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Automatic test paper design is critical in education to reduce workloads for educators and facilitate an efficient teaching process. However, current designs fail to satisfy the realistic teaching requirements of educators, including the consideration of both test quality and efficiency. This is the main reason why teachers still manually construct tests in most teaching environments. In this paper, the quality of tests is quantitatively defined while considering multiple objectives, including a flexible coverage of knowledge points, cognitive levels, and question difficulty. Then, a model based on the technique of linear programming is delicately designed to explore the optimal results for this newly defined problem. However, this technique is not efficient enough, which cannot obtain results in polynomial time. With the consideration of both test quality and generation efficiency, this paper proposes a genetic algorithm (GA) based method, named dynamic programming guided genetic algorithm with adaptive selection (DPGA-AS). In this method, a dynamic programming method is proposed in the population initialization part to improve the efficiency of the genetic algorithm. An adaptive selection method for the GA is designed to avoid prematurely falling into the local optimal for better test quality. The question bank used in our experiments is assembled based on college-level calculus questions from well-known textbooks. The experimental results show that the proposed techniques can construct test papers with both high effectiveness and efficiency. The computation time of the test assembly problem is reduced from 3 hours to 2 seconds for a 5000-size question bank as compared to a linear programming model with similar test quality. The test quality of the proposed method is better than the other baselines.

To deeply analyze the performance of paper-cutting elements in interior space design, this paper explores the artistic expression of paper-cutting elements. The BIM model is constructed based on the TVL algorithm, and a noise-reducing style migration method with an additional total variable loss function is used to fuse the texture features of a specific paper-cutting style so that the paper-cutting texture is generated in the target object area more intensively. The algorithm is supplemented with a U-shaped network structure to obtain the mask map of the target object, modify and expand the ScanNet training data set, and input a content map and a style map to generate the stylized paper cutout image automatically. The results show that compared with other elements, the stability of paper-cut elements reaches 96.31%, the image smoothness reaches 89.34%, and the retention of significant regions reaches 93.26%. In modern design, the peak signal-noise of paper-cut elements improved by 13.418d on average, the structural similarity also improved by 0.34807, and the recognition rate of paper-cut elements in the furnishing category reached 95%. Applying paper-cut art in interior space design can give interior furnishing design better visual effects, provide inspiration and ideas for interior space design innovation, and contribute to improving aesthetics.

The study of metadiscourse word resources is an important way to reveal academic knowledge constructs and genre features in English papers. This paper selects intra- and interdisciplinary English academic papers as data samples, and the text representation is based on the vector space model. The text similarity is calculated using the word movement distance model to complete the clustering based on the density peak, and then the semantic annotation of metadiscourse verb patterns is performed using the conditional random field. Then, the intra- and interdisciplinary metadiscourse annotations are compared to analyze the variation of verb patterns. The intra-disciplinary variation of metadiscourse verb patterns was mainly found using attitude markers, where the log-likelihood ratios of 48.56, 30.25, and 35.64 were obtained for affirmative, critical, and critical declarative attitudes, respectively. In interdisciplinary studies, basic disciplines preferred to use verb patterns as transitions, while applied disciplines preferred to express the author’s point of view. The study of metadiscourse verb patterns effectively enriches the linguistic resources in academic English teaching and deepens the understanding of the characteristics of disciplinary essay genres.

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pretest and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students' results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students' disorientation is one of the purposes of history in mathematics education.

Understanding the concepts related to real function is essential in learning mathematics. To determine how students understand these concepts, it is necessary to have an appropriate measurement tool. In this paper, we have created a web application using 32 items from conceptual understanding of real functions (CURF) item bank. We conducted a psychometric analysis using Rasch model on 207 first-year students. The analysis showed that CURF is a dependable and valid instrument for measuring students' CURF. The test is uni-dimensional; all items are consistent with the construct and have excellent item fit statistics. The results indicate that the items are independent of each other and unbiased towards the gender and high school background of the students.

