Search results for: mathematical

Authors: Arpan Dwivedi, Yogesh Pahariya

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In this paper, optimal design of hybrid standalone power supply system (SAPS) is done for off grid applications in remote areas where transmission of power is difficult. The hybrid SAPS system uses two primary energy sources, wind and solar, and in addition to these diesel generator is also connected to meet the load demand in case of failure of wind and solar system. This paper presents mathematical modeling of 1.4 MW hybrid SAPS system for rural electrification. This paper firstly focuses on mathematical modeling of PV module connected in a string, secondly focuses on modeling of permanent magnet wind turbine generator (PMWTG). The hybrid controller is also designed for selection of power from the source available as per the load demand. The power output of hybrid SAPS system is analyzed for meeting load demands at urban as well as for rural areas.

Keywords: SAPS, DG, PMWTG, rural area, off-grid, PV module

Procedia PDF Downloads 249

Authors: Hakan Bozdoğan

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The goal of this paper is to evaluate the species richness, diversity and structure of in different habitats in the Kahramanmaraş Province in Turkey by using a mathematical program called as Geo-Gebra Software. The Ascalaphidae family comprises the most visually remarkable members of the order Neuroptera due to large dimensions, aerial predatory behaviour and dragonfly-like (or even butterfly-like) habits, allowing an immediate recognition also for occasional observers. Otherwise, they are one of the more poorly known families of the order in respect to biology, ecology and especially larval morphology. This discrepancy appears particularly noteworthy considering that it is a fairly large family (ca. 430 species) widely distributed in tropical and temperate areas of the World. The use of Dynamic Geometry, Analytical Softwares provides researchers a great way of visualising mathematical objects and encourage them to carry out tasks to interact with such objects and add to support of their researching. In this study we implemented; Circle with Center Through Point, Perpendicular Line, Vectors and Rays, Segments and Locus to elucidate the ecological and habitat behaviours of Butterfly-like lacewings in an analytical plane by using Geo-Gebra.

Keywords: neuroptera, Ascalaphidae, geo-gebra software, habitat selectivity

Procedia PDF Downloads 279

Authors: Easa Ali Abbasi, Akbar Allahverdizadeh, Reza Jahangiri, Behnam Dadashzadeh

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Electrical current measurement is a suitable method for the performance determination of electrical devices. There are two contact and noncontact methods in this measuring process. Contact method has some disadvantages like having direct connection with wire which may endamage the system. Thus, in this paper, a bimorph piezoelectric cantilever beam which has a permanent magnet on its free end is used to measure electrical current in a noncontact way. In mathematical modeling, based on Galerkin method, the governing equation of the cantilever beam is solved, and the equation presenting the relation between applied force and beam’s output voltage is presented. Magnetic force resulting from current carrying wire is considered as the external excitation force of the system. The results are compared with other references in order to demonstrate the accuracy of the mathematical model. Finally, the effects of geometric parameters on the output voltage and natural frequency are presented.

Keywords: cantilever beam, electrical current measurement, forced excitation, piezoelectric

Procedia PDF Downloads 232

Authors: Yunusa Aliyu Hadejia

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Cholera is a gastrointestinal disease caused by a bacterium called Vibrio Cholerae which spread as a result of eating food or drinking water contaminated with feaces from an infected person. In this work we proposed and analyzed the impact of isolating infected people and give them therapeutic treatment, the specific objectives of the research was to formulate a mathematical model of cholera transmission incorporating treatment class, to make analysis on stability of equilibrium points of the model, positivity and boundedness was shown to ensure that the model has a biological meaning, the basic reproduction number was derived by next generation matrix approach. The result of stability analysis show that the Disease free equilibrium was both locally and globally asymptotically stable when R_0< 1 while endemic equilibrium has locally asymptotically stable when R_0> 1. Sensitivity analysis was perform to determine the contribution of each parameter to the basic reproduction number. Numerical simulation was carried out to show the impact of the model parameters using MAT Lab Software.

