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Criticism of some terms and symbols of school mathematics is presented, and recommendations are given. The problem of writing decimal fractions using a comma and the resulting semicolon when separating such numbers, which contradicts not only the international symbols of mathematics, but also the general rules of the Lithuanian language, is discussed separately. The incorrect use of the concept of an elementary event not only in schools, but also in universities, is discussed in more detail.

Copyright of Lietuvos Matematikos Rinkinys is the property of Vilnius University 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.)

Deep learning (DL) is an important enabling technology for intelligent manufacturing. The DL-based industrial image pattern recognition (DLBIIPR) plays a vital role in the improvement of product quality and production efficiency. Although DL technology has been widely used in the field of natural image, industrial image often has some mixed characteristics, such as small sample, imbalance, small target, strong interference, fine-grained, temporality and semantical, which reduce the feasibility and generalization of DLBIIPR. To solve this problem, this paper provides an overview of approaches commonly used in industry by enriching the sample space and limiting the hypothesis space. In order to improve the confidence of front-line workers in using DL models, the explainable deep learning (XDL) methods are reviewed, and a case study is used to verify the effectiveness of XDL. [ABSTRACT FROM AUTHOR]

The current literature on test equating generally defines it as the process necessary to obtain score comparability between different test forms. The definition is in contrast with Lord's foundational paper which viewed equating as the process required to obtain comparability of measurement scale between forms. The distinction between the notions of scale and score is not trivial. The difference is explained by connecting these notions with standard statistical concepts as probability experiment, sample space, and random variable. The probability experiment underlying equating test forms with random scores immediately gives us the equating transformation as a function mapping the scale of one form into the other and thus supports the point of view taken by Lord. However, both Lord's view and the current literature appear to rely on the idea of an experiment with random examinees which implies a different notion of test scores. It is shown how an explicit choice between the two experiments is not just important for our theoretical understanding of key notions in test equating but also has important practical consequences. [ABSTRACT FROM AUTHOR]

Ramalingam Shanmugam,1 Karan P Singh2 1School of Health Administration, Texas State University, San Marcos, TX, 78666, USA; 2Department of Epidemiology and Biostatistics, School of Community and Rural Health, The University of Texas Health Sciences Center at Tyler, Tyler, TX, 75708, USACorrespondence: Karan P SinghDepartment of Epidemiology and Biostatistics, School of Community and Rural Health, The University of Texas Health Sciences Center at Tyler, Tyler, TX, 75708, USAEmail karan.singh@uthct.eduBackground: Challenges to manage, mitigate, or prevent the COVID-19’s pandemics are felt by medical, healthcare professionals and governing agencies. Health researchers conduct survey among the citizens to capture their opinion on COVID-19. In such surveys like in Hanafiah and Wan (2020), structural-zero (different from sampling zero) category occurs as they question about perception, knowledge, and communication regarding COVID-19.Materials: The data were collected in a survey conducted among Malaysians by Hanafiah and Wan regarding COVID-19. The survey focused on people’s response about the public communication, knowledge, and perception.Methods: One of the four question categories in the survey is mutually exclusive with the other three questions. Consequently, there will be no entry in that category. Such group is called structurally zero category in the literature. The literature never probed the migrative split to other categories of the unknown proportion belonging to the structural zero category. In this article, the probability-based new and innovative method configures what proportion in that mutually exclusive category and it is the essence of our method.Results: The mutually exclusive nature of subquestions manufactured structural zero in their data. A careful analysis of the data has created so far unknown probability concepts in the literature, which we named as “Exodus probabilities” in this article. Its discovery and utility are illustrated and elaborated with application in COVID-19. This methodology is also useful in applications in engineering, epidemiology, marketing, communication networking, etc.Conclusion: What is quite novel about the discovery of the exodus probability in this article is the evolution of the concepts from the structural-zero category. In such situation, when a category is eliminated, the proportions of the sample might have uncommunicatively transited to other viable categories and our research question is all about configuring their proportions. This is an innovative approach.Keywords: public knowledge, perception, communication, sample space, dependent probabilities, Venn layout, odds, odds ratio, survey outcomes

