Mathematical Terms Research Articles

Teaching the Analysis of Newton’s Cooling Model to Engineering Students

To apply mathematical methods to physical or other real life problem, we have to formulate the problem in mathematical terms. It means that, we have to construct the mathematical model for the problem. Many physical problems shows the relationships between changing quantities. The rates of change are represented mathematically by derivatives. In this case the mathematical models involve equations relating an unknown function and one or more of its derivatives. These equations are the differential equations. In this article, teaching the analysis of Newton's cooling model to engineering students is presented as one of the applications of separable differential equations.

Students talk about difficulties they have in solving math problems

The ability to solve students' mathematical problems cannot be diagnosed clearly just by using test questions; it must also be seen by looking at students' responses to the problem-solving process. As a result, the purpose of this study is to investigate students' mathematical problem-solving skill as well as their responses to the problem-solving process. This study is descriptive-qualitative in nature. Three junior high schools (SMP) in Aceh participated in this study, with 76 class VIII students serving as research subjects. Tests, observations, and interviews were used as data collection techniques. Quantitative data were descriptively analyzed using proportions, while qualitative data were descriptively analyzed using coding. The results showed that 25 percent of students wrote down what was known and asked, which was an indication of problem comprehension; 21 percent of students were able to devise problem-solving strategies; and 15 percent of students had done calculations correctly. correct, 11 percent of students checked their answers again. Based on the responses given by students, there were some difficulties experienced by students when solving math problems, namely difficulty understanding reading texts, using mathematical terms, making problem connections, making decisions, uncertainty in solving problems, time, carelessness, and boredom. The findings of this study are expected to serve as a resource for teachers and education practitioners in developing focus, discipline, and patience in problem solving and selecting learning models appropriate to the needs of their students.

Numerical study of the parametric optimization of the forced oscillation frequencies of the shell of a minimal surface on a trapezoidal contour under thermal and power loading

This research paper discusses various methods and approaches to the optimal design of structures. Methods for solving the optimization problem can be divided into two large groups. The first group includes methods that are based on the use of the necessary conditions for the extremes of the objective function. The second group consists of mathematical programming methods: linear, convex, dynamic programming, and random search. In mathematical terms, optimal design problems are optimization problems - the search for an extremum of the objective function and the values of the parameters at which the extremum is achieved. The choice of the optimality criterion is one of the main problems of optimal design. The most widely developed problems are those that have the optimization criterion of weight or volume of the structure while satisfying the conditions of strength, rigidity and stability.
 Optimal design problemsare also divided into three large groups. The first group is parametric optimization problems, which involve the optimization of one or more parameters, called design variables, to minimize or maximize the objective function. The second group is topological optimization, in which unnecessary material is discarded, where the Mises stress is zero, thereby minimizing the objective function. The third group is optimization of the shape of the object under study, when the shape corresponds to internal forces, the shell with the smallest area is modeled on a given cone (shells of minimal surfaces), as well as methods of applied geometry, where the surface shape is modeled for a certain load.
 To perform the parametric optimization of the forced vibrations of the shell of the minimum surface on a trapezoidal contour, the objective function is the weight of the spatial structure. The variables in the parametric optimization problem are the thickness of the finite elements from 1 to 100 mm. The structure constraint is imposed on the first forced oscillation frequency of 0.250 Hz. This type of problem is used to prevent resonance from process equipment that can affect the natural frequencies of the structure under external load.Subject of this study is an interesting applied problem for construction mechanics, as it is the first time to display the application of two types of optimization on one research object.
 The results of a numerical study of the parametric optimization of the minimum surface shell on a trapezoidal cage under thermal power loading. The parametric optimization helped to reduce the weight of the shell by 13.4%, which is 1810 kg of sheet steel. The first forced oscillation frequency meets the constraint of the optimization calculation. We constructed 10 forced vibration frequency shapes of the shell before and after optimization, and also presented the distribution of the shell thickness after the optimization calculation.