Keywords: mathematical model, treatment, stability, sensitivity

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Authors: D. Kumar, S. Kumar, A. G. Memon, R. A. Memon, K. Harijan

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A considerable amount of energy is usually lost due to compression of insulation in Heating, ventilation, and air conditioning (HVAC) duct. In this paper, the economic impact of compression of insulation is estimated. Relevant mathematical models were used to estimate the optimal thickness at the points of compression. Furthermore, the payback period is calculated for the optimal thickness at the critical parts of supply air duct (SAD) and return air duct (RAD) considering natural gas (NG) and liquefied petroleum gas (LPG) as fuels for chillier operation. The mathematical model is developed using preliminary data obtained for an HVAC system of a pharmaceutical company. The higher heat gain and cooling loss, due to compression of thermal insulation, is estimated using relevant heat transfer equations. The results reveal that maximum energy savings (ES) in SAD is 34.5 and 40%, while in RAD is 22.9% and 29% for NG and LPG, respectively. Moreover, the minimum payback period (PP) for SAD is 2 and 1.6years, while in RAD is 4.3 and 2.7years for NG and LPG, respectively. The optimum insulation thickness (OIT) corresponding to maximum ES and minimum PP is estimated to be 35 and 42mm for SAD, while 30 and 38mm for RAD in case of NG and LPG, respectively.

Keywords: optimum insulation thickness, life cycle cost analysis, payback period, HVAC system

Procedia PDF Downloads 216

Authors: Wenzhe Li, Xiaoyu Ying, Grace Ding

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Architecture plane form is an important consideration in the design of green buildings due to its significant impact on energy performance. The most effective method to consider energy performance in the early design stages is parametric modelling. This paper presents a methodology to program plane forms using MATLAB language, generating 16 kinds of plane forms by changing four designed parameters. DesignBuilder (an energy consumption simulation software) was proposed to simulate the energy consumption of the generated planes. A regression mathematical model was established to study the relationship between the plane forms and their energy consumption. The main finding of the study suggested that there was a cubic function relationship between the depth-ratio of U-shaped buildings and energy consumption, and there is also a cubic function relationship between the width-ratio and energy consumption. In the design, the depth-ratio of U-shaped buildings should not be less than 2.5, and the width-ratio should not be less than 2.

Keywords: graphic parameterization, green building design, mathematical model, plane form

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Authors: Aleksandar Hatzivelkos

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The term ”compromise” is mostly used casually within the social choice theory. It is usually used as a mere result of the social choice function, and this omits its deeper meaning and ramifications. This paper is based on a mathematical model for the description of a compromise as a version of the Sorites paradox. It introduces a formal definition of d-measure of divergence from a compromise and models a notion of compromise that is often used only colloquially. Such a model for vagueness phenomenon, which lies at the core of the notion of compromise enables the introduction of new mathematical structures. In order to maximize compromise, different methods can be used. In this paper, we explore properties of a social welfare function TdM (from Total d-Measure), which is defined as a function which minimizes the total sum of d-measures of divergence over all possible linear orderings. We prove that TdM satisfy strict Pareto principle and behaves well asymptotically. Furthermore, we show that for certain domain restrictions, TdM satisfy positive responsiveness and IIIA (intense independence of irrelevant alternatives) thus being equivalent to Borda count on such domain restriction. This result gives new opportunities in social choice, especially when there is an emphasis on compromise in the decision-making process.

Keywords: borda count, compromise, measure of divergence, minimization

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Authors: Thomas Arink, Isam Janajreh

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The petroleum industry generates significant amounts of waste in the form of drill cuttings, contaminated soil and oily sludge. Drill cuttings are a product of the off-shore drilling rigs, containing wet soil and total petroleum hydrocarbons (TPH). Contaminated soil comes from different on-shore sites and also contains TPH. The oily sludge is mainly residue or tank bottom sludge from storage tanks. The two main treatment methods currently used are incineration and thermal desorption (TD). Thermal desorption is a method where the waste material is heated to 450ºC in an anaerobic environment to release volatiles, the condensed volatiles can be used as a liquid fuel. For the thermal desorption unit dry contaminated soil is mixed with moist drill cuttings to generate a suitable mixture. By thermo gravimetric analysis (TGA) of the TD feedstock it was found that less than 50% of the TPH are released, the discharged material is stored in landfill. This study proposes co-gasification of petroleum waste with waste tires as an alternative to thermal desorption. Co-gasification with a high-calorific material is necessary since the petroleum waste consists of more than 60 wt% ash (soil/sand), causing its calorific value to be too low for gasification. Since the gasification process occurs at 900ºC and higher, close to 100% of the TPH can be released, according to the TGA. This work consists of three parts: 1. a mathematical gasification model, 2. a reactive flow CFD model and 3. experimental work on a drop tube reactor. Extensive material characterization was done by means of proximate analysis (TGA), ultimate analysis (CHNOS flash analysis) and calorific value measurements (Bomb calorimeter) for the input parameters of the mathematical and CFD model. The mathematical model is a zero dimensional model based on Gibbs energy minimization together with Lagrange multiplier; it is used to find the product species composition (molar fractions of CO, H2, CH4 etc.) for different tire/petroleum feedstock mixtures and equivalence ratios. The results of the mathematical model act as a reference for the CFD model of the drop-tube reactor. With the CFD model the efficiency and product species composition can be predicted for different mixtures and particle sizes. Finally both models are verified by experiments on a drop tube reactor (1540 mm long, 66 mm inner diameter, 1400 K maximum temperature).

