Search Results (17)

After establishing some basic facts on binary relations and sequential convergences, we prove a relational modification of a false, but interesting lemma of Paweł Pasteczka on the constancy of the composition of certain set-valued functions [There is at most one continuous invariant mean, Aequat. Math. 96 (2022), 833–841.]. In particular, we prove that if F is an inclusion-increasing, compact-valued, closed relation of the half line $X=[0,+\infty [$ to a sequential convergence space $Y=Y(lim)$, and G is an inclusion-continuous relation of Y to X such that their composition relation $\Phi =G\circ F$ is inclusion-left-continuous, then $\Phi$ is a constant relation. Full article

This study investigates the effects of math training on math and cognitive performance among 8–9 year-old students with low attention. Fifty-six students with low attention were randomly assigned to a training group (n = 24) and a passive control group (n = 32). They completed math problem-solving, calculation fluency and PASS cognitive processing tests both before and after training. The children in the training group received 3 days of training per week for a total of 21 days using the math modules of The Children’s Mathematics and Cognition Training Manual in Chinese. The results showed that the training group’s math problem-solving performance improved significantly. Moreover, the cognitive performance on the CAS-2 in the planning and simultaneous processing tests for the training group was enhanced. The implications of these findings are discussed with consideration of the interpretability being constrained by the fact that no active control condition was applied. Full article

The traditional educational system, in certain aspects, limits personalized learning. This is mainly evident in the fact that average students, who do not have any learning difficulties, are required to solve the same tasks from the same textbook in the same order. Artificial intelligence and other smart learning tools present great opportunities for implementing a personalized learning system. Our previous surveys and literature reviews also show that educators see the greatest potential in personalized education for the assimilation of artificial intelligence into education. In this context, we have developed educational software called “Learn with M.E. as Math Educator”, which facilitates more personalized teaching of basic mathematical operations. This study presents the structure and operation of this application. We tested the usability of the software in several institutions. Our research target group consists of elementary school students, specifically those aged 11–15. This article provides a detailed overview of the accuracy and educational outcomes of the completed application. We evaluated the application and its effectiveness using both qualitative and quantitative methods. Our research design combined elements of educational technology development and effectiveness assessment. To evaluate student performance, we employed a control group methodology. Data were analyzed by comparing test results between students using the software and those receiving traditional instruction. We examined user satisfaction through survey questionnaires. Teachers’ opinions were gathered through structured interviews, and their responses were categorized using a SWOT analysis. The findings indicated that the use of the software significantly improved students’ mathematics performance compared to the control group. Students provided positive feedback on the software’s user interface, describing it as user-friendly and motivating. Teachers regarded the software as an effective educational tool, facilitating differentiated instruction and enhancing student engagement. The results suggest that digital educational tools, such as the developed software, can provide substantial added value in education. Full article

Interferometric synthetic aperture radar (InSAR) processing techniques have been widely used to derive surface deformation or retrieve terrain elevation. Over the development of the past few decades, most research has mainly focused on its application, new techniques for improved accuracy, or the investigation of a particular error source and its correction method. Therefore, a thorough discussion about each error source and its influence on InSAR-derived products is rarely addressed. Additionally, InSAR is a challenging topic for beginners to learn due to the intricate mathematics and the necessary signal processing knowledge required to grasp the core concepts. This results in the fact that existing papers about InSAR are easy to understand for those with a technical background but difficult for those without. To cope with the two issues, this paper aims to provide an organized, comprehensive, and easily understandable review of the InSAR error budget. In order to assist readers of various backgrounds in comprehending the concepts, we describe the error sources in plain language, use the most fundamental math, offer clear examples, and exhibit numerical and visual comparisons. In this paper, InSAR-related errors are categorized as intrinsic height errors or location-induced errors. Intrinsic height errors are further divided into two subcategories (i.e., systematic and random error). These errors can result in an incorrect number of phase fringes and introduce unwanted phase noise into the output interferograms, respectively. Location-induced errors are the projection errors caused by the slant-ranging attribute of the SAR systems and include foreshortening, layover, and shadow effects. The main focus of this work is on systematic and random error, as well as their effects on InSAR-derived topographic and deformation products. Furthermore, because the effects of systematic and random errors are greatly dependent on radar wavelengths, different bands are utilized for comparison, including L-band, S-band, C-band, and X-band scenarios. As examples, we used the parameters of the upcoming NISAR operation to represent L-band and S-band, ERS-1 and Sentinel-1 to represent C-band, and TerraSAR-X to represent X-band. This paper seeks to bridge this knowledge gap by presenting an approachable exploration of InSAR error sources and their implications. This robust and accessible analysis of the InSAR error budget is especially pertinent as more SAR data products are made available (e.g., NISAR, ICEYE, Capella, Umbra, etc.) and the SAR user-base continues to expand. Finally, a commentary is offered to explore the error sources that were not included in this work, as well as to present our thoughts and conclusions. Full article

