Search results for: mathematical competency

Authors: Shashi Kant Mishra

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In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPEC). We establish necessary and sufficient optimality conditions for the SIMPEC, using convexificators. We study the Wolfe type dual problem for the SIMPEC under the ∂∗convexity assumptions. A Mond-Weir type dual problem is also formulated and studied for the SIMPEC under the ∂∗-convexity, ∂∗-pseudoconvexity and ∂∗quasiconvexity assumptions. Weak duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification (GS-ACQ).

Keywords: mathematical programming problems with equilibrium constraints, optimality conditions, semi-infinite programming, convexificators

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Authors: Fatemeh Yazdanmehr, Iulian Nistor

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The scope of the current study is the evaluation of the electric field effect on electrostatic desalting mathematical modeling with laboratory data. This research study was focused on developing a model for an existing operation desalting unit of one of the Iranian heavy oil field with a 75 MBPD production capacity. The high temperature of inlet oil to dehydration unit reduces the oil recovery, so the mathematical modeling of desalter operation parameters is very significant. The existing production unit operating data has been used for the accuracy of the mathematical desalting plant model. The inlet oil temperature to desalter was decreased from 110 to 80°C, and the desalted electrical field was increased from 0.75 to 2.5 Kv/cm. The model result shows that the desalter parameter changes meet the water-oil specification and also the oil production and consequently annual income is increased. In addition to that, changing desalter operation conditions reduces environmental footprint because of flare gas reduction. Following to specify the accuracy of selected electrostatic desalter electrical field, laboratory data has been used. Experimental data are used to ensure the effect of electrical field change on desalter. Therefore, the lab test is done on a crude oil sample. The results include the dehydration efficiency in the presence of a demulsifier and under electrical field (0.75 Kv) conditions at various temperatures. Comparing lab experimental and electrostatic desalter mathematical model results shows 1-3 percent acceptable error which confirms the validity of desalter specification and operation conditions changes.

Keywords: desalter, electrical field, demulsification, mathematical modeling, water-oil separation

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Authors: M. A. Khanday, Aasma Rafiq, Khalid Nazir

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This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in the human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick’s principle and the law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The results illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the results that the drug concentration decreases in the first compartment and gradually increases in other subsequent compartments.

Keywords: Laplace transform, diffusion, eigenvalue method, mathematical model

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Authors: Karen K. Perez-Ramirez, Genevieve Dupont, Virginia Gonzalez-Velez

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Pancreatic alpha-cells participate on glucose regulation together with beta cells. They release glucagon hormone when glucose level is low to stimulate gluconeogenesis from the liver. As other excitable cells, alpha cells generate Ca2+ and metabolic oscillations when they are stimulated. It is known that the glucose level can trigger or silence this activity although it is not clear how this occurs in normal and diabetic people. In this work, we propose an electric-metabolic mathematical model implemented in Matlab to study the effect of different glucose levels on the electrical response and Ca2+ oscillations of an alpha cell. Our results show that Ca2+ oscillations appear in opposite phase with metabolic oscillations in a window of glucose values. The model also predicts a direct relationship between the level of glucose and the intracellular adenine nucleotides showing a self-regulating pathway for the alpha cell.

Keywords: Ca2+ oscillations, mathematical model, metabolic oscillations, pancreatic alpha cell

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Authors: Toru Shionoya, Yosuke Kurihara, Takashi Kaburagi, Kajiro Watanabe

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Mass-produced bidirectional microphones have attractive characteristics. They work as a microphone as well as a sensor with high gain over a wide frequency range; they are also highly reliable and economical. We present novel multiple functional uses of the microphones. A mathematical model for explaining the high-pass-filtering characteristics of bidirectional microphones was presented. Based on the model, the characteristics of the microphone were investigated, and a novel use for the microphone as a sensor with a wide frequency range was presented. In this study, applications for using the microphone as a security sensor and a human biosensor were introduced. The mathematical model was validated through experiments, and the feasibility of the abovementioned applications for security monitoring and the biosignal monitoring were examined through experiments.