Keywords: computational fluid dynamics (CFD), drop tube reactor, gasification, Gibbs energy minimization, petroleum waste, waste tires

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Authors: Natalia Podkhodova, Olga Sheremeteva, Mariia Soldaeva

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Creating favorable conditions for students’ comprehension of mathematical content is one of the primary problems in teaching mathematics in secondary school. Psychology research has demonstrated that positive comprehension becomes possible when new information becomes part of student’s subjective experience and when linkages between the attributes of notions and various ways of their presentations can be established. The fact of comprehension includes the ability to build a working situational model and thus becomes an important means of solving mathematical problems. The article describes the implementation of a holistic approach to teaching mathematics designed to address the primary challenges of such teaching, specifically, the challenge of students’ comprehension. This approach consists of (1) establishing links between the attributes of a notion: the sense, the meaning, and the term; (2) taking into account the components of student’s subjective experience -emotional and value, contextual, procedural, communicative- during the educational process; (3) links between different ways to present mathematical information; (4) identifying and leveraging the relationships between real, perceptual and conceptual (scientific) mathematical spaces by applying real-life situational modeling. The article describes approaches to the practical use of these foundational concepts. Identifying how proposed methods and technology influence understanding of material used in teaching mathematics was the research’s primary goal. The research included an experiment in which 256 secondary school students took part: 142 in the experimental group and 114 in the control group. All students in these groups had similar levels of achievement in math and studied math under the same curriculum. In the course of the experiment, comprehension of two topics -'Derivative' and 'Trigonometric functions'- was evaluated. Control group participants were taught using traditional methods. Students in the experimental group were taught using the holistic method: under the teacher’s guidance, they carried out problems designed to establish linkages between notion’s characteristics, to convert information from one mode of presentation to another, as well as problems that required the ability to operate with all modes of presentation. The use of the technology that forms inter-subject notions based on linkages between perceptional, real, and conceptual mathematical spaces proved to be of special interest to the students. Results of the experiment were analyzed by presenting students in each of the groups with a final test in each of the studied topics. The test included problems that required building real situational models. Statistical analysis was used to aggregate test results. Pierson criterion was used to reveal the statistical significance of results (pass-fail the modeling test). A significant difference in results was revealed (p < 0.001), which allowed the authors to conclude that students in the study group showed better comprehension of mathematical information than those in the control group. Also, it was revealed (used Student’s t-test) that the students of the experimental group performed reliably (p = 0.0001) more problems in comparison with those in the control group. The results obtained allow us to conclude that increasing comprehension and assimilation of study material took place as a result of applying implemented methods and techniques.

Keywords: comprehension of mathematical content, holistic approach to teaching mathematics in secondary school, subjective experience, technology of the formation of inter-subject notions

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Authors: Ayşegül Çabuk, Mine Işıksal

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Mathematics is a sense-making activity so that it requires meaningful learning. Hence based on this idea, meaningful mathematical connections are necessary to learn mathematics. At that point, the major question has become that which educational methods can provide opportunities to provide mathematical connections and to understand mathematics. The amalgam of reasoning and proof can be the one of the methods that creates opportunities to learn mathematics in a meaningful way. However, even if reasoning and proof should be included from prekindergarten to grade 12, studies in literature generally include secondary school students and pre-service mathematics teachers. With the light of the idea that the amalgam of reasoning and proof has significant effect on middle school students' mathematical learning, this study aims to investigate middle grade students' tendencies while reasoning the correctness of statements related to numbers. The sample included 272 middle grade students, specifically 69 of them were sixth grade students (25.4%), 101 of them were seventh grade students (37.1%) and 102 of them were eighth grade students (37.5%). Data was gathered through an achievement test including 2 essay types of problems about algebra. The answers of two items were analyzed both quantitatively and qualitatively in terms of students' solutions strategies while reasoning the correctness of the statements. Similar on the findings in the literature, most of the students, in all grade levels, used numerical examples to judge the statements. Moreover the results also showed that the majority of these students appear to believe that providing one or more selected examples is sufficient to show the correctness of the statement. Hence based on the findings of the study, even students in earlier ages have proving and reasoning abilities their reasoning's generally based on the empirical evidences. Therefore, it is suggested that examples and example-based reasoning can be a fundamental role on to generate systematical reasoning and proof insight in earlier ages.

