Search results for: mathematical and trait anxiety.

Authors: Gilbert Makanda, Roelf Sypkens

Abstract:

A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: Differential equations, knowledge acquisition, least squares nonlinear, dynamical systems.

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Authors: Kamel Hashem, Ibrahim Arman

Abstract:

Information and Communication Technologies (ICT) in mathematical education is a very active field of research and innovation, where learning is understood to be meaningful and grasping multiple linked representation rather than rote memorization, a great amount of literature offering a wide range of theories, learning approaches, methodologies and interpretations, are generally stressing the potentialities for teaching and learning using ICT. Despite the utilization of new learning approaches with ICT, students experience difficulties in learning concepts relevant to understanding mathematics, much remains unclear about the relationship between the computer environment, the activities it might support, and the knowledge that might emerge from such activities. Many questions that might arise in this regard: to what extent does the use of ICT help students in the process of understanding and solving tasks or problems? Is it possible to identify what aspects or features of students' mathematical learning can be enhanced by the use of technology? This paper will highlight the interest of the integration of information and communication technologies (ICT) into the teaching and learning of mathematics (quadratic functions), it aims to investigate the effect of four instructional methods on students- mathematical understanding and problem solving. Quantitative and qualitative methods are used to report about 43 students in middle school. Results showed that mathematical thinking and problem solving evolves as students engage with ICT activities and learn cooperatively.

Keywords: Dynamic Geometry Software, Information and Communication Technologies, Visualization, Mathematical Education.

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Authors: Narges Razeghi

Abstract:

In studies on psychological health and children-s personality development and in researches on emotional distresses, children-s behavioral disorders associated with mother deprivation, are known as the major cause of mental disorders. Therefore, for identification of children-s attachment styles in nursery-s children are of significant importance. For this purpose, to compare the attachment styles between children of nursery with those provided care by their families, the Separation Anxiety Test (SAT) of Slough and et al was administered on 72 children (36 in nursery and 36 family-cared). The results indicated, almost half of children in both groups have insecure attachment styles. Tendency ratio of both groups of children towards Secure and Ambivalent Insecure styles are almost the same. However the avoidant style of attachment in children of nursery is more than those provided care by their families. The children under family care compared to the children of nursery, in the situations of separation from their mothers in the first day of school and sleeping in their room, have shown more self reliance.

Keywords: Attachment style, Separation Anxiety Test (SAT), Children, Nursery, Emotional and Behavioral Disorders

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Authors: V. S. Klimash, Ye Min Thu

Abstract:

Thyristor rectifiers, inverters grid-tied, and AC voltage regulators are widely used in industry, and on electrified transport, they have a lot in common both in the power circuit and in the control system. They have a common mathematical structure and switching processes. At the same time, the rectifier, but the inverter units and thyristor regulators of alternating voltage are considered separately both theoretically and practically. They are written about in different books as completely different devices. The aim of this work is to combine them into one class based on the unity of the equations describing electromagnetic processes, and then, to show this unity on the mathematical model and experimental setup. Based on research from mathematics to the product, a conclusion is made about the methodology for the rapid conduct of research and experimental design work, preparation for production and serial production of converters with a unified bundle. In recent years, there has been a transition from thyristor circuits and transistor in modular design. Showing the example of thyristor rectifiers and AC voltage regulators, we can conclude that there is a unity of mathematical structures and grid-tied thyristor converters.

Keywords: Direct current, alternating current, rectifier, AC voltage regulator, generalized mathematical model.

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Authors: Worachat Wannawong, Usa W. HumphriesPrungchan Wongwises, Suphat Vongvisessomjai

Abstract:

The mathematical modeling of storm surge in sea and coastal regions such as the South China Sea (SCS) and the Gulf of Thailand (GoT) are important to study the typhoon characteristics. The storm surge causes an inundation at a lateral boundary exhibiting in the coastal zones particularly in the GoT and some part of the SCS. The model simulations in the three dimensional primitive equations with a high resolution model are important to protect local properties and human life from the typhoon surges. In the present study, the mathematical modeling is used to simulate the typhoon–induced surges in three case studies of Typhoon Linda 1997. The results of model simulations at the tide gauge stations can describe the characteristics of storm surges at the coastal zones.