Keywords: bidirectional microphone, low-frequency, mathematical model, frequency response

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Authors: Robert L. Burdett, Bayan Bevrani

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Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways, these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

Keywords: capacity analysis, capacity expansion, railways, track sub division, track duplication

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Authors: Ledeza Jordan Babiano

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Translating statements into mathematical notations is one of the processes in word problem-solving. However, based on the literature, students still have difficulties with this skill. The purpose of this study was to investigate the translation errors of the students when they translate algebraic word problems into mathematical structures and locate the errors via the lens of the Translation-Verification Model. Moreover, this qualitative research study employed content analysis. During the data-gathering process, the students were asked to answer a six-item algebra word problem questionnaire, and their answers were analyzed by experts through blind coding using the Translation-Verification Model to determine their translation errors. After this, a focus group discussion was conducted, and the data gathered was analyzed through thematic analysis to determine the causes of the students’ translation errors. It was found out that students’ prevalent error in translation was the interpretation error, which was situated in the Attribute construct. The emerging themes during the FGD were: (1) The procedure of translation is strategically incorrect; (2) Lack of comprehension; (3) Algebra concepts related to difficulty; (4) Lack of spatial skills; (5) Unprepared for independent learning; and (6) The content of the problem is developmentally inappropriate. These themes boiled down to the major concept of independent learning preparedness in solving mathematical problems. This concept has subcomponents, which include contextual and conceptual factors in translation. Consequently, the results provided implications for instructors and professors in Mathematics to innovate their teaching pedagogies and strategies to address translation gaps among students.

Keywords: mathematical structure, algebra word problems, translation, errors

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Authors: Abrudan Dumitru

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Civil infrastructures require permanent attention from the moment of taking over to the moment of demolition. One important aspect that is mandatory to be taken into consideration is crack detection. This operation, to detect cracks that can appear during the lifetime of the civil infrastructure, requires specialized personnel and, depending on the civil infrastructure, can require specialized skills (such as climbing). To overcome this issue with regard to specialized manpower, image processing is used. In our days images can be easily acquired using an unmanned aircraft vehicle system known also as a drone. The main advantages of a drone for civil infrastructure image acquisition are it can be operated at different heights, weather conditions are not an issue, being suitable to be used on rainy, windy, sunny days and so on. In this paper, we used a dataset that contains three types of images: with cracks, without cracks and with noise. To remove the noise presented in images, mathematical morphology operators (MMO) are used.

Keywords: VGG16, VGG19, image processing, mathematical morphology

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Authors: Yasaman Azarmjoo

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Since ancient times, it has been said that mathematics is the mother of all sciences and the foundation of basic concepts in every field and profession. It would be great if, after learning this subject, we could enable students to create games and activities based on the same mathematical concepts. This article explores the design of various mathematical activities in the form of games, utilizing different mathematical topics such as algebra, equations, binary systems, and one-to-one correspondence. The theoretical significance of this article lies in uncovering alternative approaches to teaching and learning mathematics. By employing creative and interactive methods such as game design, it challenges the traditional perception of mathematics as a difficult and laborious subject. The theoretical significance of this article lies in demonstrating that mathematics can be made more accessible and enjoyable, which can result in heightened interest and engagement in the subject. In general, this article reveals another aspect of mathematics.

Keywords: playing with mathematics, algebra and equations, binary systems, one-to-one correspondence

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Authors: Krisstalova Dana, Mazal Jan

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This article deals with geographical conditions in terrain and their effect on the movement of vehicles, their effect on speed and safety of movement of people and vehicles. Finding of the optimal routes outside the communication is studied in the army environment, but it occur in civilian as well, primarily in crisis situation, or by the provision of assistance when natural disasters such as floods, fires, storms etc., have happened. These movements require the optimization of routes when effects of geographical factors should be included. The most important factor is the surface of a terrain. It is based on several geographical factors as are slopes, soil conditions, micro-relief, a type of surface and meteorological conditions. Their mutual impact has been given by coefficient of deceleration. This coefficient can be used for the commander`s decision. New approaches and methods of terrain testing, mathematical computing, mathematical statistics or cartometric investigation are necessary parts of this evaluation.

Keywords: movement in a terrain, geographical factors, surface of a field, mathematical evaluation, optimization and searching paths

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Authors: Nitin Ghule, S. G. Taji

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A mathematical model of hot-wall condensers used in refrigerators is presented. The model predicts the heat transfer characteristics of condenser and the effects of various design and operating parameters on condenser tube length and capacity. A finite element approach was used to model the condenser. The condenser tube is divided into elemental units, with each element consisting of adhesive tape, refrigerant tube and outer metal sheet. The heat transfer characteristics of each section are then analyzed by considering the heat transfer through the tube wall, tape and the outer sheet. Variations in inner heat transfer coefficient and pressure drop are considered depending on temperature, fluid phase, type of flow and orientation of tube. Variation in outer heat transfer coefficient is also taken into account. Various materials were analysed for the tube, tape and outer sheet.