Keywords: reasoning, mathematics learning, middle grade students

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Authors: Aneta Oblouková, Eva Vítková

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The article deals with the issue of water and sewerage charge rate prices in the Czech Republic. The research is specifically focused on the analysis of the development of the average prices of water and sewerage charge rate in the Czech Republic in the years 1994-2021 and on the validation of the chosen methodology relevant for the prediction of the development of the average prices of water and sewerage charge rate in the Czech Republic. The research is based on data collection. The data for this research was obtained from the Czech Statistical Office. The aim of the paper is to validate the relevance of the mathematical linear trend estimate technique for the calculation of the predicted average prices of water and sewerage charge rates. The real values of the average prices of water and sewerage charge rates in the Czech Republic in the years 1994-2018 were obtained from the Czech Statistical Office and were converted into a mathematical equation. The same type of real data was obtained from the Czech Statistical Office for the years 2019-2021. Prediction of the average prices of water and sewerage charge rates in the Czech Republic in the years 2019-2021 were also calculated using a chosen method -a linear trend estimation technique. The values obtained from the Czech Statistical Office and the values calculated using the chosen methodology were subsequently compared. The research result is a validation of the chosen mathematical technique to be a suitable technique for this research.

Keywords: Czech Republic, linear trend estimation, price prediction, water and sewerage charge rate

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Authors: Jiahui Song

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In order to predict or explain a complicated biological process, it is important first to construct mathematical models that can be used to yield analytical solutions. Through numerical simulation, mathematical model results can be used to test scenarios that might not be easily attained in a laboratory experiment, or to predict parameters or phenomena. High-intensity, nanosecond pulse electroporation has been a recent development in bioelectrics. The dynamic pore model can be achieved by including a dynamic aspect and a dependence on the pore population density into pore formation energy equation to analyze and predict such electroporation effects. For greater accuracy, with inclusion of atomistic details, molecular dynamics (MD) simulations were also carried out during this study. Besides inducing pores in cells, external voltages could also be used in principle to modulate action potential generation in nerves. This could have an application in electrically controlled ‘pain management’. Also a simple model-based rate equation treatment of the various cellular bio-chemical processes has been used to predict the pulse number dependent cell survival trends.

Keywords: model, high-intensity, nanosecond, bioelectrics

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Authors: Linda A. O’Higgins, Astrid Wingler, Jorge Oliveira

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The growth of Chlorella vulgaris was characterized as a function of irradiance in a laboratory turbidostat (1 L) and compared to batch growth in sunlit modules (5–25 L) of the commercial Phytobag photobioreactor. The effects of variable sunlight and culture density were deconvoluted by a mathematical model. The analysis showed that algal growth was light-limited due to shading by external construction elements and due to light attenuation within the algal bags. The model was also used to predict maximum biomass productivity. The manipulative experiments and the model predictions were confronted with data from a production season of a 10m2 pilot-scale photobioreactor, Phytobag (10,000 L). The analysis confirmed light limitation in all three photobioreactors. An additional limitation of biomass productivity was caused by the nitrogen starvation that was used to induce lipid accumulation. Reduction of shading and separation of biomass and lipid production are proposed for future optimization.

Keywords: microalgae, batch cultivation, Chlorella vulgaris, Mathematical model, photobioreactor, scale-up

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Authors: Muhammad Luqman, Yusuf Kurniawan

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S-Boxes is one of the linear parts of the cryptographic algorithm. The existence of S-Box in the cryptographic algorithm is needed to maintain non-linearity of the algorithm. Nowadays, modern cryptographic algorithms use an S-Box as a part of algorithm process. Despite the fact that several cryptographic algorithms today reuse theoretically secure and carefully constructed S-Boxes, there is an evaluation characteristic that can measure security properties of S-Boxes and hence the corresponding primitives. Analysis of an S-Box usually is done using manual mathematics calculation. Several S-Boxes are presented as a Truth Table without any mathematical background algorithm. Then, it’s rather difficult to determine the strength of Truth Table S-Box without a mathematical algorithm. A comprehensive analysis should be applied to the Truth Table S-Box to determine the characteristic. Several important characteristics should be owned by the S-Boxes, they are Nonlinearity, Balancedness, Algebraic degree, LAT, DAT, differential delta uniformity, correlation immunity and global avalanche criterion. Then, a comprehensive tool will be present to automatically calculate the characteristics of S-Boxes and determine the strength of S-Box. Comprehensive analysis is done on a deterministic process to produce a sequence of S-Boxes characteristic and give advice for a better S-Box construction.

