Search results for: Problem solving courts

Authors: Alex Contarino

Abstract:

Professional sports leagues often have a “free agency” period, during which teams may sign players with expiring contracts.To promote parity, many leagues operate under a salary cap that limits the amount teams can spend on player’s salaries in a given year. Similarly, in fantasy sports leagues, salary cap drafts are a popular method for selecting players. In order to sign a free agent in either setting, teams must bid against one another to buy the player’s services while ensuring the sum of their player’s salaries is below the salary cap. This paper models the bidding process for a free agent as a constrained optimization problem that can be solved using linear programming. The objective is to determine the largest bid that a team should offer the player subject to the constraint that the value of signing the player must exceed the value of using the salary cap elsewhere. Iteratively solving this optimization problem for each available free agent provides teams with an effective framework for maximizing the talent on their rosters. The utility of this approach is demonstrated for team sport roster construction and fantasy sport drafts, using recent data sets from both settings.

Keywords: linear programming, optimization, roster management, salary cap

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

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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

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Authors: Boris Melnikov, Dmitrii Chaikovskii, Elena Melnikova

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The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for the task of restoring the DNA matrix. This restoration problem is often considered in biocybernetics. For it, we must recover the matrix of distances between DNA sequences if not all the elements of the matrix under consideration are known at the input. We consider the possibility of using this method in the testing of distance calculation algorithms between a pair of DNAs to restore the partially filled matrix.

Keywords: optimization problems, DNA matrix, partially filled matrix, traveling salesman problem, heuristic algorithms

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Authors: Badr M. Alshammari, T. Guesmi

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In recent years, the combined economic and emission power dispatch is one of the main problems of electrical power system. It aims to schedule the power generation of generators in order to minimize cost production and emission of harmful gases caused by fossil-fueled thermal units such as CO, CO₂, NO_x, and SO₂. To solve this complicated multi-objective problem, an improved version of the particle swarm optimization technique that includes non-dominated sorting concept has been proposed. Valve point loading effects and system losses have been considered. The three-unit and ten-unit benchmark systems have been used to show the effectiveness of the suggested optimization technique for solving this kind of nonconvex problem. The simulation results have been compared with those obtained using genetic algorithm based method. Comparison results show that the proposed approach can provide a higher quality solution with better performance.

Keywords: power dispatch, valve point loading effects, multiobjective optimization, Pareto solutions

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Authors: S. Mahdi Sadatmansouri, Maryam Khalili

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World, nowadays, encounters serious water scarcity problem. During the past few years, by advent of Smart Energy and Water Meter (SEWM) and its installation at the electro-pumps of the water wells, one had believed that it could be the golden key to address the groundwater resources over-pumping issue. In fact, implementation of these Smart Meters managed to control the water table drawdown for short; but it was not a sustainable approach. SEWM has been considered as law enforcement facility at first; however, for solving a complex socioeconomic problem like shared groundwater resources management, more than just enforcement is required: participation to conserve common resources. The well owners or farmers, as water consumers, are the main and direct stakeholders of this system and other stakeholders could be government sectors, investors, technology providers, privet sectors or ordinary people. Designing a socio-technical system not only defines the role of each stakeholder but also can lubricate the communication to reach the system goals while benefits of each are considered and provided. Farmers, as the key participators for solving groundwater problem, do not trust governments but they would trust a fair system in which responsibilities, privileges and benefits are clear. Technology could help this system remained impartial and productive. Social aspects provide rules, regulations, social objects and etc. for the system and help it to be more human-centered. As the design methodology, Design Thinking provides probable solutions for the challenging problems and ongoing conflicts; it could enlighten the way in which the final system could be designed. Using Human Centered Design approach of IDEO helps to keep farmers in the center of the solution and provides a vision by which stakeholders’ requirements and needs are addressed effectively. Farmers would be considered to trust the system and participate in their groundwater resources management if they find the rules and tools of the system fair and effective. Besides, implementation of the socio-technical system could change farmers’ behavior in order that they concern more about their valuable shared water resources as well as their farm profit. This socio-technical system contains nine main subsystems: 1) Measurement and Monitoring system, 2) Legislation and Governmental system, 3) Information Sharing system, 4) Knowledge based NGOs, 5) Integrated Farm Management system (using IoT), 6) Water Market and Water Banking system, 7) Gamification, 8) Agribusiness ecosystem, 9) Investment system.