Keywords: condenser, domestic refrigerator, heat transfer, mathematical model

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Authors: M. Y. Ismail, M. Inam, A. F. M. Zain, N. Misran

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Progressive phase distribution is an important consideration in reflect array antenna design which is required to form a planar wave in front of the reflect array aperture. This paper presents a detailed mathematical model in order to determine the required reflection phase values from individual element of a reflect array designed in Ku-band frequency range. The proposed technique of obtaining reflection phase can be applied for any geometrical design of elements and is independent of number of array elements. Moreover the model also deals with the solution of reflect array antenna design with both centre and off-set feed configurations. The theoretical modeling has also been implemented for reflect arrays constructed on 0.508 mm thickness of different dielectric substrates. The results show an increase in the slope of the phase curve from 4.61°/mm to 22.35°/mm by varying the material properties.

Keywords: mathematical modeling, progressive phase distribution, reflect array antenna, reflection phase

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Authors: Arnold M. Brener, Lesbek Tashimov, Ablakim S. Muratov

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The paper deals with the special model for coagulation kernels which represents new control parameters in the Smoluchowski equation for binary aggregation. On the base of the model the new approach to evaluating aggregative stability of disperse systems has been submitted. With the help of this approach the simple estimates for aggregative stability of various types of hydrophilic nano-suspensions have been obtained.

Keywords: aggregative stability, coagulation kernels, disperse systems, mathematical model

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Authors: Peter Akayuure, Michael Johnson Nabie

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Similar to many colonized nations in the world, one indelible mark left by colonial masters after Ghana’s independence in 1957 has been the fact that many contexts used to teach statistics and probability concepts are often alien and do not resonate with the social domain of our indigenous Ghanaian child. This has seriously limited the understanding, discoveries, and applications of mathematics for national developments. With the recent curriculum demands of making the Ghanaian child mathematically literate, this qualitative study involved video recordings and mathematical analysis of play sessions of an indigenous girl game called Ampe with the aim to demystify the concepts in probability theorem, which is applied in mathematics related fields of study. The mathematical analysis shows that the game of Ampe, which is widely played by school girls in Ghana, is suitable for learning concepts of the probability theorems. It was also revealed that as a girl game, the use of Ampe provides good lessons to educators, textbook writers, and teachers to rethink about the selection of mathematics tasks and learning contexts that are sensitive to gender. As we undertake to transform teacher education and student learning, the use of indigenous games should be critically revisited.

Keywords: Ampe, mathematical analysis, probability theorem, Ghanaian girl game

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Authors: Sperisa Distantina, Rieke Ulfha Noviyanti, Sri Sutriyani, Fadilah Fadilah, Mujtahid Kaavessina

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In this research, carrageenan extracted from seaweed Eucheuma cottonii was mixed with polyvinyl alcohol (PVA) and then crosslinked using glutaraldehyde (GA). The obtained hydrogel films were applied to control the drug release rate of paracetamol. The aim of this research was to develop a mathematical model that can be used to describe the mass transfer rate of paracetamol from the hydrogel film into buffer solution. The effect of weight ratio carrageenan-PVA (5: 0, 1: 0.5, 1: 1, 1: 2, 0: 5) on the parameters of the mathematical model was investigated also. Based on the experimental data, the proposed mathematical model could describe the mass transfer rate of paracetamol. The weight ratio of carrageenan-PVA greatly affected the amount of paracetamol absorbed in the hydrogel film and the mass transfer rate of paracetamol.

Keywords: carrageenan-PVA, crosslinking, glutaraldehyde, hydrogel, paracetamol, mass transfer

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Authors: Ntaganda J.M., Maniraguha J.D., Mukeshimana S., Harelimana D, Bizimungu T., Ruataganda E.

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This paper presents the design of Graphic User Interface (GUI) in Matlab as interaction tool between human and machine. The designed GUI can be used by medical doctors and other experts particularly the physiologists. Matlab packages and estimated parameters of the mathematical model of cardiovascular-respiratory system developed in Rwandan context are used in GUI. The ordinary differential equations (ODE’s) govern a mathematical model in designing GUI in Matlab and a window that sets model estimated parameters and the measured parameters by any user. For healthy subject, these measured parameters include heart rate, systolic blood and diastolic blood pressure, partial pressure of oxygen in arterial blood, partial pressure of carbon dioxide in arterial blood, concentration of bound and dissolved oxygen in the mixed venous blood entering the lungs, and concentration of bound and dissolved carbon dioxide in the mixed venous blood entering the lungs. The results of numerical test give a consistent appearance as empirically known results.