Keywords: cryptographic properties, Truth Table S-Boxes, S-Boxes characteristic, deterministic process

Procedia PDF Downloads 363

Authors: N. Alias, W. Z. W. Muhammad, M. N. M. Ibrahim, M. Mohamed, H. F. S. Saipol, U. N. Z. Ariffin, N. A. Zakaria, M. S. Z. Suardi

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This paper presents the performance comparison of some computation software for solving the boundary element method (BEM). BEM formulation is the numerical technique and high potential for solving the advance mathematical modeling to predict the production of oil well in arbitrarily shaped based on multiple leases reservoir. The limitation of data validation for ensuring that a program meets the accuracy of the mathematical modeling is considered as the research motivation of this paper. Thus, based on this limitation, there are three steps involved to validate the accuracy of the oil production simulation process. In the first step, identify the mathematical modeling based on partial differential equation (PDE) with Poisson-elliptic type to perform the BEM discretization. In the second step, implement the simulation of the 2D BEM discretization using COMSOL Multiphysic and MATLAB programming languages. In the last step, analyze the numerical performance indicators for both programming languages by using the validation of Fortran programming. The performance comparisons of numerical analysis are investigated in terms of percentage error, comparison graph and 2D visualization of pressure on oil production of multiple leases reservoir. According to the performance comparison, the structured programming in Fortran programming is the alternative software for implementing the accurate numerical simulation of BEM. As a conclusion, high-level language for numerical computation and numerical performance evaluation are satisfied to prove that Fortran is well suited for capturing the visualization of the production of oil well in arbitrarily shaped.

Keywords: performance comparison, 2D visualization, COMSOL multiphysic, MATLAB, Fortran, modelling and simulation, boundary element method, reservoir pressure

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Authors: Ranjit Biswas

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The existing subject Algebra is incomplete to support mathematical computations being done by scientists of all areas: Mathematics, Physics, Statistics, Chemistry, Space Science, Cosmology etc. even starting from the era of great Einstein. A huge hidden gap in the subject ‘Algebra’ is unearthed. All the scientists today, including mathematicians, physicists, chemists, statisticians, cosmologists, space scientists, and economists, even starting from the great Einstein, are lucky that they got results without facing any contradictions or without facing computational errors. Most surprising is that the results of all scientists, including Nobel Prize winners, were proved by them by doing experiments too. But in this paper, it is rigorously justified that they all are lucky. An algebraist can define an infinite number of new algebraic structures. The objective of the work in this paper is not just for the sake of defining a distinct algebraic structure, but to recognize and identify a major gap of the subject ‘Algebra’ lying hidden so far in the existing vast literature of it. The objective of this work is to fix the unearthed gap. Consequently, a different algebraic structure called ‘Region’ has been introduced, and its properties are studied.

Keywords: region, ROR, RORR, region algebra

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Authors: Cihan Çetinkaya, Eren Özceylan, Kerem Elibal

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This paper presents a solution method for selection of production facility. The motivation has been taken from a real life case, an automotive subcontractor which has two production facilities at different cities and parts. The problem is to decide which part(s) should be produced at which facility. To the best of our knowledge, until this study, there was no scientific approach about this problem at the firm and decisions were being given intuitively. In this study, some logistic cost parameters have been defined and with these parameters a mathematical model has been constructed. Defined and collected cost parameters are handling cost of parts, shipment cost of parts and shipment cost of welding fixtures. Constructed multi-objective mathematical model aims to minimize these costs while aims to balance the workload between two locations. Results showed that defined model can give optimum solutions in reasonable computing times. Also, this result gave encouragement to develop the model with addition of new logistic cost parameters.

Keywords: automotive subcontract, facility assignment, logistic costs, multi-objective models

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Authors: Seyedmirsajad Mokhtarimousavi, Danial Talebi, Hamidreza Asgari

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Gate Assignment Problem (GAP) is one of the most substantial issues in airport operation. In principle, GAP intends to maintain the maximum capacity of the airport through the best possible allocation of the resources (gates) in order to reach the optimum outcome. The problem involves a wide range of dependent and independent resources and their limitations, which add to the complexity of GAP from both theoretical and practical perspective. In this study, GAP was mathematically formulated as a three-objective problem. The preliminary goal of multi-objective formulation was to address a higher number of objectives that can be simultaneously optimized and therefore increase the practical efficiency of the final solution. The problem is solved by applying the second version of Non-dominated Sorting Genetic Algorithm (NSGA-II). Results showed that the proposed mathematical model could address most of major criteria in the decision-making process in airport management in terms of minimizing both airport/airline cost and passenger walking distance time. Moreover, the proposed approach could properly find acceptable possible answers.