Keywords: human centered design, participatory management, smart energy and water meter (SEWM), social object, socio-technical system, water table drawdown

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Authors: Terence Soule, Tami Al Ghamdi

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To study how to transfer knowledge from multiple source problems to the target problem, we modeled the Transfer Learning (TL) process using Genetic Algorithms as the model solver. TL is the process that aims to transfer learned data from one problem to another problem. The TL process aims to help Machine Learning (ML) algorithms find a solution to the problems. The Genetic Algorithms (GA) give researchers access to information that we have about how the old problem is solved. In this paper, we have five different source problems, and we transfer the knowledge to the target problem. We studied different scenarios of the target problem. The results showed combined knowledge from multiple source problems improves the GA performance. Also, the process of combining knowledge from several problems results in promoting diversity of the transferred population.

Keywords: transfer learning, genetic algorithm, evolutionary computation, source and target

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Authors: Nayer Fardows, Zarash Nayer, Sarah Nayer Jaffar, Daud Nayer

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This paper analyses the issues related to communal properties of minorities in the cantonment area of Pakistan allotted in the mid-eighteenth centuries by the British Government to facilitate soldiers. These properties were old grants on which churches, institutes, hospitals, and residences were built. The ownership of these properties remained with British Government, but after the creation of Pakistan, changes by putting Government of Pakistan as the landlord of the property disturbed the inheritors as they remained as, holder of occupancy. The government of Pakistan issued a policy in 1997 to convert the status of old grant properties to regular lease. However, heavy taxes and high court’s decisions made it difficult to solve the issue. The study was conducted on six old grant properties of Edwardes College Peshawar cantonment situated in Khyber Pakhtunkhwa, Pakistan. The paper is descriptive research with a qualitative approach collecting data through government rules, acts, ordinance and decisions of the high courts. The result leads to three aspects; 1) holder of occupancy status of old grant properties in cantonment is similar as allotment of other properties by the government, 2) imposition of heavy taxes on conversion of property from old grant to regular lease restricted inheritors to further construct or transfer, 3) imposition of higher courts ban on conversion of communal properties contradict government policy of conversion. The paper recommends the Government of Pakistan a solution to maintain the status quo for communal properties that fall within the old grant.

Keywords: British Government, communal properties, cantonment, old grant, institutions

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Authors: Ocotlán Díaz-Parra, Jorge A. Ruiz-Vanoye, Alejandro Fuentes-Penna, Beatriz Bernabe-Loranca, Patricia Ambrocio-Cruz, José J. Hernández-Flores

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The Maritime Platform Transport Problem of Solid, Special and Dangerous Waste consist of to minimize the monetary value of carry different types of waste from one location to another location using ships. We offer a novel mathematical, the characterization of the problem and the use CPLEX to find the optimal values to solve the Solid, Special and Hazardous Waste Transportation Problem of offshore platforms instances of Mexican state-owned petroleum company (PEMEX). The set of instances used are WTPLib real instances and the tool CPLEX solver to solve the MPTPSSDW problem.

Keywords: oil platform, transport problem, waste, solid waste

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Authors: Kalpana Dahiya

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This paper discusses a two-level hierarchical time minimization transportation problem, which is an important class of transportation problems arising in industries. This problem has been studied by various researchers, and a number of polynomial time iterative algorithms are available to find its solution. All the existing algorithms, though efficient, have some shortcomings. The current study proposes an alternate solution algorithm for the problem that is more efficient in terms of computational time than the existing algorithms. The results justifying the underlying theory of the proposed algorithm are given. Further, a detailed comparison of the computational behaviour of all the algorithms for randomly generated instances of this problem of different sizes validates the efficiency of the proposed algorithm.

Keywords: global optimization, hierarchical optimization, transportation problem, concave minimization

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Authors: Farzaneh Rajabighamchi, Stan van Hoesel, Christof Defryn

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The generalized traveling salesman problem (GTSP) is an extension of the traveling salesman problem (TSP) where the set of nodes is partitioned into clusters, and the salesman must visit exactly one node per cluster. In this research, we apply the definition of the GTSP to an order picker routing problem with multiple locations per product. As such, each product represents a cluster and its corresponding nodes are the locations at which the product can be retrieved. To pick a certain product item from the warehouse, the picker needs to visit one of these locations during its pick tour. As all products are scattered throughout the warehouse, the product clusters not separated geographically. We propose an exact LP model as well as heuristic and meta-heuristic solution algorithms for the order picking problem with multiple product locations.

