Search results for: solving engineering problems

Authors: Kamariah Abu Bakar, Jennifer Way

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This study investigated how young children (six years old) constructed and used representations in mathematics classroom; particularly in problem solving. The purpose of this study is to explore the ways children used representations in solving addition problems and to determine whether their representations can play a supportive role in understanding the problem situation and solving them correctly. Data collection includes observations, children’s artifact, photographs and conversation with children during task completion. The results revealed that children were able to construct and use various representations in solving problems. However, they have certain preferences in generating representations to support their problem solving.

Keywords: young children, representations, addition, problem solving

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Authors: Verónica Díaz Quezada

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The importance given to the development of the problem solving skill and the requirement to solve problems framed in mathematical or real life contexts, in practice, they are not evidence in relation to the teaching of proportional variations. This qualitative and descriptive study aims to (1) to improve problem solving ability of high school students in Chile, (ii) to elaborate and describe a didactic intervention strategy based on learning situations in proportional variations, focused on solving types of routine problems of various contexts and non-routine problems. For this purpose, participant observation was conducted, test of mathematics problems and an opinion questionnaire to thirty-six high school students. Through the results, the highest academic performance is evidenced in the routine problems of purely mathematical context, realistic, fantasy context, and non-routine problems, except in the routine problems of real context and compound proportionality problems. The results highlight the need to consider in the curriculum different types of problems in the teaching of mathematics that relate the discipline to everyday life situations

Keywords: algebra, high school, proportion variations, nonroutine problem solving, routine problem solving

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Authors: Liberto Pombal, Christian Dieter Jaekel

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The objective of this work is to establish theoretical and numerical conditions for Solving Extended Linear Complementarity Problems (XLCP), with emphasis on the Horizontal Linear Complementarity Problem (HLCP). Two new strategies for solving complementarity problems are presented, using differentiable and penalized functions, which resulted in a natural formalization for the Linear Horizontal case. The computational results of all suggested strategies are also discussed in depth in this paper. The implication in practice allows solving and optimizing, in an innovative way, the (forestry) problems of the value chain of the industrial wood sector in Angola.

Keywords: complementarity, box constrained, optimality conditions, wood and environment

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Authors: Keng Keh Lim, Zaleha Ismail, Yudariah Mohammad Yusof

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This paper aims to find out how students using convergent and divergent thinking in creative problem solving to solve mathematical problems creatively. Eight engineering undergraduates in a local university took part in this study. They were divided into two groups. They solved the mathematical problems with the use of creative problem solving skills. Their solutions were collected and analyzed to reveal all the processes of problem solving, namely: problem definition, ideas generation, ideas evaluation, ideas judgment, and solution implementation. The result showed that the students were able to solve the mathematical problem with the use of creative problem solving skills.

Keywords: convergent thinking, divergent thinking, creative problem solving, creativity

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

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Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Fadi Awawdeh

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In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: identification problems, semigroup theory, methods for inverse problems, scientific computing

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Authors: Veronica Diaz Quezada

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The society of the 21st century requires training of engineers capable of solving routine and non-routine problems in applications of the limit of real functions, as part of the course Calculus I. For this purpose, research was conducted with a methodological design that combines quantitative and qualitative procedures and that aims, to identify and to characterize the types of problems according to their nature and context, through the application of a mathematics test; to know— through a questionnaire— the opinion of difficulties in their solution, previous and missing knowledge of some students of three engineering careers of a state university in Chile. This research is completed with three case studies. The results favor the performance of students in solving problems of a fantasist and realistic context, but these do not guarantee mathematical skills which are necessary to solve non-routine problems of limit applications. In conclusion, through this research, it became clear that the students of the three engineerings do not have all the necessary skills to solve problems of application of the limit of a function of the real variable.

Keywords: case studies, engineering program, limits, problem solving

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Authors: Ayşe Yurdakul, Eckehard Schnieder

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Because of the growing multidisciplinarity and multilinguality, communication problems in different technical fields grows more and more. Therefore, each technical field has its own specific language, terminology which is characterised by the different definition of terms. In addition to definition problems, there are also relation problems between terms. Among these problems of relation, there are the synonymy, antonymy, hypernymy/hyponymy, ambiguity, risk of confusion, and translation problems etc. Thus, the terminology management system iglos of the Institute for Traffic Safety and Automation Engineering of the Technische Universität Braunschweig has the target to solve these problems by a methodological standardisation of term definitions with the aid of the iglos sign model and iglos relation types. The focus of this paper should be on solving definition and relation problems between terms in English navigation terminology.

