Search results for: mathematical

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: 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: 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

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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

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Authors: N. Philipova

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The influence of the geometric parameters of trapezoidal labyrinth channel on the emitter discharge is investigated in this work. The impact of the dentate angle, the dentate spacing, and the dentate height are studied among the geometric parameters of the labyrinth channel. Numerical simulations of the water flow movement are performed according to central cubic composite design using Commercial codes GAMBIT and FLUENT. Inlet pressure of the dripper is set up to be 1 bar. The objective of this paper is to derive a mathematical model of the emitter discharge depending on the dentate angle, the dentate spacing, the dentate height of the labyrinth channel. As a result, the obtained mathematical model is a second-order polynomial reporting 2-way interactions among the geometric parameters. The dentate spacing has the most important and positive influence on the emitter discharge, followed by the simultaneous impact of the dentate spacing and the dentate height. The dentate angle in the observed interval has no significant effect on the emitter discharge. The obtained model can be used as a basis for a future emitter design.

Keywords: drip irrigation, labyrinth channel hydrodynamics, numerical simulations, Reynolds stress model.

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Authors: Mohammadali Abedini Sanigy, Jiangang Fei

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In this paper, a mathematical optimization model was developed to maximize the profit in a vegetable production planning problem. It serves as a decision support system that assists farmers in land allocation to crops and harvest scheduling decisions. The developed model can handle different rotation rules in two consecutive cycles of production, which is a common practice in organic production system. Moreover, different production methods of the same crop were considered in the model formulation. The main strength of the model is that it is not restricted to predetermined production periods, which makes the planning more flexible. The model is classified as a mixed integer programming (MIP) model and formulated in PYOMO -a Python package to formulate optimization models- and solved via Gurobi and CPLEX optimizer packages. The model was tested with secondary data from 'Australian vegetable growing farms', and the results were obtained and discussed with the computational test runs. The results show that the model can successfully provide reliable solutions for real size problems.

Keywords: crop rotation, harvesting, mathematical model formulation, vegetable production

Procedia PDF Downloads 189

Authors: Takuya Sumi, Syoko Nukaya, Takashi Kaburagi, Hiroshi Tanaka, Kajiro Watanabe, Yosuke Kurihara

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We propose an unconstrained measurement system for scratching motion based on mathematical model of unconstrained bed sensing method which could measure the bed vibrations due to the motion of the person on the bed. In this paper, we construct mathematical model of the unconstrained bed monitoring system, and we apply the unconstrained bed sensing method to the system for detecting scratching motion. The proposed sensors are placed under the three bed feet. When the person is lying on the bed, the output signals from the sensors are proportional to the magnitude of the vibration due to the scratching motion. Hence, we could detect the subject’s scratching motion from the output signals from ceramic sensors. We evaluated two scratching motions using the proposed system in the validity experiment as follows: First experiment is the subject’s scratching the right side cheek with his right hand, and; second experiment is the subject’s scratching the shin with another foot. As the results of the experiment, we recognized the scratching signals that enable the determination when the scratching occurred. Furthermore, the difference among the amplitudes of the output signals enabled us to estimate where the subject scratched.

Keywords: unconstrained bed sensing method, scratching, body movement, itchy, piezoceramics

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Authors: Tahir Nawaz Cheema, Dumitru Baleanu, Ali Raza

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In this research work, we design intelligent computing through Bayesian Regularization artificial neural networks (BRANNs) introduced to solve the mathematical modeling of infectious diseases (Covid-19). The dynamical transmission is due to the interaction of people and its mathematical representation based on the system's nonlinear differential equations. The generation of the dataset of the Covid-19 model is exploited by the power of the explicit Runge Kutta method for different countries of the world like India, Pakistan, Italy, and many more. The generated dataset is approximately used for training, testing, and validation processes for every frequent update in Bayesian Regularization backpropagation for numerical behavior of the dynamics of the Covid-19 model. The performance and effectiveness of designed methodology BRANNs are checked through mean squared error, error histograms, numerical solutions, absolute error, and regression analysis.

