Search results for: trajectories mathematical proves

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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Authors: Marinka K. Baghdasaryan, Siranush M. Muradyan, Avgen A. Gasparyan

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Analytical expressions of the current and angular errors, as well as the frequency characteristics of an induction converter describing the relation with its structural parameters, the core and winding characteristics are obtained. Based on estimation of the dependences obtained, a mathematical problem of parametric optimization is formulated which can successfully be used for investigation and diagnosing an induction converter.

Keywords: induction converters, magnetic circuit material, current and angular errors, frequency response, mathematical formulation, structural parameters

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Authors: Jose Francisco Ferreira Ribeiro, Alexandre Bevilacqua Leoneti, Andre Lucirton Costa

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This paper presents a mathematical model in binary variables 0/1 to make the assignment of surgical procedures to the operating rooms in a hospital. The proposed mathematical model is based on the generalized assignment problem, which maximizes the sum of preferences for the use of the operating rooms by doctors, respecting the time available in each room. The corresponding program was written in Visual Basic of Microsoft Excel, and tested to schedule surgeries at St. Lydia Hospital in Ribeirao Preto, Brazil.

Keywords: generalized assignment problem, logistics, optimization, scheduling

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Authors: Dairo Jose Hernandez Paez

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The quantum theory of atoms in molecules (QTAIM) allows us to obtain topological information on electronic density in quantum mechanical systems. The QTAIM starts by considering the electron density as a continuous mathematical object. On the other hand, the discretization of electron density is also a mathematical object, which, from discrete mathematics, would allow a new approach to its topological study. From this point of view, it is necessary to develop a series of steps that provide the theoretical support that guarantees its application. Some of the steps that we consider most important are mentioned below: (1) obtain good representations of the electron density through computational calculations, (2) design a methodology for the discretization of electron density, and construct the simplicial complex. (3) Make an analysis of the discrete vector field associating the simplicial complex. (4) Finally, in this research, we propose to use the discrete Morse theory as a mathematical tool to carry out studies of electron density topology.

Keywords: discrete mathematics, Discrete Morse theory, electronic density, computational calculations

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Authors: Kayijuka Idrissa

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This work investigates a mathematical study for traffic flow and traffic density in Kigali city roads and the data collected from the national police of Rwanda in 2012. While working on this topic, some mathematical models were used in order to analyze and compare traffic variables. This work has been carried out on Kigali roads specifically at roundabouts from Kigali Business Center (KBC) to Prince House as our study sites. In this project, we used some mathematical tools to analyze the data collected and to understand the relationship between traffic variables. We applied the Poisson distribution method to analyze and to know the number of accidents occurred in this section of the road which is from KBC to Prince House. The results show that the accidents that occurred in 2012 were at very high rates due to the fact that this section has a very narrow single lane on each side which leads to high congestion of vehicles, and consequently, accidents occur very frequently. Using the data of speeds and densities collected from this section of road, we found that the increment of the density results in a decrement of the speed of the vehicle. At the point where the density is equal to the jam density the speed becomes zero. The approach is promising in capturing sudden changes on flow patterns and is open to be utilized in a series of intelligent management strategies and especially in noncurrent congestion effect detection and control.

Keywords: statistical methods, traffic flow, Poisson distribution, car moving technics

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Authors: Neelam Kumar

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Science is stratified, with an unequal distribution of research facilities and rewards among scientists. Gender stratification is one of the most prevalent phenomena in the world of science. In most countries gender segregation, horizontal as well as vertical, stands out in the field of science and engineering. India is no exception. This paper aims to examine: (1) gender and science associations, historical as well as contemporary, (2) women’s enrolment and gender differences in selection of academic fields, (2) women as professional researchers, (3) career path and recognition/trajectories. The paper reveals that in recent years the gender–science relationship has changed, but is not totally free from biases. Women’s enrolment into various science disciplines has shown remarkable and steady increase in most parts of the world, including India, yet they remain underrepresented in the S&T workforce, although to a lesser degree than in the past.