Keywords: airport management, gate assignment problem, mathematical modeling, genetic algorithm, NSGA-II

Procedia PDF Downloads 299

Authors: Luis Miguel Méndez Díaz

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In this article, a mathematics teaching-learning strategy will be presented, specifically differential calculus in one variable, in a fun and competitive space in which the action on the part of the student is manifested and not only the repetition of information on the part of the teacher. Said action refers to motivating, problematizing, summarizing, and coordinating a game of dominoes whose thematic cards are designed around the basic and main contents of differential calculus. The strategies for teaching this area are diverse and precisely the game of dominoes is one of the most used strategies in the practice of mathematics because it stimulates logical reasoning and mental abilities. The objective on this investigation is to identify the way in which the game of dominoes affects the learning and understanding of fundamentals concepts of differential calculus in one variable through experimentation carried out on students of the first semester of the School of Engineering and Sciences of the Technological Institute of Monterrey Campus Querétaro. Finally, the results of this study will be presented and the use of this strategy in other topics around mathematics will be recommended to facilitate logical and meaningful learning in students.

Keywords: collaborative learning, logical-mathematical intelligence, mathematical games, multiple intelligences

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Authors: Nur Aidya Hanum Aizam, Vikneswary Uvaraja

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The agenda of showing the scheduled time for performing certain tasks is known as timetabling. It widely used in many departments such as transportation, education, and production. Some difficulties arise to ensure all tasks happen in the time and place allocated. Therefore, many researchers invented various programming model to solve the scheduling problems from several fields. However, the studies in developing the general integer programming model for many timetabling problems are still questionable. Meanwhile, this thesis describe about creating a general model which solve different types of timetabling problems by considering the basic constraints. Initially, the common basic constraints from five different fields are selected and analyzed. A general basic integer programming model was created and then verified by using the medium set of data obtained randomly which is much similar to realistic data. The mathematical software, AIMMS with CPLEX as a solver has been used to solve the model. The model obtained is significant in solving many timetabling problems easily since it is modifiable to all types of scheduling problems which have same basic constraints.

Keywords: AIMMS mathematical software, integer linear programming, scheduling problems, timetabling

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Authors: Amal A. Abdel-Sattar

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The curriculum of architecture department in Prince Sultan University includes ‘Building Surveying’ course which is usually a part of civil engineering courses. As a fundamental requirement of the course, it requires a strong background in mathematics and physics, which are not usually preferred subjects to the architecture students and many of them are not giving the required and necessary attention to these courses during their preparation year before commencing their architectural study. This paper introduces the concept and the methodology of the student-centered learning approach in the course of building surveying for architects. One of the major outcomes is the improvement in the students’ involvement in the course and how this will cover and strength their analytical weak points and improve their mathematical skills. The study is conducted through three semesters with a total number of 99 students. The effectiveness of the student-centered learning approach is studied using the student survey at the end of each semester and teacher observations. This survey showed great acceptance of the students for these methods. Also, the teachers observed a great improvement in the students’ mathematical abilities and how keener they became in attending the classes which were clearly reflected on the low absence record.

Keywords: architecture, building surveying, student-centered learning, teaching and learning

Procedia PDF Downloads 252

Authors: D. S. C. Soares, D. G. Costa, J. T. S., A. K. S. Abud, T. P. Nunes, A. M. Oliveira Júnior

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Mathematical models of drying are used for the purpose of understanding the drying process in order to determine important parameters for design and operation of the dryer. The jackfruit is a fruit with high consumption in the Northeast and perishability. It is necessary to apply techniques to improve their conservation for longer in order to diffuse it by regions with low consumption. This study aimed to analyse several mathematical models (Page, Lewis, and Midilli) to indicate one that best fits the conditions of convective drying process using performance indicators associated with each model: accuracy (Af) and noise factors (Bf), mean square error (RMSE) and standard error of prediction (% SEP). Jackfruit drying was carried out in convective type tray dryer at a temperature of 50°C for 9 hours. It is observed that the model Midili was more accurate with Af: 1.39, Bf: 1.33, RMSE: 0.01%, and SEP: 5.34. However, the use of the Model Midilli is not appropriate for purposes of control process due to need four tuning parameters. With the performance indicators used in this paper, the Page model showed similar results with only two parameters. It is concluded that the best correlation between the experimental and estimated data is given by the Page’s model.