Keywords: mathematical models, beysian regularization, bayesian-regularization backpropagation networks, regression analysis, numerical computing

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Authors: H. Namazi, H. T. N. Kuan

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It is known that in humans, the adaptation to a given odor occurs within a quite short span of time (typically one minute) after the odor is presented to the brain. Different models of human olfaction have been developed by scientists but none of these models consider the diffusion phenomenon in olfaction. A novel microscopic model of the human olfaction is presented in this paper. We develop this model by incorporating the transient diffusivity. In fact, the mathematical model is written based on diffusion of the odorant within the mucus layer. By the use of the model developed in this paper, it becomes possible to provide quantification of the objective strength of odor.

Keywords: diffusion, microscopic model, mucus layer, olfaction

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Authors: Verónica Díaz Quezada

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The importance given to the development of the problem solving skill and the requirement to solve problems framed in mathematical or real life contexts, in practice, they are not evidence in relation to the teaching of proportional variations. This qualitative and descriptive study aims to (1) to improve problem solving ability of high school students in Chile, (ii) to elaborate and describe a didactic intervention strategy based on learning situations in proportional variations, focused on solving types of routine problems of various contexts and non-routine problems. For this purpose, participant observation was conducted, test of mathematics problems and an opinion questionnaire to thirty-six high school students. Through the results, the highest academic performance is evidenced in the routine problems of purely mathematical context, realistic, fantasy context, and non-routine problems, except in the routine problems of real context and compound proportionality problems. The results highlight the need to consider in the curriculum different types of problems in the teaching of mathematics that relate the discipline to everyday life situations

Keywords: algebra, high school, proportion variations, nonroutine problem solving, routine problem solving

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Authors: Benaliouche Hana, Abdessemed Djamal, Meniai Abdessalem, Lesage Geoffroy, Heran Marc

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This paper presents a dynamic mathematical model of activated sludge which is able to predict the formation and degradation kinetics of SMP (Soluble microbial products) in membrane bioreactor systems. The model is based on a calibrated version of ASM1 with the theory of production and degradation of SMP. The model was calibrated on the experimental data from MBR (Mathematical modeling Membrane bioreactor) pilot plant. Analytical expressions have been developed, describing the concentrations of the main state variables present in the sludge matrix, with the inclusion of only six additional linear differential equations. The objective is to present a new dynamic mathematical model of activated sludge capable of predicting the formation and degradation kinetics of SMP (UAP and BAP) from the submerged membrane bioreactor (BRMI), operating at low organic load (C / N = 3.5), for two sludge retention times (SRT) fixed at 40 days and 60 days, to study their impact on membrane fouling, The modeling study was carried out under the steady-state condition. Analytical expressions were then validated by comparing their results with those obtained by simulations using GPS-X-Hydromantis software. These equations made it possible, by means of modeling approaches (ASM1), to identify the operating and kinetic parameters and help to predict membrane fouling.

Keywords: Activated Sludge Model No. 1 (ASM1), mathematical modeling membrane bioreactor, soluble microbial products, UAP, BAP, Modeling SMP, MBR, heterotrophic biomass

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Authors: C. Matasane, C. Dwarika, R. Naidoo

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The mathematical analysis on radiation obtained and the development of the solar photovoltaic (PV) array groundwater pumping is needed in the rural areas of Thohoyandou, Limpopo Province for sizing and power performance subject to the climate conditions within the area. A simple methodology approach is developed for the directed coupled solar, controller and submersible ground water pump system. The system consists of a PV array, pump controller and submerged pump, battery backup and charger controller. For this reason, the theoretical solar radiation obtained for optimal predictions and system performance in order to achieve different design and operating parameters. Here the examination of the PV schematic module in a Direct Current (DC) application is used for obtainable maximum solar power energy for water pumping. In this paper, a simple efficient photovoltaic water pumping system is presented with its theoretical studies and mathematical modeling of photovoltaics (PV) system.