Keywords: iglos, iglos sign model, methodological resolutions, navigation terminology, common language, technical language, positioning, definition problems, relation problems

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Authors: Veronica Diaz Quezada

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In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: engineering education, errors, limits, mathematics competences, problem solving

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Authors: A. Giannakopoulos, S. B. Buckley

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Problem solving in any field is recognised as a prerequisite for any advancement in knowledge. For example in South Africa it is one of the seven critical outcomes of education together with critical thinking. As a systematic way to problem solving was initiated in mathematics by the great mathematician George Polya (the father of problem solving), more detailed and comprehensive ways in problem solving have been developed. This paper is based on the findings by the author and subsequent recommendations for further research in problem solving and critical thinking. Although the study was done in mathematics, there is no doubt by now in almost anyone’s mind that mathematics is involved to a greater or a lesser extent in all fields, from symbols, to variables, to equations, to logic, to critical thinking. Therefore it stands to reason that mathematical principles and learning cannot be divorced from any field. In management of knowledge situations, the types of problems are similar to mathematics problems varying from simple to analogical to complex; from well-structured to ill-structured problems. While simple problems could be solved by employees by adhering to prescribed sequential steps (the process), analogical and complex problems cannot be proceduralised and that diminishes the capacity of the organisation of knowledge creation and innovation. The low efficiency in some organisations and the low pass rates in mathematics prompted the author to view problem solving as a product. The authors argue that using mathematical approaches to knowledge management problem solving and treating problem solving as a product will empower the employee through further training to tackle analogical and complex problems. The question the authors asked was: If it is true that problem solving and critical thinking are indeed basic skills necessary for advancement of knowledge why is there so little literature of knowledge management (KM) about them and how they are connected and advance KM?This paper concludes with a conceptual model which is based on general accepted principles of knowledge acquisition (developing a learning organisation), knowledge creation, sharing, disseminating and storing thereof, the five pillars of knowledge management (KM). This model, also expands on Gray’s framework on KM practices and problem solving and opens the doors to a new approach to training employees in general and domain specific areas problems which can be adapted in any type of organisation.

Keywords: critical thinking, knowledge management, mathematics, problem solving

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Authors: Gizem Akcan, Erdinc Ozturk

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When it is examined as historically, it has caught attention that homosexual people try to behave as heterosexual or come out to have a place in community. Homosexual people have identity confusion during identity development, they have high levels of need for absolute truth and their psychological well being is affected negatively because of high levels of need for absolute truth and they have problems about self concept clarity. People who have problems about self concept clarity have problems on problem solving and show lots of symptoms of stress. People who have clear self concept use healthier coping strategies to solve problems. The purpose of this study is to show whether need for absolute truth predicts problem solving and symptoms of stress via mediator effect of self concept clarity or not on homosexual men. The participants of this study were 200 homosexual men. The ages of participants were 20-50. In addition, Demographic Information Form, Self Concept Clarity Scale, Need for Absolute Truth Scale, Stres Self-Assessment Checklist and Problem Solving Inventory were applied to the participants. The assessment of the data was made with confirmatory factor analysis and structural equation modeling analysis. According to the results of this study, need for absolute truth predicts problem solving and symptoms of stress via mediator effect of self concept clarity on homosexual men.

