A DISCUSSION ON THE PHYSICAL INTERPRETATION OF MEASUREMENTS OF TRIBOLOGICAL WEAR

Physical sense and practical significance of major measurements of tribological wear are analysed here. Definitions and methods of assessing these measurements are proposed on the basis of the laws of energy and mass conservation. Contributions of energy and displacement of particular friction forces corresponding to each element of a friction couple are addressed. Energy expenditure that causes wear is introduced into the definition of wear resistance. Planning and thermodynamic analysis of a tribological experiment and the application of thermodynamic concepts and quantities to the description and the interpretation of results are recommended. The author believes application of wear measures that have an unequivocal physical interpretation will limit problems with the incomparability and the irreproducibility of tribological results and issues with transferring them to real objects.

Interface Models in Coupled Thermoelasticity

This work proposes new interface conditions between the layers of a three-dimensional composite structure in the framework of coupled thermoelasticity. More precisely, the mechanical behavior of two linear isotropic thermoelastic solids, bonded together by a thin layer, constituted of a linear isotropic thermoelastic material, is studied by means of an asymptotic analysis. After defining a small parameter ε, which tends to zero, associated with the thickness and constitutive coefficients of the intermediate layer, two different limit models and their associated limit problems, the so-called soft and hard thermoelastic interface models, are characterized. The asymptotic expansion method is reviewed by taking into account the effect of higher-order terms and defining a generalized thermoelastic interface law which comprises the above aforementioned models, as presented previously. A numerical example is presented to show the efficiency of the proposed methodology, based on a finite element approach developed previously.

Preservice Mathematics Teachers' Representation Transformation Competence Levels in the Process of Solving Limit Problems

In this study, representations used by preservice mathematics teachers in the process of solving limit problems were determined, the inter-representation transformation competence levels were investigated and the relationship between them was examined. In this context, “Limit Representation Transformation Test” with a reliability of .908 was administered to 50 preservice teachers attending to a state university in the Central of Turkey. Preservice teachers had most difficulty in solving problems that had verbal representation inputs, especially they achieved low performances in transformation from verbal to numerical representation. Although, in general, they achieved the highest performance in the problem that had numerical representation input, they also achieved very high performances in the problems that had graphical and algebraic representation inputs. Specifically, they performed very well in the problems that required transformation from an algebraic representation to a verbal representation. Moreover, significant positive correlations were found among preservice teachers’ representation transformation competence levels.

A Definite Explanation of the Concept of Limit in Teaching

The limit idea is the basic idea of calculus. Almost all concepts in mathematical analysis are inseparable from the limit, but the limit is a concept that is difficult to understand accurately. By assuming that there is a certain point closest to the limit value, this paper provides a reasonable explanation for the infinitesimal paradox and a new answer to the question why the limit value is accurate in teaching. At the same time, this method is applied to the derivative and used to understand a common practical problem in mathematics. The analysis shows that this method is effective for the accurate understanding of limit problems.

Preservice mathematics teachers’ competencies in the process of transformation between representations for the concept of limit: A qualitative study

In this study, external representations and the problems encountered related transformation process between representations towards limit concept were investigated. "Limit Representation Conversion Test" was administered to 41 preservice mathematics teachers studying at a state university in central Turkey during 2018–2019 academic years. In this study, which was designed with the case study model, which is one of the qualitative research models, the data were analyzed by content analysis. Unstructured interviews were made with preservice mathematics teachers whose explanations were insufficient or differed and the problems encountered were determined. It was observed that preservice mathematics teachers had most difficulties in the verbal representation type questions. It was revealed that preservice mathematics teachers who gave the wrong answers mostly had deficiencies in the concept and the process and could not fully understand the limit problems. It was determined that preservice mathematics teachers had difficulties in knowing the concept of limit point, determining the function and interpreting verbal data. It was seen that preservice mathematics teachers who proceeded towards the concept and process answered wrong due to mathematical operations errors and carelessness. When the wrong answers were examined, it was observed that errors were gathered under the themes "lack of content knowledge" and "lack of reading comprehension" for verbal type input; under the theme "carelessness" for graphical type input; under the theme "lack of content knowledge" for algebraic and numerical type input.

