Search results for: mathematical definitions

Authors: M. Saeed, A. Shahidzadeh

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Interaction between teachers and learners requires applying a set of samples (examples) which helps to create coordination between the goals and methods. The main result and achievement and application of samples (examples) are that they can bring the teacher and learner to a shared understanding of the concept. mathematical concepts, and also one of the challenging issues in the discussion of the function is to find the collision points of functions of and, regarding that the example space of teachers is different in this issue, this paper aims to present an example space including several problems of the secondary school with the help of intuition and drawing various graphs of functions of and for more familiarity of teachers.

Keywords: inverse function, educational example, Mathematic example, example space

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Authors: Fábio A. S. Mota, Mauro A. S. S. Ravagnani, E. P. Carvalho

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In the present paper the design of plate heat exchangers is formulated as an optimization problem considering two mathematical modeling. The number of plates is the objective function to be minimized, considering implicitly some parameters configuration. Screening is the optimization method used to solve the problem. Thermal and hydraulic constraints are verified, not viable solutions are discarded and the method searches for the convergence to the optimum, case it exists. A case study is presented to test the applicability of the developed algorithm. Results show coherency with the literature.

Keywords: plate heat exchanger, optimization, modeling, simulation

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Authors: Bojan Radisic, Katarina Stavlic

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The paper describes two economics terms consumer surplus and producer surplus using the definite integrals (the Riemann integral). The consumer surplus is the difference between what consumers are willing to pay and actual price. The producer surplus is the difference between what producers selling at the current price, rather than at the price they would have been are willing to accept. Using the definite integrals describe terms and mathematical formulas of the consumer surplus and the producer surplus and will be applied to the numerical examples.

Keywords: consumer surplus, producer surplus, definite integral, integration

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Authors: Iman Jabbar

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Within the scope of professionalism and in order to compete with the modern world, teachers, are expected to develop their teaching skills and activities in addition to their professional knowledge. At the college level, the teacher should be able to face classroom challenges through his engagement with the learning situation to understand the students and their needs. In our field of TESOL, the role of the English teacher is no longer restricted to teaching English texts, but rather he should endeavor to enhance the students’ skills such as communication and critical analysis. Within the literature of professionalism, there are certain strategies and tools that an English teacher should adopt to develop his competence and performance. Reflective practice, which is an exploratory process, is one of these strategies. Another strategy contributing to classroom development is motivation. It is crucial in students’ learning as it affects the quality of learning English in the classroom in addition to determining success or failure as well as language achievement. This is a qualitative study grounded on interpretive perspectives of teachers and students regarding the process of professional development. This study aims at (a) understanding how teachers at the college level conceptualize reflective practice and motivation inside EFL classroom, and (b) exploring the methods and strategies that they implement to practice reflection and motivation. This study and is based on two questions: 1. How do EFL teachers perceive and view reflection and motivation in relation to their teaching and professional development? 2. How can reflective practice and motivation be developed into practical strategies and actions in EFL teachers’ professional context? The study is organized into two parts, theoretical and practical. The theoretical part reviews the literature on the concept of reflective practice and motivation in relation to professional development through providing certain definitions, theoretical models, and strategies. The practical part draws on the theoretical one, however; it is the core of the study since it deals with two issues. It involves the research design, methodology, and methods of data collection, sampling, and data analysis. It ends up with an overall discussion of findings and the researcher's reflections on the investigated topic. In terms of significance, the study is intended to contribute to the field of TESOL at the academic level through the selection of the topic and investigating it from theoretical and practical perspectives. Professional development is the path that leads to enhancing the quality of teaching English as a foreign or second language in a way that suits the modern trends of globalization and advanced technology.