Keywords: gender, science, universal, women

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Authors: Jihan Abdulazeez Ahmed, Adnan Mohsin Abdulazeez Brifcani

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This paper suggests a new internal architecture of holon based on feature selection model using the combination of Bees Algorithm (BA) and Artificial Neural Network (ANN). BA is used to generate features while ANN is used as a classifier to evaluate the produced features. Proposed system is applied on the Wine data set, the statistical result proves that the proposed system is effective and has the ability to choose informative features with high accuracy.

Keywords: artificial neural network, bees algorithm, feature selection, Holon

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Authors: Jincan Li, Mingyu Gao, Zhiwei He, Yuxiang Yang, Zhongfei Yu, Yuanyuan Liu

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Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories.

Keywords: kinematic constraints, motion planning, trigonometric function, 6-DOF robots

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Authors: Misho Matsankov, Stoyan Petrov

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The paper presents the methodology and the obtained mathematical models for determining the value of the grounding resistance of a disconnected conductor in a three-phase power line, for which the contact voltage is safe, by taking into account the potentials, induced by the non-disconnected phase conductors. The mathematical models have been obtained by implementing the experimental design techniques.

Keywords: contact voltage, experimental design, induced voltage, safety

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Authors: Silvia Lucciarini, Antonio Corasaniti

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The issue of democracy in capitalist countries has once again become the focus of debate in recent years. A number of socio-economic and political tensions have triggered discussion of this topic from various perspectives and disciplines. Political developments, the rise of both right-wing parties and populism and the constant growth of inequalities in a context of welfare downsizing, have led scholars to question if European capitalist countries are really capable of creating and redistributing resources and look for elements that might make democratic capital in European countries more dense. The aim of the work is to shed light on the trajectories, intensity and convergence or divergence between political and associative participation, on one hand, and organization, on the other, as these constitute two of the main points of connection between the norms, values and actions that bind citizens to the state. Using the European Social Survey database, some studies have sought to analyse degrees of unionization by investigating the relationship between systems of industrial relations and vulnerable groups (in terms of value-oriented practices or political participation). This paper instead aims to investigate the relationship between union participation and civil/political participation, comparing union members and non-members and then distinguishing between employees and self-employed professionals to better understand participatory behaviors among different workers. The first component of the research will employ a multilinear logistic model to examine a sample of 10 countries selected according to a grid that combines the industrial relations models identified by Visser (2006) and the Welfare State systems identified by Esping-Andersen (1990). On the basis of this sample, we propose to compare the choices made by workers and their propensity to join trade unions, together with their level of social and political participation, from 2002 to 2016. In the second component, we aim to verify whether workers within the same system of industrial relations and welfare show a similar propensity to engage in civil participation through political bodies and associations, or if instead these tendencies take on more specific and varied forms. The results will allow us to see: (1) if political participation is higher among unionized workers than it is among the non-unionized. (2) what are the differences in unionisation and civil/political participation between self-employed, temporary and full-time employees and (3) whether the trajectories within industrial relations and welfare models display greater inclusiveness and participation, thereby confirming or disproving the patterns that have been documented among the different European countries.

Keywords: union membership, participation, democracy, industrial relations, welfare systems

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Authors: David Glassmeyer

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Quantitative reasoning is necessary to robustly understand mathematical concepts ranging from elementary to university levels. Quantitative reasoning involves identifying and representing quantities and the relationships between these quantities. Without reasoning quantitatively, students often resort to memorizing formulas and procedures, which have negative impacts when they encounter mathematical topics in the future. This study investigated how high school students’ quantitative reasoning could be fostered within a unit on arc measure and angle relationships. Arc measure, or the measure of a central angle that cuts off a portion of a circle’s circumference, is often confused with arclength. In this study, the researcher redesigned an activity to clearly distinguish arc measure and arc length by using a quantitative reasoning framework. Data were collected from high school students to determine if this approach impacted their understanding of these concepts. Initial data indicates the approach was successful in supporting students’ quantitative reasoning of these topics. Implications for the work are that teachers themselves may also benefit from considering mathematical definitions from a quantitative reasoning framework and can use this activity in their own classrooms.