The Group Nurturance Inventory - Initial Psychometric Evaluation Using Rasch and Factor Analysis

This paper describes the development and psychometric evaluation of a behavioral assessment instrument primarily intended for use with workgroups. The instrument is based on the Nurturing Environments framework which describes four domains important for health, well-being, and productivity; minimizing toxic social interactions, teaching and reinforcing prosocial behaviors, limiting opportunities for problem behaviors, and promoting psychological flexibility. In this article, questionnaire data of perceived frequency of behaviors relevant to nurturance are analyzed using both classic and modern test theory. The results indicate a 23-item instrument that best fit a bifactor model with a general nurturance factor explaining 87.1% of the variance in unit-weighted total scores, and three specific factors (toxic behavior, prosocial behavior, and behaviors that limit problems). Rasch analysis showed that the response scale works adequately, item fit is satisfactory, and no significant differential item functioning. Targeting is skewed towards lower levels of nurturance and item thresholds are distributed over the range of participant abilities. The instrument is freely available to use and adapt under a CC-BY license and intended as a tool that is easy for any group to use and interpret to identify key behaviors to improve their psychosocial work environment. By using a two-dimensional assessment with ratings of both frequency and perceived importance of behaviors the instrument can help facilitate a participatory group development process. We provide recommendations for how to work with a group based on their data, and how to optimize the measurement precision further. The next steps in research are suggested, such as group-level analysis, collecting observational data, and validation against concrete longitudinal outcomes. This instrument could help promote transparent assessment practices in organizational and group development.

Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth

In this paper, we prove the multiplicity of nontrivial solutions for a class of fractional-order elliptic equation with magnetic field. Under appropriate assumptions, firstly, we prove that the system has at least two different solutions by applying the mountain pass theorem and Ekeland’s variational principle. Secondly, we prove that these two solutions converge to the two solutions of the limit problem. Finally, we prove the existence of infinitely many solutions for the system and its limit problems, respectively.

Faktor Penyebab Siswa tidak dapat Menyelesaikan Soal Materi Limit Fungsi Aljabar

Indikasi banyaknya jumlah siswa yang tidak dapat menyelesaikan soal limit fungsi aljabar yang diberikan di kelas XI MAN 1 Pekanbaru, menggambarkan adanya permasalahan siswa. Penelitian ini bertujuan untuk menganalisis faktor penyebab siswa tidak menyelesaikan soal limit fungsi aljabar, khususnya siswa di kelas XI SMA/MA. Metode penelitian yang digunakan adalah penelitian deskriptif kualitatif. Subjek pada penelitian ini adalah 22 orang siswa kelas XI IIS 4 MAN 1 Pekanbaru tahun pelajaran 2019/2020. Instrumen yang digunakan dalam penelitian ini adalah angket untuk mengetahui faktor penyebab siswa tidak menyelesaikan soal limit fungsi aljabar berupa faktor fisiologis, faktor psikologis, faktor materi, faktor lingkungan sekolah, faktor lingkungan keluarga, dan faktor lingkungan masyarakat. Hasil analisis menunjukkan bahwa faktor terbesar yang menyebabkan siswa tidak menyelesaikan soal materi limit fungsi aljabar yaitu faktor materi (50%) dan yang paling sedikit adalah faktor fisiologis (18%). Hasil penelitian ini dapat menjadi rujukan bagi guru untuk dapat lebih menekankan konsep limit fungsi dalam bentuk akar dengan menggunakan strategi dan model pembelajaran yang sesuai dengan karakteristik siswa dan kebutuhan materi.Students' Causative Factor Unable to Solve The Algebraic Limit Function’s ProblemsAbstractThe indication that many of the students were not able to solve the algebraic function limit’s problems given in class XI MAN 1 Pekanbaru, it pointed out that there were some student's problem. This research aims to analyze the factors that caused many of the students were not able to solve the algebraic function limit’s problems, especially students in class XI SMA/MA. The method used in this research was descriptive qualitative research. The subject of this research were 22 students of class XI IIS 4 MAN 1 Pekanbaru in the academic year 2019/2020. The instrument used in this research was a questionnaire to determine the factors caused students were not able to solve the algebraic function limit problems in the form of physiological factors, psychological factors, topic factors, school environmental factors, family environmental factors, and community environmental factors. The analysis results showed that the biggest factor caused students were not able to solve the problems about algebraic function limit was the topic factors (50%) and the least factor was the physiological factors (18%). The results of this study can be a reference for teachers to be able to emphasize the concept of limit functions in the form of roots by using strategies and learning models that are in accordance with student characteristics and material needs.