Keywords: Graphic User Interface, mathematical model, cardiovascur-respiratory system, walking physical activity, blood pressure, oxygen

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Authors: Zeta Dooly, Aidan Duane

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The collaborative European funded research and development landscape provides prime environmental conditions for multi-disciplinary teams to learn and enhance their knowledge beyond the capability of training and learning within their own organisation cocoons. Whilst the emergence of the academic entrepreneur has changed the focus of educational institutions to that of quasi-businesses, the training and professional development of lecturers and academic staff are often not formalised to the same level as industry. This research focuses on industry and academic collaborative research funded by the European Commission. The impact of research is scalable if an optimum research network is created and managed effectively. This paper investigates network embeddedness, the nature of relationships, links, and nodes within a research network, and the enhancement of the network’s knowledge. The contribution of this paper extends our understanding of establishing and maintaining effective collaborative research networks. The effects of network embeddedness are recognized in the literature as pertinent to innovation and the economy. Network theory literature claims that networks are essential to innovative clusters such as Silicon valley and innovation in high tech industries. This research provides evidence to support the impact collaborative research has on the disparate individuals toward their innovative contributions to their organisations and their own professional development. This study adopts a qualitative approach and uncovers some of the challenges of multi-disciplinary research through case study insights. The contribution of this paper recommends the establishment of scaffolding to accommodate cooperation in research networks, role appointment, and addressing contextual complexities early to avoid problem cultivation. Furthermore, it suggests recommendations in relation to network formation, intra-network challenges in relation to open data, competition, friendships, and competency enhancement. The network capability is enhanced by the adoption of the relevant theories; network theory, open innovation, and social exchange, with the understanding that the network structure has an impact on innovation and social exchange in research networks. The research concludes that there is an opportunity to deepen our understanding of the impact of network reuse and network hoping that provides scaffolding for the network members to enhance and build upon their knowledge using a progressive approach.

Keywords: research networks, competency building, network theory, case study

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Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

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We have conducted the optimal synthesis of root-mean-squared objective filter to estimate the state vector in the case if within the observation channel with memory the anomalous noises with unknown mathematical expectation are complement in the function of the regular noises. The synthesis has been carried out for linear stochastic systems of continuous-time.

Keywords: mathematical expectation, filtration, anomalous noise, memory

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Authors: Neha J. Nandaniya

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In the present research paper researcher put focuses on the opinions of pre-service teachers have been taken regarding online language teaching, which was held during the COVID-19 pandemic and is still going on. The researcher developed a three-point rating scale in Google Forms to find out the views of trainees on online language learning, in which 167 B. Ed. trainees having language content and method gave their responses. After scoring the responses obtained by the investigator, the chi-square value was calculated, and the findings were concluded. The major finding of the study is language learning is not as effective as offline teaching mode.

Keywords: online language teaching, ICT competency, B. Ed. trainees, COVID-19 pandemic

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Authors: Wasif Mughees, Malik Al-Ahmad

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This research presents the graphical design analysis and mathematical programming technique to dig out the possible water allocation distribution to minimize water usage in process units. The study involves the mass and property integration in its core methodology. Tehran Oil Refinery is studied to implement the focused water pinch technology for regeneration, reuse and recycling of water streams. Process data is manipulated in terms of sources and sinks, which are given in terms of properties. Sources are the streams to be allocated. Sinks are the units which can accept the sources. Suspended Solids (SS) is taken as a single contaminant. The model minimizes the mount of freshwater from 340 to 275m3/h (19.1%). Redesigning and allocation of water streams was built. The graphical technique and mathematical programming shows the consistency of results which confirms mass transfer dependency of water streams.

Keywords: minimization, water pinch, process integration, pollution prevention

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Authors: Fatima Faiza Ahmed, Syed Farrukh Hussain

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The last few decades have seen a large proportion of our population bending towards e-learning technologies, starting from learning tools used in primary and elementary schools to competency based e-learning systems specifically designed for applications like finance and marketing. The huge diversity in this crowd brings about a large number of challenges for the designers of these e-learning systems, one of which is the adaptability of such systems. This paper focuses on adaptability in the learning material in an e-learning course and how artificial intelligence and the semantic web can be used as an effective tool for this purpose. The study proved that the semantic web, still a hot topic in the area of computer science can prove to be a powerful tool in designing and implementing adaptable e-learning systems.

