Search results for: fuzzy mathematical programming

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: Keerti Kembhavi, M. R. Archana, V. Anjaneyappa

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Most asphalt pavement condition evaluation use rating frameworks in which asphalt pavement distress is estimated by type, extent, and severity. Rating is carried out by the pavement condition rating (PCR), which is tedious and expensive. This paper presents the development of a low-cost technique for image pavement distress analysis that permits the identification of pothole and cracks. The paper explores the application of image processing tools for the detection of potholes and cracks. Longitudinal cracking and pothole are detected using Fuzzy-C- Means (FCM) and proceeded with the Spectral Theory algorithm. The framework comprises three phases, including image acquisition, processing, and extraction of features. A digital camera (Gopro) with the holder is used to capture pavement distress images on a moving vehicle. FCM classifier and Spectral Theory algorithms are used to compute features and classify the longitudinal cracking and pothole. The Matlab2016Ra Image preparing tool kit utilizes performance analysis to identify the viability of pavement distress on selected urban stretches of Bengaluru city, India. The outcomes of image evaluation with the utilization semi-computerized image handling framework represented the features of longitudinal crack and pothole with an accuracy of about 80%. Further, the detected images are validated with the actual dimensions, and it is seen that dimension variability is about 0.46. The linear regression model y=1.171x-0.155 is obtained using the existing and experimental / image processing area. The R2 correlation square obtained from the best fit line is 0.807, which is considered in the linear regression model to be ‘large positive linear association’.

Keywords: crack detection, pothole detection, spectral clustering, fuzzy-c-means

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Authors: Masoud Safdari, Jacob Fish

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Despite vast amount of existing theoretical knowledge, the implementation of a universal multiscale modeling, analysis, and simulation software framework remains challenging. Existing multiscale software and solutions are often domain-specific, closed-source and mandate a high-level of experience and skills in both multiscale analysis and programming. Furthermore, tools currently existing for Atomistic-to-Continuum (AtC) multiscaling are developed with the assumptions such as accessibility of high-performance computing facilities to the users. These issues mentioned plus many other challenges have reduced the adoption of multiscale in academia and especially industry. In the current work, we introduce Multiscale Hub (MsHub), an effort towards making AtC more accessible through cloud services. As a joint effort between academia and industry, MsHub provides a universal web-enabled framework for practical multiscaling. Developed on top of universally acclaimed scientific programming language Python, the package currently provides an open-source, comprehensive, easy-to-use framework for AtC coupling. MsHub offers an easy to use interface to prominent molecular dynamics and multiphysics continuum mechanics packages such as LAMMPS and MFEM (a free, lightweight, scalable C++ library for finite element methods). In this work, we first report on the design philosophy of MsHub, challenges identified and issues faced regarding its implementation. MsHub takes the advantage of a comprehensive set of tools and algorithms developed for AtC that can be used for a variety of governing physics. We then briefly report key AtC algorithms implemented in MsHub. Finally, we conclude with a few examples illustrating the capabilities of the package and its future directions.

Keywords: atomistic, continuum, coupling, multiscale

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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

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Authors: P. Hooshangitabrizi, I. Contreras, N. Bhuiyan

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This work presents an online scheduling problem which accommodates multiple requests of patients for chemotherapy treatments in a cancer center of a major metropolitan hospital in Canada. To solve the problem, an adaptive flexible approach is proposed which systematically combines two optimization models. The first model is intended to dynamically schedule arriving requests in the form of waiting lists whereas the second model is used to reschedule the already booked patients with the goal of finding better resource allocations when new information becomes available. Both models are created as mixed integer programming formulations. Various controllable and flexible parameters such as deviating the prescribed target dates by a pre-determined threshold, changing the start time of already booked appointments and the maximum number of appointments to move in the schedule are included in the proposed approach to have sufficient degrees of flexibility in handling arrival requests and unexpected changes. Several computational experiments are conducted to evaluate the performance of the proposed approach using historical data provided by the oncology clinic. Our approach achieves outstandingly better results as compared to those of the scheduling system being used in practice. Moreover, several analyses are conducted to evaluate the effect of considering different levels of flexibility on the obtained results and to assess the performance of the proposed approach in dealing with last-minute changes. We strongly believe that the proposed flexible adaptive approach is very well-suited for implementation at the clinic to provide better patient-care services and to utilize available resource more efficiently.

