Search results for: mathematical literacy

Authors: Zineb Nougrara

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In this paper, we propose a novel methodology for extracting a road network and its nodes from satellite images of Algeria country. This developed technique is a progress of our previous research works. It is founded on the information theory and the mathematical morphology; the information theory and the mathematical morphology are combined together to extract and link the road segments to form a road network and its nodes. We, therefore, have to define objects as sets of pixels and to study the shape of these objects and the relations that exist between them. In this approach, geometric and radiometric features of roads are integrated by a cost function and a set of selected points of a crossing road. Its performances were tested on satellite images of Algeria country.

Keywords: satellite image, road network, nodes, image analysis and processing

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Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

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In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: bifurcation, heteroclinic orbits, steady state, traveling wave

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Authors: Nafisa Banu

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The present study is an attempt to analyze the regional disparities in the level of education in West Bengal. The data based on secondary sources obtained from a census of India. The study is divided into four sections. The first section presents introductions, objectives and brief descriptions of the study area, second part discuss the methodology and data base, while third and fourth comprise the empirical results, interpretation, and conclusion respectively. For showing the level of educational development, 8 indicators have been selected and Z- score and composite score techniques have been applied. The present study finds out there are large variations of educational level due to various historical, economical, socio-cultural factors of the study area.

Keywords: education, regional disparity, literacy rate, Z-score, composite score

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Authors: Farzad Pargar

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We introduce the preventive maintenance and renewal scheduling problem for a multi-unit system over a finite and discretized time horizon. Given the latest possible time for carrying out the next maintenance and renewal projects after the previous ones and considering several common set-up costs, the introduced scheduling model tries to minimize the cost of projects by grouping them and simultaneously finding the optimal balance between doing maintenance and renewal. We present a 0-1 pure integer linear programming that determines which projects should be performed together on which location and in which period (e.g., week or month). We consider railway track as a case for our study and test the performance of the proposed model on a set of test problems. The experimental results show that the proposed approach performs well.

Keywords: maintenance, renewal, scheduling, mathematical programming model

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Authors: S. Benkraouda, Z. Djelloul-Khedda, B. Yagoubi

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we present a method for early detection of forest fires from a thermal infrared satellite image, using the image matrix of the probability of belonging. The principle of the method is to compare a theoretical mathematical model to an experimental model. We considered that each line of the image matrix, as an embodiment of a non-stationary random process. Since the distribution of pixels in the satellite image is statistically dependent, we divided these lines into small stationary and ergodic intervals to characterize the image by an adequate mathematical model. A standard deviation was chosen to generate random variables, so each interval behaves naturally like white Gaussian noise. The latter has been selected as the mathematical model that represents a set of very majority pixels, which we can be considered as the image background. Before modeling the image, we made a few pretreatments, then the parameters of the theoretical Gaussian model were extracted from the modeled image, these settings will be used to calculate the probability of each interval of the modeled image to belong to the theoretical Gaussian model. The high intensities pixels are regarded as foreign elements to it, so they will have a low probability, and the pixels that belong to the background image will have a high probability. Finally, we did present the reverse of the matrix of probabilities of these intervals for a better fire detection.

Keywords: forest fire, forest fire detection, satellite image, normal distribution, theoretical gaussian model, thermal infrared matrix image

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Authors: Isabella Lima Leite de Freitas

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The importance of astronomy for humanity is unquestionable. Despite being a robust science, capable of bringing new discoveries every day and quickly increasing the ability of researchers to understand the universe more deeply, scientific research in this area can also help in various applications outside the domain of astronomy. The objective of this study was to review and conduct a descriptive analysis of published studies that presented the importance of astronomy in the area of education. A narrative review of the literature has been performed, considering the articles published in the last five years. As astronomy involves the study of physics, chemistry, biology, mathematics and technology, one of the studies evaluated presented astronomy as the gateway to science, demonstrating the presence of astronomy in 52 school curricula in 37 countries, with celestial movement the dominant content area. Another intervention study, evaluating individuals aged 4-5 years, demonstrated that the attribution of personal characteristics to cosmic bodies, in addition to the use of comprehensive astronomy concepts, favored the learning of science in preschool-age children, considering the use of practical activities of accompaniment and free drawing. Aiming to measure scientific literacy, another study developed in Turkey, motivated the authorities of this country to change the teaching materials and curriculum of secondary schools after the term “astronomy” appeared as one of the most attractive subjects for young people aged 15 to 24. There are also reports in the literature of the use of pedagogical tools, such as the representation of the Solar System on a human scale, where students can walk along the orbits of the planets while studying the laws of dynamics. The use of this tool favored the teaching of the relationship between distance, duration and speed over the period of the planets, in addition to improving the motivation and well-being of students aged 14-16. An important impact of astronomy on education was demonstrated in the study that evaluated the participation of high school students in the Astronomical Olympiads and the International Astronomy Olympiad. The study concluded that these Olympics have considerable influence on students who pursue a career in teaching or research later on, many of whom are in the area of astronomy itself. In addition, the literature indicates that the teaching of astronomy in the digital age has facilitated the availability of data for researchers, but also for the general population. This fact can increase even more the curiosity that the astronomy area has always instilled in people and promote the dissemination of knowledge on an expanded scale. Currently, astronomy has been considered an important ally in strengthening the school curricula of children, adolescents and young adults. This has been used as teaching tools, in addition to being extremely useful for scientific literacy, being increasingly used in the area of education.