Problem solving in chemical kinetics poses substantial challenges for university students since it often involves significant use of mathematics as a tool and language, with challenging translations and transitions between chemical phenomena and mathematical representations. In this paper, we present key findings from a study investigating chemistry students solving tasks centred around the steady-state approximation. Building upon the mathematical modelling cycle (MMC), qualitative analysis of the data collected using a think-aloud protocol led to the development of the extended MMC. This empirically derived extended MMC offers a more detailed account of the processes involved in mathematical modelling of chemical phenomena, highlighting aspects such as the occurrence of deliberation and evaluation throughout the modelling cycle, as well as the varying characteristics, points of activation and roles of extra-mathematical resources during problem solving. We further introduce and use problem-solving trajectories as a tool for visualising and analysing the complex and diverse approaches used by students in their attempts at reaching a solution. Overall, the extended MMC provides a finer-grained model of the cognitive and metacognitive activities that students engage in, offering further insights for research and practice.

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]

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]

In this paper, we consider a Li-Yau gradient estimate on the positive solution to the following nonlinear parabolic equation ∂/∂t f = Δf + af (ln f)p with Neumann boundary conditions on a compact Riemannian manifold satisfying the integral Ricci curvature assumption, where p ≥ 0 is a real constant. This contrasts Olivé's gradient estimate, which works mainly for the heat equation rather than nonlinear parabolic equations and the result can be regarded as a generalization of the Li-Yau [P. Li, S. T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math., 156 (1986), 153-201] and Olivé [X. R. Olive, Neumann Li-Yau gradient estimate under integral Ricci curvature bounds, Proc. Amer. Math. Soc., 147 (2019), 411-426] gradient estimates. [ABSTRACT FROM AUTHOR]

In recent years, there has been an increasing amount of literature on online teaching and learning. Teaching mathematics in the fourth industrial revolution offers entry-level mathematics teachers formidable challenges. Despite using various teaching aids in explaining the learning area, entry-level mathematics teachers, those with zero to three years of teaching experience, have experienced challenges in blended teaching during the COVID-19 pandemic. Such challenges could support the preconceived notion identified by others that the field of learning (mathematics) is difficult. This paper hinged on constructivist epistemology and investigated the challenges that entry-level mathematics teachers face in conducting blended teaching in the Sedibeng West District of Gauteng Province in the Republic of South Africa. Eight entrylevel mathematics teachers were purposely sampled from four selected schools that participated in the article. This article adopted a case study design and responses were analysed thematically. The focus group interviews were used as tools to collect data in this study. The study revealed a variety of perceptions that entry-level mathematics teachers shared about the impact of blended teaching in mathematics learning. These included, but were not limited to, the use of teaching programs or software, the effects of load shedding and blended teaching challenges related to learners' performance and behaviour. The results of this study could provide program developers, subject advisors, school principals with other members of the management team, and mathematics teachers to support the entry-level mathematics teacher's confidence, sense of future and communication skills, as well as foster multigenerational connections in blended teaching. [ABSTRACT FROM AUTHOR]

Microteaching has been viewed as a professional development tool that gives pre-service teachers the chance to strengthen their teaching skills. This paper presents an overview of the research on microteaching in mathematics teacher education, noting its prospects and challenges while also making recommendations for modifications to its application. A thorough analysis of 28 empirical papers on microteaching in mathematics teacher preparation that were published between 2000 and 12 May 2023, was conducted. Findings demonstrate that microteaching is an effective approach for enhancing pre-service teachers' core mathematics teaching skills. It is suggested that microteaching, which begins in a laboratory setting with the development of essential teaching skills, should not end there; it should give trainee teachers an opportunity to learn and practice in a real classroom context. Microteaching activities require more time, more supervisors, and more resources to function at its maximum capacity. Technology has also demonstrated greater promise when it comes to enhancing microteaching's position in facilitating the development of pre-service mathematics teachers' instructional skills. [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]

In this paper, we propose an iterative algorithm, which is based on the Mann iterative method for solving simultaneously common fixed point problem with a finite family of demicontractive mappings and systems of variational inequalities involving an infinite family of strongly accretive operators. Under suitable assumptions, we prove the strong convergence of this algorithm in Banach spaces. Application to systems of constrained convex minimization problem is provided to support our main results. The results of this paper improve and extend results of [M. Eslamian, C. R. Math. Acad. Sci. Paris, 355 (2017), 1168–1177], and of many others. [ABSTRACT FROM AUTHOR]

