Search results for: solving complex problems

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: 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: 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: 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: 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: Jason Digalakis, John Cotronis

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Memetic algorithms (MAs) are useful for solving optimization problems. It is quite difficult to search the search space of the optimization problem with large dimensions. There is a challenge to use all the cores of the system. In this study, a sequential implementation of the memetic algorithm is converted into a concurrent version, which is executed on the cores of both CPU and GPU. For this reason, CUDA and OpenMP libraries are operated on the parallel algorithm to make a concurrent execution on CPU and GPU, respectively. The aim of this study is to compare CPU and GPU implementation of the memetic algorithm. For this purpose, fourteen benchmark functions are selected as test problems. The obtained results indicate that our approach leads to speedups up to five thousand times higher compared to one CPU thread while maintaining a reasonable results quality. This clearly shows that GPUs have the potential to acceleration of MAs and allow them to solve much more complex tasks.

Keywords: memetic algorithm, CUDA, GPU-based memetic algorithm, open multi processing, multimodal functions, unimodal functions, non-linear optimization problems

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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: Ferzat Anka

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Many types of problems can be solved using traditional analytical methods. However, these methods take a long time and cause inefficient use of resources. In particular, different approaches may be required in solving complex and global engineering problems that we frequently encounter in real life. The bigger and more complex a problem, the harder it is to solve. Such problems are called Nondeterministic Polynomial time (NP-hard) in the literature. The main reasons for recommending different metaheuristic algorithms for various problems are the use of simple concepts, the use of simple mathematical equations and structures, the use of non-derivative mechanisms, the avoidance of local optima, and their fast convergence. They are also flexible, as they can be applied to different problems without very specific modifications. Thanks to these features, it can be easily embedded even in many hardware devices. Accordingly, this approach can also be used in trend application areas such as IoT, big data, and parallel structures. Indeed, the metaheuristic approaches are algorithms that return near-optimal results for solving large-scale optimization problems. This study is focused on the new metaheuristic method that has been merged with the chaotic approach. It is based on the chaos theorem and helps relevant algorithms to improve the diversity of the population and fast convergence. This approach is based on Chimp Optimization Algorithm (ChOA), that is a recently introduced metaheuristic algorithm inspired by nature. This algorithm identified four types of chimpanzee groups: attacker, barrier, chaser, and driver, and proposed a suitable mathematical model for them based on the various intelligence and sexual motivations of chimpanzees. However, this algorithm is not more successful in the convergence rate and escaping of the local optimum trap in solving high-dimensional problems. Although it and some of its variants use some strategies to overcome these problems, it is observed that it is not sufficient. Therefore, in this study, a newly expanded variant is described. In the algorithm called Ex-ChOA, hybrid models are proposed for position updates of search agents, and a dynamic switching mechanism is provided for transition phases. This flexible structure solves the slow convergence problem of ChOA and improves its accuracy in multidimensional problems. Therefore, it tries to achieve success in solving global, complex, and constrained problems. The main contribution of this study is 1) It improves the accuracy and solves the slow convergence problem of the ChOA. 2) It proposes new hybrid movement strategy models for position updates of search agents. 3) It provides success in solving global, complex, and constrained problems. 4) It provides a dynamic switching mechanism between phases. The performance of the Ex-ChOA algorithm is analyzed on a total of 8 benchmark functions, as well as a total of 2 classical and constrained engineering problems. The proposed algorithm is compared with the ChoA, and several well-known variants (Weighted-ChoA, Enhanced-ChoA) are used. In addition, an Improved algorithm from the Grey Wolf Optimizer (I-GWO) method is chosen for comparison since the working model is similar. The obtained results depict that the proposed algorithm performs better or equivalently to the compared algorithms.