Keywords: astronomy, education area, teaching, review

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Authors: Emiliano Lustrissimi, Bonifacio Bianco, Sebastiano Caravaggi, Antonio Rosato

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A mathematical framework has been designed to enhance the configuration of an end-of-production-line (EOL) test bench. This system can be used to assess the performance of electric motors or axles intended for electric vehicles. The model has been developed to predict the behaviour of EOL test benches and electric motors/axles under various boundary conditions, eliminating the need for extensive physical testing and reducing the corresponding power consumption. The suggested model is versatile, capable of being utilized across various types of electric motors or axles, and adaptable to accommodate varying power ratings of electric motors or axles. The maximum performance to be guaranteed by the EMs according to the car maker's specifications are taken as inputs in the model. Then, the required performance of each main EOL test bench component is calculated, and the corresponding systems available on the market are selected based on manufacturers’ catalogues. In this study, an EOL test bench has been designed according to the proposed model outputs for testing a low-power (about 22 kW) electric axle. The performance of the designed EOL test bench has been measured and used to validate the proposed model and assess both the consistency of the constraints as well as the accuracy of predictions in terms of electric demands. The comparison between experimental and predicted data exhibited a reasonable agreement, allowing to demonstrate that, despite some discrepancies, the model gives an accurate representation of the EOL test benches' performance.

Keywords: electric motors, electric vehicles, end-of-production-line test bench, mathematical model, field tests

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Authors: Jian-Jun Shu

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It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Y. Smirlis, G. Koronakos, S. Plitsos

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Shipbrokers assist the ship companies in chartering or selling and buying vessels, acting as intermediates between them and the market. They facilitate deals, providing their expertise, negotiating skills, and knowledge about ship market bargains. Their role is very important as it affects the profitability and market position of a shipping company. Due to their significant contribution, the shipping companies have to employ systematic procedures to evaluate the shipbrokers’ services in order to select the best and, consequently, to achieve the best deals. Towards this, in this paper, we consider shipbrokers as financial service providers, and we formulate the problem of evaluating and selecting shipbrokers’ services as a multi-criteria decision making (MCDM) procedure. The proposed methodology comprises a first normalization step to adjust different scales and orientations of the criteria and a second step that includes the mathematical model to evaluate the performance of the shipbrokers’ services involved in the assessment. The criteria along which the shipbrokers are assessed may refer to their size and reputation, the potential efficiency of the services, the terms and conditions imposed, the expenses (e.g., commission – brokerage), the expected time to accomplish a chartering or selling/buying task, etc. and according to our modelling approach these criteria may be assigned different importance. The mathematical programming model performs a comparative assessment and estimates for the shipbrokers involved in the evaluation, a relative score that ranks the shipbrokers in terms of their potential performance. To illustrate the proposed methodology, we present a case study in which a shipping company evaluates and selects the most suitable among a number of sale and purchase (S&P) brokers. Acknowledgment: This study is supported by the OptiShip project, implemented within the framework of the National Recovery Plan and Resilience “Greece 2.0” and funded by the European Union – NextGenerationEU programme.

