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Let $ R $ be a ring with identity. The commuting graph of $ R $ is the graph associated to $ R $ whose vertices are non-central elements in $ R $, and distinct vertices $ A $ and $ B $ are adjacent if and only if $ AB = BA $. In this paper, we completely determine the automorphism group of the commuting graph of $ 2\times 2 $ matrix ring over $ \mathbb{Z}_{p^{s}} $, where $ \mathbb{Z}_{p^{s}} $ is the ring of integers modulo $ p^{s} $, $ p $ is a prime and $ s $ is a positive integer.

Investigating the research trends within a scientific domain by analyzing semantic information extracted from scientific journals has been a topic of interest in the natural language processing (NLP) field. A research trend evaluation is generally based on the time evolution of the term occurrence or the term topic, but it neglects an important aspect—research publication latency. The average time lag between the research and its publication may vary from one month to more than one year, and it is a characteristic that may have significant impact when assessing research trends, mainly for rapidly evolving scientific areas. To cope with this problem, the present paper is the first work that explicitly considers research publication latency as a parameter in the trend evaluation process. Consequently, we provide a new trend detection methodology that mixes auto-ARIMA prediction with Mann–Kendall trend evaluations. The experimental results in an electronic design automation case study prove the viability of our approach.

Simonas Vainbergas, a teacher of Jewish primary schools in prewar Lithuania (1894?), was one of few his colleagues that actively collaborated with Lithuanian pedagogical journals. He published in them 11 papers in didactics of mathematics about teaching mathematics at primary schools. The said papers helped young teachers of primary schools to improve their qualification. There is a great probability that S. Vainbergas was a victim of holocaust.

Recently, there has been a growing emphasis on basic number processing competencies (such as the ability to judge which of two numbers is larger) and their role in predicting individual differences in school-relevant math achievement. Children's ability to compare both symbolic (e.g. Arabic numerals) and nonsymbolic (e.g. dot arrays) magnitudes has been found to correlate with their math achievement. The available evidence, however, has focused on computerized paradigms, which may not always be suitable for universal, quick application in the classroom. Furthermore, it is currently unclear whether both symbolic and nonsymbolic magnitude comparison are related to children's performance on tests of arithmetic competence and whether either of these factors relate to arithmetic achievement over and above other factors such as working memory and reading ability. In order to address these outstanding issues, we designed a quick (2 minute) paper-and-pencil tool to assess children's ability to compare symbolic and nonsymbolic numerical magnitudes and assessed the degree to which performance on this measure explains individual differences in achievement. Children were required to cross out the larger of two, single-digit numerical magnitudes under time constraints. Results from a group of 160 children from grades 1-3 revealed that both symbolic and nonsymbolic number comparison accuracy were related to individual differences in arithmetic achievement. However, only symbolic number comparison performance accounted for unique variance in arithmetic achievement. The theoretical and practical implications of these findings are discussed which include the use of this measure as a possible tool for identifying students at risk for future difficulties in mathematics.

Very recently, P. Saha et al. [A global optimality result in probabilistic spaces using control function. Optimization. 2021;70:2387–2400] studied the existence of best proximity points for Banach type ϕ-proximal contractions in the framework of Menger probabilistic metric spaces. In this paper, we present a simple proof of their main existence result which is based on a fixed point theorem for ϕ-contractive self-mappings in complete Menger PM-spaces due to B.S. Choudhury and K. Das [A new contraction principle in Menger spaces. Acta Math Sin. 2008;24:13791386]. [ABSTRACT FROM AUTHOR]

Computer-based interventions are being used more in the classroom. Student responses to these interventions often contribute to decisions making regarding important outcomes. It is important to understand the effect of these interventions within the context of the intervention as well as across related context. The current study examined the generalization of math fact fluency gains resulting from a computer-based intervention to paper-and-pencil performance. A total of 31 second grade students completed fluency drills on the computer or with paper and pencil. Pretest-posttest performance on both computer and paper and pencil for all students was evaluated using a doubly multivariate repeated measure ANOVA. Results indicated that gains achieved on the computer did not generalize to paper-and-pencil performance., (Copyright © 2012 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.)