Keywords: lateral boundary, mathematical modeling, numericalsimulations, three dimensional primitive equations, storm surge.

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Authors: Troy L. Story

Abstract:

Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.

Keywords: Differential geometry, exterior calculus, Hamiltonian geometry, mathematical economics.

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Authors: Pinaki Pratim Acharjya, Esha Dutta

Abstract:

In image segmentation contour detection is one of the important pre-processing steps in recent days. Contours characterize boundaries and contour detection is one of the most difficult tasks in image processing. Hence it is a problem of fundamental importance in image processing. Contour detection of an image decreases the volume of data considerably and useless information is removed, but the structural properties of the image remain same. In this research, a robust and effective contour detection technique has been proposed using mathematical morphology. Three different contour detection results are obtained by using morphological dilation and erosion. The comparative analyses of three different results also have been done.

Keywords: Image segmentation, contour detection, mathematical morphology.

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Authors: Shashank.B. Thakre, Lalit.B. Bhuyar, Samir.J. Deshmukh

Abstract:

Oxygen transfer, the process by which oxygen is transferred from the gaseous to liquid phase, is a vital part of the waste water treatment process. Because of low solubility of oxygen and consequent low rate of oxygen transfer, sufficient oxygen to meet the requirement of aerobic waste does not enter through normal surface air water interface. Many theories have come up in explaining the mechanism of gas transfer and absorption of non-reacting gases in a liquid, of out of which, Two film theory is important. An exiting mathematical model determines approximate value of Overall Gas Transfer coefficient. The Overall Gas Transfer coefficient, in case of Penetration theory, is 1.13 time more than that obtained in case of Two film theory. The difference is due to the difference in assumptions in the two theories. The paper aims at development of mathematical model which determines the value of Overall Gas Transfer coefficient with greater accuracy than the existing model.

Keywords: Theories, Dissolved oxygen, Mathematical model, Gas Transfer coefficient, Accuracy.

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Authors: Evgeniy Burlutskiy

Abstract:

The paper presents a one-dimensional transient mathematical model of compressible thermal multi-component gas mixture flows in pipes. The set of the mass, momentum and enthalpy conservation equations for gas phase is solved. Thermo-physical properties of multi-component gas mixture are calculated by solving the Equation of State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. Gas mixture viscosity is calculated on the basis of the Lee-Gonzales-Eakin (LGE) correlation. Numerical analysis on rapid decompression in conventional dry gases is performed by using the proposed mathematical model. The model is validated on measured values of the decompression wave speed in dry natural gas mixtures. All predictions show excellent agreement with the experimental data at high and low pressure. The presented model predicts the decompression in dry natural gas mixtures much better than GASDECOM and OLGA codes, which are the most frequently-used codes in oil and gas pipeline transport service.

Keywords: Mathematical model, Rapid Gas Decompression

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Authors: S. Grishin

Abstract:

This article is dedicated to development of mathematical models for determining the dynamics of concentration of hazardous substances in urban turbulent atmosphere. Development of the mathematical models implied taking into account the time-space variability of the fields of meteorological items and such turbulent atmosphere data as vortex nature, nonlinear nature, dissipativity and diffusivity. Knowing the turbulent airflow velocity is not assumed when developing the model. However, a simplified model implies that the turbulent and molecular diffusion ratio is a piecewise constant function that changes depending on vertical distance from the earth surface. Thereby an important assumption of vertical stratification of urban air due to atmospheric accumulation of hazardous substances emitted by motor vehicles is introduced into the mathematical model. The suggested simplified non-linear mathematical model of determining the sought exhaust concentration at a priori unknown turbulent flow velocity through non-degenerate transformation is reduced to the model which is subsequently solved analytically.

