Journal articles: 'Strategies to solve geometric problems'

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Eker, Barış, and H. Levent Akın. "Using evolution strategies to solve DEC-POMDP problems." Soft Computing 14, no. 1 (December 9, 2008): 35–47. http://dx.doi.org/10.1007/s00500-008-0388-7.

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Lin, Ming Hua, and Jung Fa Tsai. "Optimal Design of a Speed Reducer." Applied Mechanics and Materials 376 (August 2013): 327–30. http://dx.doi.org/10.4028/www.scientific.net/amm.376.327.

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The mathematical model for optimal design of a speed reducer is a generalized geometric programming problem that is non-convex and not easy be globally solved. This paper applies a deterministic approach including convexification strategies and piecewise linearization techniques to globally solve speed reducer design problems. A practical speed reducer design problem is solved to demonstrate that this study obtains a better solution than other methods.

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Pangastuti, Ratna. "Media Puzzle untuk Mengenal Bentuk Geometri." JECED : Journal of Early Childhood Education and Development 1, no. 1 (December 27, 2019): 50–59. http://dx.doi.org/10.15642/jeced.v1i1.496.

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Learning media are all things that can be used to channel learning materials so that they can stimulate the attention, interests, thoughts and feelings of students (students) in learning activities to achieve certain learning goals. Learning media is a tool or other material that provides a complete form of information and can support the teaching and learning process. Learning in the introduction of geometric shapes in early childhood really requires appropriate learning strategies and media, so to maximize the child's ability to introduce geometric shapes can use puzzle media. Compiling geometric shapes puzzles can improve cognitive for children. Cognitive skills (cognitive skills) associated with the ability to learn and solve problems in children. Moreover, it can improve social skills for children. By using the content analysis method and the study documentation, this research tries to describe the puzzle media to introduce geometric shapes to early childhood

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Kochikov, Igor V., Svetlana A. Sharapova, Anatoly G. Yagola, and Alexander V. Tikhonravov. "Correlation of errors in inverse problems of optical coatings monitoring." Journal of Inverse and Ill-posed Problems 28, no. 6 (December 1, 2020): 915–21. http://dx.doi.org/10.1515/jiip-2020-0079.

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AbstractOn-line optical monitoring of multilayer coating production requires solving inverse identification problems of determining the thicknesses of coating layers. Regardless of the algorithm used to solve inverse problems, the errors in the thicknesses of the deposited layers are correlated by the monitoring procedure. Studying the correlation of thickness errors is important for the production of the most complex optical coatings. We develop a general geometric approach to study this correlation. It is based on a statistical analysis of large numbers of error vectors obtained during computational experiments on optical coating production. The application of the proposed approach is demonstrated using computational manufacturing experiments on the production of a 50-layer filter with four different monitoring strategies. A special coefficient is introduced to evaluate the strength of the error correlation effect. The results obtained confirm that the introduced parameter can be used as a measure of the strength of the correlation effect in practical applications.

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Yang, Feng Wei, Chandrasekhar Venkataraman, Vanessa Styles, and Anotida Madzvamuse. "A Robust and Efficient Adaptive Multigrid Solver for the Optimal Control of Phase Field Formulations of Geometric Evolution Laws." Communications in Computational Physics 21, no. 1 (December 5, 2016): 65–92. http://dx.doi.org/10.4208/cicp.240715.080716a.

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AbstractWe propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution laws. The optimal control of geometric evolution laws arises in a number of applications in fields including material science, image processing, tumour growth and cell motility. Despite this, many open problems remain in the analysis and approximation of such problems. In the current work we focus on a phase field formulation of the optimal control problem, hence exploiting the well developed mathematical theory for the optimal control of semilinear parabolic partial differential equations. Approximation of the resulting optimal control problemis computationally challenging, requiring massive amounts of computational time and memory storage. The main focus of this work is to propose, derive, implement and test an efficient solution method for such problems. The solver for the discretised partial differential equations is based upon a geometric multigrid method incorporating advanced techniques to deal with the nonlinearities in the problem and utilising adaptive mesh refinement. An in-house two-grid solution strategy for the forward and adjoint problems, that significantly reduces memory requirements and CPU time, is proposed and investigated computationally. Furthermore, parallelisation as well as an adaptive-step gradient update for the control are employed to further improve efficiency. Along with a detailed description of our proposed solution method together with its implementation we present a number of computational results that demonstrate and evaluate our algorithms with respect to accuracy and efficiency. A highlight of the present work is simulation results on the optimal control of phase field formulations of geometric evolution laws in 3-D which would be computationally infeasible without the solution strategies proposed in the present work.