Keywords: renewable energy sources, solar groundwater pumping, theoretical and mathematical analysis of photovoltaic (PV) system, theoretical solar radiation

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Authors: M. K. Balyan

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The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: dynamical diffraction, hologram, object image, X-ray holography

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Authors: Ivan Baravy

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Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Mitat Uysal, Aynur Uysal

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Artificial Intelligence (AI) is fundamentally driven by mathematics, with many of its core algorithms rooted in mathematical principles such as linear algebra, probability theory, calculus, and optimization techniques. This paper explores the deep connection between AI and mathematics, highlighting the role of mathematical concepts in key AI techniques like machine learning, neural networks, and optimization. To demonstrate this connection, a case study involving the implementation of a neural network using Python is presented. This practical example illustrates the essential role that mathematics plays in training a model and solving real-world problems.

Keywords: AI, mathematics, machine learning, optimization techniques, image processing

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Authors: Rasikh Tariq, Fatima Z. Benarab

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Evaporative coolers has a minimum potential to reach the wet-bulb temperature of intake air which is not enough to handle a large cooling load; therefore, it is not a feasible option to overcome cooling requirement of a building. The invention of Maisotsenko (M) cycle has led evaporative cooling technology to reach the sub-wet-bulb temperature of the intake air; therefore, it brings an innovation in evaporative cooling techniques. In this work, we developed a mathematical model of the Maisotsenko based air cooler by applying energy and mass balance laws on different air channels. The governing ordinary differential equations are discretized and simulated on MATLAB. The temperature and the humidity plots are shown in the simulation results. A parametric study is conducted by varying working air inlet conditions (temperature and humidity), inlet air velocity, geometric parameters and water temperature. The influence of these aforementioned parameters on the cooling effectiveness of the HMX is reported.  Results have shown that the effectiveness of the M-Cycle is increased by increasing the ambient temperature and decreasing absolute humidity. An air velocity of 0.5 m/sec and a channel height of 6-8mm is recommended.

Keywords: HMX, maisotsenko cycle, mathematical modeling, numerical simulation, parametric study

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Authors: Liliana M. Marinelli, Cristina T. Varanese

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In the last few years, students from higher education have difficulties in grasping mathematical concepts which support physical matters, especially those in the first years of this education. Classical Physics teaching turns to be complex when students are not able to make use of mathematical tools which lead to the conceptual structure of Physics. When derivation and integration rules are not used or developed in parallel with other disciplines, the physical meaning that we attempt to convey turns to be complicated. Due to this fact, it could be of great use to see the Classical Mechanics from an axiomatic approach, where the correspondence rules give physical meaning, if we expect students to understand concepts clearly and accurately. Using the Minkowski point of view adapted to a two-dimensional space and time where vectors, matrices, and straight lines (worked from an affine space) give mathematical and physical rigorosity even when it is more abstract. An interesting option would be to develop the disciplinary contents from an axiomatic version which embraces the Classical Mechanics as a particular case of Relativistic Mechanics. The observation about the increase in the difficulties stated by students in the first years of education allows this idea to grow as a possible option to improve performance and understanding of the concepts of this subject.

Keywords: axioms, classical physics, physical concepts, relativity

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Authors: Saeideh Salimpour, Sophie-Charlotte Viaux, Ahmed Azab, Mohammed Fazle Baki

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The Facility Layout Problem (FLP) is key to the efficient and cost-effective operation of a system. This paper presents a hybrid heuristic- and mathematical-programming-based approach that divides the problem conceptually into those of clustering and sequencing. First, clusters of vertically aligned facilities are formed, which are later on sequenced horizontally. The developed methodology provides promising results in comparison to its counterparts in the literature by minimizing the inter-distances for facilities which have more interactions amongst each other and aims at placing the facilities with more interactions at the centroid of the shop.