The home learning environment includes parental activities, attitudes, affect, knowledge, and resources devoted to supporting children’s development, including literacy and mathematics skills. These factors are related to the academic performance of preschool children (aged 3 to 6 years), before formal schooling and possibly beyond. In the present research, we examined the home learning environment of Canadian families as reported by either the mother (n = 51) or father (n = 30) of their Grade 3 child (n = 81; M_age = 8.7 years; range 8 to 9 years of age). Importantly, mothers’ and fathers’ reports of the home learning environment for school children were similar. For literacy, parents’ knowledge of children’s books and attitudes toward literacy were related to children’s vocabulary skills; home literacy was not related to word reading skills. For mathematics, parents’ reports of the frequency of activities such as practicing arithmetic facts and their attitudes toward mathematics were related to children’s arithmetic fluency. Other aspects of the home learning environment (time spent helping with homework, parents’ math anxiety) were not related to children’s performance. These results suggest some continuity between home learning environments and academic skills after children’s transition to school. Full article

Knowing the importance of mathematics and its relationship with veterinary medicine plays an important role for students. To promote interest in this relationship, we developed the workshop “Math in Nature” that utilizes the surrounding environment for stimulating pattern-recognition and observational skills. It consisted of four sections: A talk by a professional researcher, a question-and-answer section, a mathematical pattern identification session, and a discussion of the ideas proposed by students. The effectiveness of the program to raise interest in mathematics was evaluated using a questionnaire applied before and after the workshop. Following the course, a higher number of students agreed with the fact that biological phenomena can be explained and predicted by applying mathematics, and that it is possible to identify mathematical patterns in living beings. However, the students’ perspectives regarding the importance of mathematics in their careers, as well as their interest in deepening their mathematical knowledge, did not change. Arguably, “Math in Nature” could have exerted a positive effect on the students’ interest in mathematics. We thus recommend the application of similar workshops to improve interests and skills in relevant subjects among undergraduate students. Full article

Many studies of bilingual arithmetic report better performance when verifying arithmetic facts in the language of learning (LA+) over the other language (LA−). This could be due to language-specific memory representations, processes established during learning, or to language and task factors not related to math. The current study builds on a small number of event-related potential (ERP) studies to test this question while controlling language proficiency and eliminating potential task confounds. Adults proficient in two languages verified single-digit multiplications presented as spoken number words in LA+ and LA−, separately. ERPs and correctness judgments were measured from solution onset. Equivalent P300 effects, with larger positive amplitude for correct than incorrect solutions, were observed in both languages (Experiment 1A), even when stimuli presentation rate was shortened to increase difficulty (Experiment 1B). This effect paralleled the arithmetic correctness effect for trials presented as all digits (e.g., 2 4 8 versus 2 4 10), reflecting efficient categorization of the solutions, and was distinct from an N400 generated in a word–picture matching task, reflecting meaning processing (Experiment 2). The findings reveal that the language effects on arithmetic are likely driven by language and task factors rather than differences in memory representation in each language. Full article