Keywords: professional development, motivation, reflection, learning

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Authors: Seval Kula-Kartal

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Developing students’ reading comprehension skills is an aim that is difficult to accomplish and requires to follow long-term and systematic teaching and assessment processes. In these processes, teachers need tools to provide guidance to them on what reading comprehension is and which comprehension skills they should develop. Due to a lack of clear and evidence-based frameworks defining reading comprehension skills, especially in Turkiye, teachers and students mostly follow various processes in the classrooms without having an idea about what their comprehension goals are and what those goals mean. Since teachers and students do not have a clear view of comprehension targets, strengths, and weaknesses in students’ comprehension skills, the formative feedback processes cannot be managed in an effective way. It is believed that detecting and defining influential comprehension skills may provide guidance both to teachers and students during the feedback process. Therefore, in the current study, some of the reading comprehension frameworks that define comprehension skills operationally were examined. The aim of the study is to develop a simple and clear framework that can be used by teachers and students during their teaching, learning, assessment, and feedback processes. The current study is qualitative research in which documents related to reading comprehension skills were analyzed. Therefore, the study group consisted of recourses and frameworks which made big contributions to theoretical and operational definitions of reading comprehension. A content analysis was conducted on the resources included in the study group. To determine the validity of the themes and sub-categories revealed as the result of content analysis, three educational assessment experts were asked to examine the content analysis results. The Fleiss’ Cappa coefficient revealed that there is consistency among themes and categories defined by three different experts. The content analysis of the reading comprehension frameworks revealed that comprehension skills could be examined under four different themes. The first and second themes focus on understanding information given explicitly or implicitly within a text. The third theme includes skills used by the readers to make connections between their personal knowledge and the information given in the text. Lastly, the fourth theme focus on skills used by readers to examine the text with a critical view. The results suggested that fundamental reading comprehension skills can be examined under four themes. Teachers are recommended to use these themes in their reading comprehension teaching and assessment processes. Acknowledgment: This research is supported by Pamukkale University Scientific Research Unit within the project, whose title is Developing A Reading Comprehension Rubric.

Keywords: reading comprehension, assessing reading comprehension, comprehension taxonomies, educational assessment

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Authors: Arash Kosari, Ali Araghi

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A mathematical model for an optical-fiber communication channel is developed which results in an expression that calculates the throughput and loss of the corresponding link. The data are assumed to be transmitted by using of separate photons with different polarizations. The derived model also shows the dependency of data throughput with length of the channel and depolarization factor. It is observed that absorption of photons affects the throughput in a more intensive way in comparison with that of depolarization. Apart from that, the probability of depolarization and the absorption of radiated photons are obtained.

Keywords: absorption, data throughput, depolarization, optical fiber

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Authors: Karen Koellner, Nanette Seago, Jennifer Jacobs, Helen Garnier

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Although studies of teacher professional development (PD) are prevalent, surprisingly most have only produced incremental shifts in teachers’ learning and their impact on students. There is a critical need to understand what teachers take up and use in their classroom practice after attending PD and why we often do not see greater changes in learning and practice. This paper is based on a mixed methods efficacy study of the Learning and Teaching Geometry (LTG) video-based mathematics professional development materials. The extent to which the materials produce a beneficial impact on teachers’ mathematics knowledge, classroom practices, and their students’ knowledge in the domain of geometry through a group-randomized experimental design are considered. Included is a close-up examination of a small group of teachers to better understand their interpretations of the workshops and their classroom uptake. The participants included 103 secondary mathematics teachers serving grades 6-12 from two US states in different regions. Randomization was conducted at the school level, with 23 schools and 49 teachers assigned to the treatment group and 18 schools and 54 teachers assigned to the comparison group. The case study examination included twelve treatment teachers. PD workshops for treatment teachers began in Summer 2016. Nine full days of professional development were offered to teachers, beginning with the one-week institute (Summer 2016) and four days of PD throughout the academic year. The same facilitator-led all of the workshops, after completing a facilitator preparation process that included a multi-faceted assessment of fidelity. The overall impact of the LTG PD program was assessed from multiple sources: two teacher content assessments, two PD embedded assessments, pre-post-post videotaped classroom observations, and student assessments. Additional data were collected from the case study teachers including additional videotaped classroom observations and interviews. Repeated measures ANOVA analyses were used to detect patterns of change in the treatment teachers’ content knowledge before and after completion of the LTG PD, relative to the comparison group. No significant effects were found across the two groups of teachers on the two teacher content assessments. Teachers were rated on the quality of their mathematics instruction captured in videotaped classroom observations using the Math in Common Observation Protocol. On average, teachers who attended the LTG PD intervention improved their ability to engage students in mathematical reasoning and to provide accurate, coherent, and well-justified mathematical content. In addition, the LTG PD intervention and instruction that engaged students in mathematical practices both positively and significantly predicted greater student knowledge gains. Teacher knowledge was not a significant predictor. Twelve treatment teachers self-selected to serve as case study teachers to provide additional videotapes in which they felt they were using something from the PD they learned and experienced. Project staff analyzed the videos, compared them to previous videos and interviewed the teachers regarding their uptake of the PD related to content knowledge, pedagogical knowledge and resources used. The full paper will include the case study of Ana to illustrate the factors involved in what teachers take up and use from participating in the LTG PD.