Keywords: Urban ecology, time-dependent mathematical model, exhaust concentration, turbulent and molecular diffusion, airflow velocity.

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Authors: Miloš Šeda

Abstract:

In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.

Keywords: Flow shop, job shop, mixed integer model, representation scheme.

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Authors: M.R.Shabgard, R.M.Shotorbani

Abstract:

FW4 is a newly developed hot die material widely used in Forging Dies manufacturing. The right selection of the machining conditions is one of the most important aspects to take into consideration in the Electrical Discharge Machining (EDM) of FW4. In this paper an attempt has been made to develop mathematical models for relating the Material Removal Rate (MRR), Tool Wear Ratio (TWR) and surface roughness (Ra) to machining parameters (current, pulse-on time and voltage). Furthermore, a study was carried out to analyze the effects of machining parameters in respect of listed technological characteristics. The results of analysis of variance (ANOVA) indicate that the proposed mathematical models, can adequately describe the performance within the limits of the factors being studied.

Keywords: Electrical Discharge Machining (EDM), linearregression technique, Response Surface Methodology (RSM)

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Authors: S. Jursová, P. Pustějovská, S. Brožová, J. Bilík

Abstract:

The paper deals with possibilities of interpretation of iron ore reducibility tests. It presents a mathematical model developed at Centre ENET, VŠB – Technical University of Ostrava, Czech Republic for an evaluation of metallurgical material of blast furnace feedstock such as iron ore, sinter or pellets. According to the data from the test, the model predicts its usage in blast furnace technology and its effects on production parameters of shaft aggregate. At the beginning, the paper sums up the general concept and experience in mathematical modelling of iron ore reduction. It presents basic equation for the calculation and the main parts of the developed model. In the experimental part, there is an example of usage of the mathematical model. The paper describes the usage of data for some predictive calculation. There are presented material, method of carried test of iron ore reducibility. Then there are graphically interpreted effects of used material on carbon consumption, rate of direct reduction and the whole reduction process.

Keywords: Blast furnace technology, iron ore reduction, mathematical model, prediction of iron ore reduction.

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Authors: Aaron A. R. Nwabude

Abstract:

The research investigates the “impact of VLE on mathematical concepts acquisition of the special education needs (SENs) students at KS4 secondary education sector" in England. The overall aim of the study is to establish possible areas of difficulties to approach for above or below knowledge standard requirements for KS4 students in the acquisition and validation of basic mathematical concepts. A teaching period, in which virtual learning environment (Fronter) was used to emphasise different mathematical perception and symbolic representation was carried out and task based survey conducted to 20 special education needs students [14 actually took part]. The result shows that students were able to process information and consider images, objects and numbers within the VLE at early stages of acquisition process. They were also able to carry out perceptual tasks but with limiting process of different quotient, thus they need teacher-s guidance to connect them to symbolic representations and sometimes coach them through. The pilot study further indicates that VLE curriculum approaches for students were minutely aligned with mathematics teaching which does not emphasise the integration of VLE into the existing curriculum and current teaching practice. There was also poor alignment of vision regarding the use of VLE in realisation of the objectives of teaching mathematics by the management. On the part of teacher training, not much was done to develop teacher-s skills in the technical and pedagogical aspects of VLE that is in-use at the school. The classroom observation confirmed teaching practice will find a reliance on VLE as an enhancer of mathematical skills, providing interaction and personalisation of learning to SEN students.