Math fluency is the ability to solve arithmetic facts quickly and accurately (i.e., addition and subtraction problems up to 20, and multiplication and division problems from the multiplication table). Curricula in primary school devote a significant period of time for learning and retrieval of arithmetic facts. Recently, a new computerized tool to assess math fluency—the BGU-MF (Ben-Gurion University Math Fluency) test—was developed and found to be a reliable and valid tool for adults. In the current study, we examine the performance of first to sixth-grade children in math fluency using the BGU-MF. The results present the performance of MF during childhood and emphasize that it continues to develop during primary school. Importantly, proficiency of MF differed by operations, and the automaticity of math facts was acquired in different grades. Moreover, we found that the BGU-MF is a reliable and valid tool not only for adults but also for children during primary school. Our study has educational implications for the teaching, practice, and retrieval of arithmetic facts. Full article

Derived math fact fluency becomes more imperative across all mathematical content areas during a students’ mathematics development. However, many of them struggle to automate the most basic math facts sufficiently and therefore are not able to deal with more complex mathematical problems. This leads to the fact that many of them are already left behind in the early years of their school careers whether they have diagnosed learning disabilities or not. In this single-case research project, we evaluated a peer-tutoring approach designed to extend the number of automated single-digit addition tasks for four struggling elementary students through a multicomponent motivational system including immediate correction of errors, graphical feedback on performance, positive reinforcement, direct instruction flashcards, and a racetrack game. A multiple-baseline design (ABE) across subjects was applied to assess the effects of the treatment. The results indicate significant and large effects of the intervention on the number of automated math facts for the participants. This substantiates the assumption that the math-fact recall performance of struggling students can be improved through the method of peer tutoring even with the limited resources available in everyday school life. Full article

Background. Skill learning (e.g., reading, spelling and maths) has been predominantly treated separately in the neuropsychological literature. However, skills (as well as their corresponding deficits), tend to partially overlap. We recently proposed a multi-level model of learning skills (based on the distinction among competence, performance, and acquisition) as a framework to provide a unitary account of these learning skills. In the present study, we examined the performance of an unselected group of third- to fifth-grade children on standard reading, spelling, and maths tasks, and tested the relationships among these skills with a network analysis, i.e., a method particularly suited to analysing relations among different domains. Methods. We administered a battery of reading, spelling, and maths tests to 185 third-, fourth-, and fifth-grade children (103 M, 82 F). Results. The network analysis indicated that the different measures of the same ability (i.e., reading, spelling, and maths) formed separate clusters, in keeping with the idea that they are based on different competences. However, these clusters were also related to each other, so that three nodes were more central in connecting them. In keeping with the multi-level model of learning skills, two of these tests (arithmetic facts subtest and spelling words with ambiguous transcription) relied heavily on the ability to recall specific instances, a factor hypothesised to underlie the co-variation among learning skills. Conclusions. The network analysis indicated both elements of association and of partial independence among learning skills. Interestingly, the study was based on standard clinical instruments, indicating that the multi-level model of learning skills might provide a framework for the clinical analysis of these learning skills. Full article

One of the main goals of this paper is to obtain new contractive conditions using the method of a strictly increasing mapping $\mathbf{F}:(0,+\infty )\to (-\infty ,+\infty )$. According to the recently obtained results, this was possible (Wardowski’s method) only if two more properties $\left(F_2\right)$ and $\left(F_3\right)$ were used instead of the aforementioned strictly increasing $\left(F_1\right)$. Using only the fact that the function $\mathbf{F}$ is strictly increasing, we came to new families of contractive conditions that have not been found in the existing literature so far. Assuming that $\alpha (\mathfrak{u},\mathfrak{v})=1$ for every $\mathfrak{u}$ and $\mathfrak{v}$ from metric space $\Xi$, we obtain some contractive conditions that can be found in the research of Rhoades (Trans. Amer. Math. Soc. 1977, 222) and Collaco and Silva (Nonlinear Anal. TMA 1997). Results of the paper significantly improve, complement, unify, generalize and enrich several results known in the current literature. In addition, we give examples with results in line with the ones we obtained. Full article