Keywords: optimization, metaheuristic, chimp optimization algorithm, engineering constrained problems

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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: 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: 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: 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: 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: 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: 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: Robin Lok Wang Ma

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The purpose of this paper is to investigate how engineering students’ motivation and interests are maintained in their journeys. In recent years, different pedagogies of teaching, including entrepreneurship, experiential and lifelong learning, as well as dream builder, etc., have been widely used for education purposes. University advocates hands-on practice, learning by experiencing and experimenting throughout different courses. Students are not limited to gaining knowledge via traditional lectures, laboratory demonstrations, tutorials, and so on. The capability to identify both complex problems and their corresponding solutions in daily life are one of the criteria/skill sets required for graduates to obtain their careers at professional organizations and companies. A project-based course, namely Mechatronic Design and Prototyping, was developed for students to design and build a physical prototype for solving existing problems in their daily lives, thereby encouraging them as an entrepreneur to explore further possibilities to commercialize their designed prototypes and launch them to the market. Feedbacks from students show that they are keen to propose their own ideas freely with guidance from the instructor instead of using either suggested or assigned topics. Proposed ideas of the prototypes reflect that if students’ interests are maintained, they acquire the knowledge and skills they need, including essential communication, logical thinking, and, more importantly, problem solving for their lifelong learning journey.

Keywords: problem solving, lifelong learning, entrepreneurship, engineering

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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: 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: 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: Amal Machtalay

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In this survey, we aim to review the rapidly growing literature on numerical methods to solve different forms of mean field problems, namely mean field games (MFG), mean field controls (MFC), potential MFGs, and master equations, as well as their corresponding recent applications. Here, we distinguish two families of numerical methods: iterative methods based on mesh generation and those called mesh-free, normally related to neural networking and learning frameworks.

Keywords: mean-field games, numerical schemes, partial differential equations, complex systems, machine learning

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Authors: Tien-Ling Yeh, Jo-Han Chan

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The percentage of dual-earner couples has become higher and higher each year. Family lifestyles in Taiwan have also been changing. This fact reflects the importance of family communication and parent-child relationship. This study aimed to explore the influences of family lifestyles and accompany forms on children’s capability to solve problems. The research process included two phases: (1) literature review, to explore the characteristics of children’s capability to solve problems and methods to measure this capability; and (2) questionnaire analyses, to explore the influences of lifestyles and accompany time and forms of modern families on their children’s capability to solve problems. The questionnaires were issued in October and November, 2016. A total of 300 questionnaires were retrieved, among which 250 were valid. The findings are summarized below: -The linguistic performances of the children from families of the busy and haggling lifestyle or the intermittent childcare lifestyle were rather good. Besides being interested in learning, these children could solve problems or difficulties independently. -The capability to ‘analyze problems’ of children from families with accompanying time during 19:00-19:30 (family dinner time) or 22:00-23:30 (before bedtime) was good. When facing a complex problem, these children could identify the most important factor in the problem. When seeing a problem, they would first look for the cause. If they encountered a bottleneck while solving a problem, they would review the context of the problem and related conditions to come up with another solution. -According to the literature, learning toys with numbers and symbols to learn to read can help develop children’s logic thinking, which is helpful to solve problems. Interestingly, some study suggested that children playing with fluid constructive toys are less likely to give up what they are doing and more likely to identify problems in their daily life. Some of them can even come up with creative and effective solutions.

Keywords: accompany, lifestyle, parent-child, problem-solving

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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

Abstract:

108 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in the Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not correctly solve 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, they did not treat the astronomical and physical phenomena in a physical way based on the correct physical laws obtained from the solution of the geodesic equations in the Schwarzschild metric. Therefore, some former scholars mentioned that Einstein’s theoretical basis of a general theory of relativity was obscure and incorrect, but they did not give a correct physical solution to the problems. Furthermore, since the general theory of relativity has not given a quantitative solution to obscure and incorrect problems, the generalization of gravitational theory has not yet been successfully completed, although former scholars have thought of it and tried to do it. In order to solve the problems, it is necessary to explore the obscure and incorrect problems in a general theory of relativity based on the physical laws and to find out the methodology for solving the problems. Therefore, as the first step toward achieving this purpose, the right solution of the geodesic equation in the Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results have been presented, the obscure and incorrect problems have been shown, and an analysis of them has been made based on 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, Poincaré

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