Keywords: chemotherapy scheduling, multi-appointment modeling, optimization of resources, satisfaction of patients, mixed integer programming

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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: Deyadeen Ali Alshibani

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In the literature, the multi-armed bandit problem as a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. There are several different algorithms models and their applications on this problem. In this paper, we evaluate the Regret-regression through comparing with Q-learning method. A simulation on determination of optimal treatment regime is presented in detail.

Keywords: optimal, bandit problem, optimization, dynamic programming

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Authors: E. Y. Igde, S. Aydogan, F. E. Boran, D. Akay

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Patent data have an increasingly important role in economic growth, innovation, technical advantages and business strategies and even in countries competitions. Analyzing of patent data is crucial since patents cover large part of all technological information of the world. In this paper, we have used the linguistic summarization technique to prove the validity of the hypotheses related to patent data stated in the literature.

Keywords: data mining, fuzzy sets, linguistic summarization, patent data

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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: 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

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Authors: Konstantinos Pikos, Dimitrios Kaimaris

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Although designing building blocks is a procedure used by many planners around the world, there isn’t an automated tool that will help planners and designers achieve their goals with lesser effort. The difficulty of the subject lies in the repeating process of manually drawing lines, while not only it is mandatory to maintain the desirable offset but to also achieve a lesser impact to the existing building stock. In this paper, using Geographical Information Systems (GIS) and the Python programming language, an automated tool integrated into ArcGIS PRO, is being presented. Despite its simplistic enviroment and the lack of specialized building legislation due to the complex state of the field, a planner who is aware of such technical information can use the tool to draw an initial approach of the final building blocks in an area with pre-existing buildings in an attempt to organize the usually sprawling suburbs of a city or any continuously developing area. The tool uses ESRI’s ArcPy library to handle the spatial data, while interactions with the user is made throught Tkinter. The main process consists of a modification of building edgescoordinates, using NumPy library, in an effort to draw the line of best fit, so the user can get the optimal results per block’s side. Finally, after the tool runs successfully, a table of primary planning information is shown, such as the area of the building block and its coverage rate. Regardless of the primary stage of the tool’s development, it is a solid base where potential planners with programming skills could invest, so they can make the tool adapt to their individual needs. An example of the entire procedure in a test area is provided, highlighting both the strengths and weaknesses of the final results.

Keywords: arcPy, GIS, python, building blocks

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Authors: Arash Parehkar, S. Jamshid Mousavi, Shoubo Bayazidi, Vahid Karami, Laleh Shahidi, Arash Azaranfar, Ali Moridi, M. Shabakhti, Tayebeh Ariyan, Mitra Tofigh, Kaveh Masoumi, Alireza Motahari

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Water resource systems modelling have constantly been a challenge through history for human being. As the innovative methodological development is evolving alongside computer sciences on one hand, researches are likely to confront more complex and larger water resources systems due to new challenges regarding increased water demands, climate change and human interventions, socio-economic concerns, and environment protection and sustainability. In this research, an automatic calibration scheme has been applied on the Gilan’s large-scale water resource model using mathematical programming. The water resource model’s calibration is developed in order to attune unknown water return flows from demand sites in the complex Sefidroud irrigation network and other related areas. The calibration procedure is validated by comparing several gauged river outflows from the system in the past with model results. The calibration results are pleasantly reasonable presenting a rational insight of the system. Subsequently, the unknown optimized parameters were used in a basin-scale linear optimization model with the ability to evaluate the system’s performance against a reduced inflow scenario in future. Results showed an acceptable match between predicted and observed outflows from the system at selected hydrometric stations. Moreover, an efficient operating policy was determined for Sefidroud dam leading to a minimum water shortage in the reduced inflow scenario.