Keywords: warehouse optimization, order picking problem, generalised travelling salesman problem, heuristic algorithm

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Authors: Ivan Baravy

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

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

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Authors: A. A. Soliman

Abstract:

The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

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Authors: Elham Kiyani

Abstract:

In this paper, we first introduce the concept of Q-efficient solutions in a real linear space not necessarily endowed with a topology, where Q is some nonempty (not necessarily convex) set. We also used the scalarization technique including the Gerstewitz function generated by a nonconvex set to characterize these Q-efficient solutions. The algebraic concepts of interior and closure are useful to study optimization problems without topology. Studying nonconvex vector optimization is valuable since topological interior is equal to algebraic interior for a convex cone. So, we use the algebraic concepts of interior and closure to define Q-weak efficient solutions and Q-Henig proper efficient solutions of set-valued optimization problems, where Q is not a convex cone. Optimization problems with set-valued maps have a wide range of applications, so it is expected that there will be a useful analytical tool in optimization theory for set-valued maps. These kind of optimization problems are closely related to stochastic programming, control theory, and economic theory. The paper focus on nonconvex problems, the results are obtained by assuming generalized non-convexity assumptions on the data of the problem. In convex problems, main mathematical tools are convex separation theorems, alternative theorems, and algebraic counterparts of some usual topological concepts, while in nonconvex problems, we need a nonconvex separation function. Thus, we consider the Gerstewitz function generated by a general set in a real linear space and re-examine its properties in the more general setting. A useful approach for solving a vector problem is to reduce it to a scalar problem. In general, scalarization means the replacement of a vector optimization problem by a suitable scalar problem which tends to be an optimization problem with a real valued objective function. The Gerstewitz function is well known and widely used in optimization as the basis of the scalarization. The essential properties of the Gerstewitz function, which are well known in the topological framework, are studied by using algebraic counterparts rather than the topological concepts of interior and closure. Therefore, properties of the Gerstewitz function, when it takes values just in a real linear space are studied, and we use it to characterize Q-efficient solutions of vector problems whose image space is not endowed with any particular topology. Therefore, we deal with a constrained vector optimization problem in a real linear space without assuming any topology, and also Q-weak efficient and Q-proper efficient solutions in the senses of Henig are defined. Moreover, by means of the Gerstewitz function, we provide some necessary and sufficient optimality conditions for set-valued vector optimization problems.

Keywords: algebraic interior, Gerstewitz function, vector closure, vector optimization

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Authors: Hassan M. H. Mustafa

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This piece of research addresses an interesting comparative analytical study. Which considers two concepts of diverse algorithmic computational intelligence approaches related tightly with Neural and Non-Neural Systems. The first algorithmic intelligent approach concerned with observed obtained practical results after three neural animal systems’ activities. Namely, they are Pavlov’s, and Thorndike’s experimental work. Besides a mouse’s trial during its movement inside figure of eight (8) maze, to reach an optimal solution for reconstruction problem. Conversely, second algorithmic intelligent approach originated from observed activities’ results for Non-Neural Ant Colony System (ACS). These results obtained after reaching an optimal solution while solving Traveling Sales-man Problem (TSP). Interestingly, the effect of increasing number of agents (either neurons or ants) on learning performance shown to be similar for both introduced systems. Finally, performance of both intelligent learning paradigms shown to be in agreement with learning convergence process searching for least mean square error LMS algorithm. While its application for training some Artificial Neural Network (ANN) models. Accordingly, adopted ANN modeling is a relevant and realistic tool to investigate observations and analyze performance for both selected computational intelligence (biological behavioral learning) systems.

Keywords: artificial neural network modeling, animal learning, ant colony system, traveling salesman problem, computational biology

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Authors: Leila Maleki, Ezatollah Ahmadi

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The aim of this study was to investigate the effectiveness of memory training exercise on cognitive flexibility. The method of this study was experimental. The statistical population selected 40 students 14 years old, samples were chosen by available sampling method and then they were replaced in experimental (training program) group and control group randomly and answered to Wisconsin Card Sorting Test; covariance test results indicated that there were a significant in post-test scores of experimental group (p<0.005).