Keywords: need for absolute truth, self concept clarity, symptoms of stress, problem solving

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Authors: Irena Smetackova

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The important part of school mathematics are word problems which represent the connection between school knowledge and life reality. To find the reasons why students consider word problems to be difficult, it is necessary to take into consideration the motivational settings, besides mathematical knowledge and reading skills. Our goal is to identify whether the familiar or unfamiliar context of math word problem influences solving success rate and if so, whether the reasons are motivational or cognitive. For this purpose, we conducted three steps study in group of fifty pupils 9-10 years old. In the first step, we asked pupils to create ‘the best’ word problems for entered numerical formula. The set of 19 word problems with different contexts were selected. In the second step, pupils were asked to evaluate (without solving) how they like each item and how easy it is for them. The 6 word problems with low preference and low estimated success rate were selected and combined with other 6 problems with high preference and success rate. In the third step, the same pupils were asked to solve the word problems. The analysis showed that pupils attitudes and solving toward word problems varied by the context. The strong gender patterns both in preferred contexts and in estimated success rates were identified however the real success rate did not differ so strongly. The success gap between word problems with and without preferred contexts were stronger than the gap between problems with and without real experience with the context. The hypothesis that motivational factors are more important than cognitive factors was confirmed.

Keywords: mathematics, context of reality, motivation, cognition, word problems

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Authors: B. Özlük, A. Karaaslan

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This study has been conducted as a supplementary and relationship seeking study with the purpose of measuring the tendency and success of support among peers amid nursing students studying at university in solving interpersonal problems. The population of the study (N:279) is comprised of nursing students who are studying at one state and one private university in the province of Konya, while its sample is comprised of 231 nursing students who agreed to take part in the study voluntarily. As a result of this study, it has been determined that the peer support and interpersonal problem solving characteristics among students were at medium levels and that the interpersonal problem solving skills of students studying in the third year were higher than those of first and second year students. While the interpersonal problem solving characteristics of students who are aged 20 and over were found to be higher, no difference could be determined in terms of the interpersonal problem solving skills and tendencies among students, based on their gender and where they reside. A positive – to a medium degree – and significant relationship was determined between peer support and interpersonal problem solving skills, and it is possible to say that as peer support increases, so do the skills and tendencies to solve problems.

Keywords: nursing students, peer support, interpersonal problem, problem solving

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Authors: Myunghoun Jang

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Most engineering colleges in South Korea have engineering design classes in order to develop and enhance a student's creativity and problem-solving ability. Many cases about engineering design class are shown in journals and magazines, but a case lasting many years is few. The engineering design class in the Department of Architectural Engineering, Jeju National University was open in 2009 and continues to this year. 3-5 teams in every year set up their problems found their solutions and produced good results. Three of the results obtained patents. The class also provides students with opportunities to improve communication skill because they have many discussions in solving their problems.

Keywords: engineering design, architectural engineering, team-based learning, construction safety

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Authors: R. M. Rizk-Allah

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This paper presents co-evolutionary fruit fly optimization algorithm based on firefly algorithm (CFOA-FA) for solving unconstrained optimization problems. The proposed algorithm integrates the merits of fruit fly optimization algorithm (FOA), firefly algorithm (FA) and elite strategy to refine the performance of classical FOA. Moreover, co-evolutionary mechanism is performed by applying FA procedures to ensure the diversity of the swarm. Finally, the proposed algorithm CFOA- FA is tested on several benchmark problems from the usual literature and the numerical results have demonstrated the superiority of the proposed algorithm for finding the global optimal solution.

Keywords: firefly algorithm, fruit fly optimization algorithm, unconstrained optimization problems

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Authors: Sidharth Talan, Rajlakshmi G. Majumdar

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Problem-solving skill is one the few skills which is constantly endeavored to improve upon by the professionals and academicians around the world in order to sustain themselves in the ever-growing competitive environment. The given paper focuses on evaluating a hypothesized relationship between the problems solving efficiency of an individual with spaced repetitions, conducted with a time interval of one day over a period of two weeks. The paper has utilized uni-variate regression analysis technique to assess the best fit curve that can explain the significant relationship between the given two variables. The paper has incorporated Anagrams solving as the appropriate testing process for the analysis. Since Anagrams solving involves rearranging a jumbled word to form a correct word, it projects to be an efficient process to observe the attention span, visual- motor coordination and the verbal ability of an individual. Based on the analysis for a sample population of 30, it was observed that problem-solving efficiency of an individual, measured in terms of the score in each test was found to be significantly correlated with time period measured in days.

Keywords: Anagrams, histogram plot, moving average curve, spacing effect

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Authors: Yixun Shi

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Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed.

