Search

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.

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.

The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states W ( N ) depends on the size N of the system. Here we propose a scaling expansion of the phasespace volume W ( N ) of a stochastic system. The corresponding expansion coefficients (exponents) define the universality class the system belongs to. Systems within the same universality class share the same statistics and thermodynamics. For sub-exponentially growing systems such expansions have been shown to exist. By using the scaling expansion this classification can be extended to all stochastic systems, including correlated, constraint and super-exponential systems. The extensive entropy of these systems can be easily expressed in terms of these scaling exponents. Systems with super-exponential phasespace growth contain important systems, such as magnetic coins that combine combinatorial and structural statistics. We discuss other applications in the statistics of networks, aging, and cascading random walks.

O presente trabalho avaliou a variabilidade amostral dos parâmetros da distribuição gama, relativos a séries mensais de precipitação pluvial, nas regiões de Campinas-SP e Pelotas-RS, que têm dados para os períodos de 1890-2006 e 1890-2005, respectivamente. Assim, os espaços amostrais considerados foram de 58, 39 e 29 anos para Campinas e 58 e 29 anos para Pelotas. As análises foram feitas usando o teste da razão da máxima verossimilhança. Os resultados apontaram significativas alterações amostrais. Não houve indicações de tendências contínuas (redução ou aumento) no regime mensal de precipitação pluvial na região de Campinas-SP. Em contrapartida, esse teste indicou, para a localidade de Pelotas-RS, tendência de elevação no regime desse elemento meteorológico ocorrida entre as amostras relativas aos anos de 1948 a 1976 e 1977 a 2005.The present work evaluated the sample variability of the Gamma distribution parameters fitted to monthly precipitation series in the regions of Campinas-SP and Pelotas-RS, which have data for the 1890-2006 and 1890-2005 periods, respectively. So, the sample spaces considered were of 58, 39 and 29 years for Campinas, and of 58 and 29 years for Pelotas. Analyses were done using the likelihood ratio test. The analyses showed significant sample alterations. No trend was detected in monthly precipitation series of the region of Campinas-SP. Increasing trends was detected in the monthly precipitation series of the region of Pelotas-RS considering the 1948 to 1976 and 1977 to 2005 samples.