Search results for: mathematical thinking

Authors: Elham Rajabian

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The ascent of cybersecurity incidents is a rising threat to most organisations in general, while the impact of the incidents is unique to each of the organizations. It is a need for behavioural sciences to concentrate on employees’ behaviour in order to prepare key security mitigation opinions versus cybersecurity incidents. There are noticeable differences among users of a computer system in terms of complying with security behaviours. We can discuss the people's differences under several subjects such as delaying tactics on something that must be done, the tendency to act without thinking, future thinking about unexpected implications of present-day issues, and risk-taking behaviours in security policies compliance. In this article, we introduce high-profile cyber-attacks and their impacts on weakening cyber resiliency in organizations. We also give attention to human errors that influence network security. Human errors are discussed as a part of psychological matters to enhance compliance with the security policies. The organizational challenges are studied in order to shape a sustainable cyber risks management approach in the related work section. Insiders’ behaviours are viewed as a cyber security gap to draw proper cyber resiliency in section 3. We carry out the best cybersecurity practices by discussing four CIS challenges in section 4. In this regard, we provide a guideline and metrics to measure cyber resilience in organizations in section 5. In the end, we give some recommendations in order to build a cybersecurity culture based on individual behaviours.

Keywords: cyber resilience, human factors, cybersecurity behavior, attitude, usability, security culture

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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: Jennifer K. Bowerman, Rhonda L. Reich

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The purpose of this paper is to explore the concepts ACDC (Amore, Consciousness, Discipline, and Commitment) which the authors first discovered as a philosophy and framework for recruitment and organizational development in a successful start-up tech company in Brazil. This paper represents an exploration of these concepts as a potential pedagogical foundation for undergraduate business education in the classroom. It explores whether their application has potential to build emotional and practical resilience in the face of constant organizational and societal change. Derived from Holonomy this paper explains the concepts and develops a narrative around how change influences the operation of organizations. Using examples from leading edge organizational theorists, it explains why a different educational approach grounded in ACDC concepts may not only have relevance for the working world, but also for undergraduates about to enter that world. The authors propose that in the global context of constant change, it makes sense to develop an approach to education, particularly business education, beyond cognitive knowledge, models and tools, in such a way that emotional and practical resilience and creative thinking may be developed. Using the classroom as an opportunity to explore these concepts, and aligning personal passion with the necessary discipline and commitment, may provide students with a greater sense of their own worth and potential as they venture into their ever-changing futures.

Keywords: ACDC, holonomic thinking, organizational learning, organizational change, business pedagogy

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Authors: Yuliya Lipshits-Braziler

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For many young adults, career decision making is a difficult and complex process that may lead to indecision. Indecision is frequently associated with great psychological distress and low levels of well-being. One important resource for dealing with indecision is career decision self-efficacy (CDSE), which refers to people’s beliefs about their ability to successfully accomplish certain tasks involved in career choice. Drawing from Social Cognitive Theory, it has been hypothesized that CDSE correlates with (a) people’s likelihood to engage in or avoid career decision making tasks, (b) the amount of effort put into the decision making process, (c) the people’s persistence in decision making efforts when faced with difficulties, and (d) the eventual success in arriving at career decisions. Based on these assumptions, the present study examines the associations between the CDSE and 14 strategies for coping with career indecision among young adults. Using the structural equation modeling (SEM), the results showed that CDSE is positively associated with the use of productive coping strategies, such as information-seeking, problem-solving, positive thinking, and self-regulation. In addition, CDSE was negatively associated with nonproductive coping strategies, such as avoidance, isolation, ruminative thinking, and blaming others. Contrary to our expectations, CDSE was not significantly correlated with instrumental help-seeking, while it was negatively correlated with emotional help-seeking. The results of this study can be used to facilitate the development of interventions aiming to reinforce young adults’ career decision making self-efficacy, which may provide them with a basis for overcoming career indecision more effectively.

