Search results for: bouncing ball problem

Authors: Mohammad Farid

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In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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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: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Subhayan Maity

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Complete scenario of cosmic evolution from emergent phase to late time acceleration (i.e. non-singular ever expanding Universe) is a popular preference in the recent cosmology. Yet one can’t exclude the idea that other type of evolution pattern of the Universe may also be possible. Especially, the bouncing scenario is becoming a matter of interest now a days. The present work is an exhibition of such a different pattern of cosmic evolution where the evolution of Universe has been shown as a cyclic thermodynamic process. Under diffusion mechanism (non-equilibrium thermodynamic process), the cosmic evolution has been modelled as [ emergent - accelerated expansion - decelerated expansion - decelerated contraction - accelerated contraction - emergent] .

Keywords: non-equilibrium thermodynamics, non singular evolution of universe, cyclic evolution, diffusive fluid

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second.

Keywords: circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem

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Authors: Kinjal Trivedi, Ramesh V. Upadhyay

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Magnetic fluid as a nanolubricant is a most recent field of study due to its unusual properties that can be tuned by applying a magnetic field. In present work, four ball tester has been used to investigate the tribological properties of the magnetic fluid having a 4 wt% of nanoparticles. The structural characterization of fluid shows crystallite size of particle is 11.7 nm and particles are nearly spherical in nature. The magnetic characterization shows the fluid saturation magnetization is 2.2 kA/m. The magnetic field applied using permanent strip magnet (0 to 1.6 mT) on the faces of the lock nut and fixing a solenoid (0 to 50 mT) around a shaft, such that shaft rotates freely. The magnetic flux line for both the systems analyzed using finite elemental analysis. The coefficient of friction increases with the application of magnetic field using permanent strip magnet compared to zero field value. While for the solenoid, it decreases at 20 mT. The wear scar diameter is lower for 1.1 mT and 20 mT when the magnetic field applied using permanent strip magnet and solenoid, respectively. The coefficient of friction and wear scar reduced by 29 % and 7 % at 20 mT using solenoid. The worn surface analysis carried out using Scanning Electron Microscope and Atomic Force Microscope to understand the wear mechanism. The results are explained on the basis of structure formation in a magnetic fluid upon application of magnetic field. It is concluded that the tribological properties of magnetic fluid depend on magnetic field and its applied direction.

Keywords: four ball tester, magnetic fluid, nanolubricant, tribology

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Authors: G. Mazor, I. Ladizhensky, A. Shapiro, D. Nemirovsky

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A lot of researches was dedicated to the evaluation of the efficiency of the uniform constant and temporary coatings enhancing a heat transfer rate. Our goal is an investigation of the sand coatings distributed by both uniform and non-uniform forms. The sand of different sizes (0.2-0.4-0.6 mm) was attached to a copper ball (30 mm diameter) surface by means of PVA adhesive as a uniform layer. At the next stage, sand spots were distributed over the ball surface with an areal density that ranges between one spot per 1.18 cm² (for low-density spots) and one spot per 0.51 cm² (for high-density spots). The spot's diameter value varied from 3 to 6.5 mm and height from 0.5 to 1.5 mm. All coatings serve as a heat transfer enhancer during the quenching in liquid nitrogen. Highest heat flux densities, achieved during quenching, lie in the range 10.8-20.2 W/cm², depending on the sand layer structure. Application of the enhancing coating increases an amount of heat, evacuated by highly effective nucleate and transition boiling, by a factor of 4.5 as compared to the bare sample. The non-uniform sand coatings were increasing the heat transfer rate value under all pool boiling conditions: nucleate boiling, transfer boiling and the most severe film boiling. A combination of uniform sand coating together with high-density sand spots increased the average heat transfer rate by a factor of 3.