Keywords: auto-calibration, Gilan, large-scale water resources, simulation

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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: 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: Adrian Forca, Simeon Cainday III

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The Electronic Payment Recording with Payment History Retrieval Module is developed intendedly for the College of Science and Technology. This system software innovates the manual process of recording the payments done in the department through the development of electronic payment recording system software shifting from the slow and time-consuming procedure to quick yet reliable and accurate way of recording payments because it immediately generates receipts for every transaction. As an added feature to its software process, generation of recorded payment report is integrated eliminating the manual reporting to a more easy and consolidated report. As an added feature to the system, all recorded payments of the students can be retrieved immediately making the system transparent and reliable payment recording software. Viewing the whole process, the system software will shift from the manual process to an organized software technology because the information will be stored in a logically correct and normalized database. Further, the software will be developed using the modern programming language and implement strict programming methods to validate all users accessing the system, evaluate all data passed into the system and information retrieved to ensure data accuracy and reliability. In addition, the system will identify the user and limit its access privilege to establish boundaries of the specific access to information allowed for the store, modify, and update making the information secure against unauthorized data manipulation. As a result, the System software will eliminate the manual procedure and replace with an innovative modern information technology resulting to the improvement of the whole process of payment recording fast, secure, accurate and reliable software innovations.

Keywords: collection, information system, manual procedure, payment

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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

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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: 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: Geetha Baskaran, Andrzej Barjiela, Rong Qu

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Motivation: Nurse scheduling is a complex combinatorial optimization problem. It is also known as NP-hard. It needs an efficient re-scheduling to minimize some trade-off of the measures of violation by reducing selected constraints to soft constraints with measurements of their violations. Problem Statement: In this paper, we extend our novel approach to solve the nurse scheduling problem by transforming it through Information Granulation. Approach: This approach satisfies the rules of a typical hospital environment based on a standard benchmark problem. Generating good work schedules has a great influence on nurses' working conditions which are strongly related to the level of a quality health care. Domain transformation that combines the strengths of operation research and artificial intelligence was proposed for the solution of the problem. Compared to conventional methods, our approach involves judicious grouping (information granulation) of shifts types’ that transforms the original problem into a smaller solution domain. Later these schedules from the smaller problem domain are converted back into the original problem domain by taking into account the constraints that could not be represented in the smaller domain. An Integer Programming (IP) package is used to solve the transformed scheduling problem by expending the branch and bound algorithm. We have used the GNU Octave for Windows to solve this problem. Results: The scheduling problem has been solved in the proposed formalism resulting in a high quality schedule. Conclusion: Domain transformation represents departure from a conventional one-shift-at-a-time scheduling approach. It offers an advantage of efficient and easily understandable solutions as well as offering deterministic reproducibility of the results. We note, however, that it does not guarantee the global optimum.

Keywords: domain transformation, nurse scheduling, information granulation, artificial intelligence, simulation

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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: 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

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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

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

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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

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Authors: Joon-Hoon Park

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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

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Authors: Zhanna Dedovets

Abstract:

Fostering a mathematical style of thinking is crucial for cultivating intellectual personalities capable of thriving in modern society. Intuitive thinking stands as a cornerstone among the components of mathematical cognition, playing a pivotal role in grasping mathematical truths across various disciplines. This article delves into the exploration of leveraging search activities rooted in students' intuitive thinking, particularly when tackling geometric problems. Emphasizing both student engagement with the task and their active involvement in the search process, the study underscores the importance of heuristic procedures and the freedom for students to chart their own problem-solving paths. Spanning several years (2019-2023) at the Physics and Mathematics Lyceum of Dushanbe, the research engaged 17 teachers and 78 high school students. After assessing the initial levels of intuitive thinking in both control and experimental groups, the experimental group underwent training following the authors' methodology. Subsequent analysis revealed a significant advancement in thinking levels among the experimental group students. The methodological approaches and teaching materials developed through this process offer valuable resources for mathematics educators seeking to enhance their students' learning experiences effectively.

Keywords: teaching of mathematics, intuitive thinking, heuristic procedures, geometric problem, students.

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