Keywords: arc length, arc measure, quantitative reasoning, student content knowledge

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Authors: A. Giniatoulline

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We consider the internal oscillations of the ocean which are caused by the gravity force and the Coriolis force, for different models with changeable density, heat transfer, and salinity. Traditionally, the mathematical description of the resonance effect is related to the growing amplitude as a result of input vibrations. We offer a different approach: the study of the relation between the spectrum of the internal oscillations and the properties of the limiting amplitude of the solution for the harmonic input vibrations of the external forces. Using the results of the spectral theory of self-adjoint operators in Hilbert functional spaces, we prove that there exists an explicit relation between the localization of the frequency of the external input vibrations with respect to the essential spectrum of proper inner oscillations and the non-uniqueness of the limiting amplitude. The results may find their application in various problems concerning mathematical modeling of turbulent flows in the ocean.

Keywords: computational fluid dynamics, essential spectrum, limiting amplitude, rotating fluid, spectral theory, stratified fluid, the uniqueness of solutions of PDE equations

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Authors: Zahid Ullah, Atlas Khan

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In today's data-driven world, the role of mathematics in bridging the gap between theory and applications is becoming increasingly vital. This abstract highlights the significance of mathematics as a powerful tool for analyzing, interpreting, and extracting meaningful insights from vast amounts of data. By integrating mathematical principles with real-world applications, researchers can unlock the full potential of data-driven decision-making processes. This abstract delves into the various ways mathematics acts as a bridge connecting theoretical frameworks to practical applications. It explores the utilization of mathematical models, algorithms, and statistical techniques to uncover hidden patterns, trends, and correlations within complex datasets. Furthermore, it investigates the role of mathematics in enhancing predictive modeling, optimization, and risk assessment methodologies for improved decision-making in diverse fields such as finance, healthcare, engineering, and social sciences. The abstract also emphasizes the need for interdisciplinary collaboration between mathematicians, statisticians, computer scientists, and domain experts to tackle the challenges posed by the data-driven landscape. By fostering synergies between these disciplines, novel approaches can be developed to address complex problems and make data-driven insights accessible and actionable. Moreover, this abstract underscores the importance of robust mathematical foundations for ensuring the reliability and validity of data analysis. Rigorous mathematical frameworks not only provide a solid basis for understanding and interpreting results but also contribute to the development of innovative methodologies and techniques. In summary, this abstract advocates for the pivotal role of mathematics in bridging theory and applications in a data-driven world. By harnessing mathematical principles, researchers can unlock the transformative potential of data analysis, paving the way for evidence-based decision-making, optimized processes, and innovative solutions to the challenges of our rapidly evolving society.

Keywords: mathematics, bridging theory and applications, data-driven world, mathematical models

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Authors: Mark Kwaku Mensah Obeng

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In the late 1990s and early 2000s, nationals of sub-Saharan Africa who had initially settled in the Middle East and other parts of south east Asia moved to Guangzhou in response to the 1997/8 Asian financial crisis in numbers never witnessed. They were later joined by many more as the Chinese economy improved and as the economic relationship between China and Africa improved. This paper tells the story of identifiable sets of Ghanaians in Guangzhou, China in the 21st century. It details out their respective characteristics and their activities in China, their migratory trajectories and the motivations for travelling to China. Also analyzed is how they are coping with life in the unknown destination. It finally attempt predicting the future of the Ghanaian community in China in terms of their level of community participation and integration.

