Search results for: mathematical programming

Authors: Tala Toonsi, Marah Alagha, Lina Alnowaiser, Hala Rajab

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This report is about the Photomath app, which is an AI application that uses image recognition technology, specifically optical character recognition (OCR) algorithms. The (OCR) algorithm translates the images into a mathematical equation, and the app automatically provides a step-by-step solution. The application supports decimals, basic arithmetic, fractions, linear equations, and multiple functions such as logarithms. Testing was conducted to examine the usage of this app, and results were collected by surveying ten participants. Later, the results were analyzed. This paper seeks to answer the question: To what level the artificial intelligence features are accurate and the speed of process in this app. It is hoped this study will inform about the efficiency of AI in Photomath to the users.

Keywords: photomath, image recognition, app, OCR, artificial intelligence, mathematical equations.

Procedia PDF Downloads 170

Authors: Javad Khaligh, Aghileh Heydari, Ali Akbar Heydari

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Mathematical epidemiological models for the spread of disease through a population are used to predict the prevalence of a disease or to study the impacts of treatment or prevention measures. Initial conditions for these models are measured from statistical data collected from a population since these initial conditions can never be exact, the presence of chaos in mathematical models has serious implications for the accuracy of the models as well as how epidemiologists interpret their findings. This paper confirms the chaotic behavior of a model for dengue fever and SI by investigating sensitive dependence, bifurcation, and 0-1 test under a variety of initial conditions.

Keywords: epidemiological models, SEIR disease model, bifurcation, chaotic behavior, 0-1 test

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Authors: Wlodzimierz Ogryczak, Michal Przyluski, Tomasz Sliwinski

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In problems of portfolio selection, the reward-risk ratio criterion is optimized to search for a risky portfolio with the maximum increase of the mean return in proportion to the risk measure increase when compared to the risk-free investments. In the classical model, following Markowitz, the risk is measured by the variance thus representing the Sharpe ratio optimization and leading to the quadratic optimization problems. Several Linear Programming (LP) computable risk measures have been introduced and applied in portfolio optimization. In particular, the Mean Absolute Deviation (MAD) measure has been widely recognized. The reward-risk ratio optimization with the MAD measure can be transformed into the LP formulation with the number of constraints proportional to the number of scenarios and the number of variables proportional to the total of the number of scenarios and the number of instruments. This may lead to the LP models with huge number of variables and constraints in the case of real-life financial decisions based on several thousands scenarios, thus decreasing their computational efficiency and making them hardly solvable by general LP tools. We show that the computational efficiency can be then dramatically improved by an alternative model based on the inverse risk-reward ratio minimization and by taking advantages of the LP duality. In the introduced LP model the number of structural constraints is proportional to the number of instruments thus not affecting seriously the simplex method efficiency by the number of scenarios and therefore guaranteeing easy solvability. Moreover, we show that under natural restriction on the target value the MAD risk-reward ratio optimization is consistent with the second order stochastic dominance rules.

Keywords: portfolio optimization, reward-risk ratio, mean absolute deviation, linear programming

Procedia PDF Downloads 405

Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

Procedia PDF Downloads 147

Authors: Ana Maria Reis D'Azevedo Breda, Catarina Maria Neto da Cruz

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The Japanese art of origami provides a rich context for designing exploratory mathematical activities for children and young people. By folding a simple sheet of paper, fascinating and surprising planar and spatial configurations emerge. Equally surprising is the unfolding process, which also produces striking patterns. The procedure of folding, unfolding, and folding again allows the exploration of interesting geometric patterns. When adequately and systematically done, we may deduce some of the mathematical rules ruling origami. As the child/youth folds the sheet of paper repeatedly, he can physically observe how the forms he obtains are transformed and how they relate to the pattern of the corresponding unfolding, creating space for the understanding/discovery of mathematical principles regulating the folding-unfolding process. As part of a 2023 Summer Academy organized by a Portuguese university, a session entitled “Folding, Thinking and Generalizing” took place. Twenty-three students attended the session, all enrolled in the 2nd cycle of Portuguese Basic Education and aged between 10 and 12 years old. The main focus of this session was to foster the development of critical cognitive and socio-emotional skills among these young learners using origami. These skills included creativity, critical analysis, mathematical reasoning, collaboration, and communication. Employing a qualitative, descriptive, and interpretative analysis of data collected during the session through field notes and students’ written productions, our findings reveal that structured origami-based activities not only promote student engagement with mathematical concepts in a playful and interactive but also facilitate the development of socio-emotional skills, which include collaboration and effective communication between participants. This research highlights the value of integrating origami into educational practices, highlighting its role in supporting comprehensive cognitive and emotional learning experiences.