Keywords: career decision self-efficacy, career indecision, coping strategies, career counseling

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Authors: Tiptunya Duangsri, Panwilai Chomchid, Natchanok Jansawang

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This research study was to investigate of education decisions must be made which a part of it should be passed on to future generations as obligatory for all members of a chemistry class for students who will prepare themselves for a special position. The descriptions of instructional design were provided and the recent criticisms are discussed. This research study to an outline of an integrative framework for the description of information and the instructional design model give structure to negotiate a semblance of conscious understanding. The aims of this study are to describe the instructional design model for comparisons between students’ genders of their effects on STEM educational learning achievement motives to their science attitudes and logical thinking abilities with a sample size of 18 students at the 11th grade level with the cluster random sampling technique in Mahawichanukul School were designed. The chemistry learning environment was administered with the STEM education method. To build up the 5-instrument lesson instructional plan issues were instructed innovations, the 30-item Logical Thinking Test (LTT) on 5 scales, namely; Inference, Recognition of Assumptions, Deduction, Interpretation and Evaluation scales was used. Students’ responses of their perceptions with the Test Of Chemistry-Related Attitude (TOCRA) were assessed of their attitude in science toward chemistry. The validity from Index Objective Congruence value (IOC) checked by five expert specialist educator in two chemistry classroom targets in STEM education, the E1/E2 process were equaled evidence of 84.05/81.42 which results based on criteria are higher than of 80/80 standard level with the IOC from the expert educators. Comparisons between students’ learning achievement motives with STEM educational model on stoichiometry issue in chemistry classes with different genders were differentiated at evidence level of .05, significantly. Associations between students’ learning achievement motives on their posttest outcomes and logical thinking abilities, the predictive efficiency (R2) values indicate that 69% and 70% of the variances in different male and female student groups of their logical thinking abilities. The predictive efficiency (R2) values indicate that 73%; and 74% of the variances in different male and female student groups of their science attitudes toward chemistry were associated. Statistically significant on students’ perceptions of their chemistry learning classroom environment and their science attitude toward chemistry when using the MCI and TOCRA, the predictive efficiency (R2) values indicated that 72% and 74% of the variances in different male and female student groups of their chemistry classroom climate, consequently. Suggestions that supporting chemistry or science teachers from science, technology, engineering and mathematics (STEM) in addressing complex teaching and learning issues related instructional design to develop, teach, and assess traditional are important strategies with a focus on STEM education instructional method.

Keywords: development, the instructional design model, students learning achievement motives, science attitudes with STEM educational model, stoichiometry issue, chemistry classes, genders

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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: 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: 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: 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: M. Bortolini, E. Ferrari, F. G. Galizia, C. Mora

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In the last decades, an increasing set of companies adopted lean philosophy to improve their productivity and efficiency promoting the so-called continuous improvement concept, reducing waste of time and cutting off no-value added activities. In parallel, increasing attention rises toward green practice and management through the spread of the green supply chain pattern, to minimise landfilled waste, drained wastewater and pollutant emissions. Starting from a review on contributions deepening lean and green principles applied to supply chain management, the most relevant drivers to measure the performance of industrial processes are pointed out. Specific attention is paid on the role of cost because it is of key importance and it crosses both lean and green principles. This analysis leads to figure out an original reference framework for integrating lean and green principles in designing and managing supply chains. The proposed framework supports the application, to the whole value chain or to parts of it, e.g. distribution network, assembly system, job-shop, storage system etc., of the lean-green integrated perspective. Evidences show that the combination of the lean and green practices lead to great results, higher than the sum of the performances from their separate application. Lean thinking has beneficial effects on green practices and, at the same time, methods allowing environmental savings generate positive effects on time reduction and process quality increase.