Interdisciplinary Studies in Music Research the Substance of Study and Implications of Fine Arts, Mathematics, and Philosophy

Interdisciplinary studies in music education research can integrate various disciplines that can help enrich the understanding of fine arts, mathematics, and philosophy. In terms of fine arts, this approach can help students understand the relationship between fine arts and music to enrich their experience in understanding and producing works of art. In terms of mathematics, mathematical elements found in music theory can be applied in music education, so that students can understand how mathematical principles can be applied in the arts. In terms of philosophy, an understanding of ontology, epistemology as well as axiology can help students consider the meaning and value of musical artworks. Interdisciplinary study in music research implies that students can gain a richer and more multidimensional learning experience, and develop skills and understanding that are holistic and beneficial to their future lives.

Development and initial validation of a mathematics-specific spatial vocabulary scale

This study describes the development and initial validation of a mathematics-specific spatial vocabulary measure for upper elementary school students. Reviews of spatial vocabulary items, mathematics textbooks, and Mathematics Common Core State Standards identified 720 mathematical terms, 148 of which had spatial content (e.g., edge). In total, 29 of these items were appropriate for elementary students, and a pilot study (59 fourth graders) indicated that nine of them were too difficult (< 50% correct) or too easy (> 95% correct). The remaining 20 items were retained as a spatial vocabulary measure and administered to 181 (75 girls, mean age = 119.73 months, SD =4.01) fourth graders, along with measures of geometry, arithmetic, spatial abilities, verbal memory span, and mathematics attitudes and anxiety. A Rasch model indicated that all 20 items assessed an underlying spatial vocabulary latent construct. The convergent and discriminant validity of the vocabulary measure was supported by stronger correlations with theoretically related (i.e., geometry) than with more distantly related (i.e., arithmetic) mathematics content and stronger relations with spatial abilities than with verbal memory span or mathematics attitudes and anxiety. Simultaneous regression analyses and structural equation models, including all measures, confirmed this pattern, whereby spatial vocabulary was predicted by geometry knowledge and spatial abilities but not by verbal memory span, mathematics attitudes and anxiety. Thus, the measure developed in this study helps in assessing upper elementary students' mathematics-specific spatial vocabulary.

Dynamical behaviour of discrete logistic equation with Allee effect in an uncertain environment

The Allee effect refers to a natural occurrence where the average individual fitness of a population or species is correlated with population size or density. A demographic Allee effect having a threshold population size constitutes a strong Allee effect. On the contrary, it is called the weak Allee effect when it lacks an adequate population size. This paper revisits a single-species logistic growth model under the combined impacts of the strong Allee effect, discrete population dynamics, and an impreciseness phenomenon. Several existing literatures on models with deterministic and continuous time frames address the Allee effect’s significance. The population growth model may disobey the continuous time frame of dynamics. The difference equation may be a fruitful substitute for the traditional differential equation to trace a discrete logistic population growth model phenomenon. Also, initial information and the population growth model’s associated coefficient may sometimes be vague. Fuzzy logic is a suitable tool to describe such vagueness in mathematical terms. We have discussed the proposed model through the different fuzzy scenarios to realize the relative impact of different fuzzy parameters. This paper also includes the studies of equilibrium points and their corresponding stability analysis for each case. This paper differs from the existing literature on Allee effect in that it contributes an alternative approach to manifest the logistic growth model in a discrete time frame under uncertainty. Numerical results show the fuzzy impact of different parameters of the model. One of the significant insights of the outcome is that the extinction or highly growing population depends on the parameter’s values rather than the population size only.