Keywords: geometry, mathematics professional development, pedagogical content knowledge, teacher learning

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Authors: Hassan Al Salman

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We consider a nonlinear parabolic cross diffusion model arising in applied mathematics. A fully practical piecewise linear finite element approximation of the model is studied. By using entropy-type inequalities and compactness arguments, existence of a global weak solution is proved. Providing further regularity of the solution of the model, some uniqueness results and error estimates are established. Finally, some numerical experiments are performed.

Keywords: cross diffusion model, entropy-type inequality, finite element approximation, numerical analysis

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Authors: Lottie Lane

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It is habitually assumed and stated that the World Bank should engage and comply with international human rights standards. However, the basis for holding the Bank to such standards is unclear. Most advocates of the idea invoke aspects of international law to argue that the Bank has existing obligations to act in compliance with human rights standards. The Bank itself, however, does not appear to accept such arguments, despite having endorsed the importance of human rights for a considerable length of time. A substantial challenge is that under the current international human rights law framework, the World Bank is considered a non-state actor, and as such, has no direct human rights obligations. In the absence of clear legal duties for the Bank, it is necessary to look at the tools available beyond the international human rights framework to encourage the Bank to comply with human rights standards. This article critically examines several bases for arguing that the Bank should comply and engage with human rights through its policies and practices. Drawing on the Bank’s own ‘good governance’ approach as well as the United Nations’ ‘human rights-based-approach’ to development, a new basis is suggested. First, the relationship between the World Bank and human rights is examined. Three perspectives are considered: (1) the legal position – what the status of the World Bank is under international human rights law, and whether it can be said to have existing legal human rights obligations; (2) the Bank’s own official position – how the Bank envisages its relationship with and role in the protection of human rights; and (3) the relationship between the Bank’s policies and practices and human rights (including how its attitudes are reflected in its policies and how the Bank’s operations impact human rights enjoyment in practice). Here, the article focuses on two examples – the (revised) 2016 Environmental and Social Safeguard Policies and the 2012 case-study regarding Gambella, Ethiopia. Both examples are widely considered missed opportunities for the Bank to actively engage with human rights. The analysis shows that however much pressure is placed on the Bank to improve its human rights footprint, it is extremely reluctant to do so explicitly, and the legal bases available are insufficient for requiring concrete, ex ante action by the Bank. Instead, the Bank’s own ‘good governance’ approach to development – which it has been advocating since the 1990s – can be relied upon. ‘Good governance’ has been used and applied by many actors in many contexts, receiving numerous different definitions. This article argues that human rights protection can now be considered a crucial component of good governance, at least in the context of development. In doing so, the article explains the relationship and interdependence between the two concepts, and provides three rationales for the Bank to take a ‘human rights-based approach’ to good governance. Ultimately, this article seeks to look beyond international human rights law and take a governance approach to provide a convincing basis upon which to argue that the World Bank should comply with human rights standards.

Keywords: World Bank, international human rights law, good governance, human rights-based approach

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Authors: Anna Avramenko, Heikki Haario

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This paper reports the development and application of a 2D depth-averaged model. The main goal of this contribution is to apply the depth averaged equations to a wind park model in which the treatment of the geometry, introduced on the mathematical model by the mass and momentum source terms. The depth-averaged model will be used in future to find the optimal position of wind turbines in the wind park. K-E and 2D LES turbulence models were consider in this article. 2D CFD simulations for one hill was done to check the depth-averaged model in practise.