Keywords: shipbrokers, multi-criteria decision making, mathematical programming, service-provider selection

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Authors: Michael Naderhirn, Marco Pavone

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Problem statement, motivation, and aim of work: So far, the development of control algorithms was done by control engineers in a way that the controller would fit a specification by testing. When it comes to the certification of an autonomous car in highly complex scenarios, the challenge is much higher since such a controller must mathematically guarantee to implement the rules of the road while on the other side guarantee aspects like safety and real time executability. What if it becomes reality to solve this demanding problem by combining Formal Verification and System Theory? The aim of this work is to present a workflow to solve the above mentioned problem. Summary of the presented results / main outcomes: We show the usage of an English like language to transform the rules of the road into system specification for an autonomous car. The language based specifications are used to define system functions and interfaces. Based on that a formal model is developed which formally correctly models the specifications. On the other side, a mathematical model describing the systems dynamics is used to calculate the systems reachability set which is further used to determine the system input boundaries. Then a motion planning algorithm is applied inside the system boundaries to find an optimized trajectory in combination with the formal specification model while satisfying the specifications. The result is a control strategy which can be applied in real time independent of the scenario with a mathematical guarantee to satisfy a predefined specification. We demonstrate the applicability of the method in simulation driving scenarios and a potential certification. Originality, significance, and benefit: To the authors’ best knowledge, it is the first time that it is possible to show an automated workflow which combines a specification in an English like language and a mathematical model in a mathematical formal verified way to synthesizes a controller for potential real time applications like autonomous driving.

Keywords: formal system verification, reachability, real time controller, hybrid system

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Authors: Juliet Sorensen, Anna Maitland

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Introduction: Characterized by lack of water and sanitation, food insecurity, and low access to hospitals and clinics, informal urban settlements in Lagos, Nigeria have very poor health outcomes. With little education and a general inability to demand basic rights, these communities are often disempowered and isolated from understanding, claiming, or owning their health needs. Utilizing community-based participatory research characterized by interdisciplinary, cross-cultural partnerships, evidence-based assessments, and both primary and secondary source research, a holistic health education and advocacy program was developed in Lagos to address health barriers for targeted communities. This includes a first of its kind guide formulated to teach community-based health educators how to transmit health information to low-literacy Nigerian audiences while supporting behavior change models and social support mechanisms. This paper discusses the interdisciplinary contributions to developing a health education program while also looking at the need for greater beneficiary ownership and implementation of health justice and access. Methods: In March 2016, an interdisciplinary group of medical, legal, and business graduate students and faculty from Northwestern University conduced a Health Needs Assessment (HNA) in Lagos with a partner and a local non-governmental organization. The HNA revealed that members of informal urban communities in Lagos were lacking basic health literacy, but desired to remedy this lacuna. Further, the HNA revealed that even where the government mandates specific services, many vulnerable populations are unable to access these services. The HNA concluded that a program focused on education, advocacy, and organizing around anatomy, maternal and sexual health, infectious disease and malaria, HIV/AIDS, emergency care, and water and sanitation would respond to stated needs while also building capacity in communities to address health barriers. Results: Based on the HNA, including both primary and secondary source research on integrated health education approaches and behavior change models and responsive, adaptive material development, a holistic program was developed for the Lagos partners and first implemented in November 2016. This program trained community-nominated health educators in adult, low-literacy, knowledge exchange approaches, utilizing information identified by communities as a priority. After a second training in March 2017, these educators will teach community-based groups and will support and facilitate behavior change models and peer-support methods around basic issues like hand washing and disease transmission. They will be supported by community paralegals who will help ensure that newly trained community groups can act on education around access, such as receiving free vaccinations, maternal health care, and HIV/AIDS medicines. Materials will continue to be updated as needs and issues arise, with a focus on identifying best practices around health improvements that can be shared across these partner communities. Conclusion: These materials are the first of their kind, and address a void of health information and understanding pervasive in informal-urban Lagos communities. Initial feedback indicates high levels of commitment and interest, as well as investment by communities in these materials, largely because they are responsive, targeted, and build community capacity. This methodology is an important step in dignity-based health justice solutions, albeit in the process of refinement.

Keywords: community health educators, interdisciplinary and cross cultural partnerships, health justice and access, Nigeria

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Authors: J. Ritonja, B. Grcar

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For the synchronous generator simulation and analysis and for the power system stabilizer design and synthesis a mathematical model of synchronous generator is needed. The model has to accurately describe dynamics of oscillations, while at the same time has to be transparent enough for an analysis and sufficiently simplified for design of control system. To study the oscillations of the synchronous generator against to the rest of the power system, the model of the synchronous machine connected to an infinite bus through a transmission line having resistance and inductance is needed. In this paper, the linearized reduced order dynamic model of the synchronous generator connected to the infinite bus is presented and analysed in details. This model accurately describes dynamics of the synchronous generator only in a small vicinity of an equilibrium state. With the digression from the selected equilibrium point the accuracy of this model is decreasing considerably. In this paper, the equations’ descriptions and the parameters’ determinations for the linearized reduced order mathematical model of the synchronous generator are explained and summarized and represent the useful origin for works in the areas of synchronous generators’ dynamic behaviour analysis and synchronous generator’s control systems design and synthesis. The main contribution of this paper represents the detailed analysis of the accuracy of the linearized reduced order dynamic model in the entire synchronous generator’s operating range. Borders of the areas where the linearized reduced order mathematical model represents accurate description of the synchronous generator’s dynamics are determined with the systemic numerical analysis. The thorough eigenvalue analysis of the linearized models in the entire operating range is performed. In the paper, the parameters of the linearized reduced order dynamic model of the laboratory salient poles synchronous generator were determined and used for the analysis. The theoretical conclusions were confirmed with the agreement of experimental and simulation results.