Keywords: cognitive flexibility, working memory exercises, problem solving, reaction time

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Authors: Elham Kiyani, S. Mansour Vaezpour, Javad Tavakoli

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In this paper, we first introduce a new distance function in a linear space not necessarily endowed with a topology. The algebraic concepts of interior and closure are useful to study optimization problems without topology. So, we define Q-weak efficient solutions generated by the algebraic interior of a set Q, where Q is not necessarily convex. Studying nonconvex vector optimization is valuable since, for a convex cone K in topological spaces, we have int(K)=cor(K), which means that topological interior of a convex cone K is equal to the algebraic interior of K. Moreover, we used the scalarization technique including the distance function generated by the vectorial closure of a set to characterize these Q-weak efficient solutions. Scalarization is a useful approach for solving vector optimization problems. This technique reduces the optimization problem to a scalar problem which tends to be an optimization problem with a real-valued objective function. For instance, Q-weak efficient solutions of vector optimization problems can be characterized and computed as solutions of appropriate scalar optimization problems. In the convex case, linear functionals can be used as objective functionals of the scalar problems. But in the nonconvex case, we should present a suitable objective function. It is the aim of this paper to present a new distance function that be useful to obtain sufficient and necessary conditions for Q-weak efficient solutions of general optimization problems via scalarization.

Keywords: weak efficient, algebraic interior, vector closure, linear space

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Authors: Daniel Pinheiro Da Silva Junior, Aline Paes, Daniel De Oliveira, Christiano Lacerda Ghuerren, Marcio Duran

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The Courts of Accounts are institutions responsible for overseeing and point out irregularities of Public Administration expenses. They have a high demand for processes to be analyzed, whose decisions must be grounded on severity laws. Despite the existing large amount of processes, there are several cases reporting similar subjects. Thus, previous decisions on already analyzed processes can be a precedent for current processes that refer to similar topics. Identifying similar topics is an open, yet essential task for identifying similarities between several processes. Since the actual amount of topics is considerably large, it is tedious and error-prone to identify topics using a pure manual approach. This paper presents a tool based on Machine Learning and Natural Language Processing to assists in building a labeled dataset. The tool relies on Topic Modelling with Latent Dirichlet Allocation to find the topics underlying a document followed by Jensen Shannon distance metric to generate a probability of similarity between documents pairs. Furthermore, in a case study with a corpus of decisions of the Rio de Janeiro State Court of Accounts, it was noted that data pre-processing plays an essential role in modeling relevant topics. Also, the combination of topic modeling and a calculated distance metric over document represented among generated topics has been proved useful in helping to construct a labeled base of similar and non-similar document pairs.

Keywords: courts of accounts, data labelling, document similarity, topic modeling

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Authors: Cagri Memis, Muzaffer Kapanoglu

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The school bus routing problem (SBRP) is a variant of the Vehicle Routing Problem (VRP) classified as a location-allocation-routing problem. In this study, the SBRP is decomposed into two sub-problems: (1) bus route generation and (2) bus stop selection to solve large instances of the SBRP in reasonable computational times. To solve the first sub-problem, we propose a genetic algorithm to generate bus routes. Once the routes have been fixed, a sub-problem remains of allocating students to stops considering the capacity of the buses and the walkability constraints of the students. While the exact method solves small-scale problems, treating large-scale problems with the exact method becomes complex due to computational problems, a deficiency that the genetic algorithm can overcome. Results obtained from the proposed approach on 150 instances up to 250 stops show that the matheuristic algorithm provides better solutions in reasonable computational times with respect to benchmark algorithms.

Keywords: genetic algorithm, matheuristic, school bus routing problem, vehicle routing problem

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Hernández Eva Selene, Reyna Mary Carmen, Rivera Héctor, Barragán Irving

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We propose an approach that jointly addresses the layout of a facility and the scheduling of a sequence of jobs. In real production, these two problems are interrelated. However, they are treated separately in the literature. Our approach is an extension of the job shop problem with transportation delay, where the location of the machines is selected among possible sites. The model minimizes the makespan, using the short processing times rule with two algorithms; the first one considers all the permutations for the location of machines, and the second only a heuristic to select some specific permutations that reduces computational time. Some instances are proved and compared with literature.