The Rubik's Cube mechanism (RCM) is a kind of reconfigurable mechanism with multiple characteristics such as multiple configurations, variable topology, strong coupling, and reconfigurability. Crossover research on the RCM with mathematics, chemistry, cryptography, and other disciplines has led to important breakthroughs and progress. It is obvious that the invention and creation of a new RCM can provide important ideological inspiration and theoretical guidance for the accelerated iterative updating of Rubik's Cube products and the expansion of their applications. This paper investigates the type synthesis method for a regular hexagonal prism (RHP) RCM (RHPRCM). Through analysis of the reconfigurable movement process of the RCM, two mechanism factors are abstracted, a type synthesis process for the RHPRCM is proposed, a symmetry layout method for the RCM's revolute axis based on the RHP space polyhedron is proposed, and an analysis method for the intersection of the revolute pair contact surfaces (RPCSs) based on the adjacency matrix is proposed. Taking a revolute axis passing through the center of an RHP and having only one RPCS for each revolute axis as an example, an RHPRCM with different topological structures is synthesized. The relevant research in this paper can provide methodological guidance for the synthesis of other spatial RCMs. [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]

I argue that since technology is already changing the way we do mathematics, we can use this technology to allow mathematics to be more congressive without human mathematicians becoming redundant in the face of technological advances. In thinking about what it means to "do mathematics," I examine the following aspects of technology in mathematics: teaching and learning, asking questions, collaboration, dissemination, and the act of doing research. This is not intended to be a rigorous analysis but an informed reflection based on my experience as a mathematician. [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]

In this paper, we gave some generalized Young type inequalities due to Zuo and Li [J. Math. Inequal., 16 (2022), 1169-1178], and we also presented a new Young type inequality. As applications, we obtained some operator inequalities and matrix versions inequalities including the Hilbert-Schmidt norm and trace. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notion of (incident) higher-order generalized epiderivative for a set-valued map and obtain a crucial result of the epiderivative. Then we use this result to establish the higher-order sufficient and necessary optimality conditions of a constrained set-valued optimization problem. By virtue of the epiderivatives and the optimality conditions, we establish the higher-order mixed duality problem for the set-valued optimization problem and obtain the corresponding duality theorems. [ABSTRACT FROM AUTHOR]

In this paper, we provide necessary and sufficient conditions for the existence of solutions for variational inequalities and sufficient conditions for the existence of solutions for quasi-Ky Fan minimax inequality, quasi-variational inequalities, and generalized variational inequalities. As applications, we apply these results to derive existence results for strong Nash equilibria in generalized games which generalize some existence theorems for Nash equilibria in generalized games in the literature and the existence theorem for strong Nash equilibria in normal-form games by Nessah and Tian [J. Math. Anal. Appl. 414 (2014), 871-885]. We also provide sufficient conditions for the uniqueness of strong Nash equilibria in certain generalized games. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the idea of gH-weak subdifferential for interval-valued functions (IVFs) and show how to calculate gH-weak subgradients. It is observed that a nonempty gH-weak subdifferential set is convex and closed. In characterizing the class of functions for which the gH-weak subdifferential set is nonempty, it is identified that this class is the collection of gH-lower Lipschitz IVFs. In checking the validity of the sum rule of gH-weak subdifferential for a pair of IVFs, a counterexample is obtained, which reflects that the sum rule does not hold. However, under a mild restriction on one of the IVFs, one-sided inclusion for the sum rule holds. As applications, we employ gH-weak subdifferential to provide a few optimality conditions for nonsmooth IVFs. Further, a necessary optimality condition for interval optimization problems with a difference of two nonsmooth IVFs as the objective is established. Next, a necessary and sufficient condition via augmented normal cone and gH-weak subdifferential of IVFs for finding weak efficient points is presented. Lastly, in investigating a 'sup-relation' between gH-direction derivative and gH-weak subgradients, we approximately compute gH-weak subgradient at each iterative step. In the sequel, we propose W -gH-weak subgradient method to identify a weak efficient solution of an unconstrained nonsmooth IOP. We apply the proposed method to solve an interval optimization problem by taking a test example. We present a convergence analysis of the proposed method for constant and diminishing step sizes. [ABSTRACT FROM AUTHOR]

