-Bézier surfaces using known boundary control points. The mean curvature and Gaussian curvature of these q-Bernstein-Bézier surfaces are computed by finding the respective fundamental coefficients. We also investigate the shape operator dependency for timelike and spacelike q-Bernstein-Bézier surfaces in Minkowski space- R13 , and provide biquadratic and bicubic q-Bernstein-Bézier surfaces as illustrative examples for different values of the shape controlling parameter q. [ABSTRACT FROM AUTHOR]

In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder's inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N and T = R ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011). [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 were concerned with the multiplicity of the large periodic solutions to a super-linear wave equation with a general variable coefficient. In general, the variable coefficient ρ(·) needs to be satisfied ess inf ηρ(·) > 0 with ηρ(·) = 1/2 ρ/ρ − 1/4 ( ρ/ρ )² . Especially, the case ηρ(·) = 0 is presented as an open problem in [Trans. Amer. Math. 349: 2015–2048, 1997]. Here, without any restrictions on ηρ(·), we established the multiplicity of large periodic solutions for the Dirichlet-Neumann boundary condition and Dirichlet-Robin boundary condition when the period T = 2π 2a−1/b with a, b ∈ N + . The key ingredient of the proof is the combination of the variational method and an approximation argument. Since the sign of ηρ(·) can change, our results can be applied to the classical wave equation [ABSTRACT FROM AUTHOR]

Given a connected (molecular) graph G, its Harary index H(G) is defined by the reciprocal sum of the distances between all unordered pairs of vertices of G. Lower bounds on the graph vulnerability parameters binding number and toughness have been often used to determine that the graph has a certain property. Recently, Yatauro [Discrete Appl. Math. 338 (2023) 56-68] gave a sharp upper bound of W (G) (Wiener index) to ensure that G has a determined lower bound (greater than or equal to 1) for the binding number or toughness. In this paper, we supply an upper bound on H(G) to ensure that G has a determined lower bound (between 0 and 1) for the binding number or toughness, and show that these bounds are best possible in some sense. [ABSTRACT FROM AUTHOR]

In the paper, we investigate the uniqueness problem of a meromorphic function and its difference operator to the most general setting via two shared set problems and thus improve a recent result of Chen–Chen (Bull Malays Math Sci Soc 35(3): 765-774, 2012). [ABSTRACT FROM AUTHOR]

In this paper, we obtain the Harary index and the hyper-Wiener index of the H-generalized join of graphs and the generalized corona product of graphs. As a consequence, we deduce some of the results in (Das et al. in J. Inequal. Appl. 2013:339, 2013) and (Khalifeh et al. in Comput. Math. Appl. 56:1402–1407, 2008). Moreover, we calculate the Harary index and the hyper-Wiener index of the ideal-based zero-divisor graph of a ring. [ABSTRACT FROM AUTHOR]

Howe and Tan (Bull Am Math Soc 28:1–74, 1993) investigated a degenerate principal series representation of indefinite orthogonal groups O (b + , b -) and explicitly described its composition series. In particular it contains a unique unitarizable irreducible submodule Π , which is isomorphic to a cohomological representation. In this paper we construct orthogonal automorphic forms locally corresponding to Π as theta liftings of holomorphic Mp 2 (R) cusp forms by using the Borcherds' method (Invent Math 132:491–562, 1998). We propose a special choice of Schwartz functions to define the liftings, which yields precise descriptions of their Fourier expansions. [ABSTRACT FROM AUTHOR]

The idempotent divisor graph of a commutative ring R is a graph with a vertex set in R* = R-{0}, where any distinct vertices x and y are adjacent if and only if x.y = e, for some non-unit idempotent element e^2 = e ∈ R, and is denoted by Л(R). Our goal in this work is to transform the planar idempotent divisor graph after coloring its regions into optical art by depending on the reflection of vertices, edges, and planes on the x or y-axes. That is, we achieve Op art solely through pure mathematics in this paper. [ABSTRACT FROM AUTHOR]

In recent decades, with the continuous changes in the mathematics curriculum, many geometry-related topics were neglected or removed from our classroom activities. Thus, some teachers pursue these topics as independent students' projects. There is also a growing interest in various courses and workshops dealing with practical geometric pattern design. The author has taught courses and conducted workshops on geometry and pattern design at the Istanbul Design Center for many years. Participants in these events were high school and university students, artists, and architects. In this paper, we will discuss selected concepts of geometry used by Seljuk architects in designing the famous Seljuk geometric mosaics and stone carvings. We will show how these geometric concepts were used in selected examples from mosques, tombs, hans, and madrasas. We will also demonstrate using geometry software, e.g., Geometer's Sketchpad or GeoGebra, for constructing geometric patterns. [ABSTRACT FROM AUTHOR]