Keywords: eigenvalue analysis, mathematical model, power system stability, synchronous generator

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Authors: Aya Al Masri, Stefaan Carpentier, Fabrice Leroy, Thibault Julien, Safoin Aktaou, Malorie Martin, Fouad Maaloul

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Introduction: During an 'Interventional Radiology (IR)' procedure, the patient's skin-dose may become very high for a burn, necrosis and ulceration to appear. In order to prevent these deterministic effects, an accurate calculation of the patient skin-dose mapping is essential. For most machines, the 'Dose Area Product (DAP)' and fluoroscopy time are the only information available for the operator. These two parameters are a very poor indicator of the peak skin dose. We developed a mathematical model that reconstructs the magnitude (delivered dose), shape, and localization of each irradiation field on the patient skin. In case of critical dose exceeding, the system generates warning alerts. We present the results of its comparison with clinical studies. Materials and methods: Two series of comparison of the skin-dose mapping of our mathematical model with clinical studies were performed: 1. At a first time, clinical tests were performed on patient phantoms. Gafchromic films were placed on the table of the IR machine under of PMMA plates (thickness = 20 cm) that simulate the patient. After irradiation, the film darkening is proportional to the radiation dose received by the patient's back and reflects the shape of the X-ray field. After film scanning and analysis, the exact dose value can be obtained at each point of the mapping. Four experimentation were performed, constituting a total of 34 acquisition incidences including all possible exposure configurations. 2. At a second time, clinical trials were launched on real patients during real 'Chronic Total Occlusion (CTO)' procedures for a total of 80 cases. Gafchromic films were placed at the back of patients. We performed comparisons on the dose values, as well as the distribution, and the shape of irradiation fields between the skin dose mapping of our mathematical model and Gafchromic films. Results: The comparison between the dose values shows a difference less than 15%. Moreover, our model shows a very good geometric accuracy: all fields have the same shape, size and location (uncertainty < 5%). Conclusion: This study shows that our model is a reliable tool to warn physicians when a high radiation dose is reached. Thus, deterministic effects can be avoided.

Keywords: clinical experimentation, interventional radiology, mathematical model, patient's skin-dose mapping.

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Authors: Petri Solanti, Russell Klein

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Many designers are asking for an automated path from an abstract mathematical MATLAB model to a high-quality Register-Transfer Level (RTL) hardware description. Manual transformations of MATLAB or intermediate code are needed, when the design abstraction is changed. Design conversion is problematic as it is multidimensional and it requires many different design steps to translate the mathematical representation of the desired functionality to an efficient hardware description with the same behavior and configurability. Yet, a manual model conversion is not an insurmountable task. Using currently available design tools and an appropriate design methodology, converting a MATLAB model to efficient hardware is a reasonable effort. This paper describes a simple and flexible design methodology that was developed together with several design teams.

Keywords: design methodology, high-level synthesis, MATLAB, verification

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Authors: Alexander N. Savostyanov, Tatyana A. Dolgorukova, Elena A. Esipenko, Mikhail S. Zaleshin, Margherita Malanchini, Anna V. Budakova, Alexander E. Saprygin, Yulia V. Kovas

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The present study compared spectral-power indexes and cortical topography of brain activity in a sample characterized by different levels of trait and mathematical anxiety. 52 healthy Russian-speakers (age 17-32; 30 males) participated in the study. Participants solved an error recognition task under 3 conditions: A lexical condition (simple sentences in Russian), and two numerical conditions (simple arithmetic and complicated algebraic problems). Trait and mathematical anxiety were measured using self-repot questionnaires. EEG activity was recorded simultaneously during task execution. Event-related spectral perturbations (ERSP) were used to analyze spectral-power changes in brain activity. Additionally, sLORETA was applied in order to localize the sources of brain activity. When exploring EEG activity recorded after tasks onset during lexical conditions, sLORETA revealed increased activation in frontal and left temporal cortical areas, mainly in the alpha/beta frequency ranges. When examining the EEG activity recorded after task onset during arithmetic and algebraic conditions, additional activation in delta/theta band in the right parietal cortex was observed. The ERSP plots reveled alpha/beta desynchronizations within a 500-3000 ms interval after task onset and slow-wave synchronization within an interval of 150-350 ms. Amplitudes of these intervals reflected the accuracy of error recognition, and were differently associated with the three (lexical, arithmetic and algebraic) conditions. The level of trait anxiety was positively correlated with the amplitude of alpha/beta desynchronization. The level of mathematical anxiety was negatively correlated with the amplitude of theta synchronization and of alpha/beta desynchronization. Overall, trait anxiety was related with an increase in brain activation during task execution, whereas mathematical anxiety was associated with increased inhibitory-related activity. We gratefully acknowledge the support from the №11.G34.31.0043 grant from the Government of the Russian Federation.