Keywords: adaptable e-learning, HTMLParser, information extraction, semantic web

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Authors: Erim Koyun

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This paper aim to construct a mathematical model for Underwater vehicles under load variation test conditions. Propeller effects on underwater vehicle are investigated. Body with counter rotating propeller model is analyzed by CFD methods, thus forces and moment are obtained. Propeller effects of vehicle’s hydrodynamic performance under load variation conditions will be investigated. Additionally, pressure contour is examined for differences between different load conditions. Axial force equation is established using hydrodynamic coefficients, which contains resistance, thrust, and additional coefficients occurs due to load variations. Additional coefficients helps to express completely axial force on underwater vehicle. When the vehicle accelerates, additional force occurs besides thrust force increment. This is propeller effect on the body. Hence, mathematical model cover this effect. For CFD analysis, the incompressible, three-dimensional, and unsteady Reynolds Averaged Navier-Stokes equations will be used Numerical results is verified with experimental results for verification. The overall goal of this study is to present complementary mathematical model for body with counter rotating propeller.

Keywords: counter rotating propeller, CFD, hydrodynamic mathematic model, hydrodynamics analysis, thrust deduction

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Authors: Hanife Merve Öztürk, Sıdıka Dalgan

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In this project, a capacity analysis study is done at TAT A. Ş. Maret Plant. Production capacity of products which generate 80% of sales amount are determined. Obtained data entered the LEKIN Scheduling Program and we get production schedules by using heuristic methods. Besides heuristic methods, as mathematical model, disjunctive programming formulation is adapted to flexible job shop problems by adding a new constraint to find optimal schedule solution.

Keywords: scheduling, flexible job shop problem, shifting bottleneck heuristic, mathematical modelling

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Authors: Aqeela Mir, Akhtar Nawaz Malik, Javaid Iqbal

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The paper presents a survey based approach in order to observe the level of awareness regarding Mechatronics in society of Pakistan and the factors affecting the future development trend of Mechatronics in Pakistan. With the help of these surveys a new direction for making a Mathematical model for the future development trend of Mechatronics in Pakistan is also suggested.

Keywords: mechatronics society survey, future development trend of mechatronics in pakistan, probability estimation, mathematical model

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Authors: Tamara Díaz-Chang, Elizabeth-H Arredondo

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This article presents the results of mixed approach research, where the ocular movements of students are examined while they solve questionnaires related to some abstract mathematical concepts. The objective of this research is to determine possible correlations between the parameters of ocular activity and the level of difficulty of the tasks. The difficulty level categories were established based on two types of criteria: a subjective one, through an evaluation, carried out by the subjects, and a behavioral one, related to obtaining the correct solution. Correlations of these criteria with ocular activity parameters, which were considered indicators of mental effort, were identified. The analysis of the data obtained allowed us to observe discrepancies in the categorization of difficulty levels based on subjective and behavioral criteria. There was a negative correlation of the eye movement parameters with the students' opinions on the level of difficulty of the questions, while a strong positive and significant correlation was noted between most of the parameters of ocular activity and the level of difficulty, determined by the percentage of correct answers. The results obtained by the analysis of the data suggest that eye movement parameters can be taken as indicators of the difficulty level of the tasks related to the study of some abstract mathematical concepts at the university.

Keywords: abstract mathematical concepts, cognitive neuroscience, eye-tracking, university education

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Authors: Hassan Karimi, Fred Piercy, Ruoxi Chen, Ana L. Jaramillo-Sierra, Wei-Ning Chang, Manjushree Palit, Catherine Martosudarmo, Angelito Antonio