In this paper, I attempt to describe Mark Burgin's results in non-Diophantine mathematics, which are important for the foundation of mathematics and its application in quantum field theory. In particular, the elimination of divergences in quantum electrodynamics is described. [ABSTRACT FROM AUTHOR]

Separation of variables is a common method for producing an analytical based solution to partial differential equations. Despite the wide application of this method, often the physical phenomena described by the differential equations are not adequately involved in the discourse over the appropriate methods to solve a given problem, particularly in mathematics curricula. However, as mathematics is the tool to better understanding of the physical world, the meaning of the differential equation, boundary conditions, and initial conditions cannot be detached from the methods used to solve the differential equations. Failure to recognize the physical conditions being studied can lead to solution methods that are invalid or unphysical. This paper demonstrates how awareness of the physical nature of the system being investigated and its relationship to the mathematics can guide the selection of the relevant solution methods. To illustrate the importance of the comprehension of the physical meaning behind the mathematical equations and representations and the need to avoid rote application a solution technique, the logic behind the selection of the appropriate solution techniques for the one-dimensional transient heat conduction equation is considered under different imposed conditions which lead to different trends in system operation. [ABSTRACT FROM AUTHOR]

Anemia is a global public health problem, especially common among children in developing countries, which affects their physical and mental health development. However, there is currently a lack of research on the relationship between anemia and academic performance. The objective of this study was to explore the association between anemia and academic performance, and the possible factors mediating this association among Chinese children. The data for this study came from the baseline survey of the Chinese Education Panel Survey Elementary School Cohort. The cohort was conducted from September 2018 to June 2019 in 160 elementary schools, covering 20 provinces and 40 counties/districts throughout China. Paper-based questionnaires were used, completed by 4th grade students, parents, head teachers, main teachers, and principals. The data used included questionnaire responses, physical measurements, and academic performance of 17,695 students. Based on students' hemoglobin levels and school altitude data, we grouped them into anemia and nonanemia categories using WHO criteria. The anemia group had 1,154 individuals, while the nonanemia group had 16,541 individuals. An ordinary least squares regression and mediation effect analysis were conducted. Our findings found the prevalence of anemia was 6.52% among Chinese Grade 4 students. Students without anemia had a higher average test score for three academic subjects than students with anemia (P < 0.001); their test scores for Chinese, Mathematics, and English were also higher (P < 0.05). Multivariate regression analysis showed a negative association between anemia and average test scores as well as individual test scores for the three subjects. Mediation analysis found that anemia affected academic performance directly (P < 0.05), and indirectly by decreasing the cognition score (P < 0.05). The indirect effect was 19.9% of the total effect. Findings highlighted anemia affected academic performance both directly and indirectly. Nutrition-related interventions should be implemented to prevent a decrease in academic performance among students with anemia. [ABSTRACT FROM AUTHOR]

In this paper, we study the Onsager-Machlup function and its relationship to the Freidlin-Wentzell function for measures equivalent to arbitrary infinite dimensional Gaussian measures. The Onsager-Machlup function can serve as a density on infinite dimensional spaces, where a uniform measure does not exist, and has been seen as the Lagrangian for the "most likely element". The Freidlin-Wentzell rate function is the large deviations rate function for small-noise limits and has also been identified as a Lagrangian for the "most likely element". This leads to a conundrum - what is the relationship between these two functions? We show both pointwise and G-convergence (which is essentially the convergence of minimizers) of the Onsager-Machlup function under the small-noise limit to the Freidlin-Wentzell function - and give an expression for both. That is, we show that the small-noise limit of the most likely element is the most likely element in the small noise limit for infinite dimensional measures that are equivalent to a Gaussian. Examples of measures include the law of solutions to path-dependent stochastic differential equations and the law of an infinite system of random algebraic equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the hypothesis testing of correlation between two m-uniform hypergraphs on n unlabelled nodes. Under the null hypothesis, the hypergraphs are independent, while under the alternative hypothesis, the hyperdges have the same marginal distributions as in the null hypothesis but are correlated after some unknown node permutation. We focus on two scenarios: the hypergraphs are generated from the Gaussian-Wigner model and the dense Erdös-Rényi model. We derive the sharp information-theoretic testing threshold. Above the threshold, there exists a powerful test to distinguish the alternative hypothesis from the null hypothesis. Below the threshold, the alternative hypothesis and the null hypothesis are not distinguishable. The threshold involves m and decreases as m gets larger. This indicates testing correlation of hypergraphs (m = 3) becomes easier than testing correlation of graphs (m = 2). [ABSTRACT FROM AUTHOR]