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Evidiasari, Serli, Subanji Subanji, and Santi Irawati. "Students’ Spatial Reasoning in Solving Geometrical Transformation Problems." Indonesian Journal on Learning and Advanced Education (IJOLAE) 1, no. 2 (August 29, 2019): 38–51. http://dx.doi.org/10.23917/ijolae.v1i2.8703.

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This study describes spatial reasoning of senior high school students in solving geometrical transformation problems. Spatial reasoning consists of three aspects: spatial visualization, mental rotation, and spatial orientation. The approach that is used in this study is descriptive qualitative. Data resource is the test result of reflection, translation, and rotation problems then continued by interview. Collecting data process involves 35 students. They are grouped to three spatial reasoning aspects then selected one respondent to be the most dominant of each aspect. The results of this study are: (1) the students with spatial visualization aspect used drawing strategy and non-spatial strategy in solving geometrical transformation problems. She transformed every vertex of the object and drew assistance lines which connect every vertex of the object to center point; (2) the students with mental rotation aspect used holistic and analytic strategies in solving geometrical transformation problems. Using holistic strategy means imagining the whole of transformational objects to solve easy problems. While using analytic strategy means transforming some components of objects to solve hard problems; (3) the students with spatial orientation didn’t involve mental imagery and she only could determine the position and orientation of the object in solving geometrical transformation problems

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Rufai, Mufutau Ajani, and Higinio Ramos. "Numerical Solution for Singular Boundary Value Problems Using a Pair of Hybrid Nyström Techniques." Axioms 10, no. 3 (August 25, 2021): 202. http://dx.doi.org/10.3390/axioms10030202.

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This manuscript presents an efficient pair of hybrid Nyström techniques to solve second-order Lane–Emden singular boundary value problems directly. One of the proposed strategies uses three off-step points. The obtained formulas are paired with an appropriate set of formulas implemented for the first step to avoid singularity at the left end of the integration interval. The fundamental properties of the proposed scheme are analyzed. Some test problems, including chemical kinetics and physical model problems, are solved numerically to determine the efficiency and validity of the proposed approach.

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Xu, Xinlin, Zhongbo Hu, Qinghua Su, and Zenggang Xiong. "Multiobjective Collective Decision Optimization Algorithm for Economic Emission Dispatch Problem." Complexity 2018 (November 13, 2018): 1–20. http://dx.doi.org/10.1155/2018/1027193.

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The collective decision optimization algorithm (CDOA) is a new stochastic population-based evolutionary algorithm which simulates the decision behavior of human. In this paper, a multiobjective collective decision optimization algorithm (MOCDOA) is first proposed to solve the environmental/economic dispatch (EED) problem. MOCDOA uses three novel learning strategies, that is, a leader-updating strategy based on the maximum distance of each solution in an external archive, a wise random perturbation strategy based on the sparse mark around a leader, and a geometric center-updating strategy based on an extreme point. The proposed three learning strategies benefit the improvement of the uniformity and the diversity of Pareto optimal solutions. Several experiments have been carried out on the IEEE 30-bus 6-unit test system and 10-unit test system to investigate the performance of MOCDOA. In terms of extreme solutions, compromise solution, and three metrics (SP, HV, and CM), MOCDOA is compared with other existing multiobjective optimization algorithms. It is demonstrated that MOCDOA can generate the well-distributed and the high-quality Pareto optimal solutions for the EED problem and has the potential to solve the multiobjective optimization problems of other power systems.

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Ma, Chaoqun, Hui Wu, and Xiang Lin. "Nonzero-Sum Stochastic Differential Portfolio Games under a Markovian Regime Switching Model." Mathematical Problems in Engineering 2015 (2015): 1–18. http://dx.doi.org/10.1155/2015/738181.