Keywords: convex programming, interior point method, linear systems, vector division

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Authors: Allen A. Espinosa, Larkins A. Trinidad

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The present study investigated collegiate students’ problem solving strategies and misconceptions in solving stoichiometric problems and later on formulate a teaching framework from the result of the study. The study found out that the most prominent strategies among students are the mole method and the proportionality method, which are both algorithmic by nature. Misconception was also noted as some students rely on Avogadro’s number in converting between moles. It is suggested therefore that the teaching of stoichiometry should not be confined to demonstration. Students should be involved in the process of thinking of ways to solve the problem.

Keywords: stoichiometry, Svogadro’s number, mole method, proportionality method

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Authors: Carol Okigbo

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Mathematical problem solving has long been accorded an important place in mathematics curricula at every education level in both advanced and emerging economies. Its classroom approaches have varied, such as teaching for problem-solving, teaching about problem-solving, and teaching mathematics through problem-solving. It requires engaging in tasks for which the solution methods are not eminent, making sense of problems and persevering in solving them by exhibiting processes, strategies, appropriate attitude, and adequate exposure. Teachers play important roles in helping students acquire competency in problem-solving; thus, they are expected to be good problem-solvers and have proper conceptions of problem-solving. Studies show that teachers’ conceptions influence their decisions about what to teach and how to teach. Therefore, how teachers view their roles in teaching problem-solving will depend on their pedagogical conceptions of problem-solving. If teaching problem-solving is a major component of secondary school mathematics instruction, as recommended by researchers and mathematics educators, then it is necessary to establish teachers’ conceptions, what they do, and how they approach problem-solving. This study is designed to determine secondary school teachers’ conceptions regarding mathematical problem solving, its current situation, how teachers’ conceptions relate to their demographics, as well as the interaction patterns in the mathematics classroom. There have been many studies of mathematics problem solving, some of which addressed teachers’ conceptions using single-method approaches, thereby presenting only limited views of this important phenomenon. To address the problem more holistically, this study adopted an integrated mixed methods approach which involved a quantitative survey, qualitative analysis of open-ended responses, and ethnographic observations of teachers in class. Data for the analysis came from a random sample of 327 secondary school mathematics teachers in two Nigerian states - Anambra State and Enugu State who completed a 45-item questionnaire. Ten of the items elicited demographic information, 11 items were open-ended questions, and 25 items were Likert-type questions. Of the 327 teachers who responded to the questionnaires, 37 were randomly selected and observed in their classes. Data analysis using ANOVA, t-tests, chi-square tests, and open coding showed that the teachers had different conceptions about problem-solving, which fall into three main themes: practice on exercises and word application problems, a process of solving mathematical problems, and a way of teaching mathematics. Teachers reported that no period is set aside for problem-solving; typically, teachers solve problems on the board, teach problem-solving strategies, and allow students time to struggle with problems on their own. The result shows a significant difference between male and female teachers’ conception of problems solving, a significant relationship among teachers’ conceptions and academic qualifications, and teachers who have spent ten years or more teaching mathematics were significantly different from the group with seven to nine years of experience in terms of their conceptions of problem-solving.

Keywords: conceptions, education, mathematics, problem solving, teacher

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Authors: Hashini E. Mohottala

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We report the combine use of Wikispaces (WikiS) and Group Problem Solving (GPS) sessions conducted in the introductory level physics classes. As a part of this new teaching tool, some essay type problems were posted on the WikiS in weekly basis and students were encouraged to participate in problem solving without providing numerical final answers but the steps. Wikispace is used as a platform for students to meet online and create discussions. Each week students were further evaluated on problem solving skills opening up more opportunity for peer interaction through GPS. Each group was given a different problem to solve and the answers were graded. Students developed a set of skills in decision-making, problem solving, communication, negotiation, critical and independent thinking and teamwork through the combination of WikiS and GPS.

Keywords: group problem solving (GPS), wikispace (WikiS), physics education, learning

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

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In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem

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Authors: A. A. Behroozpoor, M. M. Mazarei

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In this paper, a fuzzy recurrent neural network is proposed for solving the classical quadratic control problem subject to linear equality and bound constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed.