Keywords: layout problem, job shop scheduling problem, concurrent scheduling and layout problem, metaheuristic

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Authors: Avinoam Rabinovich

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CO₂ geological storage is a proven technology for reducing anthropogenic carbon emissions, which is paramount for achieving the ambitious net zero emissions goal. Core flooding experiments are an important step in any CO₂ storage project, allowing us to gain information on the flow of CO₂ and brine in the porous rock extracted from the reservoir. This information is important for understanding basic mechanisms related to CO₂ geological storage as well as for reservoir modeling, which is an integral part of a field project. In this work, a different method for constructing accurate models of CO₂-brine core flooding will be presented. Results for synthetic cases and real experiments will be shown and compared with numerical models to exhibit their predictive capabilities. Furthermore, the various mechanisms which impact the CO₂ distribution and trapping in the rock samples will be discussed, and examples from models and experiments will be provided. The new method entails solving an inverse problem to obtain a three-dimensional permeability distribution which, along with the relative permeability and capillary pressure functions, constitutes a model of the flow experiments. The model is more accurate when data from a number of experiments are combined to solve the inverse problem. This model can then be used to test various other injection flow rates and fluid fractions which have not been tested in experiments. The models can also be used to bridge the gap between small-scale capillary heterogeneity effects (sub-core and core scale) and large-scale (reservoir scale) effects, known as the upscaling problem.

Keywords: CO₂ geological storage, residual trapping, capillary heterogeneity, core flooding, CO₂-brine flow

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Authors: Alejandra Cardenas, Ona Flores, Fabiola Gretzinger

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Since the 1990s, legal strategies for the promotion and protection of maternal health rights have achieved significant gains. Successful litigation in courts around the world have shown that these rights can be judicially enforceable. Governments and international organizations have acknowledged the importance of a human rights-based approach to maternal mortality and morbidity, and obstetric violence has been recognized as a human rights issue. Despite the progress made, maternal mortality has worsened in some regions of the world, while progress has stagnated elsewhere, and mistreatment in maternal care is reported almost universally. In this context, issues of maternal autonomy and decision-making during pregnancy, labor, and delivery as a critical barrier to access quality maternal health have been largely overlooked. Indeed, despite the principles of autonomy and informed consent in medical interventions being well-established in international and regional norms, how they are applied particularly during childbirth and pregnancy remains underdeveloped. National and global legal standards and decisions related to maternal health were reviewed and analyzed to determine how maternal autonomy and decision-making during pregnancy, labor, and delivery have been protected (or not) by international and national courts. The results of this legal research and analysis lead to the conclusion that a few standards have been set by courts regarding pregnant people’s rights to make choices during pregnancy and birth; however, most undermine the agency of pregnant people. These decisions recognize obstetric violence and gender-based discrimination, but fail to protect pregnant people’s autonomy, privacy, and their right to informed consent. As current human rights standards stand today, maternal health is the only field in medicine and law in which informed consent can be overridden, and patients can be forced to submit to treatments against their will. Unconsented treatment and loss of agency during pregnancy and childbirth can have long-term physical and mental impacts, reduce satisfaction and trust in health systems, and may deter future health-seeking behaviors. This research proposes a path forward that focuses on the pregnant person as an independent agent, relying on the doctrine of self-determination during pregnancy and childbirth, which includes access to the necessary conditions to enable autonomy and choice throughout pregnancy and childbirth as a critical step towards our approaches to reduce maternal mortality, morbidity, and mistreatment, and realize the promise of access to quality maternal health as a human right.

Keywords: autonomy in childbirth and pregnancy, choice, informed consent, jurisprudential analysis

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Authors: S. H. Lee, M. J. Park, O. M. Kwon

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In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of this systems are obtained by solving a set of Linear Matrix Inequalities(LMIs). One numerical example is included to show the effectiveness of the proposed criteria.

Keywords: multi-agent, linear matrix inequalities (LMIs), kronecker product, sampled-data, Lyapunov method

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Authors: Kwan U. Kim, Jin Sim, Ryong Jin Jang, Sung Duk Kim

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108 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in the Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not correctly solve one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition, they did not treat the astronomical and physical phenomena in a physical way based on the correct physical laws obtained from the solution of the geodesic equations in the Schwarzschild metric. Therefore, some former scholars mentioned that Einstein’s theoretical basis of a general theory of relativity was obscure and incorrect, but they did not give a correct physical solution to the problems. Furthermore, since the general theory of relativity has not given a quantitative solution to obscure and incorrect problems, the generalization of gravitational theory has not yet been successfully completed, although former scholars have thought of it and tried to do it. In order to solve the problems, it is necessary to explore the obscure and incorrect problems in a general theory of relativity based on the physical laws and to find out the methodology for solving the problems. Therefore, as the first step toward achieving this purpose, the right solution of the geodesic equation in the Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results have been presented, the obscure and incorrect problems have been shown, and an analysis of them has been made based on the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild, Poincaré