Keywords: environmental sustainability, green supply chain, integrated framework, lean thinking, supply chain management

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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: Ehsan Moradi, Parisa Paikhaste, Amir Alam Beigi, Seyedeh Somayeh Bathaei

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The need for entrepreneurial sustainability is as important as the entrepreneurship category itself. By transferring competencies in a sustainable entrepreneurship framework, entrepreneurship education can make a significant contribution to the effectiveness of businesses, especially for start-up entrepreneurs. This study analyzes the essential competencies of students in the development of sustainable entrepreneurship. It is an applied causal study in terms of nature and field in terms of data collection. The main purpose of this research project is to study and explain the dimensions of sustainability entrepreneurship competencies among agricultural students. The statistical population consists of 730 junior and senior undergraduate students of the Campus of Agriculture and Natural Resources, University of Tehran. The sample size was determined to be 120 using the Cochran's formula, and the convenience sampling method was used. Face validity, structure validity, and diagnostic methods were used to evaluate the validity of the research tool and Cronbach's alpha and composite reliability to evaluate its reliability. Structural equation modeling (SEM) was used by the confirmatory factor analysis (CFA) method to prepare a measurement model for data processing. The results showed that seven key dimensions play a role in shaping sustainable entrepreneurial development competencies: systems thinking competence (STC), embracing diversity and interdisciplinary (EDI), foresighted thinking (FTC), normative competence (NC), action competence (AC), interpersonal competence (IC), and strategic management competence (SMC). It was found that acquiring skills in SMC by creating the ability to plan to achieve sustainable entrepreneurship in students through the relevant mechanisms can improve entrepreneurship in students by adopting a sustainability attitude. While increasing students' analytical ability in the field of social and environmental needs and challenges and emphasizing curriculum updates, AC should pay more attention to the relationship between the curriculum and its content in the form of entrepreneurship culture promotion programs. In the field of EDI, it was found that the success of entrepreneurs in terms of sustainability and business sustainability of start-up entrepreneurs depends on their interdisciplinary thinking. It was also found that STC plays an important role in explaining the relationship between sustainability and entrepreneurship. Therefore, focusing on these competencies in agricultural education to train start-up entrepreneurs can lead to sustainable entrepreneurship in the agricultural higher education system.

Keywords: sustainable entrepreneurship, entrepreneurship education, competency, agricultural higher education

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Authors: Mohammad Hossein Badamchi

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As Leo Strauss demonstrates in his works, Political Philosophy in the western tradition is an epistemic-naturalistic tradition insofar Hanna Arendt mentioning the deep conflict between philosophy and politics, opposed to be named “political philosopher” prefer the title “political thinker” for herself. In fact, the Western political philosophy’s tendency to derive politics from natural law and epistemic argumentations makes a paradox between the actual “the political” and the theoretical “natural politics” in the western tradition. In this paper, we want to show that Hanna Arendt, in her exploration to find a new realm of the non-naturalistic way of thinking about the political is walking on a completely different tradition of political philosophy which was first established by Al-Farabi, the founder of Islamic political philosophy around thousand years after Greek Philosophy. Despite Aristotelian Polis which is a Natural community based on true natural rationality to reach the natural purposes of mankind, Al-Farabi’s Madine (his reconstructed concept of Aristotelian Polis) is completely constructed against natural cities, which are formulated by necessity logic of natural arguments and natural deception of humanity. In fact, Farabi considers the natural understanding of politics as Ignorant ideologies used by governments to suppress people. Madine in Farabi’s work is not a natural institution but is a collaborative constitution founded by citizens. So despite Aristotelian thinking, here we don’t have just A Polis that is the one true polis, but we have various multiple Madines among one, is virtuous not by definition but by real action of citizens and civil relations. Al-Farabi’s political philosophy is not a Naturalistic-epistemic Political Philosophy but is a Phronetic Political Philosophy which Hanna Arendt wants to establish outside of western contemplative anti-active political philosophy tradition.

Keywords: al-farabi, hanna arendt, natural politics, the political, political philosophy

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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: Hau-Wei Lee, Yu-Chi Liu, Chien-Hung Liu

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A mathematical model is presented for a system that measures rotational errors in a shaft using a ball lens. The geometric optical characteristics of the ball lens mounted on the shaft allows the measurement of rotation axis errors in both the radial and axial directions. The equipment used includes two quadrant detectors (QD), two laser diodes and a ball lens that is mounted on the rotating shaft to be evaluated. Rotational errors in the shaft cause changes in the optical geometry of the ball lens. The resulting deflection of the laser beams is detected by the QDs and their output signals are used to determine rotational errors. The radial and the axial rotational errors can be calculated as explained by the mathematical model. Results from system calibration show that the measurement error is within ±1 m and resolution is about 20 nm. Using a direct drive motor (DD motor) as an example, experimental results show a rotational error of less than 20 m. The most important features of this system are that it does not require the use of expensive optical components, it is small, very easy to set up, and measurements are highly accurate.

