Search results for: mathematical cognition

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: Liang Wang, Wei Zhang

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Nowadays, sustainable development has increasingly become an important research topic of engineering education. Existing research on Engineering Education for Sustainable Development (EESD) has highlighted the importance of perceptions for ethical responsibility to address sustainable development in practice. However, whether and how the professional engineering experience affects those perceptions has not been proved, especially in a Chinese context. Our study fills this gap by investigating the perceptions bias of EESD between experienced engineers and engineering students. We specifically examined what EESD means for experienced engineers and engineering students using a triple-dimensional model to understand if there are obvious differences between the two groups. Our goal is to make the benefits of these experiences more accessible in school context. The data (n=438) came from a questionnaire created and adapted from previously published studies containing 288 students from mechanical or civil engineering and 150 civil engineers with rich working experience, and the questionnaire was distributed during Fall 2020. T-test was used to find the difference in different dimensions between the two groups. The statistical results show that there is a significant difference in the perceptions of EESD between experienced engineers and inexperienced engineering students in China. Experienced engineers tend to consider sustainable development from ecological, economic, and social perspectives, while engineering students' answers focus more on ecology and ignore economic and social dimensions to some extend. The findings provide empirical evidence that professional experience is helpful to cultivate the cognition and ability of sustainable development in engineering education. The results of this work indicate that more practical content should be added to engineering education to promote sustainable development. In addition, for the design of engineering courses and professional practice systems for sustainable development, we should not only pay attention to the ecological aspects but also emphasize the coordination of ecological, economic, and socially sustainable development (e.g., engineer's ethical responsibility).

Keywords: engineering education, sustainable development, experienced engineers, engineering students

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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: Marcin Michalak

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Biclustering is the way of two-dimensional data analysis. For several years it became possible to express such issue in terms of Boolean reasoning, for processing continuous, discrete and binary data. The mathematical backgrounds of such approach — proved ability of induction of exact and inclusion–maximal biclusters fulfilling assumed criteria — are strong advantages of the method. Unfortunately, the core of the method has quite high computational complexity. In the paper the basics of Boolean reasoning approach for biclustering are presented. In such context the problems of computation parallelization are risen.

Keywords: Boolean reasoning, biclustering, parallelization, prime implicant

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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: 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: 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: Indira Makhazhan, Azamat Taigarayev, Perizat Yerlan, Batyrbay Gulbike, Samal Abzhanova

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Aitys is a competitional performance of two or more poets creating instantly the lyrics of music concerning the social issues accompanied with the traditional instrument dombra. It is an unique music genre, because it is not practical to create music and lyrics spontaneous in anywhere else. This research study tends to approach to this particular music genre Aitys and identify its significance not only in the sense of the Kazakh cultural heritage, but also from the perspective of personal development as the improvisational , oratory, public performance skills within the ability to think critically over the social problems and represent them in convenient to public form. Through conducting this research, this paper aims to reveal the importance and beneficence of aitys in terms of both prevalence of cultural heritage and its function in personal development of the singer. In order to answer to the research question, we conducted a survey and an in-depth interview with the students of Nazarbayev University. In the survey it was asked to answer the general questions about aitys and its importance, whereas in the interview part, we asked their opinion on the importance of aitys in improving the personal skills. The results of findings was more surprising than it was expected. They agreed that the aitys lessons, workshops and concerts have high outcomes in terms improvements of improvisational, oratory, and leadership skills. Students of NU as a representors of young generation have shown a great interest in aitys, and even more interested in the topics/social issues, where the poets have to defend their usually controversial position. To conclude, the research study has focused on the importance of the aitys in personal development of different leadership skills. The given research lead us to think about the aitys as a part of cognitive musicology, where within the learning of music it represents the process of cognition as well.

Keywords: aitys, cultural heritage, Kazakh language, musicology, personal development

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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: Hammache Nadir

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The scientific study of human learning and memory is now more than 125 years old. Psychologists have conducted thousands of experiments, correlational analyses, and field studies during this time, in addition to other research conducted by those from neighboring fields. A huge knowledge base has been carefully built up over the decades. Given this backdrop, we may ask ourselves: What great changes in education have resulted from this huge research base? How has the scientific study of learning and memory changed practices in education from those of, say, a century ago? Have we succeeded in building a translational educational science to rival medical science (in which biological knowledge is translated into medical practice) or types of engineering (in which, e.g., basic knowledge in chemistry is translated into products through chemical engineering)? The answer, I am afraid, is rather mixed. Psychologists and psychological research have influenced educational practice, but in fits and starts. After all, some of the great founders of American psychology—William James, Edward L. Thorndike, John Dewey, and others—are also revered as important figures in the history of education. And some psychological research and ideas have made their way into education—for instance, computer-based cognitive tutors for some specific topics have been developed in recent years—and in years past, such practices as teaching machines, programmed learning, and, in higher education, the Keller Plan were all important. These older practices have not been sustained. Was that because they failed or because of a lack of systematic research showing they were effective? At any rate, in 2012, we cannot point to a well-developed translational educational science in which research about learning and memory, thinking and reasoning, and related topics is moved from the lab into controlled field trials (like clinical trials in medicine) and the tested techniques, if they succeed, are introduced into broad educational practice. We are just not there yet, and one question that arises is how we could achieve a translational educational science.