Let X1, X2, . . ., Xn be a sequence of coherent random variables, i.e., satisfying the equalities Xj = P(A|Gj), j = 1, 2, . . ., n, almost surely for some event A. This paper contains the proof of the estimate P (max 1=i

The Degree Corrected Stochastic Block Model (DCSBM) is a probabilistic model for random networks with community structure in which vertices of the same community are allowed to have distinct degree distributions. On the modeling side, this property makes the DCSBM more suitable for real-life complex networks. On the statistical side, it is more challenging due to a large number of parameters. In this paper, we prove that the penalized marginal likelihood estimator, when assuming prior distributions for the parameters, is strongly consistent for estimating the number of communities. We consider dense or semi-sparse random networks, and our estimator is unbounded, in the sense that the number of communities k considered can be as big as n, the number of nodes in the network. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of solutions in connection to a non-local multiterm boundary value problem (BVP) with differential equations equipped with the Riemann-Liouville (RL) fractional derivative in the sense of Atangana-Baleanu of variable-order. The results about the existence property are investigated and proved via Krasnoselskii's fixed point theorem. Note that all theorems in the present research are studied based on piece-wise constant functions defined on generalized intervals. We shall convert our main BVP with the RL-fractional derivative of the Atangana-Baleanu type of variable-order to an equivalent BVP of constant order of the RL-Atangana-Baleanu derivative. In the next step, we examine the Ulam-Hyers stability for the supposed variable-order RL-Atangana-Baleanu BVP. Finally, we provide some examples to validate that our results are applicable. [ABSTRACT FROM AUTHOR]

In this paper, we study the Liouville-type theorem for the stationary barotropic compressible Navier–Stokes equations in R 3 . Based on a fairly general framework of a kind of local mean oscillations integral and Morrey spaces, we prove that the velocity and the density of the flow are trivial without any integrability assumption on the gradient of the velocity. [ABSTRACT FROM AUTHOR]

For a hybrid stochastic system, most existing feedback controllers need to observe modes at continuous times, which is feasible when the system's mode is observable and does not incur any cost. However, in most cases, the mode is not readily apparent, and identifying it always incurs a certain expense. Therefore, in order to reduce control costs, when designing a feedback controller, both the state and the mode should be observed at discrete moments. This paper introduces an intermittent feedback controller for stabilizing an unstable hybrid stochastic system through discrete delayed observations of state and mode. By utilizing M-matrix theory, intermittent control approach, and the comparison principle, we propose sufficient conditions for the stabilization theory of hybrid stochastic systems. An illustrative example is taken to validate the proposed theory. [ABSTRACT FROM AUTHOR]

s t r i n g U t i l s. c o n v e r t A b s t r a c t M a t h H t m l (formulaUtilTools.convertMathHtml( s t r i n g U t i l s. c o n v e r t M m l (!article.abstractinfoEn)),'en') Compared to the standard variational inequalities, inverse variational inequalities are more suitable for pricing American options with indefinite payoff. This paper investigated the initial-boundary value problem of inverse variational inequalities constituted by a class of non-divergence type parabolic operators. We established the existence and Hölder continuity of weak solutions. Since the comparison principle in the case of standard variational inequalities is no longer applicable, we constructed an integral inequality using differential inequalities to determine the global upper bound of the solution. By combining it with the continuous method, we obtained the existence of weak solutions. Additionally, by employing truncation factors, we obtained the lower bound of weak solutions in the cylindrical subdomain, thereby obtaining the Hölder continuity. [ABSTRACT FROM AUTHOR]

The notion of generalized quantum cluster algebras was introduced as a natural generalization of Berenstein and Zelevinsky's quantum cluster algebras as well as Chekhov and Shapiro's generalized cluster algebras. In this paper, we focus on a generalized quantum cluster algebra of Kronecker type which possesses infinitely many cluster variables. We obtain the cluster multiplication formulas for this algebra. As an application of these formulas, a positive bar-invariant basis is explicitly constructed. Both results generalize those known for the Kronecker cluster algebra and quantum cluster algebra. [ABSTRACT FROM AUTHOR]