Keywords: ball lens, quadrant detector, axial error, radial error

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Authors: Sadia Arshad

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The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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Authors: Ozgul Kartal, Wade Tillett, Lyn D. English

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Despite its global significance in curricula, mathematical modeling encounters persistent disparities in recognition and emphasis within regular mathematics classrooms and teacher education across countries with diverse educational and cultural traditions, including variations in the perceived role of mathematical modeling. Over the past two decades, increased attention has been given to the integration of mathematical modeling into national curriculum standards in the U.S. and other countries. Therefore, the mathematics education research community has dedicated significant efforts to investigate various aspects associated with the teaching and learning of mathematical modeling, primarily focusing on exploring the applicability of modeling in schools and assessing students', teachers', and preservice teachers' (PTs) competencies and engagement in modeling cycles and processes. However, limited attention has been directed toward examining potential resistance hindering teachers and PTs from effectively implementing mathematical modeling. This study focuses on how PTs, without prior modeling experience, resist and/or embrace mathematical modeling and its pedagogy as they learn about models and modeling perspectives, navigate the modeling process, design and implement their modeling activities and lesson plans, and experience the pedagogy enabling modeling. Model eliciting activities (MEAs) were employed due to their high potential to support the development of mathematical modeling pedagogy. The mathematical modeling module was integrated into a mathematics methods course to explore how PTs embraced or resisted mathematical modeling and its pedagogy. The module design included reading, reflecting, engaging in modeling, assessing models, creating a modeling task (MEA), and designing a modeling lesson employing an MEA. Twelve senior undergraduate students participated, and data collection involved video recordings, written prompts, lesson plans, and reflections. An open coding analysis revealed acceptance and resistance toward teaching mathematical modeling. The study identified four overarching themes, including both acceptance and resistance: pedagogy, affordance of modeling (tasks), modeling actions, and adjusting modeling. In the category of pedagogy, PTs displayed acceptance based on potential pedagogical benefits and resistance due to various concerns. The affordance of modeling (tasks) category emerged from instances when PTs showed acceptance or resistance while discussing the nature and quality of modeling tasks, often debating whether modeling is considered mathematics. PTs demonstrated both acceptance and resistance in their modeling actions, engaging in modeling cycles as students and designing/implementing MEAs as teachers. The adjusting modeling category captured instances where PTs accepted or resisted maintaining the qualities and nature of the modeling experience or converted modeling into a typical structured mathematics experience for students. While PTs displayed a mix of acceptance and resistance in their modeling actions, limitations were observed in embracing complexity and adhering to model principles. The study provides valuable insights into the challenges and opportunities of integrating mathematical modeling into teacher education, emphasizing the importance of addressing pedagogical concerns and providing support for effective implementation. In conclusion, this research offers a comprehensive understanding of PTs' engagement with modeling, advocating for a more focused discussion on the distinct nature and significance of mathematical modeling in the broader curriculum to establish a foundation for effective teacher education programs.

Keywords: mathematical modeling, model eliciting activities, modeling pedagogy, secondary teacher education

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Authors: Jamal Hussain Al-Smail

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Hydrogen fuel cells (HFCs) are environmentally friendly, energy converter devices that convert the chemical energy of the reactants (oxygen and hydrogen) to electricity through electrochemical reactions. The level of the electricity production of HFCs mainly increases depending on the oxygen distribution in the HFC’s cathode gas diffusion layer (GDL). With a constant porosity of the GDL, the electrochemical reaction can have a great variation that reduces the cell’s productivity and stability. Our findings bring a methodology in finding porosity designs of the diffusion layer to improve the oxygen distribution such that it results in a stable oxygen-hydrogen reaction. We first introduce a mathematical model involving the mass and momentum transport equations, in which a porosity function of the GDL is incorporated as a control for the fluid flow. We then derive numerical methods for solving the mathematical model. In conclusion, we present our numerical results to show how to design the GDL porosity to result in a uniform oxygen distribution.