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Authors: Areej Isam Barham

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The implementation of Japanese lesson study approach in the mathematics classroom has been grown worldwide as a model of professional development for teachers. In Qatar, the implementation of IMPULS-QU lesson study program aimed to establish a robust organizational improvement model of professional development for mathematics teachers in Qatar schools. This study describes the implementation of a lesson study model at Al-Markhyia Independent Primary School through different stages; and discusses how the planning process, the research lesson, and the post discussion participates in providing teachers and researchers with a successful research lesson for teacher professional development. The research followed a case study approach in one mathematics classroom. Two teachers and one professional development specialist participated the planning process. One teacher conducted the research lesson study by introducing a problem solving related to the concept of the ‘Mean’ in a mathematics class, 21 students in grade 6 participated in solving the mathematic problem, 11 teachers, 4 professional development specialists, and 4 mathematics professors observed the research lesson. All previous participants except the students participated in a pre and post-lesson discussion within this research. This study followed a qualitative research approach by analyzing the collected data through different stages in the research lesson study. Observation, field notes, and semi-structured interviews conducted to collect data to achieve the research aims. One feature of this lesson study research is that this research describes the implementation for a lesson study as a new experience for one mathematics teacher and 21 students after 3 years of conducting IMPULS-QU project in Al-Markhyia school. The research describes various stages through the implementation of this lesson study model starting from the planning process and ending by the post discussion process. Findings of the study also address the impact of lesson study approach in teaching mathematics for the development of teachers from their point views. Results of the study show the benefits of using lesson study from the point views of participated teachers, theory perceptions about the essential features of lesson study, and their needs for future development. The discussion of the study addresses different features and issues related to the implementation of IMPULS-QU lesson study model in the mathematics classroom. In the light of the study, the research presents recommendations and suggestions for future professional development.

Keywords: lesson study, mathematics education, mathematics teaching experience, teacher professional development

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Authors: Kizito Ugochukwu Nwajeria

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This paper presents a spectral quasi-linearization technique (SQLT) for solving time fractional diffusion wave equations in boundary value problems. The proposed method integrates spectral approximations for spatial derivatives with a quasi-linearization approach to address the nonlinearity introduced by fractional time derivatives. Time fractional differential equations typically formulated using Caputo or Riemann-Liouville derivatives, model complex phenomena such as anomalous diffusion and wave propagation, which are not captured by classical integer-order models. The SQLT method iteratively linearizes the nonlinear terms at each time step, transforming the original problem into a series of linear subproblems, which can be efficiently solved. Using high-order spectral methods such as Chebyshev or Legendre polynomials for spatial discretization, the technique achieves high accuracy in approximating the solution. A convergence analysis is provided, demonstrating the method's efficiency and establishing error bounds. Numerical experiments on a range of test problems confirm the effectiveness of SQLT in solving fractional diffusion wave equations with various boundary conditions. The method offers a robust framework for addressing time fractional differential equations in diverse fields, including materials science, bioengineering, and anomalous transport phenomena.

Keywords: spectral methods, quasilinearization, time-fractional diffusion-wave equations, boundary value problems, fractional calculus

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Authors: Seyedali Seyedkavoosi, Mohammad Obadat, Seantorrion Boyle

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The purpose of this study is to assess the effectiveness of a nontraditional experiential learning strategy in improving the success and interest of mechanical engineering students, using the Kinematics/Dynamics of Machine course as a case study. This upper-division technical course covers a wide range of topics, including mechanism and machine system analysis and synthesis, yet the complexities of ideas like acceleration, motion, and machine component relationships are hard to explain using standard teaching techniques. To solve this problem, a thorough design project was created that gave students hands-on experience developing, manufacturing, and testing their inventions. The main goals of the project were to improve students' grasp of machine design and kinematics, to develop problem-solving and presenting abilities, and to familiarize them with professional software. A questionnaire survey was done to evaluate the effect of this technique on students' performance and interest in mechanical engineering. The outcomes of the study shed light on the usefulness of nontraditional experiential learning approaches in engineering education.

Keywords: experiential learning, nontraditional teaching, hands-on design project, engineering education

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Authors: Divyesh Patel, Tanuja Srivastava

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This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

Keywords: discrete tomography, exactly-1-4-adjacency, simulated annealing, binary matrices

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Authors: Narumol Chintaganun

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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.

Keywords: central differencing scheme, STG, advection equation, burgers equation

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Authors: Abdel-Maksoud Abdel-Kader Soliman

Abstract:

The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

Procedia PDF Downloads 494