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We consider a nonzero-sum stochastic differential portfolio game problem in a continuous-time Markov regime switching environment when the price dynamics of the risky assets are governed by a Markov-modulated geometric Brownian motion (GBM). The market parameters, including the bank interest rate and the appreciation and volatility rates of the risky assets, switch over time according to a continuous-time Markov chain. We formulate the nonzero-sum stochastic differential portfolio game problem as two utility maximization problems of the sum process between two investors’ terminal wealth. We derive a pair of regime switching Hamilton-Jacobi-Bellman (HJB) equations and two systems of coupled HJB equations at different regimes. We obtain explicit optimal portfolio strategies and Feynman-Kac representations of the two value functions. Furthermore, we solve the system of coupled HJB equations explicitly in a special case where there are only two states in the Markov chain. Finally we provide comparative statics and numerical simulation analysis of optimal portfolio strategies and investigate the impact of regime switching on optimal portfolio strategies.

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Qiao, H., B. S. Dalay, and R. M. Parkin. "Fine Motion Strategies for Robotic Peg-Hole Insertion." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 209, no. 6 (November 1995): 429–48. http://dx.doi.org/10.1243/pime_proc_1995_209_173_02.

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The robotic assembly operation has a prominent role in industry due to the fact that (a) it accounts for a substantial proportion of production cycle times and (b) it requires high precision. The peg-hole insertion operation, which is a simplified industrial application model, has special prominence. In terms of the hardware, various complex six-component force sensors, passive compliance and vibration systems have been designed for this purpose alone. In the control area, the disturbance filter and real-time control have been applied to the system to enhance performance. Techniques using geometric concepts such as pre-images and back-projections, models of the contact configurations, pattern recognition and fine motion analysis have been studied. The objective of this paper is to illustrate a method that combines these ideas together to solve practical problems. In this paper: 1. General contact configurations and contact motions between the peg and hole are presented. 2. An important problem in the identification of the contact configuration according to the force sensors is studied. It is concluded that the complete identification of the contact configuration should depend not only on the signals from the force sensors but also on the knowledge about the range of the initial state of the peg and clever utilization of the environment. 3. Various strategies with and without force sensors are proposed. Motion and model analysis is used to study the general identification and motion problems in the peg-hole insertion system. Pre-image and back-projection concepts are employed to enable practical implementation of the method which used Petri nets. Selecting the configuration parameters that can be (a) easily measured and (b) used to decide the incremental motion steps through the procedure were found to be complex and critical tasks that enabled success. These strategies have been verified through experimental trials. It is apparent that the fine motion strategy has a wide application in the robotic peg-hole insertion operation.

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Abu-Dakka, Fares J., Bojan Nemec, Aljaž Kramberger, Anders Glent Buch, Norbert Krüger, and Ales Ude. "Solving peg-in-hole tasks by human demonstration and exception strategies." Industrial Robot: An International Journal 41, no. 6 (October 20, 2014): 575–84. http://dx.doi.org/10.1108/ir-07-2014-0363.

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Purpose – The purpose of this paper is to propose a new algorithm based on programming by demonstration and exception strategies to solve assembly tasks such as peg-in-hole. Design/methodology/approach – Data describing the demonstrated tasks are obtained by kinesthetic guiding. The demonstrated trajectories are transferred to new robot workspaces using three-dimensional (3D) vision. Noise introduced by vision when transferring the task to a new configuration could cause the execution to fail, but such problems are resolved through exception strategies. Findings – This paper demonstrated that the proposed approach combined with exception strategies outperforms traditional approaches for robot-based assembly. Experimental evaluation was carried out on Cranfield Benchmark, which constitutes a standardized assembly task in robotics. This paper also performed statistical evaluation based on experiments carried out on two different robotic platforms. Practical implications – The developed framework can have an important impact for robot assembly processes, which are among the most important applications of industrial robots. Our future plans involve implementation of our framework in a commercially available robot controller. Originality/value – This paper proposes a new approach to the robot assembly based on the Learning by Demonstration (LbD) paradigm. The proposed framework enables to quickly program new assembly tasks without the need for detailed analysis of the geometric and dynamic characteristics of workpieces involved in the assembly task. The algorithm provides an effective disturbance rejection, improved stability and increased overall performance. The proposed exception strategies increase the success rate of the algorithm when the task is transferred to new areas of the workspace, where it is necessary to deal with vision noise and altered dynamic characteristics of the task.