The human capability to react or adapt to upcoming changes strongly relies on the ability to forecast them [...]

Perception is an individual's ability to respond, interpret, and distinguish a view of any information to a stimulus. So the aims of this study was to find out: (1) students' perceptions of the use of an equation editor in writing mathematical notation as assignments for calculus class I papers, (2) students' perceptions of writing calculus I paper assignments using the manual method (handwriting). The research subjects consisted of 16 students majoring in Extension Informatics Engineering (afternoon class) Semester I. The type of research was descriptive qualitative. Data collection techniques are interviews. The analysis stage is to analyze the results of the interviews. The results of the study concluded that: (1) 11 (eleven) students agreed to use the equation editor in writing calculus I paper assignments,the rest were still confused about the use of the equation editor; and (2) all students do not agree if the paper is written using the manual method (handwriting) because the results are not neat and take a long time.

After World War II, Hermann Druckrey and Karl Küpfmüller spent many months in allied internment camps in Germany. In camp Hammelburg, the scholars formed a research collaboration which resulted in two very important publications. Druckrey informed Adolf Butenandt about the co-operation in personal letters which have recently become accessible. Through this new source, the origins of the Druckrey-Küpfmüller papers of 1948-1949 have been confirmed and some further details have been added.

Recent developments in microscopy and image processing have made digital measurements on high-resolution images of fibrous materials possible. This helps to gain a better understanding of the structure and other properties of the material at micro level. In this paper SEM image segmentation based on mathematical morphology is proposed. In fact, paper models images (Whatman, Murillo, Watercolor, Newsprint paper) selected in the context of the Euro Mediterranean PaperTech Project have different distributions of fibers and fillers, caused by the presence of SiAl and CaCO3 particles. It is a microscopy challenge to make filler particles in the sheet distinguishable from the other components of the paper surface. This objectif is reached here by using switable strutural elements and mathematical morphology operators.

Paper waste in the mockups design with regular, irregular, and amorphous patterns is a critical problem in digital printing presses. Paper waste reduction directly impacts production costs, generating business and environmental benefits. This problem can be mapped to the two-dimensional irregular bin-packing problem. In this paper, an iterated local search algorithm using a novel neighborhood structure to detect overlaps between amorphous shapes is introduced. This algorithm is used to solve the paper waste problem, modeled as one 2D irregular bin-packing problem. The experimental results show that this approach works efficiently and effectively to detect and correct the overlaps between regular, irregular, and amorphous figures.

Tablet‐based technology has become a conduit for the administration of curriculum‐based measurement (CBM) tools. Using tablets to administer CBM probes has many advantages; however, little is known about how students perform on CBMs when administered via a tablet. The current investigation compared digits correct per minute obtained from 44 third‐grade students on CBM addition fluency probes administered via three different modalities. Students completed the probes using traditional paper and pencil, a tablet using their fingers to write the answer, or a tablet application using a keyboard to type the answer. A within‐subjects group design showed students performed significantly better on the tablet when using their finger to write the answer, even though most students (58%) indicated this was their least preferred modality. The discussion focuses on the implications for educators and the use of different CBM modalities for interindividual and intraindividual comparisons. Practitioner points: Third‐grade students responded to math facts faster when writing with their fingers on an iPad, even compared to paper and pencil.The results are inconsistent with other studies that found students were faster when using paper and pencil.Finally, most third‐grade students preferred answering addition facts with a pencil on paper. [ABSTRACT FROM AUTHOR]

Abstract In a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied a uniformly convex and 2-uniformly smooth real Banach space with the Opial property and best smoothness constant κ satisfying the condition 0 < κ < 1 2 $0