Keywords: affective, education, cognition, pshychology

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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: 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: Hiroko Komatsu, Kaori Yagasaki

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Background: Cancer-related cognitive impairment is a common problem seen in cancer patients undergoing chemotherapy. Physical activity may show beneficial effects on the cognitive function in such patients. Therefore, we have developed a self-directed home yoga program for cancer patients with cognitive symptoms during chemotherapy. This program involves a DVD presenting a combination of yoga courses based on patient preferences to be practiced at home. This study was performed to examine the feasibility of this program. In addition, we also examined changes in cognitive function and quality of life (QOL) in these patients participating in the program. Methods: This prospective feasibility study was conducted in a 500-bed general hospital in Tokyo, Japan. The study population consisted of breast cancer patients undergoing chemotherapy as the initial therapy. This feasibility study used a convenience sample with estimation of recruitment rate in a single facility with the availability of trained nurses and physicians to ensure safe yoga intervention. The aim of the intervention program was to improve cognitive function by means of both physical and mental activation via yoga, consisting of physical practice, breathing exercises, and meditation. Information on the yoga program was provided as a booklet, with an instructor-guided group yoga class during the orientation, and a self-directed home yoga program on DVD with yoga logs. Results: The recruitment rate was 44.7%, and the study population consisted of 18 women with a mean age of 43.9 years. This study showed high rates of retention, adherence, and acceptability of the yoga program. Improvements were only observed in the cognitive aspects of fatigue, and there were serious adverse events during the program. Conclusion: The self-directed home yoga program discussed here was both feasible and safe for breast cancer patients showing cognitive symptoms during chemotherapy. The patients also rated the program as useful, interesting, and satisfactory. Participation in the program was associated with improvements in cognitive fatigue but not cognitive function.

Keywords: yoga, cognition, breast cancer, chemotherapy, quality of life

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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: Sandeep Goyal, Sandeep Saluja

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Natural antioxidants have major role in maintenance of health. Green tea extract principally contains epigallocatechin-3-gallate (EGCG), as its abundant antioxidant constituent. Green tea is consumed daily worldwide as antioxidant to combat CNS diseases and has traditional importance also. EGCG has neuroprotective potential in various animal models of Parkinson disease, Alzheimer’s disease etc. but its exact mechanism has not been ruled out. The present study has been designed to investigate the anti-inflammatory, antioxidant and mitochondrial modulating mechanism of neuroprotective effect of epigallocatechin-3-gallate against rodent model of rotenone induced Parkinson’s disease (PD). The behavioural alterations were assessed by using open field test apparatus, Chatilon’s grip strength test apparatus and elevated plus maze for determining the locomotor activity, grip strength and cognition respectively. Biochemically, various parameters to assess oxidative stress, neuroinflammation and neurochemical estimations were performed on rat brain homogenates. A histological examination of rat brain striatum was done to check the neurodegeneration. Epigallocatechin-3-gallate (EGCG) at 10 & 20 mg/kg, were investigated for their neuroprotective potential along with levodopa as a standard agent. Minocycline, a microglial activation inhibitor, was administered alone and in combination with EGCG. EGCG and minocycline produced ameliorative effect against rotenone induced PD like symptoms by significantly reduced behavioral, biochemical and histological alterations. Results of our study reveal the neuroprotective effect of EGCG and minocycline against rotenone induced PD. Results of our study indicate that EGCG exerted neuroprotective effect against rotenone induced PD via its antioxidant, anti-inflammatory and mitochondrial modulating mechanisms and substantiate its previously reported and traditional claims for its use in CNS diseases.