Keywords: Africa in China, Ghana, motivation, Guangzhou

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Authors: Carlos Alberto Carvalho Castro, Nancy Del Ducca Barbedo, Edmilsom Otoni Côrrea

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With increase the production oil and lines transmission gases that are in ample expansion, the industries medium and great transport they had to adapt itself to supply the demand manufacture in this fabrication segment. In this context, two welding processes have been more extensively used: the GMAW (Gas Metal Arc Welding) and the FCAW (Flux Cored Arc Welding). In this work, welds using these processes were carried out in flat position on ASTM A-36 carbon steel plates in order to make a comparative evaluation between them concerning to mechanical and metallurgical properties. A statistical tool based on technical analysis and design of experiments, DOE, from the Minitab software was adopted. For these analyses, the voltage, current, and welding speed, in both processes, were varied. As a result, it was observed that the welds in both processes have different characteristics in relation to the metallurgical properties and performance, but they present good weldability, satisfactory mechanical strength e developed mathematical models.

Keywords: Flux Cored Arc Welding (FCAW), Gas Metal Arc Welding (GMAW), Design of Experiments (DOE), mathematical models

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Authors: Hanifeh Imanian, Morteza Kolahdoozan

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The purpose of this study is to present a mathematical phrase for calculating the dispersion rate of spilled oil in water column under non-breaking waves. In this regard, a multiphase numerical model is applied for which waves and oil phase were computed concurrently, and accuracy of its hydraulic calculations have been proven. More than 200 various scenarios of oil spilling in wave waters were simulated using the multiphase numerical model and its outcome were collected in a database. The recorded results were investigated to identify the major parameters affected vertical oil dispersion and finally 6 parameters were identified as main independent factors. Furthermore, some statistical tests were conducted to identify any relationship between the dependent variable (dispersed oil mass in the water column) and independent variables (water wave specifications containing height, length and wave period and spilled oil characteristics including density, viscosity and spilled oil mass). Finally, a mathematical-statistical relationship is proposed to predict dispersed oil in marine waters. To verify the proposed relationship, a laboratory example available in the literature was selected. Oil mass rate penetrated in water body computed by statistical regression was in accordance with experimental data was predicted. On this occasion, it was necessary to verify the proposed mathematical phrase. In a selected laboratory case available in the literature, mass oil rate penetrated in water body computed by suggested regression. Results showed good agreement with experimental data. The validated mathematical-statistical phrase is a useful tool for oil dispersion prediction in oil spill events in marine areas.

Keywords: dispersion, marine environment, mathematical-statistical relationship, oil spill

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Authors: Qian Zhang, Dongkai Shen, Yan Shi

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A new mechanical ventilator with automatic secretion clearance function can improve the secretion clearance safely and efficiently. However, in recent modeling studies on various mechanical ventilators, it was considered that human had one lung, and the coupling effect of double lungs was never illustrated. In this paper, to expound the coupling effect of double lungs, a mathematical model of a ventilation system of a bi-level positive airway pressure (BiPAP) controlled ventilator with secretion clearance was set up. Moreover, an experimental study about the mechanical ventilation system of double lungs on BiPAP ventilator was conducted to verify the mathematical model. Finally, the coupling effect of double lungs of the mathematical ventilation was studied by simulation and orthogonal experimental design. This paper adds to previous studies and can be referred to optimization methods in medical researches.

Keywords: double lungs, coupling effect, secretion clearance, orthogonal experimental design

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Authors: Xavi Vilajosana Guillen, Emilio José Pérez Salgado

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This document presents experimental results obtained in a realistic environment using an underwater LoRa link. It aims to analyze the behavior of electromagnetic waves underwater and determine this communication capability. With this it has been tried to empirically evaluate the results obtained in the mathematical model using a commercial device with low cost and low consumption that works at frequency 433Mhz. The mathematical results obtained for wireless communication at 433Mhz underwater indicate that a communication of up to 7.5 m is possible, however experimentally 8 m has been achieved.