The development of foreign economic activity of the Eurasian states led to the introduction of rail and ferry transportation. It is important to note that the current normative documentation does not fully cover the issues of transporting combined trains by sea. This can lead to a violation of the traffic safety of both the railway ferry and the transport of containers as part of combined trains by sea. In this connection, we investigated the dynamic loading of a container as part of a combined train when transported by a railway ferry. To ensure the stability of the container relative to the frame, we suggested an improvement of the load-bearing structure of a flat wagon. Additionally, we suggested the use of a viscous linkage between containers with the aim of reducing their dynamic load. To justify the suggested solutions, we carried out a mathematical modelling of the container dynamic load. The calculation was performed in MathCad. Due to the fact that the container has its own degree of freedom when transported by sea, the accelerations were separately determined for the supporting structure of the flat wagon and for the container. We found that the total amount of acceleration that acted on the container was 3.57 m/s² (0.36 g) and on the load-bearing structure of the wagon was 2.47 m/s² (0.25 g) which were, respectively, 38% and 23% less than the acceleration values in the typical scheme of their interaction. To determine the fields of acceleration distribution relative to the load-bearing structure of a flat wagon with containers, we carried out computer modelling of their dynamic load. The maximum percentage of discrepancy between the accelerations obtained by mathematical and computer modelling was 17.7%. The study will contribute to the creation of recommendations for the safe transport of combined trains by sea, as well as to increasing the efficiency of combined transport through international transport corridors. Full article

Nowadays, many factories face changes on the global market and manufacturing is unpredictable. This fact creates a demand for developing new concepts of the factory which can represent a solution to these changes. This study presents a way for designing these new factory concepts, particularly a concept of the reconfigurable manufacturing lines. The methodology in this study uses characteristics of reconfigurable manufacturing systems for developing an algorithm for designing the basic factory layout. The methodology also combines classical math operations for designing the production layout with such approaches as simulation, cluster analysis, and LCS algorithm. This combination method with LCS algorithm and an entirely different approach to the design of the manufacturing line, has not yet been used. The accuracy of this methodology is then verified through the results of the complete algorithm containing these features. The main purpose of this study was to find new approaches to designing the reconfigurable factory layout. This article is presenting new ways that differ from the classical design method. The article suggests the new way is possible and the new systems also need new ways for designing and planning. Full article

Liquid–vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575–591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point. Full article

Electric servo system (ESS) is a servo mechanism in a control system of an aircraft, a ship, etc., which controls efficiency and directly affects the energy consumption and the dynamic characteristics of the system. However, the control performance of the ESS is affected by uncertainties such as friction, clearance, and component aging. In order to improve the control performance of the ESS, a control technology combining particle swarm optimization (PSO) and finite time servo system control (FTSSC) was introduced into ESS. In fact, it is difficult to know the uncertain physical parameters of the real ESS. In this paper, the genetic algorithm (GA) was introduced into PSO and the inertia weight was improved, which increased the parameter optimization precision and convergence speed. A new feedback controller is proposed to improve response speed and reduce errors by using FTSSC theory. The performance of the controller based on PSO identification algorithm was verified by co-simulation experiments based on Automatic Dynamic Analysis of Mechanical Systems (ADAMS) (MSC software, Los Angeles, CA, USA) and matrix laboratory (MATLAB)/Simulink (MathWorks, Natick, MA, USA). Meanwhile, the proposed strategy was validated on the servo test platform in the laboratory. Compared with the existing control strategy, the control error was reduced by 75% and the steady-state accuracy was increased by at least 50%. Full article