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Páez Rolóna, Sergio Andrés. "Fortalecimiento de la competencia matemática resolución de problemas en educación básica secundaria, mediante el aprendizaje basado en problemas (ABP)." ECOMATEMATICO 8, no. 1 (January 1, 2017): 25–33. http://dx.doi.org/10.22463/17948231.1472.

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Resumen: En la enseñanza de las matemáticas es indispensable la implementación de estrategias que permitan ligar al estudiante con su contexto inmediato, a fin de que pueda desarrollar en forma significativa su aprendizaje. La presente investigación se desarrolla con base en la metodología Aprendizaje Basado en Problemas (ABP), con el objetivo de analizar de qué manera influye en el fortalecimiento de la competencia matemática resolución de problemas. Llevado a cabo bajo un enfoque cuantitativo y un diseño pre-experimental, se realizó un análisis descriptivo de la habilidad de los estudiantes para resolver problemas previos a la metodología, luego, se compararon los resultados tanto individual como grupal obtenidos en el test y el post test; y con base en estos, se determinó en qué aspectos dicha metodología fortalece la competencia de resolución de problemas en estudiantes de educación básica secundaria. Los resultados permitieron concluir que se pudo fortalecer la competencia de resolución de problemas en el área de matemáticas, en el grado noveno, viéndose reflejado en el mejoramiento de las habilidades de los estudiantes para resolver problemas sobre área y volúmenes en figuras geométricas fundamentales. Lo anterior evidenciado en los resultados del post test, esto sirve como base para que los estudiantes le den sentido a los nuevos conocimientos, promoviendo la indagación en contextos reales, facilitando el aprendizaje significativo y generando cambios en el nivel de razonamiento.Palabras clave Competencia Matemática, Metodología Aprendizaje Basado en Problemas, Resolución de problemasAbstract: In mathematics teaching, the implementation of strategies which permit the student to link to his immediate context is indispensable, aiming to be able to develop, in a meaningful way, his learning process. This research is developed based on Learning Based on Problems methodology (LBP), taking as an objective to analyze how it influences on the strengthening of the mathematics competence problem solving. Carried out in a quantitative approach and pre-experimental design, a descriptive analysis of the ability of the students to solve problems was done before the methodology, then, the results were compared both individually and collectively gathered in the test and post-test; and based on this, it was determined on what aspects this methodology strengthen problem solving competence in high school students. The results were to conclude that the problem-solving competence in the area of mathematics could be strengthened, in the ninth grade, being reflected in the improvement of students’ abilities to solve problems in the area and in fundamental geometric figures. The above evidenced in the results of the post test, this serves as taken as a base so that the students can find new knowledge more interesting, promoting the investigation in real contexts, making the meaningful learning easier and generating changes in the reasoning level.Keywords Mathematics Competence, Methodology, Learning Based on Problems, Problem Solving.

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Xia, Yuying, and M. Friswell. "Efficient solution of the fuzzy eigenvalue problem in structural dynamics." Engineering Computations 31, no. 5 (July 1, 2014): 864–78. http://dx.doi.org/10.1108/ec-02-2013-0052.

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Purpose – Many analysis and design problems in engineering and science involve uncertainty to varying degrees. This paper is concerned with the structural vibration problem involving uncertain material or geometric parameters, specified as fuzzy parameters. The requirement is to propagate the parameter uncertainty to the eigenvalues of the structure, specified as fuzzy eigenvalues. However, the usual approach is to transform the fuzzy problem into several interval eigenvalue problems by using the α-cuts method. Solving the interval problem as a generalized interval eigenvalue problem in interval mathematics will produce conservative bounds on the eigenvalues. The purpose of this paper is to investigate strategies to efficiently solve the fuzzy eigenvalue problem. Design/methodology/approach – Based on the fundamental perturbation principle and vertex theory, an efficient perturbation method is proposed, that gives the exact extrema of the first-order deviation of the structural eigenvalue. The fuzzy eigenvalue approach has also been improved by reusing the interval analysis results from previous α-cuts. Findings – The proposed method was demonstrated on a simple cantilever beam with a pinned support, and produced very accurate fuzzy eigenvalues. The approach was also demonstrated on the model of a highway bridge with a large number of degrees of freedom. Originality/value – This proposed Vertex-Perturbation method is more efficient than the standard perturbation method, and more general than interval arithmetic methods requiring the non-negative decomposition of the mass and stiffness matrices. The new increment method produces highly accurate solutions, even when the membership function for the fuzzy eigenvalues is complex.