Keywords: 433Mhz link, internet of things, LoRa link, underwater communication

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Authors: Melisa Mete, Gary Davies, Susan Whelan

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Maintaining a good employer brand image is crucial for companies since it has numerous advantages such as better recruitment, retention and employee engagement, and commitment. This study aims to understand the relationship between employer brand image and employee satisfaction and engagement in the British context. A panel survey data (N=228) is tested via the regression models from the Hayes (2012) PROCESS macro, in IBM SPSS 23.0. The results are statistically significant and proves that the more positive employer brand image, the greater employee’ engagement and satisfaction, and the greater is employee satisfaction, the greater their engagement.

Keywords: employer brand, employer brand image, employee engagement, employee satisfaction

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Authors: Sagir M. Yusuf, Chris Baber

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In this paper, we describe how to achieve knowledge understanding and prediction (Situation Awareness (SA)) for multiple-agents conducting searching activity using Bayesian inferential reasoning and learning. Bayesian Belief Network was used to monitor agents' knowledge about their environment, and cases are recorded for the network training using expectation-maximisation or gradient descent algorithm. The well trained network will be used for decision making and environmental situation prediction. Forest fire searching by multiple UAVs was the use case. UAVs are tasked to explore a forest and find a fire for urgent actions by the fire wardens. The paper focused on two problems: (i) effective agents’ path planning strategy and (ii) knowledge understanding and prediction (SA). The path planning problem by inspiring animal mode of foraging using Lévy distribution augmented with Bayesian reasoning was fully described in this paper. Results proof that the Lévy flight strategy performs better than the previous fixed-pattern (e.g., parallel sweeps) approaches in terms of energy and time utilisation. We also introduced a waypoint assessment strategy called k-previous waypoints assessment. It improves the performance of the ordinary levy flight by saving agent’s resources and mission time through redundant search avoidance. The agents (UAVs) are to report their mission knowledge at the central server for interpretation and prediction purposes. Bayesian reasoning and learning were used for the SA and results proof effectiveness in different environments scenario in terms of prediction and effective knowledge representation. The prediction accuracy was measured using learning error rate, logarithm loss, and Brier score and the result proves that little agents mission that can be used for prediction within the same or different environment. Finally, we described a situation-based knowledge visualization and prediction technique for heterogeneous multi-UAV mission. While this paper proves linkage of Bayesian reasoning and learning with SA and effective searching strategy, future works is focusing on simplifying the architecture.

Keywords: Levy flight, distributed constraint optimization problem, multi-agent system, multi-robot coordination, autonomous system, swarm intelligence

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Authors: C. Mayr, J. Periya, A. Kariminezhad

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In this paper, we developed a learning framework for the classification of vulnerable road users (VRU) by their range-Doppler signatures. The frequency-modulated continuous-wave (FMCW) radar raw data is first pre-processed to obtain robust object range-Doppler maps per coherent time interval. The complex-valued range-Doppler maps captured from our outdoor measurements are further fed into a convolutional neural network (CNN) to learn the classification. This CNN has gone through a hyperparameter optimization process for improved learning. By learning VRU range-Doppler signatures, the three classes 'pedestrian', 'dog', and 'noise' are classified with an average accuracy of almost 95%. Interestingly, this classification accuracy holds for a combined longitudinal and lateral object trajectories.

Keywords: machine learning, radar, signal processing, autonomous driving

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Authors: Michaela Chovancova, Jakub Elcner

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Real bronchial tree is very complicated piping system. Analysis of flow and pressure losses in this system is very difficult. Due to the complex geometry and the very small size in the lower generations is examination by CFD possible only in the central part of bronchial tree. For specify the pressure losses of lower generations is necessary to provide a mathematical equation. Determination of mathematical formulas for calculating the pressure losses in the real lungs is due to its complexity and diversity lengthy and inefficient process. For these calculations is necessary the lungs to slightly simplify (same cross-section over the length of individual generation) or use one of the models of lungs. The simplification could cause deviations from real values. The article compares the values of pressure losses obtained from CFD simulation of air flow in the central part of the real bronchial tree with the values calculated in a slightly simplified real lungs by using a mathematical relationship derived from the Bernoulli equation and continuity equation. Then, evaluate the desirability of using this formula to determine the pressure loss across the bronchial tree.