Keywords: heat transfer enhancement, nucleate boiling, film boiling, transfer boiling

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Authors: Noppadon Phumeechanya, Panita Wannapiroon

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The purpose of this research is to design the ubiquitous scaffold learning environment using problem-based learning activities that enhance problem-solving skills and context awareness, and to evaluate the suitability of the ubiquitous scaffold learning environment using problem-based learning activities. We divide the research procedures into two phases. The first phase is to design the ubiquitous scaffold learning environment using problem-based learning activities, and the second is to evaluate the ubiquitous scaffold learning environment using problem-based learning activities. The sample group in this study consists of five experts selected using the purposive sampling method. We analyse data by arithmetic mean and standard deviation. The research findings are as follows; the ubiquitous scaffold learning environment using problem-based learning activities consists of three major steps, the first is preparation before learning. This prepares learners to acknowledge details and learn through u-LMS. The second is the learning process, where learning activities happen in the ubiquitous learning environment and learners learn online with scaffold systems for each step of problem solving. The third step is measurement and evaluation. The experts agree that the ubiquitous scaffold learning environment using problem-based learning activities is highly appropriate.

Keywords: ubiquitous learning environment scaffolding, learning activities, problem-based learning, problem-solving skills, context awareness

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Authors: Kamariah Abu Bakar, Jennifer Way

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This study investigated how young children (six years old) constructed and used representations in mathematics classroom; particularly in problem solving. The purpose of this study is to explore the ways children used representations in solving addition problems and to determine whether their representations can play a supportive role in understanding the problem situation and solving them correctly. Data collection includes observations, children’s artifact, photographs and conversation with children during task completion. The results revealed that children were able to construct and use various representations in solving problems. However, they have certain preferences in generating representations to support their problem solving.

Keywords: young children, representations, addition, problem solving

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Authors: Liudmyla Koliechkina, Olena Dvirna

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The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: discrete set, linear combinatorial optimization, multi-objective optimization, Pareto solutions, partial permutation set, structural graph

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Authors: Rafał Kamiński, Joel Rech, Philippe Bertrand, Christophe Desrayaud

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Titanium alloys are among the most important material in the aircraft industry, due to its low density, high strength, and corrosion resistance. However, these alloys are considered as difficult to machine because they have poor thermal properties and high reactivity with cutting tools. The Selective Laser Melting (SLM) process becomes even more popular through industry since it enables the design of new complex components, that cannot be manufactured by standard processes. However, the high temperature reached during the melting phase as well as the several rapid heating and cooling phases, due to the movement of the laser, induce complex microstructures. These microstructures differ from conventional equiaxed ones obtained by casting+forging. Parts obtained by SLM have to be machined in order calibrate the dimensions and the surface roughness of functional surfaces. The ball milling technique is widely applied to finish complex shapes. However, the machinability of titanium is strongly influenced by the microstructure. So the objective of this work is to investigate the influence of the SLM process, i.e. microstructure, on the machinability of titanium, compared to conventional forming processes. The machinability is analyzed by measuring surface roughness, cutting forces, cutting tool wear for a range of cutting conditions (depth of cut ap, feed per tooth fz, spindle speed N) in accordance with industrial practices.

Keywords: ball milling, microstructure, surface roughness, titanium

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Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

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In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: auxiliary variable, dynamic programming technique, nonlinear programming problem, optimum stratification, uniform distribution

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Authors: Guilherme Baldo Carlos

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The flexible job-shop scheduling problem (FJSP) is an NP-hard combinatorial optimization problem, which can be applied to model several applications in a wide array of industries. This problem will have its importance increase due to the shift in the production mode that modern society is going through. The demands are increasing and for products personalized and customized. This work aims to apply a meta-heuristic called a genetic algorithm (GA) to solve this problem. A GA is a meta-heuristic inspired by the natural selection of Charles Darwin; it produces a population of individuals (solutions) and selects, mutates, and mates the individuals through generations in order to find a good solution for the problem. The results found indicate that the GA is suitable for FJSP solving.

Keywords: genetic algorithm, evolutionary algorithm, scheduling, flexible job-shop scheduling

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Authors: Laissa Mae Francisco, John Rolex Ingreso, Anna Krizel Menguito, Criselda Robrigado, Rej Maegan Tuazon

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This study aims to determine and describe the existing relationship between number sense proficiency and problem-solving performance of grade seven students from Victorino Mapa High School, Manila. A paper pencil exam containing of 50-item number sense test and 5-item problem-solving test which measures their number sense proficiency and problem-solving performance adapted from McIntosh, Reys, and Bana were used as the research instruments. The data obtained from this study were interpreted and analyzed using the Pearson – Product Moment Coefficient of Correlation to determine the relationship between the two variables. It was found out that students who were low in number sense proficiency tend to be the students with poor problem-solving performance and students with medium number sense proficiency are most likely to have an average problem-solving performance. Likewise, students with high number sense proficiency are those who do excellently in problem-solving performance.