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Chiurazzi, Marcello, Alessandro Diodato, Irene Vetrò, Joan Ortega Alcaide, Arianna Menciassi, and Gastone Ciuti. "Intrinsically Distributed Probabilistic Algorithm for Human–Robot Distance Computation in Collision Avoidance Strategies." Electronics 9, no. 4 (March 25, 2020): 548. http://dx.doi.org/10.3390/electronics9040548.

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Humans and robots are becoming co-workers, both in industrial and medical applications. This new paradigm raises problems related to human safety. To accomplish and solve this issue, many researchers have developed collision avoidance strategies—mainly relying on potential field approaches—in which attractive and repulsive virtual forces are generated between manipulators and objects within a collaborative workspace. The magnitude of such virtual forces strongly depends on the relative distance between the manipulators and the approaching agents, as well on their relative velocity. In this paper, authors developed an intrinsically distributed probabilistic algorithm to compute distances between the manipulator surfaces and humans, allowing tuning the computational time versus estimation accuracy, based on the application requirements. At each iteration, the algorithm computes the human–robot distances, considering all the Cartesian points within a specific geometrical domain, built around humans’ kinematic chain, and selecting a random subset of points outside of it. Experimental validation was performed in a dynamic and unstructured condition to assess the performance of the algorithm, simulating up to six humans into the shared workspace. Tests showed that the algorithm, with the selected hardware, is able to estimate the distance between the human and the manipulator with a RMSE of 5.93 mm (maximum error of 34.86 mm).

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Pandiscio, Eric A. "Using Proportional Reasoning to Solve Geometric Problems." Mathematics Teacher 98, no. 1 (August 2004): 16–19. http://dx.doi.org/10.5951/mt.98.1.0016.

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The proportional nature of geometric work, and the ways in which proportional reasoning can be employed as a generalized problem–solving tool. A geometric construction is presented for students to solve. The author gives reasoning via proof and proportions and provides extension activities.

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Imanah, Ulil Nurul. "KEMAMPUAN MAHASISWA CALON GURU MATEMATIKA DALAM MENYELESAIKAN SOAL OLIMPIADE MATEMATIKA PADA MATERI ALJABAR DAN GEOMETRI." Journal of Mathematics Education and Science 4, no. 1 (April 30, 2021): 37–40. http://dx.doi.org/10.32665/james.v4i1.177.

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This study aims to determine the ability of pre-service mathematics teachers to solve mathematics olympiad questions on algebra and geometry. This research is quantitative descriptive. The research subjects were mathematics education students at the Faculty of Teacher Training and Education at Majapahit Islamic University in semester V of the 2020-2021 academic year who had completed Mathematical Problem-Solving courses. The subjects that study mathematical problem-solving strategies and deepen elementary and secondary mathematics olympiad problems. The research subjects were 14 people. The instrument used was four questions at the high school level mathematics olympiad, consisting of 2 questions about algebra and two questions about geometry. Based on the results of the study, it was concluded that the ability of pre-service mathematics teachers in the Mathematics Education Study Program of the Faculty of Teacher Training and Education, Majapahit Islamic University in solving math Olympiad questions on algebra and geometry was in the sufficient category with an average score of 57.68 Abstrak Penelitian ini bertujuan untuk mengetahui kemampuan mahasiswa calon guru matematika dalam menyelesaikan soal olimpiade matematika pada materi aljabar dan geometri. Penelitian ini merupakan penelitian deskriptif kuantitatif. Subyek penelitian adalah mahasiswa pendidikan matematika Fakultas Keguruan dan Ilmu Pendidikan Universitas Islam Majapahit semester V tahun akademik 2020-2021 yang telah menyelesaikan perkuliahan Pemecahan Masalah Matematika, yaitu mata kuliah yang mempelajari tentang strategi pemecahan masalah matematika dan mendalami soal-soal olimpiade matematika tingkat dasar dan menengah. Subyek penelitian berjumlah 14 orang. Instrumen yang digunakan adalah 4 soal olimpiade matematika tingkat sekolah menengah, yang terdiri dari 2 soal materi aljabar dan 2 soal materi geometri. Berdasarkan hasil penelitian diperoleh simpulan bahwa kemampuan mahasiswa calon guru matematika di Prodi Pendidikan Matematika FKIP Universitas Islam Majapahit dalam menyelesaikan soal olimpiade matematika pada materi aljabar dan geometri berada pada kategori cukup dengan nilai rata-rata 57,68.