Multi-layer additive tensor decomposition of infrared video for titanium alloy tensile testing

Infrared video (in mathematics terms, tensor) has been widely used in the tensile testing of metallic materials, such as titanium alloy and steel. The infrared video of the tensile testing process can effectively and efficiently determine the properties of metallic materials, e.g., Young’s modulus, Poisson’s ratio, yield strength, etc. The infrared video with structural properties, such as smoothness and sparsity, can be used to characterize the tensile testing process. To extract the features in the infrared video with structural properties, we propose a multi-layer additive tensor decomposition (MLATD) method based on regularization tensor regression for tensile testing. It decomposes a tensor into three classes of components: the multi-smooth layers (including background and foreground), the sparse layers (including between-tensor and in-tensor), and the noise layer. The scree plot is proposed to determine the number of multi-smooth layers, which is a downward curve of the difference between the smooth layers and the sparse layer. The alternating direction method of multipliers (ADMM) algorithm is proposed to solve the proposed method. The decomposition results of the simulation data and real-world case study revealed that the proposed method outperforms the existing state-of-the-art methods.

Digital Game Design Process for the Concept of Area

Designing a digital game using method, activities, contexts and problems which have been proved to be effective in mathematics education for a long time, will increase the effectiveness and success of the game. The purpose of this study was to reflect the digital game design process for the area concept. The design-based research method was used in the study. The digital game was developed by the researchers in a circular design process including the design, analysis, evaluation, and revision. In the design process, preliminary concepts, skills, and the way to teach them were determined with the help of the literature on the concept of area aimed to be taught via the digital game, and then the mechanics and context of the game were designed under the supervision of three instructors of mathematics. After the design stage, fifteen students were asked to play the game in order to evaluate it. The findings showed that it is important to refer to the literature and to involve mathematics instructors in the process of creating a digital game by considering how such a game should be in terms of mathematics. Getting help from students with different socio-economic levels during the game design phase will help the development of the educational and game structure of the game.

Semantic and structural challenges of translating modern English agro-engineering terminology into Ukrainian

The study analyzes semantic and structural peculiarities of translating modern English agro-engineering terminology. Agro-engineering terms represent the up-to-date level of agriculture development noted for advanced mechanization, application of various technical processes, new technologies, etc., this causing additional translation problems. Besides, agricultural terminology encapsulates field-specific lexis as well as mathematical, mechanical, biological and general scientific terms. Translation difficulties are closely related to lingual characteristics of agro-engineering terms (structural peculiarities, synonymy, homonymy). Playing a significant role in forming this segment of professional lexicon, multi-component units are difficult to translate due to their length and non-prepositional bonds in most cases. The main research methods include comparative and contrastive analysis as well as the quantitative method. The results obtained reveal that a variety of techniques applied to translating English agro-engineering terms into Ukrainian include equivalence, analogue, descriptive techniques, transliteration, grammatical and lexical transformations. Yet, the most frequent technique is equivalence. Application of different translation techniques in multicomponent phrases can cause inconsistences in the number of components in a terminological phrase in a target language. The authors suggest an algorithm of English-Ukrainian translation of agro-engineering multicomponent terms. The paper is intended for a wide range of specialists interested in translating agro-engineering texts, teaching ESP, students of translation departments and experts in the relevant field of knowledge.

The Dynamic Vectors-Based Attention Model for Chinese Mathematical Term Extraction

Term extraction aims to extract domain-specific terminology from documents. Secondary school mathematics terminology plays a guiding role in the learning and teaching of secondary school mathematics. We found that it needs to be more corpus in this field and that there are two main issues in extracting the terms from the middle school mathematics text: polysemy of one character problem and nested terms problem. Accordingly, we have constructed a secondary school mathematics corpus and proposed a model to resolve these problems, termed BERT-LLA-CRF. Using pre-training to obtain dynamic word vectors to improve the model’s understanding of text semantics and solve the problem of multiple meanings of one word, the proposed model integrates attention mechanisms and Chinese character information to solve the nested terminology problem. The experiment results show that the proposed model effectively solves those problems and achieves good middle-school mathematics term extraction results.