Keywords: anxiety, EEG, lexical and numerical error-recognition tasks, alpha/beta desynchronization

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Authors: Jaroslav Masek, Juraj Camaj, Eva Nedeliakova

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The aim of optimization of store management is not only designing the situation of store management itself including its equipment, technology and operation. In optimization of store management we need to consider also synchronizing of technological, transport, store and service operations throughout the whole process of logistic chain in such a way that a natural flow of material from provider to consumer will be achieved the shortest possible way, in the shortest possible time in requested quality and quantity and with minimum costs. The paper deals with the application of the queuing theory for optimization of warehouse processes. The first part refers to common information about the problematic of warehousing and using mathematical methods for logistics chains optimization. The second part refers to preparing a model of a warehouse within queuing theory. The conclusion of the paper includes two examples of using queuing theory in praxis.

Keywords: queuing theory, logistics system, mathematical methods, warehouse optimization

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Authors: Shirly May Balais

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This study aims to evaluate the effects of vocabulary instruction in improving the students’ learning in science. The teacher-researcher utilized the vocabulary instructional materials in enriching the science vocabulary of grade four learners. The students were also given an achievement test to determine the effects of vocabulary instructional materials. The assessment indicated that students had shown improvement in comprehension and science literacy. This also helps the students to grasp, understand, and communicate appropriate science concepts and the integration of imagery makes learning science fun. In this research, descriptive qualitative methods and observation interviews were used to describe the effects of using vocabulary instructional materials in improving the science vocabulary of grade four learners. The students’ perceptions were studied, analyzed, and interpreted qualitatively.

Keywords: instruction, learning, science, vocabulary

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Authors: Vedat Senol, Gursoy Turan, Anders Helmersson, Vortechz Andersson

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In developing a mathematical model of a real structure, the simulation results of the model may not match the real structural response. This is a general problem that arises during dynamic motion of the structure, which may be modeled by means of parameter variations in the stiffness, damping, and mass matrices. These changes in parameters need to be estimated, and the mathematical model is updated to obtain higher control performances and robustness. In this study, a linear fractional transformation (LFT) is utilized for uncertainty modeling. Further, a general approach to the design of an H∞ control of a magneto-rheological damper (MRD) for vibration reduction in a building with mass, damping, and stiffness uncertainties is presented.

Keywords: uncertainty modeling, structural control, MR Damper, H∞, robust control

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Authors: Fatemeh Asadi Farsad, Sima Modirkhameneh

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The purpose of this study was to explore the pattern of Psychological Well-Being (PWB) of Iranian male and female EFL teachers during the pandemic. It was intended to see if such a drastic change in the context and mode of teaching affects teachers' PWB. Furthermore, the possible difference between the six elements of PWB of Iranian EFL male vs. female teachers during the pandemic was investigated. The other purpose was to find out the EFL teachers’ perceptions of any modifications, and factors leading to such modifications in their PWB during pandemic. For the purpose of this investigation, a total of 81 EFL teachers (59 female, 22 male) with an age range of 25 to 35 were conveniently sampled from different cities in Iran. Ryff’s PWB questionnaire was sent to participant teachers through online platforms to elicit data on their PWB. As for their perceptions on the possible modifications and the factors involved in PWB during pandemic, a set of semi-structured interviews were run among both sample groups. The findings revealed that male EFL teachers had the highest mean on personal growth, followed by purpose of life, and self-acceptance and the lowest mean on environmental mastery. With a slightly similar pattern, female EFL teachers had the highest mean on personal growth, followed by purpose in life, and positive relationship with others with the lowest mean on environmental mastery. However, no significant difference was observed between the male and female groups’ overall means on elements of PWB. Additionally, participants perceived that their anxiety level in online classes altered due to factors like (1) Computer literacy skills, (2) Lack of social communications and interactions with colleagues and students, (3) Online class management, (4) Overwhelming workloads, and (5) Time management. The study ends with further suggestions as regards effective online teaching preparation considering teachers PWB, especially at severe situations such as covid-19 pandemic. The findings offer to determine the reformations of educational policies concerning enhancing EFL teachers’ PWB through computer literacy courses and stress management courses. It is also suggested that to proactively support teachers’ mental health, it is necessary to provide them with advisors and psychologists if possible for free. Limitations: One limitation is the small number of participants (81), suggesting that future replications should include more participants for reliable findings. Another limitation is the gender imbalance, which future studies should address to yield better outcomes. Furthermore, Limited data gathering tools suggest using observations, diaries, and narratives for more insights in future studies. The study focused on one model of PWB, calling for further research on other models in the literature. Considering the wide effect of the COVID-19 pandemic, future studies should consider additional variables (e.g., teaching experience, age, income) to understand Iranian EFL teachers’ vulnerabilities and strengths better.