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ATALLAH, MIKHAIL J., PAUL B. CALLAHAN, and MICHAEL T. GOODRICH. "P-COMPLETE GEOMETRIC PROBLEMS." International Journal of Computational Geometry & Applications 03, no. 04 (December 1993): 443–62. http://dx.doi.org/10.1142/s0218195993000282.

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In this paper we show that it is impossible to solve a number of “natural” two-dimensional geometric problems in polylog time with a polynomial number of processors (unless P=NC). Thus, we disprove a popular belief that there are no natural P-complete geometric problems in the plane. The problems we address include instances of polygon triangulation, planar partitioning, and geometric layering. Our results are based on non-trivial reductions from the monotone circuit value and planar circuit value problems.

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Ehrgott, Matthias, Horst W. Hamacher, and Stefan Nickel. "Geometric methods to solve max-ordering location problems." Discrete Applied Mathematics 93, no. 1 (April 1999): 3–20. http://dx.doi.org/10.1016/s0166-218x(99)00005-0.

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Martin, Tami. "Calculus students’ ability to solve geometric related-rates problems." Mathematics Education Research Journal 12, no. 2 (September 2000): 74–91. http://dx.doi.org/10.1007/bf03217077.

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Magnani, Lorenzo. "Thinking through drawing." Knowledge Engineering Review 28, no. 3 (July 30, 2013): 303–26. http://dx.doi.org/10.1017/s026988891300026x.

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AbstractThe concept ofmanipulative abductionis devoted to capture the role of action in many interesting cognitive situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. We observe that many external things, usually inert from an epistemological point of view, can be transformed intoepistemic mediators. I will present some details derived from the history of the discovery of the non-Euclidean geometries that illustrate the relationships between strategies for anomaly resolution and visual thinking. Geometrical diagrams are external representations that play both amirrorrole (to externalize rough mental models) and anunveilingrole (as gateways to imaginary entities). I describe them as epistemic mediators able to perform various explanatory, non-explanatory, and instrumental abductive tasks (discovery of new properties or new propositions/hypotheses, provision of suitable sequences of models as able to convincingly verifying theorems, etc.). I am also convinced that they can be exploited and studied in everyday non-mathematical applications also to the aim of promoting new trends in artificial intelligence modeling of various aspects of hypothetical reasoning: finding routes, road signs, buildings maps, for example, in connection with various zooming effects of spatial reasoning. I also think that the cognitive activities of optical, mirror, and unveiling diagrams can be studied in other areas of manipulative and model-based reasoning, such as the ones involving creative, analogical, and spatial inferences, both in science and everyday situations so that this can extend the epistemological, computational, and the psychological theory.

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Filippini, Mattia, and Piergiorgio Alotto. "An optimization tool for coaxial magnetic gears." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 5 (September 4, 2017): 1526–39. http://dx.doi.org/10.1108/compel-02-2017-0068.