Keywords: REFERENCES [1] Xia, Y, A new neural network for solving linear and quadratic programming problems. IEEE Transactions on Neural Networks, 7(6), 1996, pp.1544–1548. [2] Xia, Y., & Wang, J, A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Transactions on Neural Networks, 16(2), 2005, pp. 379–386. [3] Xia, Y., H, Leung, & J, Wang, A projection neural network and its application to constrained optimization problems. IEEE Transactions Circuits and Systems-I, 49(4), 2002, pp.447–458.B. [4] Q. Liu, Z. Guo, J. Wang, A one-layer recurrent neural network for constrained seudoconvex optimization and its application for dynamic portfolio optimization. Neural Networks, 26, 2012, pp. 99-109.

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Authors: Temitayo Ogunsanwo

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Problem-solving is an important way of learning way of learning because it propels children to use previous experiences to deal with new situations. The purpose of this study is to find out the attitude of pre-service teachers to problem-solving as a strategy for promoting early mathematics learning in children. This qualitative study employed a descriptive design to investigate the experiences of twenty second-year undergraduate early childhood education Pre-service teachers in a teaching practice and their attitude towards five-year-old children’s problem-solving strategies in mathematics. Pre-service teachers were exposed to different strategies for teaching children how to solve problems in mathematics. They were taken through a micro teaching in class using different strategies to teach problem-solving in different topics in the five-year-old mathematics curriculum. The students were then made to teach five-year-olds in neighbouring schools for three weeks, working in pairs, observing and recording children’s problem-solving activities and strategies. After the three weeks exercise, their experiences and attitude towards children’s problem-solving strategies were collected using open-ended questions and analysed in themes. Findings were discussed.

Keywords: attitude, early mathematics learning, experience, pre-service teachers, problem-solving, strategies

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Authors: Kwan-u Kim, Jin-Sim, Ryong-Jin Jang, Sung-Duk Kim

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106 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not solve correctly one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition to it, they did not treat the astronomical and physical phenomena in a physical way based on the exact physical laws obtained from the solution of the geodesic equations in Schwarzschild metric, so some former scholars mentioned that Einstein’s theoretical basis of general theory of relativity was obscure and incorrect, but they have not given a correct physical solution to the problems. Furthermore, because general theory of relativity has not given a quantitative solution to the obscure and incorrect problems, generalization of gravitational theory although the former scholars thought of it and tried to do it. In order to solve the problems it is necessary to explore theobscure and incorrect problems in general theory of relativity based on the physical laws and to find out the methodology of solving the problems. Therefore, first of all, as the first sarytep for achieving the purpose, the correct solution of the geodesic equation in Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results has been presented, the obscure and incorrect problems have been showed and an analysis of them has been made on the basis of the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild

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Authors: Karen Odendaal

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Accounting transactions are becoming more complex, and more extensive accounting guidance is provided on a continuous basis. It is widely perceived that conceptual teaching of accounting contributes to lifelong learning. Such a conceptual teaching approach also contributes to effective accounting problem-solving. This framework-based approach is rooted in educational psychologies such as constructivism and Ausubel’s subsumption theory. This study aimed at investigating the ability of students to solve complex accounting problems by using only concepts underlying the Conceptual Framework. An assignment was administered to pre-graduate students at a South African university and this study made use of an interpretative research design which implemented multiple research instruments to investigate the ability of students to solve complex accounting problems using only concepts underlying the Conceptual Framework. Student perceptions were analysed and were aided by a related reflective questionnaire. The importance of the study indicates the necessity of Accounting educators to enhance a conceptual understanding among students as a mechanism for problem-solving of accounting issues. The results indicate that the ability of students to solve accounting problems effectively using only the Conceptual Framework depends on the complexity of the scenario and the students’ familiarity with the problem. The study promotes a balanced and more conceptual (rather than only technical) preference to the problem-solving of complex accounting problems. The study indubitably promotes considerable emphasis on the importance of the Conceptual Framework in accounting education and the promotion of life-long learning in the subject field.