Keywords: depth-averaged equations, numerical modeling, CFD, wind park model

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Authors: Khalid Alshaikh

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Corporate Social Responsibility (CSR) in Libya has recently gained momentum, especially with the rise of the social issues ensued by the recent war. CSR is a new organisational culture designing its features and route within the Libyan financial institutions. Now, both the public and private banks invest in this construct trusting that its powers are capable of improving the economic, social and environmental problems the conflict has created. On the other hand, the Libyan commercial banks recognise the benefits of utilising CSR to entice investors and ensure their continuations in the national and international markets. Nevertheless, as a new concept, CSR necessitates an in-depth exploration and analysis to help its transition from the margins of religion to the mainstream of society and businesses. This can assist in constructing its activities to bring about change nation-wide. Therefore, this paper intends to explore the current definitions attached to this term through tracing back its historical beginnings. Then, it investigates its trends both in the public and private banks to identify where its sustainable development materialises. Lastly, it seeks to understand the key challenges that obscure its success in the Libyan environment. The research methodology used both public and private banks as case study and qualitative research to interview ten Board of Directors (BoDs) and eleven Chief Executive Managers (CEOs) to discover how CSR is defined and the core CSR activities practiced by the Libyan Commercial Banks (LCBs) and the key constraints that CSR faces and make it unsuccessful. The findings suggest that CSR is still influenced by the power of religion. Nevertheless, the Islamic perspective is more consistent with the social contract concept of CSR. The LCBs do not solely focus on the economic side of maximizing profits, but also concentrate on its morality. The issue is that CSR activities are not enough to achieve good charity publicly and needs strategies to address major social issues. Moreover, shareholders do not support CSR activities. Their argument is that the only social responsibility of businesses is to maximize profits, while the government should deal with the existing social issues. Finally, although the LCBs endeavour to embed CSR in their organisational culture, it is still important that different stakeholders need to do much more to entrench this construct through their core functions. The Central bank of Libya needs also to boost its standing to be more influential and ensure that the right discussions about CSR happen with the right stakeholders involved.

Keywords: corporate social responsibility, private banks, public banks, stakeholders

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Authors: Zdzislaw Kaminski, Zbigniew Czyz, Tytus Tulwin

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This paper describes the geometrical model, algorithm and CFD simulation of an airflow around a Vertical Axis Wind Turbine rotor. A solver, ANSYS Fluent, was applied for the numerical simulation. Numerical simulation, unlike experiments, enables us to validate project assumptions when it is designed to avoid a costly preparation of a model or a prototype for a bench test. This research focuses on the rotor designed according to patent no PL 219985 with its blades capable of modifying their working surfaces, i.e. absorbing wind kinetic energy. The operation of this rotor is based on a regulation of blade angle α between the top and bottom parts of blades mounted on an axis. If angle α increases, the working surface which absorbs wind kinetic energy also increases. CFD calculations enable us to compare aerodynamic characteristics of forces acting on rotor working surfaces and specify rotor operation parameters like torque or turbine assembly power output. This paper is part of the research to improve an efficiency of a rotor assembly and it contains investigation of the impact of a blade angle of wind turbine working blades on the power output as a function of rotor torque, specific rotational speed and wind speed. The simulation was made for wind speeds ranging from 3.4 m/s to 6.2 m/s and blade angles of 30°, 60°, 90°. The simulation enables us to create a mathematical model to describe how aerodynamic forces acting each of the blade of the studied rotor are generated. Also, the simulation results are compared with the wind tunnel ones. This investigation enables us to estimate the growth in turbine power output if a blade angle changes. The regulation of blade angle α enables a smooth change in turbine rotor power, which is a kind of safety measures if the wind is strong. Decreasing blade angle α reduces the risk of damaging or destroying a turbine that is still in operation and there is no complete rotor braking as it is in other Horizontal Axis Wind Turbines. This work has been financed by the Polish Ministry of Science and Higher Education.

Keywords: computational fluid dynamics, mathematical model, numerical analysis, power, renewable energy, wind turbine

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Authors: Gyorgy Folk

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A finite set of cardinal needs define the human core of living well shaped on the evolutionary time scale as attested by social and life sciences of the last decades. Well-being is the purported state of living well. Living of humans akin any other living beings involves the exchange of vital substance with nature, maintaining a supportive symbiosis with an array of other living beings, living up to bonds to kin and exerting efforts to sustain living. A supportive natural environment, access to material resources, the nearness to fellow beings, and life sustaining activity are prerequisites of well-being. Well-living is prone to misinterpretation as an individual achievement, one lives well only and only if bonded to human relationships, related to a place, incorporated in nature. Akin all other forms of it, human life is a self-sustaining arrangement. One may say that the substance of life is life, and not materials, products, and services converted into life. The human being remains shaped on an evolutionary time scale and is enabled within the non-altering core of human being, invariant of cultural differences in earthly space and time. Present paper proposes the introduction of weal, the missing link in the causal chain of societal performance and the goodness of life. Interpreted differently over the ages, cultures and disciplines, instead of well-being, the construct in general use, weal is proposed as the underlying foundation of well-being. Weal stands for the totality of socialised reality as framing well-being for the individual beyond the possibility of deliberate choice. The descriptive approach to weal, mapping it under the guidance of discrete scientific disciplines reveals a limited set of cardinal aspects, labeled here the cardinal needs. Cardinal expresses the fundamental reorientation weal can bring about, needs deliver the sense of sine qua non. Weal is conceived as a oneness mapped along eight cardinal needs. The needs, approached as aspects instead of analytically isolated factors do not require mutually exclusive definitions. To serve the purpose of reorientation, weal is operationalised as a domain in multidimensional space, each dimension encompassing an optimal level of availability of the fundamental satisfiers between the extremes of drastic insufficiency and harmful excess, ensured by actual human effort. Weal seeks balance among the material and social aspects of human being while allows for cultural and individual uniqueness in attaining human flourishing.