Keywords: VLE, Mathematical Concepts Acquisition, PilotStudy, SENs, KS4, Education, Teacher

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Authors: Zuraida Alwadood, Adibah Shuib, Norlida Abd Hamid

Abstract:

This paper presents the review of past studies concerning mathematical models for rescheduling passenger railway services, as part of delay management in the occurrence of railway disruption. Many past mathematical models highlighted were aimed at minimizing the service delays experienced by passengers during service disruptions. Integer programming (IP) and mixed-integer programming (MIP) models are critically discussed, focusing on the model approach, decision variables, sets and parameters. Some of them have been tested on real-life data of railway companies worldwide, while a few have been validated on fictive data. Based on selected literatures on train rescheduling, this paper is able to assist researchers in the model formulation by providing comprehensive analyses towards the model building. These analyses would be able to help in the development of new approaches in rescheduling strategies or perhaps to enhance the existing rescheduling models and make them more powerful or more applicable with shorter computing time.

Keywords: Mathematical modelling, Mixed-integer programming, Railway rescheduling, Service delays.

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Authors: Kazuhisa Takagi

Abstract:

This paper is about movies and dynamic objects for mobile phones. Dynamic objects are the software programmed by JavaScript. They consist of geometric figures and work on HTML5-compliant browsers. Mobile phones are very popular among teenagers. They like watching movies and playing games on them. So, mathematics movies and dynamic objects would enhance teaching and learning processes. In the movies, manga characters speak with artificially synchronized voices. They teach trigonometry together with dynamic mathematical objects. Many movies are created. They are Windows Media files or MP4 movies. These movies and dynamic objects are not only used in the classroom but also distributed to students. By watching movies, students can study trigonometry before or after class.

Keywords: Dynamic mathematical object, JavaScript, Google drive, transfer jet.

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Authors: T.C. Manjunath, Student Member, B. Bandyopadhyay

Abstract:

This paper features the mathematical modeling of a single input single output based Timoshenko smart beam. Further, this mathematical model is used to design a multirate output feedback based discrete sliding mode controller using Bartoszewicz law to suppress the flexural vibrations. The first 2 dominant vibratory modes is retained. Here, an application of the discrete sliding mode control in smart systems is presented. The algorithm uses a fast output sampling based sliding mode control strategy that would avoid the use of switching in the control input and hence avoids chattering. This method does not need the measurement of the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement.

Keywords: Smart structure, Timoshenko beam theory, Discretesliding mode control, Bartoszewicz law, Finite Element Method, State space model, Vibration control, Mathematical model, SISO.

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Authors: Sheila R. Bonito

Abstract:

This study describes the relationship between motivation factors and academic performance among distance education students enrolled in a postgraduate nursing course. Students (n=96) participated in a survey that assesses student's motivational orientations from a cognitive perspective using a selfadministered questionnaire based on Pintrich-s Motivation Strategies for Learning Questionnaire (MLSQ). Results showed students- motivational factors are highest on task value (6.44, 0.71); followed by intrinsic goal orientation (6.20, 0.76), control beliefs (6.02, 0.89); extrinsic goal orientation (5.85, 1.13); self-efficacy for learning and performance (5.62, 0.84), and finally, test anxiety (4.21, 1.37). Weak positive correlations were found between academic performance and intrinsic goal orientation (r=0.13), extrinsic goal orientation (r=0.04), task value (r=0.09), control beliefs (r=0.02), and self-efficacy (r=0.05), while there was weak negative correlation with test anxiety (r=-0.04). Conclusions from the study indicate the need to focus on improving tasks and targeting intrinsic goal orientations of students to courses since these were positively correlated with academic performance and downplay the use of tests since these were negatively correlated with academic performance.

Keywords: Motivation factors, academic performance, distance education

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Authors: Turki Alotaibi

Abstract:

Student counseling programs can provide many benefits to students in schools all around the world. In theory, the government of the Kingdom of Saudi Arabia (Saudi Arabia) has committed itself to school counseling programs in educational institutions throughout the country. Student counselors face a number of burdens and obstacles that impact student counseling programs. It is also widely known that Saudi Arabia has extremely high prevalence rates for overweight and obesity, anxiety and depression, and diabetes in children. It has also been demonstrated that teachers and staff are inadequately prepared when dealing with health issues relating to diabetes in schools in Saudi Arabia. This study will clearly demonstrate how student counselors in Saudi Arabia could become 'New Educators' in Saudi schools in relation to these health issues. This would allow them to leverage their position as student counselor to improve the management of these health issues in Saudi schools, to improve the quality of care provided to school children, and to overcome burdens and obstacles that are currently negatively affecting student counseling in Saudi schools.