This paper proposes an approach to predicting fatigue crack growth under mixed-mode loading based on improved Gaussian process. In terms of analyzing the theoretical background for fatigue crack growth, a corresponding finite element model is built to generate sufficient simulation data, which is utilized to obtain the key parameters (e.g., stress intensity factor) for the fatigue crack growth process. And then, a Gaussian process model is achieved to meet the condition that the stress intensity factor is a nonlinear continuous change in crack growth, especially for mixed-mode loading. Following, an idea of local sample densification method is implemented to improve Gaussian sample generation process according to the simplified model of the crack growth path. Based on the above investigation, a fatigue crack growth prediction model using the improved Gaussian process is finished, which is subsequently verified through the test data of lower bainite steel (SCM435) material. The results show that the proposed approach has better computational accuracy and efficiency than the traditional finite element method in predicting fatigue crack growth under mixed-mode loading.

This study aims to analyze the reasoning that children and adults with the same school level use to assess and justify the fairness of games, considering aspects of probability such as randomness, sample space, and comparison of probabilities. Data collection included a Piagetian clinical interview based on games of chance. The results showed participants' judgments about the fairness of the games depended mainly on the understanding of independence of events, analysis of the sample space, and perception of proportionality when comparing probabilities, and indicated they may have misunderstandings about these ideas. The similar low performance of adults and children on probabilistic reasoning tasks, indicates that the maturity and experience of the adults were not enough to develop appropriate probabilistic reasoning and to instrumentalize it to assess the fairness of a game consistently. Thus, teaching interventions to expand and consolidate students' learning in the field of probability are recommended and the activities presented in this study may serve as a basis for such interventions. [ABSTRACT FROM AUTHOR]

We present an exploratory study of solving probabilistic tasks proposed to a sample of 55 primary school 6th grade Costa Rican children on comparison of probabilities and the construction of the sample space, analysing their strategies and errors. Comparing the results with previous investigations, an improvement is observed in the item in which the comparison of favorable and possible cases can be applied, and where the comparison of areas is necessary; however, there were no differences in the item in which the order in which the favorable cases are located is introduced as a distractor. The sample space is generally correctly built in the cases of possible and equiprobable event, but not in those of impossible or certain events. [ABSTRACT FROM AUTHOR]

Life data frequently arise in many reliability studies, such as accelerated life tests studies. This paper considers the part of life data where failure and censoring observations may exist. To develop statistical methods and theory for the analysis of these data, a new approach was proposed to obtain the exact lower and upper confidence limits for the mean life of the exponential distribution with Type-I censoring data. It is assumed that the acceleration factor is a random variable, and that the distribution of the acceleration factor is known from some empirical information or the meta analysis. A method for constructing the lower and upper confidence limits for the parameter based on an ordering relation among the sample space was proposed. Simulation studies and analyses of two examples suggest that the proposed method performed well. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador 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.)

For the past 15 years, pre-university students in many countries including the United States have encountered data analysis and probability as separate, mostly independent strands. Classroom-based research suggests, however, that some of the difficulties students have in learning basic skills in Exploratory Data Analysis stem from a lack of rudimentary ideas in probability. We describe a recent project that is developing materials to support middle-school students in coming to see the “data in chance” and the “chance in data.” Instruction focuses on four main ideas: model fit, distribution, signal-noise, and the Law of Large Numbers. Central to our approach is a new modeling and simulation capability that we are building into a future version of the data-analysis software TinkerPlots. We describe three classroom-tested probability investigations that employ an iterative model-fit process in which students evaluate successive theories by collecting and analyzing data. As distribution features become a focal point of students’ explorations, signal and noise components of data become visible as variation around an “expected” distribution in repeated samples. An important part of students’ learning experience, and one enhanced through visual aspects of TinkerPlots, is becoming able to see things in data they were previously unable to see.