Keywords: fuel cells, material porosity design, mathematical modeling, porous media

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Authors: Z. M. T. Lim, W. Q. Yow

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Diversity in individual problem-solving approaches, culture and nationality have been shown to have positive effects on collaborative creative processes in organizational and scholastic settings. For example, diverse graduate and organizational teams consisting of members with both structured and unstructured problem-solving styles were found to have more creative ideas on a collaborative idea generation task than teams that comprised solely of members with either structured or unstructured problem-solving styles. However, being different may not always provide benefits to the collaborative creative process. In particular, speaking different languages may hinder mutual engagement through impaired communication and thus collaboration. Instead, sharing similar languages may have facilitative effects on mutual engagement in collaborative tasks. However, no studies have explored the relations between language diversity and adults’ collaborative creative problem solving. Sixty-four Singaporean English-speaking bilingual undergraduates were paired up into similar or dissimilar language pairs based on the second language they spoke (e.g., for similar language pairs, both participants spoke English-Mandarin; for dissimilar language pairs, one participant spoke English-Mandarin and the other spoke English-Korean). Each participant completed the Ravens Progressive Matrices Task individually. Next, they worked in pairs to complete a collaborative divergent thinking task where they used mind-mapping techniques to brainstorm ideas on a given problem together (e.g., how to keep insects out of the house). Lastly, the pairs worked on a collaborative insight problem-solving task (Triangle of Coins puzzle) where they needed to flip a triangle of ten coins around by moving only three coins. Pairs who had prior knowledge of the Triangle of Coins puzzle were asked to complete an equivalent Matchstick task instead, where they needed to make seven squares by moving only two matchsticks based on a given array of matchsticks. Results showed that, after controlling for intelligence, similar language pairs completed the collaborative insight problem-solving task faster than dissimilar language pairs. Intelligence also moderated these relations. Among adults of lower intelligence, similar language pairs solved the insight problem-solving task faster than dissimilar language pairs. These differences in speed were not found in adults with higher intelligence. No differences were found in the number of ideas generated in the collaborative divergent thinking task between similar language and dissimilar language pairs. In conclusion, sharing similar languages seem to enrich collaborative creative processes. These effects were especially pertinent to pairs with lower intelligence. This provides guidelines for the formation of groups based on shared languages in collaborative creative processes. However, the positive effects of shared languages appear to be limited to the insight problem-solving task and not the divergent thinking task. This could be due to the facilitative effects of other factors of diversity as found in previous literature. Background diversity, for example, may have a larger facilitative effect on the divergent thinking task as compared to the insight problem-solving task due to the varied experiences individuals bring to the task. In conclusion, this study contributes to the understanding of the effects of language diversity in collaborative creative processes and challenges the general positive effects that diversity has on these processes.