In this paper, we consider an infinite inequality system defined by a family of proper lower semicontinuous quasiconvex functions in real normed linear spaces. By using the interior-point condition and approximate continuity assumption of the functions, we establish some sufficient conditions for ensuring the basic constraint qualification for quasiconvex programming. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the upper bound and H¨older continuity for a general class of parametric elliptical variational-hemivariational inequalities via regularized gap functions. More precisely, we deliver a formulation of the elliptical variational-hemivariational inequalities in the case of the perturbed parameters governed by both the set of constraints and the mappings (for brevity, PEVHI (CM)). Based on the arguments of monotonicity and properties of the Clarke's generalized directional derivative, we establish an upper bound result for the PEVHI (CM) and provide the H¨older continuity of the solution mapping for the PEVHI (CM) under suitable assumptions on the data. [ABSTRACT FROM AUTHOR]

In this paper, we completely characterize the boundedness and compactness of the differences for composition operators on the weighted Bergman spaces with Békollé weights in the open unit ball and estimate the norm and essential norm of weighted composition operators. [ABSTRACT FROM AUTHOR]

Uncertainty theory, founded in 2007, has become a branch of mathematics to model uncertainty rather than randomness. As an indispensable part of uncertainty theory, uncertain graph and uncertain network optimization has received the wide attention of many scholars. Naturally, a series of original research achievements have been obtained on uncertain graph and uncertain network optimization. This paper aims to present a state-of-the-art review on the recent advance in uncertain graph and uncertain network optimization. Furthermore, it hopes to predict the possible future research directions. Based on Web of Science database, this paper retrieves 144 related papers from 2011 to 2021 to analyze the features of published articles. More precisely, we analyze the annual number of publications, key topics and sub-fields, journals, and most-cited articles. In addition, the main results and models for uncertain graph and uncertain network optimization are summarized. Furthermore, the limitations of existing literature and the possible development trend are discussed. [ABSTRACT FROM AUTHOR]

Copyright of REMIE - Multidisciplinary Journal of Educational Research is the property of Hipatia Press 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.)

In this paper, we derived that a sufficiently large integer N can always be represented as the sum of three generalized D. H. Lehmer numbers. As a consequence, we deduced Lu and Yi's original result (Monatsh. Math., 159 (2010), 45-58). [ABSTRACT FROM AUTHOR]

Our purpose of this paper is to answer several open questions posed by Doan (AIMS Math., 6 (2021), 7895-7908). First, we present two fixed point theorems, which are positive answers to Doan's questions. Second, we establish a new type of Riech's fixed point theorem to improve a result of Doan. Finally, we offer a straightforward example illustrating that a set-valued mapping satisfying the conditions of our fixed point theorem may has more than one fixed point. [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]

In this paper, it is noted that three apparently disparate areas of mathematics—singularity analysis, complex symmetry analysis and the distributional representation of special functions—have a basic commonality in the underlying methods used. The insights obtained from the first of these provides a much-needed explanation for the effectiveness of the latter two. The consequent explanations are provided in the form of two theorems and their corollaries. [ABSTRACT FROM AUTHOR]

In this paper, an optimization approach based on an arithmetic optimization algorithm (AOA) is proposed for specifying the optimal allocation of distribution generations/generators (DGs) and capacitor banks (CBs) in radial distribution systems. The AOA is a new population-based meta-heuristic algorithm that is essentially based on using basic arithmetic operators in mathematics. The proposed approach is employed to specify the optimum placement, capacity, and power factor of DGs and CBs to decrease the distribution systems' total power loss and voltage deviation. To state the performance of the proposed approach, DGs and CBs are placed in IEEE 33-bus and 69-bus systems separately or together. When only DGs are used and the parameters of location, capacity, and power factor of DGs are determined simultaneously, the total active power loss reductions in the IEEE 33-bus and 69-bus systems are achieved at 94.42% and 98.03%, respectively. When the results of other optimization algorithms are examined, it is seen that better results are obtained with AOA. [ABSTRACT FROM AUTHOR]