Keywords: pressure gradient, airways resistance, real geometry of bronchial tree, breathing

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Authors: Abdelkhalek Bakkari

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Image segmentation is a critical step in image processing and pattern recognition. In this paper, we proposed a new robust automatic image classification based on a dynamic fuzzy c-means algorithm and mathematical morphology. The proposed segmentation algorithm (DFCM_MM) has been applied to MR perfusion images. The obtained results show the validity and robustness of the proposed approach.

Keywords: segmentation, classification, dynamic, fuzzy c-means, MR image

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Sarwat Jahan, Asker Rajin Rahman

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Management of offtake of any fluvial river is very sensitive in terms of long-term sustainability where the variation of water flow and sediment transport range are wide enough throughout a hydrological year. The Gorai River is a major distributary of the Ganges River in Bangladesh and is termed as a primary source of fresh water for the South-West part of the country. Every year, significant siltation of the Gorai offtake disconnects it from the Ganges during the dry season. As a result, the socio-economic and environmental condition of the downstream areas has been deteriorating for a few decades. To improve the overall situation of the Gorai offtake and its dependent areas, a study has been conducted by the Institute of Water Modelling, Bangladesh, in 2022. Using the mathematical morphological modeling tool MIKE 21C of DHI Water & Environment, Denmark, simulated results revealed the need for dredging/river training structures for offtake management at the Gorai offtake to ensure significant dry season flow towards the downstream. The dry season flow is found to increase significantly with the proposed river interventions, which also improves the environmental conditions in terms of salinity of the South-West zone of the country. This paper summarizes the primary findings of the analyzed results of the developed mathematical model for improving the existing condition of the Gorai River.

Keywords: Gorai river, mathematical modelling, offtake, siltation, salinity

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Authors: Emhimed Saffor

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In this paper, the problem of edge detection in digital images is considered. Three methods of edge detection based on mathematical morphology algorithm were applied on two sets (Brain and Chest) CT images. 3x3 filter for first method, 5x5 filter for second method and 7x7 filter for third method under MATLAB programming environment. The results of the above-mentioned methods are subjectively evaluated. The results show these methods are more efficient and satiable for medical images, and they can be used for different other applications.

Keywords: CT images, Matlab, medical images, edge detection

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Authors: Nessa-Amie T. Peñaflor, Antonio Cinto

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This is a descriptive research on the level of math anxiety and mathematics misconceptions in algebra. This research is composed of four parts: (1) analysis of the level of anxiety of the respondents; (2) analysis of the common mathematical misconceptions in algebra; (3) relationship of socio-demographic profile in math anxiety and mathematical misconceptions and (4) analysis of the relationship of math anxiety and misconceptions in algebra. Through the demographic profile questionnaire it was found out that most of the respondents were female. Majority had ages that ranged from 13-15. Most of them had parents who finished secondary education. The biggest portion of Grade Seven students where from families with annual family income ranging from PhP 100, 000 to PhP 299, 999. Most of them came from public school. Mathematics Anxiety Scale for Secondary and Senior Secondary School Students (MAS) and set of 10 open-ended algebraic expressions and polynomials were also administered to determine the anxiety level and the common misconceptions in algebra. Data analysis revealed that respondents had high anxiety in mathematics. Likewise, the common mathematical misconceptions of the Grade Seven students were: combining unlike terms; multiplying the base and exponents; regarding the variable x as 0; squaring the first and second terms only in product of two binomials; wrong meaning attached to brackets; writing the terms next to each other but not simplifying in using the FOIL Method; writing the literal coefficient even if the numerical coefficient is 0; and dividing the denominator by the numerator when the numerical coefficient in the numerator is smaller than the numerical coefficient of the denominator. Results of the study show that the socio-demographic characteristics were not related to mathematics anxiety and misconceptions. Furthermore, students from higher section had high anxiety than those students on the lower section. Thus, belonging to higher or lower section may affect the mathematical misconceptions of the respondents.