Keywords: Anxiety, depression, diabetes, overweight, obesity, policy recommendations, student counseling, The Kingdom of Saudi Arabia.

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Authors: M. L. Anitha, K. A. Radhakrishna Rao

Abstract:

With the advent of modern computing technology, there is an increased demand for developing recognition systems that have the capability of verifying the identity of individuals. Recognition systems are required by several civilian and commercial applications for providing access to secured resources. Traditional recognition systems which are based on physical identities are not sufficiently reliable to satisfy the security requirements due to the use of several advances of forgery and identity impersonation methods. Recognizing individuals based on his/her unique physiological characteristics known as biometric traits is a reliable technique, since these traits are not transferable and they cannot be stolen or lost. Since the performance of biometric based recognition system depends on the particular trait that is utilized, the present work proposes a fusion approach which combines Inner knuckle print (IKP) trait of the middle, ring and index fingers with the geometrical features of hand. The hand image captured from a digital camera is preprocessed to find finger IKP as region of interest (ROI) and hand geometry features. Geometrical features are represented as the distances between different key points and IKP features are extracted by applying local binary pattern descriptor on the IKP ROI. The decision level AND fusion was adopted, which has shown improvement in performance of the combined scheme. The proposed approach is tested on the database collected at our institute. Proposed approach is of significance since both hand geometry and IKP features can be extracted from the palm region of the hand. The fusion of these features yields a false acceptance rate of 0.75%, false rejection rate of 0.86% for verification tests conducted, which is less when compared to the results obtained using individual traits. The results obtained confirm the usefulness of proposed approach and suitability of the selected features for developing biometric based recognition system based on features from palmar region of hand.

Keywords: Biometrics, hand geometry features, inner knuckle print, recognition.

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Authors: Md. Ashikur Rahman Khan, M. M. Rahman

Abstract:

In electrical discharge machining (EDM), a complete and clear theory has not yet been established. The developed theory (physical models) yields results far from reality due to the complexity of the physics. It is difficult to select proper parameter settings in order to achieve better EDM performance. However, modelling can solve this critical problem concerning the parameter settings. Therefore, the purpose of the present work is to develop mathematical model to predict performance characteristics of EDM on Ti-5Al-2.5Sn titanium alloy. Response surface method (RSM) and artificial neural network (ANN) are employed to develop the mathematical models. The developed models are verified through analysis of variance (ANOVA). The ANN models are trained, tested, and validated utilizing a set of data. It is found that the developed ANN and mathematical model can predict performance of EDM effectively. Thus, the model has found a precise tool that turns EDM process cost-effective and more efficient.

Keywords: Analysis of variance, artificial neural network, material removal rate, modelling, response surface method, surface finish.

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Authors: Mahbub C. Mishu, Venketesh N. Dubey, Tamas Hickish, Jonathan Cole

Abstract:

Pressure ulcer is a common problem for today’s healthcare industry. It occurs due to external load applied to the skin. Also when the subject is immobile for a longer period of time and there is continuous load applied to a particular area of human body, blood flow gets reduced and as a result pressure ulcer develops. Body support surface has a significant role in preventing ulceration so it is important to know the characteristics of support surface under loading conditions. In this paper we have presented mathematical models of different types of viscoelastic materials and also we have shown the validation of our simulation results with experiments.

Keywords: Pressure ulcer, viscoelastic material, mathematical model, experimental validation.