Keywords: skills, origami rules, active learning, hands-on activities

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Authors: Silvia Arrate, Waldo Salud, Eloy París

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The wear of cutting tools is one of the most decisive elements when planning tunneling works, programming the maintenance stops and saving the optimum stock of spare parts during the evolution of the excavation. Being able to predict the behavior of cutting tools can give a very competitive advantage in terms of costs and excavation performance, optimized to the needs of the TBM itself. The incredible evolution of data science in recent years gives the option to implement it at the time of analyzing the key and most critical parameters related to machinery with the purpose of knowing how the cutting head is performing in front of the excavated ground. Taking this as a case study, Metro Line 3 of Guadalajara in Mexico will develop the feasibility of using Specific Energy versus data science applied over parameters of Torque, Penetration, and Contact Force, among others, to predict the behavior and status of cutting tools. The results obtained through both techniques are analyzed and verified in the function of the wear and the field situations observed in the excavation in order to determine its effectiveness regarding its predictive capacity. In conclusion, the possibilities and improvements offered by the application of digital tools and the programming of calculation algorithms for the analysis of wear of cutting head elements compared to purely empirical methods allow early detection of possible damage to cutting tools, which is reflected in optimization of excavation performance and a significant improvement in costs and deadlines.

Keywords: cutting tools, data science, prediction, TBM, wear

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Authors: Jean Berger, Nassirou Lo, Martin Noel

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Perfectly suited for natural or man-made emergency and disaster management situations such as flood, earthquakes, tornadoes, or tsunami, multi-target search path planning for a team of rescue agents is known to be computationally hard, and most techniques developed so far come short to successfully estimate optimality gap. A novel mixed-integer linear programming (MIP) formulation is proposed to optimally solve the multi-target multi-agent discrete search and rescue (SAR) path planning problem. Aimed at maximizing cumulative probability of successful target detection, it captures anticipated feedback information associated with possible observation outcomes resulting from projected path execution, while modeling agent discrete actions over all possible moving directions. Problem modeling further takes advantage of network representation to encompass decision variables, expedite compact constraint specification, and lead to substantial problem-solving speed-up. The proposed MIP approach uses CPLEX optimization machinery, efficiently computing near-optimal solutions for practical size problems, while giving a robust upper bound obtained from Lagrangean integrality constraint relaxation. Should eventually a target be positively detected during plan execution, a new problem instance would simply be reformulated from the current state, and then solved over the next decision cycle. A computational experiment shows the feasibility and the value of the proposed approach.

Keywords: search path planning, search and rescue, multi-agent, mixed-integer linear programming, optimization

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Authors: Berker Bayazit, Gulgun Kayakutlu

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The World Energy Outlook shows that energy markets will substantially change within a few forthcoming decades. First, determined action plans according to COP21 and aim of CO₂ emission reduction have already impact on policies of countries. Secondly, swiftly changed technological developments in the field of renewable energy will be influential upon medium and long-term energy generation and consumption behaviors of countries. Furthermore, share of electricity on global energy consumption is to be expected as high as 40 percent in 2040. Electrical vehicles, heat pumps, new electronical devices and digital improvements will be outstanding technologies and innovations will be the testimony of the market modifications. In order to meet highly increasing electricity demand caused by technologies, countries have to make new investments in the field of electricity production, transmission and distribution. Specifically, electricity generation mix becomes vital for both prevention of CO₂ emission and reduction of power prices. Majority of the research and development investments are made in the field of electricity generation. Hence, the prime source diversity and source planning of electricity generation are crucial for improving the wealth of citizen life. Approaches considering the CO₂ emission and total cost of generation, are necessary but not sufficient to evaluate and construct the product mix. On the other hand, employment and positive contribution to macroeconomic values are important factors that have to be taken into consideration. This study aims to constitute new investments in renewable energies (solar, wind, geothermal, biogas and hydropower) between 2018-2023 under 4 different goals. Therefore, a multi-objective programming model is proposed to optimize the goals of minimizing the CO₂ emission, investment amount and electricity sales price while maximizing the total employment and positive contribution to current deficit. In order to avoid the user preference among the goals, Dinkelbach’s algorithm and Guzel’s approach have been combined. The achievements are discussed with comparison to the current policies. Our study shows that new policies like huge capacity allotment might be discussible although obligation for local production is positive. The improvements in grid infrastructure and re-design support for the biogas and geothermal can be recommended.