Keywords: number sense, performance, problem solving, proficiency

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Authors: Pei Chin Lim

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School of Mathematics and Science of Singapore Polytechnic offers a Basic Mathematics module to students who did not pass GCE O-Level Additional Mathematics. These students are weaker in Mathematics. In particular, they struggle with word problems and tend to leave them blank in tests and examinations. In order to improve students’ problem-solving skills, the school redesigned the Basic Mathematics module to incorporate Polya’s problem-solving methodology. During tutorial lessons, students have to work through learning activities designed to raise their metacognitive awareness by following Polya’s problem-solving process. To assess the effectiveness of the redesign, students’ working for a challenging word problem in the mid-semester test were analyzed. Sixty-five percent of students attempted to understand the problem by making sketches. Twenty-eight percent of students went on to devise a plan and implement it. Only five percent of the students still left the question blank. These preliminary results suggest that with regular exposure to an explicit and systematic problem-solving approach, weak students’ problem-solving skills can potentially be improved.

Keywords: mathematics education, metacognition, problem solving, weak students

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Authors: Ahmad Alazemi, M. Sherif El-Eskandrany, Mohamad Kishk, Thanyan AlOnaizi, Ahmad Alduweesh, Shorouq Abdullaleel

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Arc melting technique followed by top-down approach, using a high-energy ball milling technique were employed to synthesize nanocrystalline of Cu50(Zr50-xNix)50 (x = 0, 10, 20 and 30 at.%) powder particles. The end-products of the alloy powders obtained after 50 h of the ball milling time were uniform in composition and had spherical-like morphology with an average particle size of 0.75 µm in diameter. The powders, which consisted of nanocrystalline grains with an average grain size of 10 nm in diameter, were used as feedstock materials for double face coating of stainless (SUS304) sheets, using cold spraying process. The coating materials enjoyed nanocrystalline structure and uniform composition. Biofilms were grown on 20-mm2 SUS304 sheets coated coupons inoculated with 1.5 × 108 CFU ml−1 E. coli. Significant biofilm inhibition was recorded in the nanoparticles coated coupons in comparison to non-coated SUS304 coupon. In conclusion, this study demonstrates that formation of biofilms can be significantly inhibited by Cu-based alloys especially in case of high (Ni) content. The inhibition of biofilm formation by nanocrystalline powders of Cu-based provides a practical approach to achieve the inhibition of biofilms formed by an emerging pathogen.

Keywords: biofilm, Cu, E.coli, FE-HRTEM/EDS, nanomaterials, nanocrystalline

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Authors: Derkaoui Orkia, Lehireche Ahmed

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The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time.

Keywords: semidefinite programming, maximum clique problem, primal-dual interior point method, relaxation

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Authors: Mehmet Hakan Karaata

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In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring.

Keywords: algorithm, cycle, graph algorithm, graph theory, network structuring

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Authors: Hashini E. Mohottala

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We report the combine use of Wikispaces (WikiS) and Group Problem Solving (GPS) sessions conducted in the introductory level physics classes. As a part of this new teaching tool, some essay type problems were posted on the WikiS in weekly basis and students were encouraged to participate in problem solving without providing numerical final answers but the steps. Wikispace is used as a platform for students to meet online and create discussions. Each week students were further evaluated on problem solving skills opening up more opportunity for peer interaction through GPS. Each group was given a different problem to solve and the answers were graded. Students developed a set of skills in decision-making, problem solving, communication, negotiation, critical and independent thinking and teamwork through the combination of WikiS and GPS.