Keywords: online teaching, psychological well-being, female and male EFL teachers, pandemic

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Authors: Aarthi Sridhar, Henri Gavin, Karah Kelly

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Rolling Isolation Systems (RISs) are simple and effective means to mitigate earthquake hazards to equipment in critical and precious facilities, such as hospitals, network collocation facilities, supercomputer centers, and museums. The RIS works by isolating components acceleration the inertial forces felt by the subsystem. The RIS consists of two platforms with counter-facing concave surfaces (dishes) in each corner. Steel balls lie inside the dishes and allow the relative motion between the top and bottom platform. Formerly, a mathematical model for the dynamics of RISs was developed using Lagrange’s equations (LE) and experimentally validated. A new mathematical model was developed using Gauss’s Principle of Least Constraint (GPLC) and verified by comparing impulse response trajectories of the GPLC model and the LE model in terms of the peak displacements and accelerations of the top platform. Mathematical models for the RIS are tedious to derive because of the non-holonomic rolling constraints imposed on the system. However, using Gauss’s Principle of Least constraint to find the equations of motion removes some of the obscurity and yields a system that can be easily extended. Though the GPLC model requires more state variables, the equations of motion are far simpler. The non-holonomic constraint is enforced in terms of accelerations and therefore requires additional constraint stabilization methods in order to avoid the possibility that numerical integration methods can cause the system to go unstable. The GPLC model allows the incorporation of more physical aspects related to the RIS, such as contribution of the vertical velocity of the platform to the kinetic energy and the mass of the balls. This mathematical model for the RIS is a tool to predict the motion of the isolation platform. The ability to statistically quantify the expected responses of the RIS is critical in the implementation of earthquake hazard mitigation.

Keywords: earthquake hazard mitigation, earthquake isolation, Gauss’s Principle of Least Constraint, nonlinear dynamics, rolling isolation system

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Authors: Amal G. Kurian

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The use of mathematical modeling has seen a considerable boost in recent times with the development of many advanced algorithms and mathematical modeling capabilities. The advantages this method has over other methods are that they are much closer to standard physics theories and thus represent a better theoretical model. They take lesser solving time and have the ability to change various parameters for optimization, which is a big advantage, especially in automotive industry. This thesis work focuses on a thorough investigation of the effects of vehicle speed and road roughness on a heavy commercial vehicle ride and structural dynamic responses. Since commercial vehicles are kept in operation continuously for longer periods of time, it is important to study effects of various physical conditions on the vehicle and its user. For this purpose, various experimental as well as simulation methodologies, are adopted ranging from experimental transfer path analysis to various road scenario simulations. To effectively investigate and eliminate several causes of unwanted responses, an efficient and robust technique is needed. Carrying forward this motivation, the present work focuses on the development of a mathematical model of a 4-axle configuration heavy commercial vehicle (HCV) capable of calculating responses of the vehicle on different road PSD inputs and vehicle speeds. Outputs from the model will include response transfer functions and PSDs and wheel forces experienced. A MATLAB code will be developed to implement the objectives in a robust and flexible manner which can be exploited further in a study of responses due to various suspension parameters, loading conditions as well as vehicle dimensions. The thesis work resulted in quantifying the effect of various physical conditions on ride comfort of the vehicle. An increase in discomfort is seen with velocity increase; also the effect of road profiles has a considerable effect on comfort of the driver. Details of dominant modes at each frequency are analysed and mentioned in work. The reduction in ride height or deflection of tire and suspension with loading along with load on each axle is analysed and it is seen that the front axle supports a greater portion of vehicle weight while more of payload weight comes on fourth and third axles. The deflection of the vehicle is seen to be well inside acceptable limits.