Keywords: energy generation policies, multi-objective linear programming, portfolio planning, renewable energy

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Authors: Abdullahi Mohammed Auwal

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Formation and change or decamping from one political party to another have now become a common trend in Nigeria. Many of the parties’ members who could not secure positions and or win elections in their parties or are not very much satisfied with the trends occurring in the party’s internal democratic principles and mechanisms, change their respective parties. This paper developed/presented and analyzed the used of non linear mathematical model for defections between two political parties using epidemiological approach. The whole population was assumed to be a constant and homogeneously mixed. Equilibria have been analytically obtained and their local and global stability discussed. Conditions for the co-existence of both the political parties have been determined, in the study of defections between People Democratic Party (PDP) and All Progressive Congress (APC) in Nigeria using numerical simulations to support the analytical results.

Keywords: model, political parties, deffection, stability, equilibrium, epidemiology

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Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda

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This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.

Keywords: adsorption, mathematical modeling, nanocarbons, numerical analysis

Procedia PDF Downloads 266

Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: gravity gradient, gravity gradient sensor, accelerometer, single-axis rotation modulation

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Authors: Gak-Gyu Kim, Won Il Jung

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According to a remarkable development of science and technology, function and role of the system of engineering fields has recently been diversified. The system has become increasingly more complex and precise, and thus, system designers intended to maximize reliability concentrate more effort at the design stage. This study deals with the reliability redundancy optimization problem (RROP) for k-out-of-n: G system configuration with cold standby and warm standby components. This paper further intends to present the optimal mathematical model through which the following three elements of (i) multiple components choices, (ii) redundant components quantity and (iii) the choice of redundancy strategies may be combined in order to maximize the reliability of the system. Therefore, we focus on the following three issues. First, we consider RROP that there exists warm standby state as well as cold standby state of the component. Second, as eliminating an approximation approach of the previous RROP studies, we construct a precise model for system reliability. Third, given transition time when the state of components changes, we present not simply a workable solution but the advanced method. For the wide applicability of RROPs, moreover, we use absorbing continuous time Markov chain and matrix analytic methods in the suggested mathematical model.

Keywords: RROP, matrix analytic methods, k-out-of-n: G system, MTTF, absorbing continuous time Markov Chain

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Authors: Hao-Wei Fu, Chung-Feng Kao

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In the era of rapid technological advancement, information technology (IT) has become integral to modern life, exerting significant influence across diverse sectors and serving as a catalyst for development in various industries. Within agriculture, the integration of IT offers substantial benefits, notably enhancing operational efficiency. Real-time monitoring systems, for instance, have been widely embraced in agriculture, effectively improving crop management practices. This study specifically addresses the management of rice panicle fertilizer, presenting the development of a web application tailored to handle data associated with rice panicle fertilizer management. Leveraging the normalized difference red edge index, this application optimizes the quantity of rice panicle fertilizer used, providing recommendations to agricultural stakeholders and service providers in the agricultural information sector. The overarching objective is to minimize costs while maximizing yields. Furthermore, a robust database system has been established to store and manage relevant data for future reference in rice cultivation management. Additionally, the study utilizes the Representational State Transfer software architectural style to construct an application programming interface (API), facilitating data creation, retrieval, updating, and deletion for users via the HyperText Transfer Protocol methods. Future plans involve integrating this API with third-party services to incorporate it into larger frameworks, thus catering to the diverse requirements of various third-party services.