Analytical thinking is dominated by binary ideas. From pairwise interactions to algebraic operations, to compositions of processes, to network models, binary structures are deeply ingrained in the fabric of most current scientific paradigms. In this paper, we introduce arity as the generic conceptualization of the order of an interaction between a discrete collection of entities and argue that there is a rich universe of higher arity ideas beyond binarity waiting to be explored. To illustrate this, we discuss several higher-order phenomena appearing in a wide range of research areas, paying special attention to instances of ternary interactions. From the point of view of formal sciences and mathematics, higher arity thinking opens up new paradigms of algebra, symbolic calculus and logic. In particular, we delve into the special case of ternary structures, as that itself reveals ample surprises: new notions of associativity (or lack thereof) in ternary operations of cubic matrices, ternary isomorphisms and ternary relations; the integration problem of 3-Lie algebras; and generalizations of adjacency in 3-uniform hypergraphs. All these are open problems that strongly suggest the need to develop new ternary mathematics. Finally, we comment on potential future research directions and remark on the transdisciplinary nature of higher arity science. [ABSTRACT FROM AUTHOR]

Summer camps can help children continue to learn beyond school, build knowledge, keep their learning skills sharp, and help them prepare for the following school year. This paper presents participants', facilitators', and researchers' experiences in a "Problem Solvers Camp" held in the Maker Lab at an Ontario University. A total of 12 junior students participated in a one-week summer camp, during which the participants developed plausible solutions for mathematical and instant problems using their creativity while learning some mathematical concepts. The creative learning spiral (CLS) model was adopted while designing the learning activities. Throughout the camp, children had the opportunity to work with virtual tech tools to design, create, and play to complete their challenges. Afterward, they shared their work for feedback and generated new ideas to promote their creative learning. The data were collected through observations, participants' work, and their portfolios to highlight the campers' experiences throughout the camp. On the last day of the camp, the researchers also ran focus group interviews. Data analysis showed that CLS might offer engaging environments that enhance children's creative and reflective thinking skills to solve real-life problems. This study enabled children to engage in all stages of the CLS during problem solving, encouraging the exchange of ideas and opinions. The implementation of the CLS model also has the potential to inspire creativity and enhance learners' fluency and elaboration skills, especially when complemented by technological or coding tools. [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]

In this paper, the recognition of fidgety speech emotion is studied, and real-world speech emotions are collected to enhance emotion recognition in practical scenarios, especially for cognitive tasks. We first focused on eliciting fidgety emotions and data acquisition for general math learning. Students practice mathematics by performing operations, solving problems, and orally responding to questions, all of which are recorded as audio data. Subsequently, the teacher evaluates the accuracy of these mathematical exercises by scoring, which reflects the cognitive outcomes of the students. Secondly, we propose an end-to-end speech emotion model based on a multi-scale one-dimensional (1-D) residual convolutional neural network. Finally, we conducted an experiment to recognize fidgety speech emotions by testing various classifiers, including SVM, LSTM, 1-D CNN, and the proposed multi-scale 1-D CNN. The experimental results show that the classifier we constructed can identify fidgety emotion well. After conducting a thorough analysis of fidgety emotions and their influence on the learning process, a clear relationship between the two was apparent. The automatic recognition of fidgety emotions is valuable for assisting on-line math teaching. [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 correction notice addresses an omission in a previously published paper titled "Ricci Vector Fields Revisited." The authors apologize for not including acknowledgements in the original paper and express their gratitude for the support received from King Saud University in Riyadh, Saudi Arabia. The authors assure readers that this correction does not impact the scientific conclusions of the paper. The correction has been approved by the Academic Editor and the original publication has been updated. The authors of the paper are Hanan Alohali, Sharief Deshmukh, and Gabriel-Eduard Vîlcu. [Extracted from the article]

Addressing the boundary value problems of fractional-order differential equations hold significant importance due to their applications in various fields. The aim of this paper was to approximate solutions for a class of boundary value problems involving Caputo fractional-order differential equations employing the AA-iterative scheme. Moreover, the stability and data dependence results of the iterative scheme were given for a certain class of mappings. Finally, a numerical experiment was illustrated to support the results presented herein. The results presented in this paper extend and unify some well-known comparable results in the existing literature.