Keywords: human well-being, development, economic theory, human needs

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Authors: Christine Demaecker

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Many researchers have underlined the importance of metaphors in specialised language. Their use of specific domains helps us understand the conceptualisations used to communicate new ideas or difficult topics. Within the wide area of specialised discourse, wine tasting is a very specific example because it is almost exclusively metaphoric. Wine tasting metaphors express various conceptualisations. They are not linguistic but rather conceptual, as defined by Lakoff & Johnson. They correspond to the linguistic expression of a mental projection from a well-known or more concrete source domain onto the target domain, which is the taste of wine. But unlike most specialised terminologies, the vocabulary is never clearly defined. When metaphorical terms are listed in dictionaries, their definitions remain vague, unclear, and circular. They cannot be replaced by literal linguistic expressions. This makes it impossible to transfer them into another language with the traditional linguistic translation methods. Qualitative research investigates whether wine tasting metaphors could rather be translated with the cognitive translation process, as well described by Nili Mandelblit (1995). The research is based on a corpus compiled from two high-profile wine guides; the Parker’s Wine Buyer’s Guide and its translation into French and the Guide Hachette des Vins and its translation into English. In this small corpus with a total of 68,826 words, 170 metaphoric expressions have been identified in the original English text and 180 in the original French text. They have been selected with the MIPVU Metaphor Identification Procedure developed at the Vrije Universiteit Amsterdam. The selection demonstrates that both languages use the same set of conceptualisations, which are often combined in wine tasting notes, creating conceptual integrations or blends. The comparison of expressions in the source and target texts also demonstrates the use of the cognitive translation approach. In accordance with the principle of relevance, the translation always uses target language conceptualisations, but compared to the original, the highlighting of the projection is often different. Also, when original metaphors are complex with a combination of conceptualisations, at least one element of the original metaphor underlies the target expression. This approach perfectly integrates into Lederer’s interpretative model of translation (2006). In this triangular model, the transfer of conceptualisation could be included at the level of ‘deverbalisation/reverbalisation’, the crucial stage of the model, where the extraction of meaning combines with the encyclopedic background to generate the target text.

Keywords: cognitive translation, conceptual integration, conceptual metaphor, interpretative model of translation, wine tasting metaphor

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Authors: Maamar Yahiaoui, Abdelrrahmene Kechich, Ismail Elkhallile Bousserhene

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This article presents a study in simulation by means of MATLAB/Simulink software of the nonlinear control in positioning of a linear synchronous machine with the esteemed force of load, to have effective control in the estimator in all tests the wished trajectory follows and the disturbance of load start. The results of simulation prove clearly that the control proposed can detect the reference of positioning the value estimates of load force equal to the actual value.

Keywords: mathematical model, Matlab, PMLSM, control, linearization, estimator, force, load, current

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Authors: Shaloom Mbambu Kabeya, Léonard Kabeya Mukeba

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Churches, cathedrals and castles beaten from antiquity to modern times were relevant from that time to the present day, and preserved as cultural heritage. Our predecessors as François 1er1, Michelangelo2, and Giotto3 left us traces. Gustave Eiffel4, Hector Guimard5 did not decrease their time to show modernization (evolution) in architecture. Plagiarism is a brake on architectural development, construction works of spirits is necessary architecture. This work explains the relationship between ancient and modern architecture. It also shows the power of mathematics in modern architecture.

Keywords: architectural modernization, heritage, mathematical architecture, materials

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Authors: Reham Banwair, Lana Alshehri, Sara Hadrawi

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The purpose of this project is to identify user satisfaction with the AI functions on Snapchat, in order to generate improvement proposals that allow its development within the app. To achieve this, a qualitative analysis was carried out through interviews to people who usually use the application, revealing their satisfaction or dissatisfaction with the usefulness of the AI. In addition, the background of the company and its introduction in these algorithms were analyzed. Furthermore, the characteristics of the three main functions of AI were explained: identify songs, solve mathematical problems, and recognize plants. As a result, it was obtained that 50% still do not know the characteristics of AI, 50% still believe song recognition is not always correct, 41.7% believe that math problems are usually accurate and 91.7% believes the plant detection tool is working properly.