Modeling and numerical analysis for mechanical characterization of soft tissue mechanism applying inverse finite element technique

Tissue-mimicking materials [e.g., polyvinyl alcohol cryogel (PVA-C)] are extensively used in clinical applications such as tissue repair and tissue engineering. Various mechanical testing techniques have been used to assess the biomechanical compatibility of tissue-mimicking materials. This article presents the development of inverse finite element (FE) techniques that are solved using numerical optimization to characterize the mechanical properties of PVA-C specimens. In this study, a numerical analysis where the displacement influence factor was employed in conjunction with a linear elastic model of finite thickness was performed. In the analysis, the effects of Poisson's ratio, specimen aspect ratio, and relative indentation depth were investigated, and a novel mathematical term was introduced to Sneddon's equation. In addition, a robust optimization algorithm was developed in MATLAB that utilized FE modeling for parameter estimation before it was rigorously validated.

EFEKTIVITAS MODEL PROBLEM BASED LEARNING METODE TUTOR SEBAYA BERBANTUAN CARD PROBLEM TERHADAP HASIL BELAJAR MATEMATIKA

Learning mathematics is frequently regarded as difficult by students, resulting in a lack of problem-solving ability. This problem occurred at SMPN 8 Jember, where, based on the results of observations, grade VII students have low problem-solving skills due to the conventional learning model used. If the problem is not addressed immediately, it is feared that it will continue with the next generation of students. This study aims to determine the effectiveness of PBL model of the peer tutor method assisted by card problems on mathematics learning outcomes in seventh-grade junior high school students with quadrilateral material. This research includes a quasi-experimental design. The data collection technique uses pretest and posttest tests to be tested with the paired samples T test and regression test (ANOVA) on the SPSS application. The results of the paired samples T test in the experimental class gave a sig value of 0.000, while in the control class it was 0.003. The sig value for the regression test for the experimental class is 0.014, while the sig value for the control class is 0.033. These results show that the PBL model of the peer tutor method assisted by card problems is more effective and influential than the PBL model of the peer tutor method to improve student mathematics learning outcomes. The study concludes that incorporating card problem learning media into the PBL model of the peer tutor method produces effective results in terms of quadrilateral material mathematics learning outcomes.

Exploration of Students’ Strategic Competence in Higher-Order Thinking Skills Based Linear Programming Topic in terms of Mathematics Learning Styles

This study is descriptive-explorative in nature employing a mixed-method approach and aiming to know students’ strategic competence in HOTS-based linear programming topic in terms of mathematics learning styles. There were 6 subjects in grade XI in Polewali Mandar that represent each learning style-strategic competence category. The instruments were questionnaire, test, and interview guidance. The questionnaire and test scores were analyzed quantitatively whereas test answers and interview results were analyzed qualitatively. The results show that of the 58 students who answered the test, they had low strategic competence in average also lack ability in each component. Visual learners are unable to formulate problem, incorrect in representing problem and unable to solve it correctly, tend to misinterpret verbal information and to involve visual presentations. An auditory learner formulated problem, however, the auditory learners are not completely correct in representing problem and unable to solve it correctly, tend to narrate the strategy, and are the best in interpreting verbal information. Meanwhile, kinesthetic learners are unable to formulate problem, not completely correct in representing problem and unable to solve it correctly, are the best in problem representation approach, but tend to be rigid in doing the strategy.

Advantages of Using Geogebra Software when Examining the Flow and Drawing a Graph of a Function

For a long time, the term function has been treated as a mandatory topic in mathematics curricula around the world. It aims to emphasize the importance of this topic of mathematics in higher education, at technical faculties. In addition to the classic way of learning blackboard and chalk, today all over the world a variety of interactive mathematical software is often used in the study of the topic functions. The software helps students to learn how to recognize functions, to examine their properties, and draw them accurately. In this paper, the importance of the mathematical term function in higher education at technical faculties is stated. It also lists the ambiguities that students face when mastering the topic of functions. Then, software for drawing graphs of functions (material that is taught in the subject Mathematics 1 at technical faculties) is listed to help students master that material more easily. Finally, a comparison is made in the results of the final exams in Mathematics 1, before students are recommended to use GeoGebra and after using the software. A conclusion is drawn from the results and the advantages of using the mathematical software are presented.