Keywords: algebra, grade 7 math, math anxiety, math misconceptions

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Authors: Atara Shriki, Ilana Lavy

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Teaching for the first time an online course dealing with the history of mathematics, we were struggling with questions related to the design of a proper learning environment (LE). Thirteen high school mathematics teachers, M.Ed. students, attended the course. The teachers were engaged in independent reading of mathematical texts, a task that is recognized as complex due to the unique characteristics of such texts. In order to support the learning processes and develop skills that are essential for succeeding in learning online (e.g. self-regulated learning skills, meta-cognitive skills, reflective ability, and self-assessment skills), the LE comprised of three components aimed at “scaffolding” the learning: (1) An online "self-feedback" questionnaires that included drill-and-practice questions. Subsequent to responding the questions the online system provided a grade and the teachers were entitled to correct their answers; (2) Open-ended questions aimed at stimulating critical thinking about the mathematical contents; (3) Reflective questionnaires designed to assist the teachers in steering their learning. Using a mixed-method methodology, an inquiry study examined the learning processes, the learners' difficulties in reading the mathematical texts and on the unique contribution of each component of the LE to the ability of teachers to comprehend the mathematical contents, and support the development of their learning skills. The results indicate that the teachers found the online feedback as most helpful in developing self-regulated learning skills and ability to reflect on deficiencies in knowledge. Lacking previous experience in expressing opinion on mathematical ideas, the teachers had troubles in responding open-ended questions; however, they perceived this assignment as nurturing cognitive and meta-cognitive skills. The teachers also attested that the reflective questionnaires were useful for steering the learning. Although in general the teachers found the LE as supportive, most of them indicated the need to strengthen instructor-learners and learners-learners interactions. They suggested to generate an online forum to enable them receive direct feedback from the instructor, share ideas with other learners, and consult with them about solutions. Apparently, within online LE, supporting learning merely with respect to cognitive aspects is not sufficient. Leaners also need an emotional support and sense a social presence.

Keywords: cognitive and meta-cognitive skills, independent reading of mathematical texts, online learning environment, self-regulated learning skills

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Authors: A. A. Okafor, C. H. Achebe, J. L. Chukwuneke, C. G. Ozoegwu

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The performance of an engine whose basic design parameters are known can be predicted with the assistance of simulation programs into the less time, cost and near value of actual. This paper presents a comprehensive mathematical model of the performance parameters of four stroke spark ignition engine. The essence of this research work is to develop a mathematical model for the analysis of engine performance parameters of four stroke spark ignition engine before embarking on full scale construction, this will ensure that only optimal parameters are in the design and development of an engine and also allow to check and develop the design of the engine and it’s operation alternatives in an inexpensive way and less time, instead of using experimental method which requires costly research test beds. To achieve this, equations were derived which describe the performance parameters (sfc, thermal efficiency, mep and A/F). The equations were used to simulate and optimize the engine performance of the model for various engine speeds. The optimal values obtained for the developed bivariate mathematical models are: sfc is 0.2833kg/kwh, efficiency is 28.77% and a/f is 20.75.

Keywords: bivariate models, engine performance, injector engine, optimization, performance parameters, simulation, spark ignition

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi

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In this paper a real-time obstacle avoidance approach for both autonomous and non-autonomous dynamical systems (DS) is presented. In this approach the original dynamics of the controller which allow us to determine safety margin can be modulated. Different common types of DS increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle especially when robot moves very fast in changeable complex environments. The method is validated by simulation and influence of different autonomous and non-autonomous DS such as important characteristics of limit cycles and unstable DS. Furthermore, the position of different obstacles in complex environment is explained. Finally, the verification of avoidance trajectories is described through different parameters such as safety factor.

Keywords: limit cycles, nonlinear dynamical system, real time obstacle avoidance, safety margin

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