Keywords: artificial intelligence, scanning, Snapchat, machine learning

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: İlhami Karahanoglu, Oguz Ceylan

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As its well-known definitions; systemic risk refers to whole economic system down-turn movement even collapse together in very severe cases. In fact, it points out the contagion effects of the defaults. Such a risk is can be depicted with the famous Chinese game of falling domino stones. During and after the Bear & Sterns and Lehman Brothers cases, it was well understood that there is a very strong effect of systemic risk in financial services sector. In this study, we concentrate on the existence of systemic risk in Turkish Banking Sector based upon the Halkbank Case during the end month of 2013; there was a political turmoil in Turkey in which the close relatives of the upper politicians were involved in illegal trading activities. In that operation, the CEO of Halkbank was also arrested and in investigation, Halkbank was considered as part of such illegal actions. That operation had an impact on Halkbanks stock value. The Halkbank stock value during that time interval decreased remarkably, the distributional profile of stock return changed and became more volatile as well as more skewed. In this study, the daily returns of 5 leading banks in Turkish banking sector were used to obtain 48 return distributions (for each month, 90-days-back stock value returns are used) of 5 banks for the period 12/2011-12/2013 (pre operation period) and 12/2013-12/2015 (post operation period). When those distributions are compared with timely manner, interestingly; the distribution of the 5 other leading banks in Turkey, public or private, had also distribution profiles which was different from the past 2011-2013 period just like Halkbank. Those 5 big banks, whose stock values are monitored with sub index in Istanbul stock exchange (BIST) as BN10, had more skewed distribution just following the Halkbank stock return movement during the post operation period, with lover mean value and as well higher volatility. In addition, the correlation between the stock value return distributions of the leading banks after Halkbank case, where the returns are more skewed to the left, increased (which is measured in monthly base before and after the operation). The dependence between those banks was stronger under the case where the stock values were falling compared with the normal market condition. Such distributional effect of stock returns between the leading banks in Turkey, which is valid for down sub-market (financial/banking sector) condition, can be evaluated as an evidence for the existence of contagious effect and systemic risk.

Keywords: financial risk, systemic risk, banking sector, return distribution, dependency structure

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Authors: Małgorzata Anna Karczmarzyk

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Who is the contemporary child? What are his/her distinctive features making him/her different from earlier generations? And how to teach in the dissimilar social reality? These questions will constitute the key to my reflections on contemporary early school education. For, to my mind, games have become highly significant for the modern model of education. There arise publications and research employing games to increase competence both in business, tutoring, or coaching, as well as in academic education . Thanks to games students and subordinates can be taught such abilities as problem thinking, creativity, consistent fulfillment of goals, resourcefulness and skills of communication.

Keywords: games, art, children, school education, integration

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Authors: E. V. Kuzmicheva

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An attention is concentrated on a service quality estimation of sport services. A typical mathematical model was developed at the base of the «general economic theory of mass service» accounting pedagogical requirements of fitness services. Also it took into account a dependence of the club member number versus on a value of square of sport facilities. Final recommendations were applied to the fitness club resulted in some improvement of the quality sport service, an increasing of the revenue from club members and profit of clubs.

Keywords: fitness club, efficiency of operation, facilities, service quality, mass service

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Authors: Esther Cabezas-Rivas

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Ordinary differential equations (ODE) are a fundamental part of the curriculum for most engineering degrees, and students typically have difficulties in the subsequent abstract mathematical calculations. To enhance their motivation and profit that they are digital natives, we propose a teamwork project that includes the creation of a video. It should explain how to model mathematically a real-world problem transforming it into an ODE, which should then be solved using the tools learned in the lectures. This idea was indeed implemented with first-year students of a BSc in Engineering and Management during the period of online learning caused by the outbreak of COVID-19 in Spain. Each group of 4 students was assigned a different topic: model a hot water heater, search for the shortest path, design the quickest route for delivery, cooling a computer chip, the shape of the hanging cables of the Golden Gate, detecting land mines, rocket trajectories, etc. These topics should be worked out through two complementary channels: a written report describing the problem and a 10-15 min video on the subject. The report includes the following items: description of the problem to be modeled, detailed obtention of the ODE that models the problem, its complete solution, and interpretation in the context of the original problem. We report the outcomes of this teaching in context and active learning experience, including the feedback received by the students. They highlighted the encouragement of creativity and originality, which are skills that they do not typically relate to mathematics. Additionally, the video format (unlike a common presentation) has the advantage of allowing them to critically review and self-assess the recording, repeating some parts until the result is satisfactory. As a side effect, they felt more confident about their oral abilities. In short, students agreed that they had fun preparing the video. They recognized that it was tricky to combine deep mathematical contents with entertainment since, without the latter, it is impossible to engage people to view the video till the end. Despite this difficulty, after the activity, they claimed to understand better the material, and they enjoyed showing the videos to family and friends during and after the project.