PRODUCTIVITY OF SELECTED SUFFIXES IN THE TERMS OF MATHEMATICS

The article deals with the analysis of mathematical terms, i.e. simple nouns. Complex terms are avoided in order to prepare a detailed lexico-grammatical analysis. The research examines the term formation within the word class of nouns. Origins of the English and Slovak terms are analysed, described and compared. Latin and Greek languages are languages of science for the English language. The original languages of terms in both languages. Furthemore, Slovak terminological equivalents are compared with the English ones in term preference the Latin/Greek term or the native term if exists. According to term formation processes, the following suffixes representing bound morphemes are analysed: -er, -or, -ion. The terms formed by affixation using the selected suffixes are compared with the Slovak counterparts in terminology of mathematics. Terms are analysed according to principles for term formation. The following principles should be followed in the formation of terms and appellations, as far as possible and as appropriate to the language: transparency; ⎯ consistency; ⎯ appropriateness, linguistic economy; ⎯ derivability and compoundability; ⎯ linguistic correctness; ⎯ preference for native language. Subject of analysis are terms taken from the Slovak National Corpus 10.0, i.e. English –Slovak Parallel Corpus 4.0 en, Slovak –English Parallel Corpus 4.0 sk and the British National Corpus. In the research, electronic corpora are applied. They use mathematical ad statistical methods to evaluate e.g. occurrence, frequency, collocability of words. The previous mentioned methods are taken into consideration and help to prepare the effective, precise and objective analysis of the planned analysis. The research is based on both languages and comparison of terms in both parts of the corpus. Specific trends and tendencies in the strategies of term formation are analysed. Descriptive method is used and the methods of quantitative and qualitative analysis are applied. Due to analysis of two languages, contrastive and comparative approaches are entailed. Terminology records of terms are examined from lexico-grammatical point of view and on the basis of term-formation tendencies in each analysed language. i.e. Slovak language and English language. Records include entry, identification number, reference to the term, synonyms, subject field, formula, abbreviation, context, reference to the context, definition, reference to the definition. 

Integration of STEAM in Teaching Modern Geometry through Batik Motifs Creation with Algebraic Surfaces

This paper explains teaching modern geometry for schools using software called Surfer and converting the algebraic surfaces into Batik motifs as one example of teaching mathematics with the integration of STEAM. Typical algebraic surfaces known in schools were, for example, cylinders and spheres which are identified as traditional geometry in this article. On the other hand, other geometrical objects that are not solely identified as traditional ones are called modern geometrical objects. The objects addressed here are governed by multiple algebraic surfaces and existed in the software called Surfer. The software is used for students to learn traditional geometry initially. After knowing how the software Surfer is doing, the software can be used for drawing more complex geometrical objects that are named to be modern geometry. This software is introduced for students in middle schools until students in the university such that technology and art are immersed in learning geometry. In this research, the activity involved creating a Batik piece which was a local textile in Indonesia based on algebraic surfaces created with Surfer. There were two methods of presenting the motif, these are after drawing the algebraic surfaces, students copied the surfaces into textiles using drawing Batik procedures. In the second method, students received some prototypes of algebraic surfaces and converted them into new patterns which were illustrated on a special paper for a copper stamp prototype later on. Using geometry as the routine topic which must be learned by any level of students in learning mathematics, the learning, innovation skills, and technology skills are direct educational values that are targeted by the activities with the approach presented in this article. The educational value is not only for the sake of mathematics and its content but also for integrating mathematics with other fields and exploring mathematical terms such that STEAM is introduced in this sense. The article here has addressed learning geometry by combining technology, art, and creating products to the related geometrical studied objects to develop learning skills, innovative skills, and technology skills that are educational values required skills in 21st-century education.