Keywords: clustering-sequencing approach, mathematical modeling, optimization, unequal facility layout problem

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Authors: Farzad Khajavi, Farzaneh Jalilfar, Faranak Jafari, Leila Shokrani

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Formulation of gliclazide in the form of extended-release tablet in 30 and 60 mg dosage forms was performed using hypromellose (HPMC K4M) as a retarding agent. Drug-release profiles were investigated in comparison with references Diamicron MR 30 and 60 mg tablets. The effect of size of powder particles, the amount of hypromellose in formulation, hardness of tablets, and also the effect of halving the tablets were investigated on drug release profile. A mathematical model which describes hypromellose behavior in initial times of drug release was proposed for the estimation of hypromellose content in modified-release gliclazide 60 mg tablet. This model is based on erosion of hypromellose in dissolution media. The model is applicable to describe release profiles of insoluble drugs. Therefore, by using dissolved amount of drug in initial times of dissolution and the model, the amount of hypromellose in formulation can be predictable. The model was used to predict the HPMC K4M content in modified-release gliclazide 30 mg and extended-release quetiapine 200 mg tablets.

Keywords: Gliclazide, hypromellose, drug release, modified-release tablet, mathematical model

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Authors: Divya Vats, Sanjay Mahajani

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The clarification of sugarcane juice plays a pivotal role in the production of non-centrifugal sugar (NCS), profoundly influencing the quality of the final NCS product. In this study, we have investigated the kinetics and mathematical modeling of the batch clarification process. The turbidity of the clarified cane juice (NTU) emerges as the determinant of the end product’s color. Moreover, this parameter underscores the significance of considering other variables as performance indicators for accessing the efficacy of the clarification process. Temperature-controlled experiments were meticulously conducted in a laboratory-scale batch mode. The primary objective was to discern the essential and optimized parameters crucial for augmenting the clarity of cane juice. Additionally, we explored the impact of pH and flocculant loading on the kinetics. Particle Image Velocimetry (PIV) is employed to comprehend the particle-particle and fluid-particle interaction. This technique facilitated a comprehensive understanding, paving the way for the subsequent multiphase computational fluid dynamics (CFD) simulations using the Eulerian-Lagrangian approach in the Ansys fluent. Impressively, these simulations accurately replicated comparable velocity profiles. The final mechanism of this study helps to make a mathematical model and presents a valuable framework for transitioning from the traditional batch process to a continuous process. The ultimate aim is to attain heightened productivity and unwavering consistency in product quality.

Keywords: non-centrifugal sugar, particle image velocimetry, computational fluid dynamics, mathematical modeling, turbidity

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Authors: Muleya Nqobile, Winston Garira

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We presented a compartmental deterministic multi-scale model which encompass internal plant defensive mechanism and pathogen interaction, then we consider nesting the model into the epidemiological model. The objective was to improve our understanding of the transmission dynamics of within host and between host of Guignardia citricapa Kiely. The inflow of infected class was scaled down to individual level while the outflow was scaled up to average population level. Conceptual model and mathematical model were constructed to display a theoretical framework which can be used for predicting or identify disease pattern.

Keywords: epidemiological model, mathematical modelling, multi-scale modelling, immunological model

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Authors: Fahad Alsharari, Mohd Salmi Md. Noorani

Abstract:

A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron-Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift AZ, x is in M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, we find a new method of calculating the topological entropy of the Motzkin shift M(M,N) without any measure theoretical discussion.

Keywords: entropy, Motzkin shift, mathematical model, theory

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Authors: Nina Philipova

Abstract:

The influence of the geometric parameters of trapezoidal labyrinth channel on the pressure losses along the labyrinth length is investigated in this work. The impact of the dentate height is studied at fixed values of the dentate angle and the dentate spacing. The objective of the work presented in this paper is to derive a mathematical model of the pressure losses along the labyrinth length depending on the dentate height. The numerical simulations of the water flow movement are performed by using Commercial codes ANSYS GAMBIT and FLUENT. Dripper inlet pressure is set up to be 1 bar. As a result, the mathematical model of the pressure losses is determined as a second-order polynomial by means Commercial code STATISTIKA. Bi-objective optimization is performed by using the mean algebraic function of utility. The optimum value of the dentate height is defined at fixed values of the dentate angle and the dentate spacing. The derived model of the pressure losses and the optimum value of the dentate height are used as a basis for a more successful emitter design.

Keywords: drip irrigation, labyrinth channel hydrodynamics, numerical simulations, Reynolds stress model

Procedia PDF Downloads 154

Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

Abstract:

In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

Procedia PDF Downloads 168