Search results for: mathematical reasoning

Authors: Louk Aourelien Andrianos, Edward Dommen, Athena Peralta

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Greed, as epitomized by overconsumption of natural resources, is at the root of ecological destruction and unsustainability of modern societies. Presently economies rely on unrestricted structural greed which fuels unlimited economic growth, overconsumption, and individualistic competitive behavior. Structural greed undermines the life support system on earth and threatens ecological integrity, social justice and peace. The World Council of Churches (WCC) has developed a program on ecological and economic justice (EEJ) with the aim to promote an economy of life where the economy is embedded in society and society in ecology. This paper aims at analyzing and assessing the economy of life (EcoLife) by offering an empirical tool to measure and monitor the root causes and effects of unsustainability resulting from human greed on global, national, institutional and individual levels. This holistic approach is based on the integrity of ecology and economy in a society founded on justice. The paper will discuss critical questions such as ‘what is an economy of life’ and ‘how to measure and control it from the effect of greed’. A model called GLIMS, which stands for Greed Lines and Indices Measurement System is used to clarify the concept of greed and help measuring the economy of life index by fuzzy logic reasoning. The inputs of the model are from statistical indicators of natural resources consumption, financial realities, economic performance, social welfare and ethical and political facts. The outputs are concrete measures of three primary indices of ecological, economic and socio-political greed (ECOL-GI, ECON-GI, SOCI-GI) and one overall multidimensional economy of life index (EcoLife-I). EcoLife measurement aims to build awareness of an economy life and to address the effects of greed in systemic and structural aspects. It is a tool for ethical diagnosis and policy making.

Keywords: greed line, sustainability indicators, fuzzy logic, eco-justice, World Council of Churches (WCC)

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Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: coherent covering location problem, efficient frontier, lagragian relaxation, data envelopment analysis

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Authors: Muhammad Hassan Khalil, Xu Jiadong

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Detection of malignant tumor inside the breast of women is a challenging field for the researchers. MWI (Microwave imaging) for breast cancer diagnosis has been of interest for last two decades, newly it suggested for finding cancerous tissues of women breast. A simple and basic idea of the mathematical modeling is used throughout this paper for imaging of malignant tumor. In this paper, the authors explained inverse scattering method in the microwave imaging and also present some simulation results.

Keywords: breast cancer detection, microwave imaging, tomography, tumor

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Authors: Mohd Sabri Minhat, Nurul Adilla Mohd Subha

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The PUSPATI TRIGA Reactor (RTP), Malaysia reached its first criticality on June 28, 1982, with power capacity 1MW thermal. The Feedback Control Algorithm (FCA) which is conventional Proportional-Integral (PI) controller, was used for present power control method to control fission process in RTP. It is important to ensure the core power always stable and follows load tracking within acceptable steady-state error and minimum settling time to reach steady-state power. At this time, the system could be considered not well-posed with power tracking performance. However, there is still potential to improve current performance by developing next generation of a novel design nuclear core power control. In this paper, the dual-mode predictions which are proposed in modelling Optimal Model Predictive Control (OMPC), is presented in a state-space model to control the core power. The model for core power control was based on mathematical models of the reactor core, OMPC, and control rods selection algorithm. The mathematical models of the reactor core were based on neutronic models, thermal hydraulic models, and reactivity models. The dual-mode prediction in OMPC for transient and terminal modes was based on the implementation of a Linear Quadratic Regulator (LQR) in designing the core power control. The combination of dual-mode prediction and Lyapunov which deal with summations in cost function over an infinite horizon is intended to eliminate some of the fundamental weaknesses related to MPC. This paper shows the behaviour of OMPC to deal with tracking, regulation problem, disturbance rejection and caters for parameter uncertainty. The comparison of both tracking and regulating performance is analysed between the conventional controller and OMPC by numerical simulations. In conclusion, the proposed OMPC has shown significant performance in load tracking and regulating core power for nuclear reactor with guarantee stabilising in the closed-loop.

Keywords: core power control, dual-mode prediction, load tracking, optimal model predictive control

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Authors: Weiping Liu

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This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods.

Keywords: stock price, multistage model, different growth model, discounted cash flow method

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Authors: Styliani Soulioti, Helen Fiddler