Keywords: drying, models, jackfruit, biotechnology

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Authors: S. P. Sharma, Som Nath Saha

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This paper deals with the analytical investigation of thermal and thermohydraulic performance of double flow solar air heaters with corrugated and flat plate absorber. A mathematical model of double flow solar air heater has been presented, and a computer program in C⁺⁺ language is developed to estimate the outlet temperature of air for the evaluation of thermal and thermohydraulic efficiency by solving the governing equations numerically using relevant correlations for heat transfer coefficients. The results obtained from the mathematical model is compared with the available experimental results and it is found to be reasonably good. The results show that the double flow solar air heaters have higher efficiency than conventional solar air heater, although the double flow corrugated absorber is superior to that of flat plate double flow solar air heater. It is also observed that the thermal efficiency increases with increase in mass flow rate; however, thermohydraulic efficiency increases with increase in mass flow rate up to a certain limit, attains the maximum value, then thereafter decreases sharply.

Keywords: corrugated absorber, double flow, solar air heater, thermos-hydraulic efficiency

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Authors: Hong Lu, Xiong Xiao

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Shaft parts are widely used in machinery industry, however, bending deformation often occurred when this kind of parts is being heat treated. This parts needs to be straightened to meet the requirement of straightness. As for the pressure straightening process, a good straightening stroke algorithm is related to the precision and efficiency of straightening process. In this paper, the relationship between straightening load and deflection during the straightening process is analyzed, and the mathematical model of the straightening process has been established. By the mathematical model, the iterative method is used to solve the straightening stroke. Compared to the traditional straightening stroke algorithm, straightening stroke calculated by this method is much more precise; because it can adapt to the change of material performance parameters. Considering that the straightening method is widely used in the mass production of the shaft parts, knowledge base is used to store the data of the straightening process, and a straightening stroke algorithm based on empirical data is set up. In this paper, the straightening process control model which combine the straightening stroke method based on iteration and straightening stroke algorithm based on empirical data has been set up. Finally, an experiment has been designed to verify the straightening process control model.

Keywords: straightness, straightening stroke, deflection, shaft parts

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Authors: Neslihan Sahin Celik, Ali Eraslan

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Mathematical model and modeling are one of the topics that have been intensively discussed in recent years. In line with the results of the PISA studies, researchers in many countries have begun to question how much students in school-education system are prepared to solve the real-world problems they encounter in their future professional lives. As a result, many mathematics educators have begun to emphasize the importance of new skills and understanding such as constructing, Hypothesizing, Describing, manipulating, predicting, working together for complex and multifaceted problems for success in beyond the school. When students increasingly face this kind of situations in their daily life, it is important to make sure that students have enough experience to work together and interpret mathematical situations that enable them to think in different ways and share their ideas with their peers. Thus, model eliciting activities are one of main tools that help students to gain experiences and the new skills required. This research study was carried on the town center of a big city located in the Black Sea region in Turkey. The participants were eighth-grade students in a middle school. After a six-week preliminary study, three students in an eighth-grade classroom were selected using criterion sampling technique and placed in a focus group. The focus group of three students was videotaped as they worked on a model eliciting activity, the Summer Job Problem. The conversation of the group was transcribed, examined with students’ written work and then qualitatively analyzed through the lens of Blum’s (1996) modeling processing cycle. The study results showed that eighth grade students can successfully work with the model eliciting, develop a model based on the two parameters and review the whole process. On the other hand, they had difficulties to relate parameters to each other and take all parameters into account to establish the model.

Keywords: middle school, modeling, mathematical modeling, summer job problem

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Authors: A. N. Santhosh, Vinay Hegde, S. Vinod Kumar, R. Giria, D. L. Rakesh, M. S. Raghu

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At present, research on automobile engineering is in high demand, particularly in the field of fuel combustion. A large number of fossil fuels are being used in combustion, which may get exhausted in the near future and are not economical. To this end, research on the use of magnetic material in combustion engines is in progress to enhance the efficiency of fuel. The present review describes the chemical, physical and mathematical theory behind the magnetic materials along with the working principle of the internal combustion engine. The effect of different magnets like ferrite magnet, Neodymium magnet, and electromagnets was discussed. The effect of magnetic field on the consumption of the fuel, brake thermal efficiency, carbon monoxide, Oxides of Nitrogen, carbon dioxide, and hydrocarbon emission, along with smoke density, have been discussed in detail. Detailed mathematical modelling that shows the effect of magnetic field on fuel combustion is elaborated. Required pictorial representations are included wherever necessary. This review article could serve as a base for studying the effect of magnetic materials on IC engines.