Keywords: antioxidants, neurotoxicity, rotenone, EGCG

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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: Yi-Hsiu Lai

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The present study aimed to elucidate the nature of semantic processing in Chinese. Language and cognition related to the issue of aging are examined from the perspective of picture naming and category fluency tasks. Twenty Chinese-speaking adults (ranging from 25 to 45 years old) and twenty Chinese-speaking seniors (ranging from 65 to 75 years old) in Taiwan participated in this study. Each of them individually completed two tasks: a picture naming task and a category fluency task. Instruments for the naming task were sixty black-and-white pictures: thirty-five object and twenty-five action pictures. Category fluency task also consisted of two semantic categories – objects (or nouns) and actions (or verbs). Participants were asked to report as many items within a category as possible in one minute. Scores of action fluency and of object fluency were a summation of correct responses in these two categories. Category effects (actions vs. objects) and age effects were examined in these tasks. Objects were further divided into two major types: living objects and non-living objects. Actions were also categorized into two major types: action verbs and process verbs. Reaction time to each picture/question was additionally calculated and analyzed. Results of the category fluency task indicated that the content of information in Chinese seniors was comparatively deteriorated, thus producing smaller number of semantic-lexical items. Significant group difference was also found in the results of reaction time. Category Effect was significant for both Chinese adults and seniors in the semantic fluency task. Findings in the present study helped characterize the nature of semantic processing in Chinese-speaking adults and seniors and contributed to the issue of language and aging.

Keywords: semantic processing, aging, Chinese, category effects

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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: Ozgu Hafizoglu

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An analogy is an essential tool of human cognition that enables connecting diffuse and diverse systems with physical, behavioral, principal relations that are essential to learning, discovery, and innovation. The Cognitive Model of Analogy (CMA) leads and creates patterns of pathways to transfer information within and between domains in science, just as happens in the brain. The connectome of the brain shows how the brain operates with mental leaps between domains and mental hops within domains and the way how analogical reasoning mechanism operates. This paper demonstrates the CMA as an evolutionary approach to science, technology, and life. The model puts forward the challenges of deep uncertainty about the future, emphasizing the need for flexibility of the system in order to enable reasoning methodology to adapt to changing conditions in the new era, especially post-pandemic. In this paper, we will reveal how to draw an analogy to scientific research to discover new systems that reveal the fractal schema of analogical reasoning within and between the systems like within and between the brain regions. Distinct phases of the problem-solving processes are divided thusly: stimulus, encoding, mapping, inference, and response. Based on the brain research so far, the system is revealed to be relevant to brain activation considering each of these phases with an emphasis on achieving a better visualization of the brain’s mechanism in macro context; brain and spinal cord, and micro context: glia and neurons, relative to matching conditions of analogical reasoning and relational information, encoding, mapping, inference and response processes, and verification of perceptual responses in four-term analogical reasoning. Finally, we will relate all these terminologies with these mental leaps, mental maps, mental hops, and mental loops to make the mental model of CMA clear.

Keywords: analogy, analogical reasoning, brain connectome, cognitive model, neurons and glia, mental leaps, mental hops, mental loops

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Authors: L. Atif, C. Rosenthal-Sabroux, M. Grundstein

Abstract:

The requirements engineering process is a crucial phase in the design of complex systems. The purpose of our research is to present a collaborative problem-driven requirements engineering approach that aims at improving the design of a Decision Support System as an Analytics application. This approach has been adopted to design a Human Resource management DSS. The Requirements Engineering process is presented as a series of guidelines for activities that must be implemented to assure that the final product satisfies end-users requirements and takes into account the limitations identified. For this, we know that a well-posed statement of the problem is “a problem whose crucial character arises from collectively produced estimation and a formulation found to be acceptable by all the parties”. Moreover, we know that DSSs were developed to help decision-makers solve their unstructured problems. So, we thus base our research off of the assumption that developing DSS, particularly for helping poorly structured or unstructured decisions, cannot be done without considering end-user decision problems, how to represent them collectively, decisions content, their meaning, and the decision-making process; thus, arise the field issues in a multidisciplinary perspective. Our approach addresses a problem-driven and collaborative approach to designing DSS technologies: It will reflect common end-user problems in the upstream design phase and in the downstream phase these problems will determine the design choices and potential technical solution. We will thus rely on a categorization of HR’s problems for a development mirroring the Analytics solution. This brings out a new data-driven DSS typology: Descriptive Analytics, Explicative or Diagnostic Analytics, Predictive Analytics, Prescriptive Analytics. In our research, identifying the problem takes place with design of the solution, so, we would have to resort a significant transformations of representations associated with the HR Analytics application to build an increasingly detailed representation of the goal to be achieved. Here, the collective cognition is reflected in the establishment of transfer functions of representations during the whole of the design process.

Keywords: DSS, collaborative design, problem-driven requirements, analytics application, HR decision making

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