Keywords: mathematical modeling, HCV, suspension, ride analysis

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Sagar Hedaoo, Fazle Baki, Ahmed Azab

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In supply chain management, network design for scalable manufacturing facilities is an emerging field of research. Facility location allocation assigns facilities to customers to optimize the overall cost of the supply chain. To further optimize the costs, capacities of these facilities can be changed in accordance with customer demands. A mathematical model is formulated to fully express the problem at hand and to solve small-to-mid range instances. A dedicated constraint has been developed to restrict emissions in line with the Kyoto protocol. This problem is NP-Hard; hence, a simulated annealing metaheuristic has been developed to solve larger instances. A case study on the USA-Canada cross border crossing is used.

Keywords: emission, mixed integer linear programming, metaheuristic, simulated annealing

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Authors: Muhammad A. Khan, Waseem Shahzad

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Analysis of protein sequences is carried out for the purpose to discover their structural and ancestry relationship. Sequence similarity determines similar protein structures, similar function, and homology detection. Biological sequences composed of amino acid residues or nucleotides provide significant information through sequence alignment. In this paper, we present a new similarity/dissimilarity measure to sequence alignment based on the primary structure of a protein. The approach finds the distance between the two given sequences using the novel sequence alignment algorithm and a mathematical model. The algorithm runs at a time complexity of O(n²). A distance matrix is generated to construct a phylogenetic tree of different species. The new similarity/dissimilarity measure outperforms other existing methods.

Keywords: alignment, distance, homology, mathematical model, phylogenetic tree

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Authors: Hussein Altartouri

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In this paper the kinematic and kinetic models of an omnidirectional holonomic mobile robot is presented. The kinematic and kinetic models form the OmniDrive model. Therefore, a mathematical model for the robot equipped with three- omnidirectional wheels is derived. This model which takes into consideration the kinematics and kinetics of the robot, is developed to state space representation. Relative analysis of the velocities and displacements is used for the kinematics of the robot. Lagrange’s approach is considered in this study for deriving the equation of motion. The drive train and the mechanical assembly only of the Festo Robotino® is considered in this model. Mainly the model is developed for motion control. Furthermore, the model can be used for simulation purposes in different virtual environments not only Robotino® View. Further use of the model is in the mechatronics research fields with the aim of teaching and learning the advanced control theories.

Keywords: mobile robot, omni-direction wheel, mathematical model, holonomic mobile robot

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Authors: El Hassene Osmani, Mounir Haddou, Naceurdine Bensalem

Abstract:

In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely, the obstacle problem. We present a relaxed formulation for the problem using smoothing functions. Since we adopt a numerical point of view, we first relax the feasible domain of the problem, then using both mathematical programming methods and penalization methods, we get optimality conditions with smooth Lagrange multipliers. Some numerical experiments using IPOPT algorithm (Interior Point Optimizer) are presented to verify the efficiency of our approach.

Keywords: complementarity problem, IPOPT, Lagrange multipliers, mathematical programming, optimal control, smoothing methods, variationally inequalities

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Authors: Ella Tyuryumina, Alexey Neznanov

Abstract:

Finding algorithms to predict the growth of tumors has piqued the interest of researchers ever since the early days of cancer research. A number of studies were carried out as an attempt to obtain reliable data on the natural history of breast cancer growth. Mathematical modeling can play a very important role in the prognosis of tumor process of breast cancer. However, mathematical models describe primary tumor growth and metastases growth separately. Consequently, we propose a mathematical growth model for primary tumor and primary metastases which may help to improve predicting accuracy of breast cancer progression using an original mathematical model referred to CoM-IV and corresponding software. We are interested in: 1) modelling the whole natural history of primary tumor and primary metastases; 2) developing adequate and precise CoM-IV which reflects relations between PT and MTS; 3) analyzing the CoM-IV scope of application; 4) implementing the model as a software tool. The CoM-IV is based on exponential tumor growth model and consists of a system of determinate nonlinear and linear equations; corresponds to TNM classification. It allows to calculate different growth periods of primary tumor and primary metastases: 1) ‘non-visible period’ for primary tumor; 2) ‘non-visible period’ for primary metastases; 3) ‘visible period’ for primary metastases. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. Thus, the CoM-IV model and predictive software: a) detect different growth periods of primary tumor and primary metastases; b) make forecast of the period of primary metastases appearance; c) have higher average prediction accuracy than the other tools; d) can improve forecasts on survival of BC and facilitate optimization of diagnostic tests. The following are calculated by CoM-IV: the number of doublings for ‘nonvisible’ and ‘visible’ growth period of primary metastases; tumor volume doubling time (days) for ‘nonvisible’ and ‘visible’ growth period of primary metastases. The CoM-IV enables, for the first time, to predict the whole natural history of primary tumor and primary metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on primary tumor sizes. Summarizing: a) CoM-IV describes correctly primary tumor and primary distant metastases growth of IV (T1-4N0-3M1) stage with (N1-3) or without regional metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and manifestation of primary metastases.