Keywords: application programming interface, HyperText Transfer Protocol, nitrogen fertilizer intelligent management, web-based application

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Authors: Yuan-Jye Tseng, Yi-Shiuan Chen

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The paper presented a sustainable design model for integrated evaluation of the design and supply chain of a product for the sustainable objectives. To design a product, there can be alternative ways to assign the detailed specifications to fulfill the same design objectives. In the design alternative cases, different material and manufacturing processes with various supply chain activities may be required for the production. Therefore, it is required to evaluate the different design cases based on the sustainable objectives. In this research, a closed-loop design model is developed by integrating the forward design model and reverse design model. From the supply chain point of view, the decisions in the forward design model are connected with the forward supply chain. The decisions in the reverse design model are connected with the reverse supply chain considering the sustainable objectives. The purpose of this research is to develop a mathematical model for analyzing the design cases by integrated evaluating the criteria in the closed-loop design and the closed-loop supply chain. The decision variables are built to represent the design cases of the forward design and reverse design. The cost parameters in a forward design include the costs of material and manufacturing processes. The cost parameters in a reverse design include the costs of recycling, disassembly, reusing, remanufacturing, and disposing. The mathematical model is formulated to minimize the total cost under the design constraints. In practical applications, the decisions of the mathematical model can be used for selecting a design case for the purpose of sustainable design of a product. An example product is demonstrated in the paper. The test result shows that the sustainable design model is useful for integrated evaluation of the design and the supply chain to achieve the sustainable objectives.

Keywords: closed-loop design, closed-loop supply chain, design evaluation, supply chain management, sustainable design model

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Authors: Cristian Patrascioiu, Loredana Negoita

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This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: heat exchanger, mathematical modelling, nonlinear equation system, Newton-Raphson algorithm

Procedia PDF Downloads 288

Authors: Gurmeet Singh Cheema, Gurjinder Singh, Amardeep Singh Kang

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Aluminium alloy 6061 is a medium to high strength heat-treatable alloy which has very good corrosion resistance and very good weldability. Friction Stir Welding was developed and this technique has attracted considerable interest from the aerospace and automotive industries since it is able to produce defect free joints particularly for light metals i.e aluminum alloy and magnesium alloy. In the friction stir welding process, welding parameters such as tool rotational speed, welding speed and tool shoulder diameter play a major role in deciding the weld quality. In this research work, an attempt has been made to understand the effect of tool rotational speed, welding speed and tool shoulder diameter on friction stir welded AA6061 aluminium alloy joints. Statistical tool such as central composite design is used to develop the mathematical relationships. The mathematical model was developed to predict mechanical properties of friction stir welded aluminium alloy joints at the 95% confidence level.

Keywords: aluminium alloy, friction stir welding, central composite design, mathematical relationship

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Authors: Onur Kaya, Halit Bayer

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Global grocery and supermarket sales are among the largest markets in the world and perishable products such as fresh produce, dairy and meat constitute the biggest section of these markets. Due to their deterioration over time, the demand for these products depends highly on their freshness. They become totally obsolete after a certain amount of time causing a high amount of wastage and decreases in grocery profits. In addition, customers are asking for higher product variety in perishable product categories, leading to less predictable demand per product and to more out-dating. Effective management of these perishable products is an important issue since it is observed that billions of dollars’ worth of food is expired and wasted every month. We consider coordinated inventory and pricing decisions for perishable products with a time and price dependent random demand function. We use stochastic dynamic programming to model this system for both periodically-reviewed and continuously-reviewed inventory systems and prove certain structural characteristics of the optimal solution. We prove that the optimal ordering decision scenario has a monotone structure and the optimal price value decreases by time. However, the optimal price changes in a non-monotonic structure with respect to inventory size. We also analyze the effect of 1 different parameters on the optimal solution through numerical experiments. In addition, we analyze simple-to-implement heuristics, investigate their effectiveness and extract managerial insights. This study gives valuable insights about the management of perishable products in order to decrease wastage and increase profits.

Keywords: age-dependent demand, dynamic programming, perishable inventory, pricing

Procedia PDF Downloads 246

Authors: Jacob A. Braun

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This paper uses mathematical modeling to show the spread of Herpes Simplex type-2 with and without the usage of condoms in a college population. The model uses four differential equations to calculate the data for the simulation. The dt increment used is one week. It also runs based on a fixated period. The period chosen was five years to represent time spent in college. The average age of the individual is 21, once again to represent the age of someone in college. In the total population, there are almost two times as many women who have Herpes Simplex Type-2 as men. Additionally, Herpes Simplex Type-2 does not have a known cure. The goal of the model is to show how condom usage affects women’s chances of receiving the virus in the hope of being able to reduce the number of women infected. In the end, the model demonstrates that condoms offer significant protection to women from the virus. Since fewer women are infected with the virus when condoms are used, in turn, fewer males are infected. Since Herpes Simplex Type-2 affects the carrier for their whole life, a small decrease of infections could lead to large ramifications over time. Specifically, a small decrease of infections at a young age, such as college, could have a very big effect on the long-term number of people infected with the virus.