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Purpose This paper aims to show a complete optimization tool that can be used for the design of coaxial magnetic gears. In the first part, the paper deals with the semi-analytic modelling of these machines and also discusses how to reduce the computational efforts. In the second part, an optimization algorithm is adopted for finding the Pareto optimal geometries. Design/methodology/approach The machine is subdivided into a set of domains according to their physical and geometrical properties, and the potential distribution is found semi-analytically in them under some simplifying hypothesis. A loss estimation is performed for both ferromagnetic and permanent magnet regions. A stochastic differential evolution (DE) algorithm for multi-objective constrained problems is then applied. Findings It is shown that the presented design tool gives results in accordance to finite element method (FEM)-based analysis keeping the advantages of robustness and simplicity of the analytical methods. The DE-based strategy performs well on the magnetic gear optimization problem. Practical implications The proposed tool appears to be a good starting point when designing coaxial magnetic gears. The optimal Pareto points can be used as initial seeds of FEM-based optimizations, resulting in a cheaper computational method with respect to a full FEM optimization. Originality/value This paper takes inspiration from recent works on magnetic gear modelling and completes the design procedure with a suitable efficiency estimation. The paper also shows how to use mature optimization strategies to solve the constrained multi-objective magnetic gear design problem.

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Sinn, Robb, Dianna J. Spence, and Margaret Poitevint. "Mathematical Exploration: A Geometric Approach to Solving Rate Problems." Mathematics Teaching in the Middle School 16, no. 5 (December 2010): 302–7. http://dx.doi.org/10.5951/mtms.16.5.0302.

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The proportional reasoning required to solve rate problems can cause difficulty for many students. However, understanding how to solve problems of this type is vital as students transition from arithmetic to algebra. A guided-discovery approach to modeling these problems using pattern blocks can help students appreciate the quantities involved and the relationships between them.

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Melissaratos, Elefterios A., and Diane L. Souvaine. "Shortest Paths Help Solve Geometric Optimization Problems in Planar Regions." SIAM Journal on Computing 21, no. 4 (August 1992): 601–38. http://dx.doi.org/10.1137/0221038.

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Biswal, M. P. "Fuzzy programming technique to solve multi-objective geometric programming problems." Fuzzy Sets and Systems 51, no. 1 (October 1992): 67–71. http://dx.doi.org/10.1016/0165-0114(92)90076-g.

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BERZINS, A. "GEOMETRIC EQUIVALENCE OF ALGEBRAS." International Journal of Algebra and Computation 11, no. 04 (August 2001): 447–56. http://dx.doi.org/10.1142/s0218196701000668.

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In this paper, we study the geometric equivalence of algebras in several varieties of algebras. We solve some of the problems formulated in [2], in particular, that of geometric equivalence for real-closed fields and finitely generated commutative groups.

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Toscano, Rosario, and Ioan Alexandru Ivan. "Heuristic Approaches for Non-Convex Problems." International Journal of Applied Industrial Engineering 2, no. 1 (January 2014): 74–98. http://dx.doi.org/10.4018/ijaie.2014010105.

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This paper aims at solving difficult optimization problems arising in many engineering areas. To this end, two recently developed optimization method will be introduced: the heuristic Kalman algorithms (HKA) and the quasi geometric programming (QGP) problems. The principle of HKA is to consider the optimization problem as a measurement process intended to give an estimate of the optimum. A specific procedure, based on the Kalman estimator, is developed to improve the quality of the estimate obtained through a measurement process. A significant advantage of HKA against other stochastic methods lies mainly in the small number of parameters which have to be set by the user. In this paper we also introduce an extension of standard geometric programming (GP) problems which we call quasi geometric programming (QGP) problems. The consideration of this particular kind of nonlinear and possibly non smooth optimization problem is motivated by the fact that many engineering problems can be formulated as a QGP. To solve this kind of problems (QGP), an algorithm is proposed which is based on the resolution of a succession of standard GP. An interesting feature of the proposed approach is that it does not need to develop specific program solver and works well with any existing solver able to solve conventional GP. In the last part of the paper, it is to shown that HKA and QGP can be efficiently used to solve difficult non-convex optimization problems. In particular, we have addressed the problem of robust structured control and on-ship spiral inductor design. Numerical experiments exemplify the resolution of this kind of problems.

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Joan-Arinyo, R., N. Mata, and A. Soto-Riera. "A Constraint Solving-Based Approach to Analyze 2D Geometric Problems With Interval Parameters." Journal of Computing and Information Science in Engineering 1, no. 4 (October 1, 2001): 341–46. http://dx.doi.org/10.1115/1.1429641.