Keywords: breast cancer, exponential growth model, mathematical modelling, primary metastases, primary tumor, survival

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Authors: Abderazak Guettaf

Abstract:

The mathematical models of the physical phenomena interacting in inductive plasma were described by the physics equations of the continuous mediums. A 3D model based on magnetic potential vector and electric scalar potential (A, V) formulation is used. The finished volume method is applied to electromagnetic equation, to obtain the field distribution inside the plasma. The numerical results of the method developed on a basic model designed starting from a real three-dimensional model were exposed. From the mathematical model 3D spreading assumptions and boundary conditions, we evaluated the electric field in the load and we have developed a numerical code made under the MATLAB environment, all verifying the effectiveness and validity of this code.

Keywords: electric field, 3D magnetic potential vector and electric scalar potential (A, V) formulation, finished volumes, annular plasma

Procedia PDF Downloads 477

Authors: A. G. Kovalenko, Y. N. Amirgaliyev, A. U. Kalizhanova, L. S. Balgabayeva, A. H. Kozbakova, Z. S. Aitkulov

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It is known that statistical information on operation of the compound multisite system is often far from the description of actual state of the system and does not allow drawing any conclusions about the correctness of its operation. For example, from the world practice of operation of systems of water supply, water disposal, it is known that total measurements at consumers and at suppliers differ between 40-60%. It is connected with mathematical measure of inaccuracy as well as ineffective running of corresponding systems. Analysis of widely-distributed systems is more difficult, in which subjects, which are self-maintained in decision-making, carry out economic interaction in production, act of purchase and sale, resale and consumption. This work analyzed mathematical models of sellers, consumers, arbitragers and the models of their interaction in the provision of dispersed single-product market of perfect competition. On the basis of these models, the methods, allowing estimation of every subject’s operating options and systems as a whole are given.

Keywords: dispersed systems, models, hydraulic network, algorithms

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Authors: Benjamin Castillo, Luis Pastenes, Fernando Cerdova

Abstract:

The contamination of food by microbial agents is a common problem in the industry, especially regarding the elaboration of animal source products. Incorrect manipulation of the machinery or on the raw materials can cause a decrease in production or an epidemiological outbreak due to intoxication. In order to improve food product quality, different methods have been used to reduce or, at least, to slow down the growth of the pathogens, especially deteriorated, infectious or toxigenic bacteria. These methods are usually carried out under low temperatures and short processing time (abiotic agents), along with the application of antibacterial substances, such as bacteriocins (biotic agents). This, in a controlled and efficient way that fulfills the purpose of bacterial control without damaging the final product. Therefore, the objective of the present study is to design a secondary mathematical model that allows the prediction of both the biotic and abiotic factor impact associated with animal source food processing. In order to accomplish this objective, the authors propose a three-dimensional differential equation model, whose components are: bacterial growth, release, production and artificial incorporation of bacteriocins and changes in pH levels of the medium. These three dimensions are constantly being influenced by the temperature of the medium. Secondly, this model adapts to an idealized situation of cross-contamination animal source food processing, with the study agents being both the animal product and the contact surface. Thirdly, the stochastic simulations and the parametric sensibility analysis are compared with referential data. The main results obtained from the analysis and simulations of the mathematical model were to discover that, although bacterial growth can be stopped in lower temperatures, even lower ones are needed to eradicate it. However, this can be not only expensive, but counterproductive as well in terms of the quality of the raw materials and, on the other hand, higher temperatures accelerate bacterial growth. In other aspects, the use and efficiency of bacteriocins are an effective alternative in the short and medium terms. Moreover, an indicator of bacterial growth is a low-level pH, since lots of deteriorating bacteria are lactic acids. Lastly, the processing times are a secondary agent of concern when the rest of the aforementioned agents are under control. Our main conclusion is that when acclimating a mathematical model within the context of the industrial process, it can generate new tools that predict bacterial contamination, the impact of bacterial inhibition, and processing method times. In addition, the mathematical modeling proposed logistic input of broad application, which can be replicated on non-meat food products, other pathogens or even on contamination by crossed contact of allergen foods.

Keywords: bacteriocins, cross-contamination, mathematical model, temperature

Procedia PDF Downloads 124