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Background: The two psychotherapy camps, the randomized clinical trials (RCTs) and the common factors model, have competitively claimed specific explanations for therapy effectiveness. Recently, scholars called for empirical evidence to show the role of common factors in therapeutic outcome in marriage and family therapy. Purpose: This cross-national study aims to explore how clinicians, across different nations and theoretical orientations, attribute the contribution of common factors to therapy outcome. Method: A brief common factors questionnaire (CFQ-with a Cronbach’s Alpha, 0.77) was developed and administered in seven nations. A series of statistical analyses (paired-samples t-test, independent sample t-test, ANOVA) were conducted: to compare clinicians perceived contribution of total common factors versus model-specific factors, to compare each pair of common factors’ categories, and to compare clinicians from collectivistic nations versus clinicians from individualistic nation. Results: Clinicians across seven nations attributed 86% to common factors versus 14% to model-specific factors. Clinicians attributed 34% of therapeutic change to client’s factors, 26% to therapist’s factors, 26% to relationship factors, and 14% to model-specific techniques. The ANOVA test indicated each of the three categories of common factors (client 34%, therapist 26%, relationship 26%) showed higher contribution in therapeutic outcome than the category of model specific factors (techniques 14%). Clinicians with psychology degree attributed more contribution to model-specific factors than clinicians with MFT and counseling degrees who attributed more contribution to client factors. Clinicians from collectivistic nations attributed larger contributions to therapist’s factors (M=28.96, SD=12.75) than the US clinicians (M=23.22, SD=7.73). The US clinicians attributed a larger contribution to client’s factors (M=39.02, SD=1504) than clinicians from the collectivistic nations (M=28.71, SD=15.74). Conclusion: The findings indicate clinicians across the globe attributed more than two thirds of therapeutic change to CFs, which emphasize the training of the common factors model in the field. CFs, like model-specific factors, vary in their contribution to therapy outcome in relation to specific client, therapist, problem, treatment model, and sociocultural context. Sociocultural expectations and norms should be considered as a context in which both CFs and model-specific factors function toward therapeutic goals. Clinicians need to foster a cultural competency specifically regarding the divergent ways that CFs can be activated due to specific sociocultural values.

Keywords: common factors, model-specific factors, cross-national survey, therapist cultural competency, enhancing therapist efficacy

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Authors: Veysel Seker

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Graphic designing and virtual reality have been affected by digital development and technological development for the last decades. This study aims to compare and evaluate digitalization and virtual reality evaluation in traditional and classical methods of the graphic designing sector in Turkey. The qualitative and quantitative studies and research were discussed and identified according to the evaluated results of the literature surveys. Moreover, the study showed that the competency gap between graphic design schools and the field should be determined and well-studied. The competencies of traditional graphic designers will have a big challenge for the purpose of the transition into the developed and evaluated digital graphic design world.

Keywords: digitalization, evaluation, graphic designing, virtual reality

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Authors: Indrajit Ghosh, Jaydip Roy

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Literacy rate is an important indicator for measurement of human development. But this is not a good one to capture the qualitative dimension of educational attainment of an individual or a society. The overall educational level of an area is an important issue beyond the literacy rate. The overall educational level can be thought of as an outcome of the educational levels of individuals. But there is no well-defined algorithm and mathematical model available to measure the overall educational level of an area. A heuristic approach based on accumulated experience of experts is effective one. It is evident that fuzzy logic offers a natural and convenient framework in modeling various concepts in social science domain. This work suggests the implementation of fuzzy logic to develop a mathematical model for measurement of educational attainment of an area in terms of Education Index. The contribution of the study is two folds: conceptualization of “Education Profile” and proposing a new mathematical model to measure educational attainment in terms of “Education Index”.

Keywords: education index, education profile, fuzzy logic, literacy

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Authors: Seyed Habib A. Rahmati, Mohamad Hasan Sadeghpour, Parsa Fallah Sheikhlari

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Location quotient (LQ) is a comparison technique that represents emphasized economic structure of single zone versus the standard area to identify specialty for every zone. In another words, the exact calculation of this metric can show the main core competencies and critical capabilities of an area to the decision makers. This research focus on the exact calculation of the LQ for an Iranian Province called Qazvin and within a case study introduces LQ of the capable industries of Qazvin. Finally, through different graphs and tables, it creates an opportunity to compare the recognized capabilities.

Keywords: location quotient, case study, province analysis, core competency

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Authors: Josephine Shamash, Stuart Smith

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We examine reasons for introducing definitions in teaching mathematics in a number of different cases. We try to determine if, where, and when to provide a definition, and which definition to choose. We characterize different types of definitions and the different purposes we may have for formulating them, and detail examples of each type. Giving a definition at a certain stage can sometimes be detrimental to the development of the concept image. In such a case, it is advisable to delay the precise definition to a later stage. We describe two models, the 'successive approximation model', and the 'model of the extending definition' that fit such situations. Detailed examples that fit the different models are given based on material taken from a number of textbooks, and analysis of the way the concept is introduced, and where and how its definition is given. Our conclusions, based on this analysis, is that some of the definitions given may cause discontinuities in the learning sequence and constitute obstacles and unnecessary cognitive conflicts in the formation of the concept definition. However, in other cases, the discontinuity in passing from definition to definition actually serves a didactic purpose, is unavoidable for the mathematical evolution of the concept image, and is essential for students to deepen their understanding.

Keywords: concept image, mathematical definitions, mathematics education, mathematics teaching

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