The iterated function system (IFS) is important in different fields like image compression. An important feature of such systems is that they can be used to generate fractals. Yet, for the obtained fractals, it is difficult to locally control them to generate new ones with desired structures at specific places. In this paper, we gave an attempt to solve this problem based on a nonuniform multiple function system. For this, we first analyzed the multiple function systems needed in the generation of the final desired fractals. Based on such analysis, the final fractals with desired structures at specific places can be generated using the nonuniform multiple function system. Moreover, these two procedures were summarized into two algorithms for convenience. Examples were also given to illustrate the performance of the nonuniform multiple function system and the two algorithms in this paper.

We have studied initial value problems for Caputo fractional differential equations with singular nonlinearities involving the p-Laplacian operator. We have given a precise mathematical analysis of the equivalence of the fractional differential equations and Volterra integral equations studied in this paper. A theorem for the global existence of the solution was proven. In addition, an example was given at the end of the article as an application of the results found in this paper.

A new class of nonlocal boundary value problems consisting of multi-term delay fractional differential equations and multipoint-integral boundary conditions is studied in this paper. We derive a more general form of the solution for the given problem by applying a fractional integral operator of an arbitrary order $ \beta_{\xi} $ instead of $ \beta_{1} $; for details, see Lemma 2. The given problem is converted into an equivalent fixed-point problem to apply the tools of fixed-point theory. The existence of solutions for the given problem is established through the use of a nonlinear alternative of the Leray-Schauder theorem, while the uniqueness of its solutions is shown with the aid of Banach's fixed-point theorem. We also discuss the stability criteria, icluding Ulam-Hyers, generalized Ulam-Hyers, Ulam-Hyers-Rassias, and generalized Ulam-Hyers-Rassias stability, for solutions of the problem at hand. For illustration of the abstract results, we present examples. Our results are new and useful for the discipline of multi-term fractional differential equations related to hydrodynamics. The paper concludes with some interesting observations.

In this paper, we dealt with the tracking control problem of a class of fractional-order uncertain systems with time delays. In order to handle the effects brought by the uncertainties, external disturbances, time-delay terms, and to overcome the obstacles caused by inputs saturation, the tracking controller, which consisted of linear control law, nonlinear law, and robust control law proposed in this paper, was designed by combining the composite nonlinear feedback control method and the properties of fractional order operators. Furthermore, the validation of this tracking controller was proved.

Abstract In continuation of Zayed and Bulboacă work in (J. Inequal. Appl. 2022:158, 2022), this paper discusses the geometric characterization of the normalized form of the generalized Bessel function defined by V ρ , r ( z ) : = z + ∑ k = 1 ∞ ( − r ) k 4 k ( 1 ) k ( ρ ) k z k + 1 , z ∈ U , $$\begin{aligned} \mathrm{V}_{\rho,r}(z):=z+\sum_{k=1}^{\infty} \frac{(-r)^{k}}{4^{k}(1)_{k}(\rho )_{k}}z^{k+1}, \quad z\in \mathbb{U}, \end{aligned}$$ for ρ , r ∈ C ∗ : = C ∖ { 0 } $\rho, r\in \mathbb{C}^{\ast}:=\mathbb{C}\setminus \{0\}$ . Precisely, we will use a sharp estimate for the Pochhammer symbol, that is, Γ ( a + n ) / Γ ( a + 1 ) > ( a + α ) n − 1 $\Gamma (a+n)/\Gamma (a+1)>(a+\alpha )^{n-1}$ , or equivalently ( a ) n > a ( a + α ) n − 1 $(a)_{n}>a(a+\alpha )^{n-1}$ , that was firstly proved by Baricz and Ponnusamy for n ∈ N ∖ { 1 , 2 } $n\in \mathbb{N}\setminus \{1,2\}$ , a > 0 $a>0$ and α ∈ [ 0 , 1.302775637 … ] $\alpha \in [0,1.302775637\ldots ]$ in (Integral Transforms Spec. Funct. 21(9):641–653, 2010), and then proved in our paper by another method to improve it using the partial derivatives and the two-variable functions’ extremum technique for n ∈ N ∖ { 1 , 2 } $n\in \mathbb{N}\setminus \{1,2\}$ , a > 0 $a>0$ and 0 ≤ α ≤ 2 $0\leq \alpha \leq \sqrt{2}$ , and used to investigate the orders of starlikeness and convexity. We provide the reader with some examples to illustrate the efficiency of our theory. Our results improve, complement, and generalize some well-known (nonsharp) estimates, as seen in the Concluding Remarks and Outlook section.