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The aim of this study was to investigate the approaches used by physiotherapists in the education of patients with chronic low back pain (cLBP) and the rationale that underpins their choice of approach. Therapeutic patient education (TPE) is considered to be an important aspect of modern physiotherapy practice, as it helps patients achieve better self-management and a better understanding of their problem. Previous studies have explored this subject, but the reasoning behind the choices physiotherapists make as educators has not been widely explored, thus making it difficult to understand areas that could be addressed in order to improve the application of TPE.A qualitative study design, guided by a constructivist epistemology was used in this research project. Semi-structured interviews were used to collect data from 7 physiotherapists. Inductive coding and thematic analysis were used, which allowed key themes to emerge. Data analysis revealed two overarching themes: 1) patient-centred versus therapist-centred educational approaches, and 2) behaviourist versus constructivist educational approaches. Physiotherapists appear to use a patient-centred-approach when they explore patients’ beliefs about cLBP and treatment expectations. However, treatment planning and goal-setting were guided by a therapist-centred approach, as physiotherapists appear to take on the role of the instructor/expert, whereas patients were viewed as students. Using a constructivist approach, physiotherapists aimed to provide guidance to patients by combining their professional knowledge with the patients’ individual knowledge, to help the patient better understand their problem, reflect upon it and find a possible solution. However, educating patients about scientific facts concerning cLBP followed a behaviourist approach, as an instructor/student relationship was observed and the learning content was predetermined and transmitted in a one-way manner. The results of this study suggest that a lack of consistency appears to exist in the educational approaches used by physiotherapists. Although patient-centeredness and constructivism appear to be the aims set by physiotherapists in order to optimise the education they provide, a student-teacher relationship appears to dominate when it comes to goal-setting and delivering scientific information.

Keywords: chronic low back pain, educational approaches, health education, patient education

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Authors: Bar Shapira-Youngster, Sima Amram-Vaknin, Yuliya Lipshits-Braziler

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The study examined how 811 Israelis experienced and coped with the COVID-19 lockdown. Stress, uncertainty, and loss of control were reported as common emotional experiences. Two main difficulties were reported: Loneliness and health and emotional concerns. Frequent explanations for the virus's emergence were: scientific or faith reasoning. The most prevalent coping strategies were distraction activities and acceptance. Reducing the use of maladaptive coping strategies has important implications for mental health outcomes. Objectives: COVID-19 has been recognized as a collective, continuous traumatic stressor. The present study examined how individuals experienced, perceived, and coped with this traumatic event during the lockdown in Israel in April 2020. Method: 811 Israelis (71.3% were women; mean age 43.7, SD=13.3)completed an online semi-structured questionnaire consisting two sections: In the first section, participants were asked to report background information. In the second section, they were asked to answer 8 open-ended questions about their experience, perception, and coping with the covid-19 lockdown. Participation was voluntary, and anonymity was assured, they were not offered compensation of any kind. The data were subjected to qualitative content analysis that seeks to classify the participants` answers into an effective number of categories that represent similar meanings. Our content analysis of participants’ answers extended far beyond simple word counts; our objective was to try to identify recurrent categories that characterized participants’ responses to each question. We sought to ensure that the categories regarding the different questions are as mutually exclusive and exhaustive as possible. To ensure robust analysis, the data were initially analyzed by the first author, and a second opinion was then sought from research colleagues. Contribution: The present research expands our knowledge of individuals' experiences, perceptions, and coping mechanisms with continuous traumatic events. Reducing the use of maladaptive coping strategies has important implications for mental health outcomes.

Keywords: Covid-19, emotional distress, coping, continuous traumatic event

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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: Per Blomqvist

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This study is part of a larger research project on creativity and writing cultures in upper secondary schools in Sweden, with the purpose of exploring how formative assessment practices can be developed to better support students' writing of subject-specific texts. The purpose of the study is to shed light on how writing has changed over time in the subjects of Social Studies and Swedish, especially regarding changes in the formative assessment practice in relation to students opportunities to take part in creative writing processes that can develop their subject specific-writing. Theoretically, the study is based on concepts and models concerning creativity, writing instructions and formative assessment, especially regarding scaffolding in relation to the development of students' subject-specific writing. The empirical data consists of video recordings of teacher groups' conversations from five upper secondary schools in Sweden, compromising a total of twenty teachers. The conversations were conducted as so-called collective remembering interviews, a method to stimulate the participants' memory through social interaction, and focused on addressing issues on how writing assessment has changed over time. Topic analysis was used to analyze the conversations in order to identify common descriptions and expressions among the teachers in each group. The result highlights two different assessment practices that are described as giving students different opportunities to take part in creative writing processes to develop their writing of subject-specific texts. One of the assessment practices is characterized by teachers focusing on explaining to the students what the grading criteria mean and showing sample texts that correspond to a certain grade. The teachers describe that this assessment practice has led to a formalized, instrumental and product-oriented writing culture that has negative consequences for the student's development of their subject-specific writing, which often lacks independent reasoning, own conclusions and understanding of concepts. The other assessment practice is characterized by students examining text qualities and discussing a variety of sample texts to understand what different texts require. These teachers describe the assessment practice as an exploratory work that leads to more creative writing processes where the students gradually deepen their understanding of subject-specific texts and develop their writing.