Keywords: group problem solving (GPS), wikispace (WikiS), physics education, learning

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Authors: Sourabh Joshi, Tarun Sharma, Anurag Sharma

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Ant Colony Optimization is heuristic Algorithm which has been proven a successful technique applied on number of combinatorial optimization problems. Two variants of Ant Colony Optimization algorithm named Ant System and Max-Min Ant System are implemented in MATLAB to solve travelling Salesman Problem and the results are compared. In, this paper both systems are analyzed by solving the some Travelling Salesman Problem and depict which system solve the problem better in term of cost and time.

Keywords: Ant Colony Optimization, Travelling Salesman Problem, Ant System, Max-Min Ant System

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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: 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: Akhentoolove Corbin, Leta De Jonge, Charmaine De Jonge

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Introduction: Various writers have promoted the adoption of the 4th R in the education curricula (relationships, respect, reasoning, religion, computing, science, art, conflict management, music) and the 5th R (responsibility). They argue that the traditional 3 Rs are not adequate for the modern environment and the requirements for students to become functional citizens in society. In particular, the developing countries of the anglophone Caribbean (most of which are tiny islands) are susceptible to the dangers and complexities of climate change and global economic volatility. These proposed additions to the 3Rs do have some justification, but this research considers Resilience as even more important and relevant in a world that is faced with the negative prospects of climate change, poverty, discrimination, and economic volatility. It is argued that the foundation for resilient citizens, workers, and workplaces, must be built in the elementary and secondary/middle schools and then through the tertiary level, to achieve an outcome of more resilient students. Government, business, and society require widespread resilience to be capable of ‘bouncing back’ and be more adaptable, transformational, and sustainable. Methodology: The paper utilises a mixed-methods approach incorporating a questionnaire and interviews to determine participants’ opinions on the importance and relevance of resilience in the schools’ curricula and to government, business, and society. The target groups are as follows: educators at all levels, education administrators, members of the business sector, public sector, and 3rd sector. The research specifically targets the anglophone Caribbean developing countries (Barbados, Guyana, Jamaica, Trinidad, St. Lucia, and St Vincent, and the Grenadines). The research utilises SPSS for data analysis. Major Findings: The preliminary findings suggest that the majority of participants support the adoption of resilience as a 4th R in the curricula of the elementary, secondary/middle schools, and tertiary level in the anglophone Caribbean. The final results will allow the researchers to reveal more specific details on any variations among the islands in the sample andto engage in an in-depth discussion of the relevance and importance of resilience as the 4th R. Conclusion: Results seem to suggest that the education system should adopt the 4th R of resilience so that educators working in collaboration with the family and community/village can develop young citizens who are more resilient and capable of manifesting the behaviours and attitudes associated with ‘bouncing back,’ adaptability, transformation, and sustainability. These findings may be useful for education decision-makers and governments in these Caribbean islands, who have the authority and responsibility for the development of education policy, laws, and regulations.

Keywords: education, resilient students, adaptable, transformational, resilient citizens, workplaces, government

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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: Jay Gohel, Anant Parghi

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A tuned liquid column damper (TLCD) is a modified passive system of tuned mass damper, where a liquid is used in place of mass in the structure. A TLCD consists of U-shaped tube with an orifice that produces damping against the liquid motion in the tube. This paper provides a state-of-the-art review on the vibration control of wind and earthquake excited structures using liquid dampers. Further, the paper will also discuss the theoretical background of TCLD, history of liquid dampers and existing literature on experimental, numerical, and analytical study. The review will also include different configuration of TLCD viz single TLCD, multi tuned liquid column damper (MTLCD), TLCD-Interior (TLCDI), tuned liquid column ball damper (TLCBD), tuned liquid column ball gas damper (TLCBGD), and pendulum liquid column damper (PLCD). The dynamic characteristics of the different configurate TLCD system and their effectiveness in reducing the vibration of structure will be discussed. The effectiveness of semi-active TLCD will be also discussed with reference to experimental and analytical results. In addition, the review will also provide the numerous examples of implemented TLCD to control the vibration in real structures. Based on the comprehensive review of literature, some important conclusions will be made and the need for future research will be identified for vibration control of structures using TLCD.

Keywords: earthquake, wind, tuned liquid column damper, passive response control, structures

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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: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: Mohsen Ziaee

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Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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