Keywords: college, condom, Herpes, mathematical modelling

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Authors: Marlone D. Severo

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A pre- and post-test quasi-experimental design was used to test the intervention of Trachtenberg Speed Math on the mathematical competency of sixty (60) matched-paired students with a poor performing grade in Mathematics from one of the biggest public national high school at the South of Metro Manila. Both control and experimental group were administered with the Attitude Towards Mathematics Inventory (ATMI) before the pretest were given and both group showed high dislike for Mathematics. Pretest showed a 53 percent accuracy for the control group and 51 percent for the experimental group using a 15-item long multiplication test without any aid of a computing device. The experimental group were taught how to use the Trachtenberg number-keys and techniques in multiplication between October 2014 to March 2015. Post-test showed an improvement in the experimental group with 96 percent accuracy for the control group and a dismal 57 percent for the control group in long-multiplication. Post-test ATMI were administered. The control group showed a great dislike towards Mathematics, while the experimental group showed a positive attitude towards the subject.

Keywords: attitude towards mathematics, mathematical competency, number-keys, trachtenberg speed math

Procedia PDF Downloads 367

Authors: Beata Jackowska-Zduniak

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We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: mathematical modeling, ordinary differential equations, endocrine system, delay differential equation

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Authors: Ofosuhene O. Apenteng, Noor Azina Ismail

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Recently tourism is a major foreign exchange earner in the World. In this paper, we propose the mathematical model to study the impact of tourists on the spread of HIV incidences using compartmental differential equation models. Simulation studies of reproduction number are used to demonstrate new insights on the spread of HIV disease. The periodogram analysis of a time series was used to determine the speed at which the disease is spread. The results indicate that with the persistent flow of tourism into a country, the disease status has increased the epidemic rate. The result suggests that the government must put more control on illegal prostitution, unprotected sexual activity as well as to emphasis on prevention policies that include the safe sexual activity through the campaign by the tourism board.

Keywords: HIV/AIDS, mathematical transmission modeling, tourists, stability, simulation

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Authors: Tiantian Li, Lusheng Wang, Zhaohui Zhan, Daming Zhu

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In this paper, we propose two string problems, and study algorithms and complexity of various versions for those problems. Let S = {s₁, s₂, . . . , sₘ} be a set of m strings. A common substring of S is a substring appearing in every string in S. Given a set of m strings S = {s₁, s₂, . . . , sₘ} and a positive integer k, we want to find a set C of k common substrings of S such that the k common substrings in C appear in the same order and have no overlap among the m input strings in S, and the total length of the k common substring in C is maximized. This problem is referred to as the longest total length of k common substrings from m input strings (LCSS(k, m) for short). The other problem we study here is called the longest total length of a set of common substrings with length more than l from m input string (LSCSS(l, m) for short). Given a set of m strings S = {s₁, s₂, . . . , sₘ} and a positive integer l, for LSCSS(l, m), we want to find a set of common substrings of S, each is of length more than l, such that the total length of all the common substrings is maximized. We show that both problems are NP-hard when k and m are variables. We propose dynamic programming algorithms with time complexity O(k n₁n₂) and O(n₁n₂) to solve LCSS(k, 2) and LSCSS(l, 2), respectively, where n1 and n₂ are the lengths of the two input strings. We then design an algorithm for LSCSS(l, m) when every length > l common substring appears once in each of the m − 1 input strings. The running time is O(n₁²m), where n1 is the length of the input string with no restriction on length > l common substrings. Finally, we propose a fixed parameter algorithm for LSCSS(l, m), where each length > l common substring appears m − 1 + c times among the m − 1 input strings (other than s1). In other words, each length > l common substring may repeatedly appear at most c times among the m − 1 input strings {s₂, s₃, . . . , sₘ}. The running time of the proposed algorithm is O((n12ᶜ)²m), where n₁ is the input string with no restriction on repeats. The LSCSS(l, m) is proposed to handle whole chromosome sequence alignment for different strains of the same species, where more than 98% of letters in core regions are identical.