Keywords: active learning, contextual teaching, models in differential equations, student-produced videos

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Authors: Wang Xingbo

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Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: algorithm, determinant, computation, eigenvalue, time complexity

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Authors: Farhaz Amyn Rajabali, Collins Odour

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Mathematics has been there for over 4000 years and has been one of the very first educational topics explored by human civilization. Throughout the years, it has become a complex study and has derived so many other subjects. With advancements in ICT, most of the computation in mathematics is done using powerful computers. In many different countries, the children in primary and secondary schools face difficulties in learning mathematics, and this has many reasons behind it, one being the students don’t engage much with the mathematical concepts hence failing to understand them deeply. The objective of this system is to help the students understand this mathematical concept interactively, which in return will encourage the love for learning and increase thorough understanding of many concepts. Research was conducted among a group of samples and about 50% of respondents replied that they had never used an augmented reality application before. This means that the chances for this system to be accepted in the market are high due to its innovative idea. Around 60% of people did recommend the use of this system to learn mathematics. The study also showed several challenges in an educational system, including but not limited to lack of resources which was chosen by 30% of respondents, the challenge to read from textbooks (34.6%) and how hard it is to visualize concepts (46.2%). The survey question asked what benefits the users see using augmented reality to learn mathematics. The responses that were picked the most were increased student engagement and using real-world examples to understand concepts, both being 65.4% and followed by easy access to learning material at 61.5%, and increased knowledge retention at 50%. This shows that there are plenty of issues with an education system that can be addressed by software applications; now that the newer generation is so enthusiastic about electronic devices, it can actually be used to deliver good knowledge and skills to the upcoming students and mitigate most of the challenges faced currently. The study concludes that the implementation of the system is a best practice for the educational system especially leveraging a new technology that has the ability to attract the attention of many young students and use it to deliver information. It will also give rise to awareness of new technology and on multiple ways it can be implemented. Addressing the educational sector in developing countries using information technology is an imperative task since these kids studying now is the future of the country and will use what they learn and understand during their childhood will help them to make decisions about their lives in the future which will not only affect them personally but also affect the whole society in general.

Keywords: AR, mathematics, system development, augmented reality

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Authors: Fuad M. Alkoot

Abstract:

The main component of a machine learning system is the classifier. Classifiers are mathematical models that can perform classification tasks for a specific application area. Additionally, many classifiers are combined using any of the available methods to reduce the classifier error rate. The benefits gained from the combination of multiple classifier designs has motivated the development of diverse approaches to multiple classifiers. We aim to investigate using fractal geometry to develop an improved classifier combiner. Initially we experiment with measuring the fractal dimension of data and use the results in the development of a combiner strategy.

Keywords: fractal geometry, machine learning, classifier, fractal dimension

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

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Authors: Arcady Ponosov

Abstract:

A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

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Authors: Eugenia Vomvoridi-Ivanovic

Abstract:

It is broadly assumed that participation in field experiences will help pre-service teachers (PSTs) bridge theory to practice. However, this is often not the case since PSTs who are placed in classrooms with large numbers of students from diverse linguistic, cultural, racial, and ethnic backgrounds (culturally diverse students (CDS)) usually observe ineffective mathematics teaching practices that are in contrast to those discussed in their teacher preparation program. Over the past decades, the educational research community has paid increasing attention to investigating out-of-school learning contexts and how participation in such contexts can contribute to the achievement of underrepresented groups in Science, Technology, Engineering, and mathematics (STEM) education and their expanded participation in STEM fields. In addition, several research studies have shown that students display different kinds of mathematical behaviors and discourse practices in out-of-school contexts than they do in the typical mathematics classroom since they draw from a variety of linguistic and cultural resources to negotiate meanings and participate in joint problem solving. However, almost no attention has been given to exploring these contexts as field experiences for pre-service mathematics teachers. The purpose of this study was to explore how participation in a community based after-school field experience promotes understanding of the content pedagogy concepts introduced in elementary mathematics methods courses, particularly as they apply to teaching mathematics to CDS. This study draws upon a situated, socio-cultural theory of teacher learning that centers on the concept of learning as situated social practice, which includes discourse, social interaction, and participation structures. Consistent with exploratory case study methodology, qualitative methods were employed to investigate how a cohort of twelve participating pre-service teacher's approach to pedagogy and their conversations around teaching and learning mathematics to CDS evolved through their participation in the after-school field experience, and how they connected the content discussed in their mathematics methods course with their interactions with the CDS in the after-school. Data were collected over a period of one academic year from the following sources: (a) audio recordings of the PSTs' interactions with the students during the after-school sessions, (b) PSTs' after-school field-notes, (c) audio-recordings of weekly methods course meetings, and (d) other document data (e.g., PST and student generated artifacts, PSTs' written course assignments). The findings of this study reveal that the PSTs benefitted greatly through their participation in the after-school field experience. Specifically, after-school participation promoted a deeper understanding of the content pedagogy concepts introduced in the mathematics methods course and gained a greater appreciation for how students learn mathematics with understanding. Further, even though many of PSTs' assumptions about the mathematical abilities of CDS were challenged and PSTs began to view CDSs' cultural and linguistic backgrounds as resources (rather than obstacles) for learning, some PSTs still held negative stereotypes about CDS and teaching and learning mathematics to CDS in particular. Insights gained through this study contribute to a better understanding of how informal mathematics learning contexts may provide a valuable context for pre-service teacher's learning to teach mathematics to CDS.

Keywords: after-school mathematics program, pre-service mathematical education of teachers, qualitative methods, situated socio-cultural theory, teaching culturally diverse students

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Authors: Jean Paul M. Milambo

Abstract:

Purpose: Aromatase inhibitors (AIs) are indicated in the treatment of hormone-receptive breast cancer in postmenopausal women in various settings. Studies have shown cardiovascular events in some developed countries. To date the data is sparce for evidence-based recommendations in African clinical settings due to lack of cancer registries, capacity building and surveillance systems. Therefore, this study was conducted to assess the feasibility of HyBeacon® probe genotyping adjunctive to standard care for timely prediction and diagnosis of Aromatase inhibitors (AIs) associated adverse events in breast cancer survivors in Africa. Methods: Cross sectional study was conducted to assess the knowledge of POCT among six African countries using online survey and telephonically contacted. Incremental cost effectiveness ratio (ICER) was calculated, using diagnostic accuracy study. This was based on mathematical modeling. Results: One hundred twenty-six participants were considered for analysis (mean age = 61 years; SD = 7.11 years; 95%CI: 60-62 years). Comparison of genotyping from HyBeacon® probe technology to Sanger sequencing showed that sensitivity was reported at 99% (95% CI: 94.55% to 99.97%), specificity at 89.44% (95% CI: 87.25 to 91.38%), PPV at 51% (95%: 43.77 to 58.26%), and NPV at 99.88% (95% CI: 99.31 to 100.00%). Based on the mathematical model, the assumptions revealed that ICER was R7 044.55. Conclusion: POCT using HyBeacon® probe genotyping for AI-associated adverse events maybe cost effective in many African clinical settings. Integration of preventive measures for early detection and prevention guided by different subtype of breast cancer diagnosis with specific clinical, biomedical and genetic screenings may improve cancer survivorship. Feasibility of POCT was demonstrated but the implementation could be achieved by improving the integration of POCT within primary health cares, referral cancer hospitals with capacity building activities at different level of health systems. This finding is pertinent for a future envisioned implementation and global scale-up of POCT-based initiative as part of risk communication strategies with clear management pathways.

Keywords: breast cancer, diagnosis, point of care, South Africa, aromatase inhibitors

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Authors: Lulu Sun

Abstract:

In Addition is an after-school mathematics program in which students and their parents build mathematical confidence and competence by solving problems they curious about. It is a program consists of mix-grade from 4th to 6th grade of 10 to 20 students, including math problem solving and other activities. This partnership will focus on the relationship between the In-Addition and the parents’ engagement; in this kind of partnership, it has the In-Addition program teaching and the family engagement. This partnership is purpose to building cooperation between the program and parents, strengthening the links between the program and families.

Keywords: program-family, family engagement, positive bias, partnership

Procedia PDF Downloads 182