Keywords: bilingualism, diversity, creativity, collaboration

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Authors: Fadwa Al Bawardi

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In March 2021, the Saudi Arabian Council of Ministers issued a decision to form a committee called the "Higher Committee for Research, Development and Innovation," a committee linked to the Council of Economic and Development Affairs, chaired by the Chairman of the Council of Economic and Development Affairs, and concerned with the development of the research, development and innovation sector in the Kingdom. In order to talk about the dimensions of this wonderful step, let us first try to answer the following questions. Is there a difference between creativity and innovation..? What are the factors of creativity in the individual. Are they mental genetic factors or are they factors that an individual acquires through learning..? The methodology included surveys that have been conducted on more than 500 individuals, males and females, between the ages of 18 till 60. And the answer is. "Creativity" is the creation of a new idea, while "Innovation" is the development of an already existing idea in a new, successful way. They are two sides of the same coin, as the "creative idea" needs to be developed and transformed into an "innovation" in order to achieve either strategic achievements at the level of countries and institutions to enhance organizational intelligence, or achievements at the level of individuals. For example, the beginning of smart phones was just a creative idea from IBM in 1994, but the actual successful innovation for the manufacture, development and marketing of these phones was through Apple later. Nor does creativity have to be hereditary. There are three basic factors for creativity: The first factor is "the presence of a challenge or an obstacle" that the individual faces and seeks thinking to find solutions to overcome, even if thinking requires a long time. The second factor is the "environment surrounding" of the individual, which includes science, training, experience gained, the ability to use techniques, as well as the ability to assess whether the idea is feasible or otherwise. To achieve this factor, the individual must be aware of own skills, strengths, hobbies, and aspects in which one can be creative, and the individual must also be self-confident and courageous enough to suggest those new ideas. The third factor is "Experience and the Ability to Accept Risk and Lack of Initial Success," and then learn from mistakes and try again tirelessly. There are some tools and techniques that help the individual to reach creative and innovative ideas, such as: Mind Maps tool, through which the available information is drawn by writing a short word for each piece of information and arranging all other relevant information through clear lines, which helps in logical thinking and correct vision. There is also a tool called "Flow Charts", which are graphics that show the sequence of data and expected results according to an ordered scenario of events and workflow steps, giving clarity to the ideas, their sequence, and what is expected of them. There are also other great tools such as the Six Hats tool, a useful tool to be applied by a group of people for effective planning and detailed logical thinking, and the Snowball tool. And all of them are tools that greatly help in organizing and arranging mental thoughts, and making the right decisions. It is also easy to learn, apply and use all those tools and techniques to reach creative and innovative solutions. The detailed figures and results of the conducted surveys are available upon request, with charts showing the %s based on gender, age groups, and job categories.

Keywords: innovation, creativity, factors, tools

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Authors: Goulet Marie-Pier, Voyer Dominic, Simoneau Victoria

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In a previous research project (2011-2019) funded by the Quebec Ministry of Education, an educational approach was developed based on the teaching and learning of place value through children's literature. Subsequently, the effect of this approach on the conceptual understanding of the concept among first graders (6-7 years old) was studied. The current project aims to create a series of children's literature to help older elementary school students (8-10 years old) in developing a conceptual understanding of complex mathematical concepts taught at their grade level rather than a more typical procedural understanding. Knowing that there are no educational material or children's books that exist to achieve our goals, four stories, accompanied by mathematical activities, will be created to support students, and their teachers, in the learning and teaching of mathematical concepts that can be challenging within their mathematic curriculum. The stories will also introduce a mathematical dialogue into the characters' discourse with the aim to address various mathematical foundations for which there are often erroneous statements among students and occasionally among teachers. In other words, the stories aim to empower students seeking a real understanding of difficult mathematical concepts, as well as teachers seeking a way to teach these difficult concepts in a way that goes beyond memorizing rules and procedures. In order to choose the concepts that will be part of the stories, it is essential to understand the current landscape regarding the main difficulties experienced by students in third and fourth grade (8-10 years old) and their teacher’s needs. From this perspective, the preliminary phase of the study, as discussed in the presentation, will provide critical insight into the mathematical concepts with which the target grade levels struggle the most. From this data, the research team will select the concepts and develop their stories in the second phase of the study. Two questions are preliminary to the implementation of our approach, namely (1) what mathematical concepts are considered the most “difficult to teach” by teachers in the third and fourth grades? and (2) according to teachers, what are the main difficulties encountered by their students in numeracy? Self-administered online questionnaires using the SimpleSondage software will be sent to all third and fourth-grade teachers in nine school service centers in the Quebec region, representing approximately 300 schools. The data that will be collected in the fall of 2022 will be used to compare the difficulties identified by the teachers with those prevalent in the scientific literature. Considering that this ensures consistency between the proposed approach and the true needs of the educational community, this preliminary phase is essential to the relevance of the rest of the project. It is also an essential first step in achieving the two ultimate goals of the research project, improving the learning of elementary school students in numeracy, and contributing to the professional development of elementary school teachers.