Application development of dictionary of mathematical terms as a learning medium

In mathematics learning in schools, teachers only focus on teaching the application of formulas in mathematical problems. However, it is not realized that students find it challenging to participate in learning because they need to learn the meaning of terms and symbols in mathematics. As a result, a decrease in student mathematics learning outcomes is inevitable. Therefore, researchers develop learning media in the form of feasible, effective, and practical applications to improve student mathematics learning outcomes. The method used is Research and Development (R&D) with 4D stages designed into 3D. The subjects of this study were 35 students from class XII IPA 3 MAN Batu Bara with instruments in the form of questionnaires and tests. The results of this study showed a percentage of 95.83% of media experts, 90% of material experts, and 96.875% of lesson teachers who represented that the product was considered feasible and practical to use. The N-Gain test results showed the effectiveness of the product by 0.8. So, the application can be used in learning as a viable, effective, and practical medium

Aggregating disjoint partial sub-orders – an internal logistics application

The problematic addressed in this work concerns an internal logistics issue that arises in warehousing. It first concerns the aggregation of a several ordered flows of loads (cartons, totes, containers, etc.) into a single flow, called the load sequencing problem. Then, this flow should be injected into the system at a maximal throughput, which gives the load injection problem. From the theoretical perspective, the load sequencing problem belongs to the class of partial-order aggregation problems, known to be NP-Hard. We describe a use-case application in logistics and formulate it in mathematical terms as a specific partial-order aggregation problem, namely disjoint partial sub-orders aggregation. We then present two exact solution methods in detail, one based on integer linear programming and the other using dynamic programming combined with a Branch & Cut scheme. All methods perform very well for randomly generated industrial instances. At the end, we provide a heuristic based on the dynamic programming algorithm. This heuristic is implemented for industrial use and gives near-optimal solutions in a very short computation time. The load injection problem falls in the category of scheduling problem (Job shop problem). In practice, this comes to compute the injection dates of loads in the collector with goal of ensuring a maximal debit exit flow with respect to the capacity of the system. We provide the formula for the injection date which achieves maximal debit exit flow. With respect to the application in hand, the proposed method outperforms the existing used method in terms of flow management and brings in practice a significant increase (up to 20%) of a number of loads proceeded for the same amount of time. Our findings are supported by numerical results.

NOTE ON THE THREE MAIN THEOREMS OF THE MULATU NUMBERS

The Mulatu numbers were studied [1] and [2]. The numbers are sequences of numbers of the form: 4,1, 5,6,11,17,28,45... The numbers have wonderful and amazing properties and patterns. 
 In mathematical terms, the sequence of the Mulatu numbers is defined by the following recurrence relation: 
 In [1] and [2] some properties and patterns of the numbers were considered. In this paper, we investigate additional properties and patterns of these fascinating numbers. Many beautiful mathematical identities involving the Mulatu numbers in relation with the two celebrity numbers of Fibonacci numbers and the Lucas numbers will be more explored. 
 2000 Mathematical Subject Classification: 11

A NOTE ON SOME INTERESTING THEOREMS OF THE MULATU NUMBERS

The Mulatu numbers were studied [1] and [2]. The numbers are sequences of numbers of the form: 4, 5,6,11,17,28,45...The numbers have wonderful and amazing properties and patterns.In mathematical terms, the sequence of the Mulatu numbers is defined by the following recurrence relation: In [1] and [2] some properties and patterns of the numbers were considered. In this paper, we investigate additionalproperties and patterns of these fascinating numbers. Many beautiful mathematical identities involving the Mulatunumbers in relation with the Fibonacci numbers and the Lucas numbers will be more explored.2000 Mathematical Subject Classification: 11