Keywords: teaching for creativity, writing processes, formative assessment, subject-specific writing

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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: 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: Samaneh Poormohammadi, Farid Golkar, Vahideh Khatibi Sarabi

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Climate change and consecutive droughts have increased the importance of using rainwater harvesting methods. One of the methods of rainwater harvesting and, in other words, the management of atmospheric water resources is the use of weather modification technologies. Weather modification (also known as weather control) is the act of intentionally manipulating or altering the weather. The most common form of weather modification is cloud seeding, which increases rain or snow, usually for the purpose of increasing the local water supply. Cloud seeding operations in Iran have been married since 1999 in central Iran with the aim of harvesting rainwater and reducing the effects of drought. In this research, we analyze the results of cloud seeding operations in the Simindashtplain in northern Iran. Rainwater harvesting with the help of cloud seeding technology has been evaluated through its effects on surface water and underground water. For this purpose, two different methods have been used to estimate runoff. The first method is the US Soil Conservation Service (SCS) curve number method. Another method, known as the reasoning method, has also been used. In order to determine the infiltration rate of underground water, the balance reports of the comprehensive water plan of the country have been used. In this regard, the study areas located in the target area of each province have been extracted by drawing maps of the influence coefficients of each area in the GIS software. It should be mentioned that the infiltration coefficients were taken from the balance sheet reports of the country's comprehensive water plan. Then, based on the area of each study area, the weighted average of the infiltration coefficient of the study areas located in the target area of each province is considered as the infiltration coefficient of that province. Results show that the amount of water extracted from the rain with the help of cloud seeding projects in Simindasht is as follows: an increase in runoff 63.9 million cubic meters (with SCS equation) or 51.2 million cubic meters (with logical equation) and an increase in ground water resources: 40.5 million cubic meters.

Keywords: rainwater harvesting, ground water, atmospheric water resources, weather modification, cloud seeding

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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: 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: 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: Fatemeh Jannesarvatan, Ghazaal Parastooei, Jimmy frerejan, Saedeh Mokhtari, Peter Van Rosmalen

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Medical and dental education increasingly emphasizes the acquisition, integration, and coordination of complex knowledge, skills, and attitudes that can be applied in practical situations. Instructional design approaches have focused on using real-life tasks in order to facilitate complex learning in both real and simulated environments. The Four component instructional design (4C/ID) model has become a useful guideline for designing instructional materials that improve learning transfer, especially in health profession education. The objective of this study was to apply the 4C/ID model in the creation of virtual patients (VPs) that dental students can use to practice their clinical management and clinical reasoning skills. The study first explored the context and concept of complication factors and common errors for novices and how they can affect the design of a virtual patient program. The study then selected key dental information and considered the content needs of dental students. The design of virtual patients was based on the 4C/ID model's fundamental principles, which included: Designing learning tasks that reflect real patient scenarios and applying different levels of task complexity to challenge students to apply their knowledge and skills in different contexts. Creating varied learning materials that support students during the VP program and are closely integrated with the learning tasks and students' curricula. Cognitive feedback was provided at different levels of the program. Providing procedural information where students followed a step-by-step process from history taking to writing a comprehensive treatment plan. Four virtual patients were designed using the 4C/ID model's principles, and an experimental design was used to test the effectiveness of the principles in achieving the intended educational outcomes. The 4C/ID model provides an effective framework for designing engaging and successful virtual patients that support the transfer of knowledge and skills for dental students. However, there are some challenges and pitfalls that instructional designers should take into account when developing these educational tools.

Keywords: 4C/ID model, virtual patients, education, dental, instructional design

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Authors: Mohaammad Ahmadpanah, Amineh Akhondi, Mohammad Haghighi, Ali Ghaleiha, Leila Jahangard, Elham Salari

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Background: Working memory includes the capability to keep and manipulate information in a short period of time. This capability is the basis of complicated judgments and has been attended to as the specific and constant character of individuals. Children with attention deficit and hyperactivity are among the people suffering from deficiency in the active memory, and this deficiency has been attributed to the problem of frontal lobe. This study utilizes a new approach with suitable tasks and methods for training active memory and assessment of the effects of the trainings. Participants: The children participating in this study were of 7-15 year age, who were diagnosed by the psychiatrist and psychologist as hyperactive and attention deficit based on DSM-IV criteria. The intervention group was consisted of 8 boys and 6 girls with the average age of 11 years and standard deviation of 2, and the control group was consisted of 2 girls and 5 boys with an average age of 11.4 and standard deviation of 3. Three children in the test group and two in the control group were under medicinal therapy. Results: Working memory training meaningfully improved the performance in not-trained areas as visual-spatial working memory as well as the performance in Raven progressive tests which are a perfect example of non-verbal, complicated reasoning tasks. In addition, motional activities – measured based on the number of head movements during computerized measuring program – was meaningfully reduced in the medication group. The results of the second test showed that training similar exercise to teenagers and adults results in the improvement of cognition functions, as in hyperactive people. Discussion: The results of this study showed that the performance of working memory is improved through training, and these trainings are extended and generalized in other areas of cognition functions not receiving any training. Trainings resulted in the improvement of performance in the tasks related to prefrontal. They had also a positive and meaningful impact on the moving activities of hyperactive children.

Keywords: attention deficit hyperactivity disorder, working memory, non-medical treatment, children

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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: 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

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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

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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

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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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