Keywords: children’s literature, conceptual understanding, elementary school, learning and teaching, mathematics

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Authors: Lee Bih Ni, Nurul Asyikin Binti Hassan

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This paper discusses the use of mnemonic and mathematical methods in enhancing the understanding of history. Mnemonics can help students from all levels including high school and in various disciplines including language, math and history. At the secondary level, students are exposed to various courses that require them to remember many facts that can be mastered through the application of mnemonic techniques. Researchers use narrative literature studies to illustrate the current state of art and science in the field of research focused. Researchers used narrative literature reviews to build a scientific base of knowledge. Researchers gather all the key points in the discussion, and put it here by referring to the specific field where the paper is essentially based. The findings suggest that the use of mnemonic techniques can improve the individual's memory by adding little effort. In implementing mnemonic techniques, it is important to integrate mathematics and history in the course as both are interconnected as mathematics has shaped our history and vice versa. This study shows that memory skills can actually be improved; the human mind can remember something more than expected.

Keywords: cognitive strategy, mnemonic technique, secondary school level study, mathematical mnemonic

Procedia PDF Downloads 111

Authors: Geetika Barman, B. S. Daya Sagar

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In this article, we proposed a pixel-wise classification of hyperspectral images using a mathematical morphology operator-based distance metric called “dilation distance” and “erosion distance”. This method involves measuring the spatial distance between the spectral features of a hyperspectral image across the bands. The key concept of the proposed approach is that the “dilation distance” is the maximum distance a pixel can be moved without changing its classification, whereas the “erosion distance” is the maximum distance that a pixel can be moved before changing its classification. The spectral signature of the hyperspectral image carries unique class information and shape for each class. This article demonstrates how easily the dilation and erosion distance can measure spatial distance compared to other approaches. This property is used to calculate the spatial distance between hyperspectral image feature vectors across the bands. The dissimilarity matrix is then constructed using both measures extracted from the feature spaces. The measured distance metric is used to distinguish between the spectral features of various classes and precisely distinguish between each class. This is illustrated using both toy data and real datasets. Furthermore, we investigated the role of flat vs. non-flat structuring elements in capturing the spatial features of each class in the hyperspectral image. In order to validate, we compared the proposed approach to other existing methods and demonstrated empirically that mathematical operator-based distance metric classification provided competitive results and outperformed some of them.

Keywords: dilation distance, erosion distance, hyperspectral image classification, mathematical morphology

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Authors: W. I. Mazyan, A. Ahmadi, M. Hoorfar

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Objectives/Scope: This paper proposes a mathematical model for calculating the solid-gas separation efficiency in cyclones. This model provides better agreement with experimental results compared to existing mathematical models. Methods: The separation ratio efficiency, ϵsp, is evaluated by calculating the outlet to inlet count ratio. Similar to mathematical derivations in the literature, the inlet and outlet particle count were evaluated based on Eulerian approach. The model also includes the external forces acting on the particle (i.e., centrifugal and drag forces). In addition, the proposed model evaluates the exact length that the particle travels inside the cyclone for the evaluation of number of turns inside the cyclone. The separation efficiency model derivation using Stoke’s law considers the effect of the inlet tangential velocity on the separation performance. In cyclones, the inlet velocity is a very important factor in determining the performance of the cyclone separation. Therefore, the proposed model provides accurate estimation of actual cyclone separation efficiency. Results/Observations/Conclusion: The separation ratio efficiency, ϵsp, is studied to evaluate the performance of the cyclone for particles ranging from 1 microns to 10 microns. The proposed model is compared with the results in the literature. It is shown that the proposed mathematical model indicates an error of 7% between its efficiency and the efficiency obtained from the experimental results for 1 micron particles. At the same time, the proposed model gives the user the flexibility to analyze the separation efficiency at different inlet velocities. Additive Information: The proposed model determines the separation efficiency accurately and could also be used to optimize the separation efficiency of cyclones at low cost through trial and error testing, through dimensional changes to enhance separation and through increasing the particle centrifugal forces. Ultimately, the proposed model provides a powerful tool to optimize and enhance existing cyclones at low cost.

Keywords: cyclone efficiency, solid-gas separation, mathematical model, models error comparison

Procedia PDF Downloads 368