Keywords: dynamic programming, algorithm, common substrings, string

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Authors: Aydin Azizi, Aburrahman Tanira

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The main source of energy used in this modern age is fossil fuels. There is a myriad of problems that come with the use of fossil fuels, out of which the issues with the greatest impact are its scarcity and the cost it imposes on the planet. Fossil fuels are the only plausible option for many vital functions and processes; the most important of these is transportation. Thus, using this source of energy wisely and as efficiently as possible is a must. The aim of this work was to explore utilising mathematical modelling and artificial intelligence techniques to enhance fuel consumption in passenger cars by focusing on the speed at which cars are driven. An artificial neural network with an error less than 0.05 was developed to be applied practically as to predict the rate of fuel consumption in vehicles.

Keywords: mathematical modeling, neural networks, fuel consumption, fossil fuel

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Authors: Artem Sedov, Aigerim Uyzbayeva, Valeriya Tyo

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The presented article is showing results of dynamic modeling with Mathlab software of optimal automatic room climate control system for two experimental houses in Astana, one of which has circle plan and the other one has square plan. These results are showing that building geometry doesn't influence on climate system PID-controls configuring. This confirms theoretical implication that optimal automatic climate control system parameters configuring should depend on building's internal space volume, envelope heat transfer, number of people inside, supply ventilation air flow and outdoor temperature.

Keywords: climate control system, climate physics, dome-like building, mathematical modeling

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Authors: M. Rodionov, Z. Dedovets

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This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.

Keywords: mathematics, motivation, secondary school, student, practical problem

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Authors: Tehrrie Konig, Cassiano Bortolozo, Daniel Metodiev, Rodolfo Mendes, Marcio Andrade, Marcio Moraes

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Gravitational mass movements are recurrent events in Brazil, usually triggered by intense rainfall. When these events occur in urban areas, they end up becoming disasters due to the economic damage, social impact, and loss of human life. To identify the landslide-susceptible areas, it is important to know the geotechnical parameters of the soil, such as cohesion, internal friction angle, unit weight, hydraulic conductivity, and hydraulic diffusivity. The measurement of these parameters is made by collecting soil samples to analyze in the laboratory and by using geophysical methodologies, such as Vertical Electrical Survey (VES). The geophysical surveys analyze the soil properties with minimal impact in its initial structure. Statistical analysis and mathematical models of physical basis are used to model and calculate the Factor of Safety for steep slope areas. In general, such mathematical models work from the combination of slope stability models and hydrological models. One example is the mathematical model TRIGRS (Transient Rainfall Infiltration and Grid-based Regional Slope- Stability Model) which calculates the variation of the Factor of Safety of a determined study area. The model relies on changes in pore-pressure and soil moisture during a rainfall event. TRIGRS was written in the Fortran programming language and associates the hydrological model, which is based on the Richards Equation, with the stability model based on the principle of equilibrium limit. Therefore, the aims of this work are modeling the slope stability of Campos do Jordão with TRIGRS, using geotechnical and geophysical methodologies to acquire the soil properties. The study area is located at southern-east of Sao Paulo State in the Mantiqueira Mountains and has a historic landslide register. During the fieldwork, soil samples were collected, and the VES method applied. These procedures provide the soil properties, which were used as input data in the TRIGRS model. The hydrological data (infiltration rate and initial water table height) and rainfall duration and intensity, were acquired from the eight rain gauges installed by Cemaden in the study area. A very high spatial resolution digital terrain model was used to identify the slopes declivity. The analyzed period is from March 6th to March 8th of 2017. As results, the TRIGRS model calculates the variation of the Factor of Safety within a 72-hour period in which two heavy rainfall events stroke the area and six landslides were registered. After each rainfall, the Factor of Safety declined, as expected. The landslides happened in areas identified by the model with low values of Factor of Safety, proving its efficiency on the identification of landslides susceptible areas. This study presents a critical threshold for landslides, in which an accumulated rainfall higher than 80mm/m² in 72 hours might trigger landslides in urban and natural slopes. The geotechnical and geophysics methods are shown to be very useful to identify the soil properties and provide the geological characteristics of the area. Therefore, the combine geotechnical and geophysical methods for soil characterization and the modeling of landslides susceptible areas with TRIGRS are useful for urban planning. Furthermore, early warning systems can be developed by combining the TRIGRS model and weather forecast, to prevent disasters in urban slopes.