In this paper, an implicit compact finite difference (CFD) scheme was constructed to get the numerical solution for time fractional diffusion-wave equation (TFDWE), in which the time fractional derivative was denoted by Caputo-Fabrizio (C-F) sense. We proved that the full discrete scheme is unconditionally stable. We also proved that the rate of convergence in time is near to O (τ 2) and the rate of convergence in space is near to O (h 4). Test problem was considered for regular domain with uniform points to validate the efficiency and accuracy of the method. The numerical results can support the theoretical claims. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic Leslie-Gower model with Beddington-DeAngelis functional response driven by the Ornstein-Uhlenbeck process is studied. Some asymptotic properties of the solution of the stochastic Leslie-Gower model are introduced: the existence and uniqueness of the global solution of the model are demonstrated, the ultimate boundedness of the model is analyzed, the existence of the stationary distribution of the model is proven, and the conditions for system extinction are discussed. Finally, numerical simulations are utilized to verify our conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we, a group of graduate students in mathematics education, discuss some of the metacognitive benefits of the non-traditional teaching methods we observed employed by one of our professors. This professor's methods challenge the common belief that well-managed class time is key for positive learning outcomes. Instead, he orients his teaching to share the exploration and sense-making phases of doing mathematics. The goal of his teaching is to share the idea that learning mathematics is a process of "refining our mathematical thinking". We argue that this approach to teaching helps students see that mathematics is a human endeavor, appreciate the cycles of learning mathematics and the importance of struggle throughout the process, and gain some insight on what it means to be an expert in mathematics. We encourage teachers and professors to move away from obsessing about structured, well-organized class time, and to instead move towards having flexible and risk-oriented class time. [ABSTRACT FROM AUTHOR]

Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demonstrate that different solutions--hiding one biscuit, arbitrarily sharing the extra biscuit, randomizing allocation, dividing the extra biscuit into three parts, and successively dividing it into smaller and smaller parts--involve different mathematical methods and evoke different human values. We discuss the construction of quantum biscuit splitting devices and the use of machine learning to divide biscuits. We argue that the multitude of different mathematically-correct solutions to this problem (each with its own ethical justification) might influence the values held by practicing mathematicians. The example we propose here has been used in teaching to help students understand why mathematics cannot be cleanly separated from human values. [ABSTRACT FROM AUTHOR]

This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, generaleducation classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student's developing identity in mathematics and, more broadly, in STEM. The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for various classroom settings are discussed in detail. [ABSTRACT FROM AUTHOR]

This paper presents some existence and uniqueness results for a solution of a system of equations. Our results extend and generalize the well-known and celebrated results of Boyd and Wong [Proc. Amer. Math. Soc. 20 (1969)], Matkowski [Dissertations Math. (Rozprawy Mat.) 127 (1975)], Proinov [Nonlinear Anal. 64 (2006)], Ri [Indag. Math. (N. S.) 27 (2016)] and many others. We also present some illustrative examples to validate our results. [ABSTRACT FROM AUTHOR]

The study of symmetry is a fascinating and unifying subject that connects various areas of mathematics in the twenty-first century. Algebraic structures offer a framework for comprehending the symmetries of geometric objects in pure mathematics. This paper introduces new concepts in algebraic structures, concentrating on semimodules over semirings and analysing the neutrosophic structure in this context. We explore the properties of neutrosophic subsemimodules and neutrosophic ideals after defining them. We discuss, utilizing neutrosophic products, the representations of neutrosophic ideals and subsemimodules, as well as the relationship between neutrosophic products and intersections. Finally, we derive equivalent criteria in terms of neutrosophic structures for a semiring to be fully idempotent. [ABSTRACT FROM AUTHOR]

This document is a correction notice for a paper titled "An Investigation on Spiking Neural Networks Based on the Izhikevich Neuronal Model: Spiking Processing and Hardware Approach." The correction addresses an error in the affiliation of one of the authors, Ehsan Nazemi. The updated affiliation should include the Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh City, Vietnam. Additionally, there was an error in the Introduction section where a paragraph with unexplained references was mistakenly copied from one of the author's theses. This paragraph has been removed, and the order of references has been adjusted accordingly. The authors assure that these corrections do not affect the scientific conclusions of the paper. [Extracted from the article]

This paper is concerned with an indirect chemotaxis-consumption model with sensitivity function χ (v). Frassu and Viglialoro (Appl. Math. Lett.; 2022; 132; 108108) showed global existence and boundedness in the case that χ is a constant. However, there is a room for improvement of the main claim. This paper improves the result and extends it in the case that χ depends on v. [ABSTRACT FROM AUTHOR]