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Authors: Rafayel A. Azizyan, Aram E. Gevogyan, Valeri B. Arakelyan, Emil S. Gevorgyan

Abstract:

The mathematical modeling of different biological processes is usually used to predict or assess behavior of systems in which these processes take place. This study deals with mathematical and computer modeling of bi-substrate enzymatic reactions with ping-pong mechanism, which play an important role in different biochemical pathways. Besides that, three models of competitive inhibition were designed using different software packages. The main objective of this study is to represent the results from in silico investigation of bi-substrate enzymatic reactions with ordered pingpong mechanism in the presence of competitive inhibitors, as well as to describe in details the inhibition effects. The simulation of the models with certain kinetic parameters allowed investigating the behavior of reactions as well as determined some interesting aspects concerning influence of different cases of competitive inhibition. Simultaneous presence of two inhibitors, competitive to the S1 and S2 substrates have been studied. Moreover, we have found the pattern of simultaneous influence of both inhibitors.

Keywords: Mathematical modeling, bi-substrate enzymatic reactions, ping-pong mechanism, competitive inhibition.

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Authors: Danilo López, Nelson Vera, Luis Pedraza

Abstract:

This paper analyzes fundamental ideas and concepts related to neural networks, which provide the reader a theoretical explanation of Long Short-Term Memory (LSTM) networks operation classified as Deep Learning Systems, and to explicitly present the mathematical development of Backward Pass equations of the LSTM network model. This mathematical modeling associated with software development will provide the necessary tools to develop an intelligent system capable of predicting the behavior of licensed users in wireless cognitive radio networks.

Keywords: Neural networks, multilayer perceptron, long short-term memory, recurrent neuronal network, mathematical analysis.

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Authors: A. Pashayev, R. Sadiqov, C. Ardil, F. Ildiz , H. Karabork

Abstract:

The new technology of fuzzy neural networks for identification of parameters for mathematical models of geofields is proposed and checked. The effectiveness of that soft computing technology is demonstrated, especially in the early stage of modeling, when the information is uncertain and limited.

Keywords: Identification, interpolation methods, neuro-fuzzy networks, geofield.

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Authors: Dong-Joong Kim, Sangho Choi, Woong Lim

Abstract:

This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.

Keywords: Commognitive framework, discourse analysis, mathematical discourse, mathematics education.

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Authors: Robert L. Burdett, Bayan Bevrani

Abstract:

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.

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Authors: Evgeniy Burlutskiy

Abstract:

The paper presents a one-dimensional transient mathematical model of thermal oil-water two-phase emulsion flows in pipes. The set of the mass, momentum and enthalpy conservation equations for the continuous fluid and droplet phases are solved. Two friction correlations for the continuous fluid phase to wall friction are accounted for in the model and tested. The aerodynamic drag force between the continuous fluid phase and droplets is modeled, too. The density and viscosity of both phases are assumed to be constant due to adiabatic experimental conditions. The proposed mathematical model is validated on the experimental measurements of oil-water emulsion flows in horizontal pipe [1,2]. Numerical analysis on single- and two-phase oil-water flows in a pipe is presented in the paper. The continuous oil flow having water droplets is simulated. Predictions, which are performed by using the presented model, show excellent agreement with the experimental data if the water fraction is equal or less than 10%. Disagreement between simulations and measurements is increased if the water fraction is larger than 10%.

Keywords: Mathematical model, Oil-Water, Pipe flows.

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Authors: S. Bennoud, M. Zergoug

Abstract:

The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models.

The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces.

The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations.

In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: Eddy current, Finite element method, Non destructive testing, Numerical simulations.

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Authors: Randhir Singh Baghel

Abstract:

In this study, the fundamental ideas guiding the dynamic area of machine learning—where models thrive and algorithms change over time—are rooted in an innate mathematical link. This study explores the fundamental ideas that drive the development of intelligent systems, providing light on the mutually beneficial link between mathematics and machine learning.

Keywords: Machine Learning, deep learning, Neural Network, optimization.

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