Keywords: landslides, susceptibility, TRIGRS, vertical electrical survey

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Authors: Sergey M. Karabanov, Dmitry V. Suvorov, Dmitry Yu. Tarabrin

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The operating principle of magnetically controlled microelectromechanical system (MEMS) switches is based on controlling the beam movement under the influence of a magnetic field. Currently, there is a MEMS switch design with a flexible ferromagnetic electrode in the form of a fixed-terminal beam, with an electrode fastened on a straight or cranked anchor. The basic performance characteristics of magnetically controlled MEMS switches (service life, sensitivity, contact resistance, fast response) are largely determined by the flexible electrode design. To ensure the stable and controlled motion of the flexible electrode, it is necessary to provide the optimal design of a flexible electrode.

Keywords: flexible electrode, magnetically controlled MEMS, mathematical modeling, mechanical stress

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Authors: Michael Lousis

Abstract:

The systematic identification of the most conspicuous and significant errors made by learners during three-years of testing of their progress in learning Arithmetic throughout the development of the Kassel Project in England and Greece was accomplished. How much retentive these errors were over three-years in the officially provided school instruction of Arithmetic in these countries has also been shown. The learners’ errors in Arithmetic stemmed from a sample, which was comprised of two hundred (200) English students and one hundred and fifty (150) Greek students. The sample was purposefully selected according to the students’ participation in each testing session in the development of the three-year project, in both domains simultaneously in Arithmetic and Algebra. Specific teaching practices have been invented and are presented in this study for subverting these learners’ errors, which were found out to be retentive to the level of the nationally provided mathematical education of each country. The invention and the development of these proposed teaching practices were founded on the rationality of the theoretical accounts concerning the explanation, prediction and control of the errors, on the conceptual metaphor and on an analysis, which tried to identify the required cognitive components and skills of the specific tasks, in terms of Psychology and Cognitive Science as applied to information-processing. The aim of the implementation of these instructional practices is not only the subversion of these errors but the achievement of the mathematical competence, as this was defined to be constituted of three elements: appropriate representations - appropriate meaning - appropriately developed schemata. However, praxis is of paramount importance, because there is no independent of science ‘real-truth’ and because praxis serves as quality control when it takes the form of a cognitive method.

Keywords: arithmetic, cognitive science, cognitive psychology, information-processing paradigm, Kassel project, level of the nationally provided mathematical education, praxis, remedial mathematical teaching practices, retentiveness of errors

Procedia PDF Downloads 315

Authors: Assem M. F. Sallam, Ah. El-S. Makled

Abstract:

This paper presents a study on the trajectory of a two stage launch vehicle. The study includes dynamic responses of motion parameters as well as the variation of angles affecting the orientation of the launch vehicle (LV). LV dynamic characteristics including state vector variation with corresponding altitude and velocity for the different LV stages separation, as well as the angle of attack and flight path angles are also discussed. A flight trajectory study for the drop zone of first stage and the jettisoning of fairing are introduced in the mathematical modeling to study their effect. To increase the accuracy of the LV model, atmospheric model is used taking into consideration geographical location and the values of solar flux related to the date and time of launch, accurate atmospheric model leads to enhancement of the calculation of Mach number, which affects the drag force over the LV. The mathematical model is implemented on MATLAB based software (Simulink). The real available experimental data are compared with results obtained from the theoretical computation model. The comparison shows good agreement, which proves the validity of the developed simulation model; the maximum error noticed was generally less than 10%, which is a result that can lead to future works and enhancement to decrease this level of error.

Keywords: launch vehicle modeling, launch vehicle trajectory, mathematical modeling, Matlab- Simulink

Procedia PDF Downloads 273

Authors: Joon-Hoon Park

Abstract:

In this paper the rationalized Haar transform is applied for distributed parameter system identification and estimation. A distributed parameter system is a dynamical and mathematical model described by a partial differential equation. And system identification concerns the problem of determining mathematical models from observed data. The Haar function has some disadvantages of calculation because it contains irrational numbers, for these reasons the rationalized Haar function that has only rational numbers. The algorithm adopted in this paper is based on the transform and operational matrix of the rationalized Haar function. This approach provides more convenient and efficient computational results.

Keywords: distributed parameter system, rationalized Haar transform, operational matrix, system identification

Procedia PDF Downloads 507