Keywords: magnetic field, energizer, fuel conditioner, fuel consumption, emission reduction

Procedia PDF Downloads 101

Authors: Hanbey Hazar, Hakan Gul

Abstract:

In this study, Thermal Barrier Coating (TBC) application is performed in order to reduce the engine emissions. Piston, exhaust, and intake valves of a single-cylinder four-cycle gasoline engine were coated with chromium carbide (Cr3C2) at a thickness of 300 µm by using the Plasma Spray coating method which is a TBC method. Gasoline engine was converted into an LPG system. The study was conducted in 4 stages. In the first stage, the piston, exhaust, and intake valves of the gasoline engine were coated with Cr3C2. In the second stage, gasoline engine was converted into the LPG system and the emission values in this engine were recorded. In the third stage, the experiments were repeated under the same conditions with a standard (uncoated) engine and the results were recorded. In the fourth stage, data obtained from both engines were loaded on Artificial Neural Networks (ANN) and estimated values were produced for every revolution. Thus, mathematical modeling of coated and uncoated engines was performed by using ANN. While there was a slight increase in exhaust gas temperature (EGT) of LPG engine due to TBC, carbon monoxide (CO) values decreased.

Keywords: LPG fuel, thermal barrier coating, artificial neural network, mathematical modelling

Procedia PDF Downloads 425

Authors: Henrik L. Funke, Lars Ulke-Winter, Sandra Gelbrich, Lothar Kroll

Abstract:

This work reports about an approach for an automatic adaptation of concrete formulations based on genetic algorithms (GA) to optimize a wide range of different fit-functions. In order to achieve the goal, a method was developed which provides a numerical description of a fibre reinforced concrete (FRC) mixture regarding the production technology and the property spectrum of the concrete. In a first step, the FRC mixture with seven fixed components was characterized by varying amounts of the components. For that purpose, ten concrete mixtures were prepared and tested. The testing procedure comprised flow spread, compressive and bending tensile strength. The analysis and approximation of the determined data was carried out by GAs. The aim was to obtain a closed mathematical expression which best describes the given seven-point cloud of FRC by applying a Gene Expression Programming with Free Coefficients (GEP-FC) strategy. The seven-parametric FRC-mixtures model which is generated according to this method correlated well with the measured data. The developed procedure can be used for concrete mixtures finding closed mathematical expressions, which are based on the measured data.

Keywords: concrete design, fibre reinforced concrete, genetic algorithms, GEP-FC

Procedia PDF Downloads 280

Authors: Rahma Adinda Sartika

Abstract:

The use of technology in learning mathematics has received a positive response from both students and teachers, so many researchers have conducted research on this theme. Based on the findings carried out in this study, 807 documents relevant to this theme have been published in Scopus from 1995-2024. After going through the stages of identification, screening, eligibility, and including, the documents that meet the criteria are 227 documents. These documents are then analyzed using the bibliometric method so that it can be seen that the most published documents in the Scopus database occurred in 2020, with 38 documents, and the lowest was from 1996 to 2000 and 2004 to 2007, namely, no documents published. The highest number of citations is in documents published in 2018, with a total of 349 citations, so the h-index is higher than the others. The country that published the most documents relevant to this theme is Indonesia with a total of 91 documents. The second largest is the United States, with a total of 28 published documents, and the third largest is China, with a total of 15 documents. Indonesia and the United States have the most working relationships between countries compared to other countries. The focus of research related to this theme is 1) mathematics learning, 2) learning systems, 3) engineering education, 4) technology and 5) mathematical concepts.

Keywords: technology, bibliometric, mathematics learning, mathematical concepts

Procedia PDF Downloads 56

Authors: Yu-Jen Chang, Yun Chen, Hei-Lam Wong

Abstract:

The Economic Lot Scheduling Problem (ELSP) is a valuable mathematical model that can support decision-makers to make scheduling decisions. The basic period approach is effective for solving the ELSP. The assumption for applying the basic period approach is that a product must use its maximum production rate to be produced. However, a product can lower its production rate to reduce the average total cost when a facility has extra idle time. The past researches discussed how a product adjusts its production rate under the common cycle approach. To the best of our knowledge, no studies have addressed how a product lowers its production rate under the basic period approach. This research is the first paper to discuss this topic. The research develops a simple fixed rate approach that adjusts the production rate of a product under the basic period approach to solve the ELSP. Our numerical example shows our approach can find a better solution than the traditional basic period approach. Our mathematical model that applies the fixed rate approach under the basic period approach can serve as a reference for other related researches.

Keywords: economic lot, basic period, genetic algorithm, fixed rate

Procedia PDF Downloads 563