The aim of this paper is to study the sufficient conditions for the existence of attractor of a generalized cyclic iterated function system composed of a complete metric space and a finite collection of generalized cyclic F-contraction mappings. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and generalize various well known results in the existing literature.

In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\mathbb{R}}^{N},$ (*) where μ > 0, s ∈ (0, 1), N ≥ 2, α ∈ (0, N), Iα∼1|x|N−α ${I}_{\alpha }\sim \frac{1}{\vert x{\vert }^{N-\alpha }}$ is the Riesz potential, and F is a general subcritical nonlinearity. The goal is to prove existence of multiple (radially symmetric) solutions u∈Hs(RN) $u\in {H}^{s}\left({\mathbb{R}}^{N}\right)$ , by assuming F odd or even: we consider both the case μ > 0 fixed and the case ∫RNu2=m>0 ${\int }_{{\mathbb{R}}^{N}}{u}^{2}=m{ >}0$ prescribed. Here we also simplify some arguments developed for s = 1 (S. Cingolani, M. Gallo, and K. Tanaka, “Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities,” Calc. Var. Partial Differ. Equ., vol. 61, no. 68, p. 34, 2022). A key point in the proof is given by the research of suitable multidimensional odd paths, which was done in the local case by Berestycki and Lions (H. Berestycki and P.-L. Lions, “Nonlinear scalar field equations II: existence of infinitely many solutions,” Arch. Ration. Mech. Anal., vol. 82, no. 4, pp. 347–375, 1983); for (*) the nonlocalities play indeed a special role. In particular, some properties of these paths are needed in the asymptotic study (as μ varies) of the mountain pass values of the unconstrained problem, then exploited to describe the geometry of the constrained problem and detect infinitely many normalized solutions for any m > 0. The found solutions satisfy in addition a Pohozaev identity: in this paper we further investigate the validity of this identity for solutions of doubly nonlocal equations under a C 1-regularity.

In this paper, we consider the general dual fractional parabolic problem ∂tαu(x,t)+Lu(x,t)=f(t,u(x,t))inRn×R. ${\partial }_{t}^{\alpha }u\left(x,t\right)+\mathcal{L}u\left(x,t\right)=f\left(t,u\left(x,t\right)\right) \text{in} {\mathbb{R}}^{n}{\times}\mathbb{R}.$ We show that the bounded entire solution u satisfying certain one-direction asymptotic assumptions must be monotone increasing and one-dimensional symmetric along that direction under an appropriate decreasing condition on f. Our result here actually solves a well-known problem known as Gibbons’ conjecture in the setting of the dual fractional parabolic equations. To overcome the difficulties caused by the nonlocal divergence type operator L $\mathcal{L}$ and the Marchaud time derivative ∂tα ${\partial }_{t}^{\alpha }$ , we introduce several new ideas. First, we derive a general weighted average inequality corresponding to the nonlocal operator L $\mathcal{L}$ , which plays a fundamental bridging role in proving maximum principles in unbounded domains. Then we combine these two essential ingredients to carry out the sliding method to establish the Gibbons’ conjecture. It is worth noting that our results are novel even for a special case of L $\mathcal{L}$ , the fractional Laplacian (−Δ)s, and the approach developed in this paper will be adapted to a broad range of nonlocal parabolic equations involving more general Marchaud time derivatives and more general non-local elliptic operators.

The aim of this paper is to determine the eigenvalue intervals of $\mu_{\mathtt{k}},~1\le \mathtt{k}\le \mathtt{n}$ for which an iterative system of a class of fractional-order differential equations with parameterized integral boundary conditions (BCs) has at least one positive solution by means of standard fixed point theorem of cone type. To the best of our knowledge, this will be the first time that we attempt to reach such findings for the topic at hand in the literature. The obtained results in the paper are illustrated with an example of their feasibility.