Keywords: accounting education, conceptual teaching, constructivism, framework-based, problem-solving

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Authors: Pei Chin Lim

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School of Mathematics and Science of Singapore Polytechnic offers a Basic Mathematics module to students who did not pass GCE O-Level Additional Mathematics. These students are weaker in Mathematics. In particular, they struggle with word problems and tend to leave them blank in tests and examinations. In order to improve students’ problem-solving skills, the school redesigned the Basic Mathematics module to incorporate Polya’s problem-solving methodology. During tutorial lessons, students have to work through learning activities designed to raise their metacognitive awareness by following Polya’s problem-solving process. To assess the effectiveness of the redesign, students’ working for a challenging word problem in the mid-semester test were analyzed. Sixty-five percent of students attempted to understand the problem by making sketches. Twenty-eight percent of students went on to devise a plan and implement it. Only five percent of the students still left the question blank. These preliminary results suggest that with regular exposure to an explicit and systematic problem-solving approach, weak students’ problem-solving skills can potentially be improved.

Keywords: mathematics education, metacognition, problem solving, weak students

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Authors: Levan Sabauri

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The purpose of this article is an examination of the meaning of theoretic aspects of audit in the context of solving of specific problems of the audit. The audit’s aim is the estimation of financial statements by the auditor, i.e. if they are prepared according to the basic requirements of current financial statements. By examination of concrete examples, we can clearly see problems created in an audit and in often cases, those contradictions which can be caused by incompliance of matters regulated by legislation and by reality. An important part of this work is the analysis of reform in the direction of business accounting, statements and audit in Georgia and its comparison with EU countries. In the article, attention is concentrated on the analysis of specific problems of auditing practice and ways of their solving by taking into consideration theoretical aspects of the audit are proposed.

Keywords: audit, auditor, auditors’ ethic code, auditor’s risk, financial statement, objectivity

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Sara Akbari

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In this study, we investigate building structures nonlinear behavior also solving analytic of nonlinear differential at vibrations. As we know most of engineering systems behavior in practical are non- linear process (especial at structural) and analytical solving (no numerical) these problems are complex, difficult and sometimes impossible (of course at form of analytical solving). In this symposium, we are going to exposure one method in engineering, that can solve sets of nonlinear differential equations with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical Method (Runge-Kutte 4th) and exact solutions. Finally, we can proof AGM method could be created huge evolution for researcher and student (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software, we can analytical solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations.

Keywords: new method AGM, vibrations, beam-column, angular frequency, energy dissipated, critical load

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Authors: Thierno Diop, Michel Fortin, Jean Deteix

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Since the precise formulation of the elastic part is irrelevant for the description of the algorithm, we shall consider a generic case. In practice, however, we will have to deal with a non linear material (for instance a Mooney-Rivlin model). We are interested in solving a finite element approximation of the problem, leading to large-scale non linear discrete problems and, after linearization, to large linear systems and ultimately to calculations needing iterative methods. This also implies that penalty method, and therefore augmented Lagrangian method, are to be banned because of their negative effect on the condition number of the underlying discrete systems and thus on the convergence of iterative methods. This is in rupture to the mainstream of methods for contact in which augmented Lagrangian is the principal tool. We shall first present the problem and its discretization; this will lead us to describe a general solution algorithm relying on a preconditioner for saddle-point problems which we shall describe in some detail as it is not entirely standard. We will propose an iterative approach for solving three-dimensional frictional contact problems between elastic bodies, including contact with a rigid body, contact between two or more bodies and also self-contact.

Keywords: frictional contact, three-dimensional, large-scale, iterative method

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Authors: Ayse Ozturk

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The study extends the prior research on modeling competencies by positioning students’ cognitive and language resources as the fundamentals for pursuing their own inquiry and expression lines through mathematical modeling. This strategy aims to answer the question that guides this study, “How do students’ group approaches to modeling tasks affect their modeling competencies over a unit of instruction?” Six bilingual tenth-grade students worked on open-ended modeling problems along with the content focused on quantities over six weeks. Each group was found to have a unique cognitive approach for solving these problems. Three different problem-solving strategies affected how the groups’ modeling competencies changed. The results provide evidence that the discussion around groups’ solutions, coupled with their reflections, advances group interpreting and validating competencies in the mathematical modeling process

Keywords: cognition, collective learning, mathematical modeling competencies, problem-solving

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