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Many applications of geometric nature can be modeled by geometric problems defined by constraints in which the constraint parameters have interval uncertainty. In a previous work, we developed a method for solving geometric constraint problems where parameters are narrow intervals in the domain of the geometric problem. Based on this work, we present a new approach to solve more general problems with non-trivial-width interval parameters that may not necessarily be in the domain of the problem. We show how our approach is successfully applied to a number of problems like solving geometric problems with tolerances, checking constraint feasibility and analyzing link motion of planar mechanisms.

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Pedersen, Mads M., and Gunner C. Larsen. "Integrated wind farm layout and control optimization." Wind Energy Science 5, no. 4 (November 12, 2020): 1551–66. http://dx.doi.org/10.5194/wes-5-1551-2020.

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Abstract. The objective of this paper is to investigate the joint optimization of wind farm layout and wind farm control in terms of power production. A successful fulfilment of this goal requires the following: (1) an accurate and fast flow model, (2) selection of the minimum set of design parameters that rules or governs the problem, and (3) selection of an optimization algorithm with good scaling properties. For control of the individual wind farm turbines with the aim of wind farm production optimization, the two most obvious strategies are wake steering based on active wind turbine yaw control and wind turbine derating. The present investigation is limited to wind turbine derating. A high-speed linearized computational fluid dynamics (CFD) Reynolds-averaged Navier–Stokes (RANS) solver models the flow field and the crucial wind turbine wake interactions inside the wind farm. The actuator disc method is used to model the wind turbines, and utilizing an aerodynamic model, the design space of the optimization problem is reduced to only three variables per turbine – two geometric and one carefully selected variable specifying the individual wind turbine derating setting for each mean wind speed and direction. The full design space is spanned by these (2N+NdNsN) parameters, where N is the number of wind farm turbines, Nd is the number of direction bins, and Ns is the number of mean wind speed bins. This design space is decomposed into two subsets, which in turn define a nested set of optimization problems to achieve a significantly faster optimization procedure compared to a direct optimization based on the full design space. Following a simplistic sanity check of the platform functionality regarding wind farm layout and control optimization, the capability of the developed optimization platform is demonstrated on a Swedish offshore wind farm. For this particular wind farm, the analysis demonstrates that the expected annual energy production can be increased by 4 % by integrating the wind farm control into the design of the wind farm layout, which is 1.2 % higher than what is achieved by optimizing the layout only.

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Meryansumayeka, Meryansumayeka, Zulkardi Zulkardi, Ratu Ilma Indra Putri, and Cecil Hiltrimartin. "Students’ Strategies in Solving PISA Mathematical Problems Reviewed from Problem-Solving Strategies." Jurnal Pendidikan Matematika 15, no. 1 (January 31, 2021): 37–48. http://dx.doi.org/10.22342/jpm.15.1.10405.37-48.

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This study purposes to describe the strategies used by students in solving PISA type problems seen from the strategy of problem solving according to Polya. The research methodology is qualitative type descriptive study. Research subjects were 6 high school students in Palembang who had different levels of mathematical ability. Data was gathered using observation, interviews, and student answer sheets on the type of PISA questions given. The results showed that the dominant strategy used by students in solving PISA type problems included making pictures when they solve problem related to geometry; looking for possible answers systematically when they try to solve problem within numeric; writing information stated and the question when the problem is in the form of storytelling; and using trial and error when the problem provide answer alternatives.

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Cheung, Ka Chun. "Optimal Reinsurance Revisited – A Geometric Approach." ASTIN Bulletin 40, no. 1 (May 2010): 221–39. http://dx.doi.org/10.2143/ast.40.1.2049226.

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AbstractIn this paper, we reexamine the two optimal reinsurance problems studied in Cai et al. (2008), in which the objectives are to find the optimal reinsurance contracts that minimize the value-at-risk (VaR) and the conditional tail expectation (CTE) of the total risk exposure under the expectation premium principle. We provide a simpler and more transparent approach to solve these problems by using intuitive geometric arguments. The usefulness of this approach is further demonstrated by solving the VaR-minimization problem when the expectation premium principle is replaced by Wang's premium principle.

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Radchenko, I. F., and Gennadiy M. Bakan. "Using R-Functions to Solve Problems in Spatial Visualization of Geometric Objects." Journal of Automation and Information Sciences 28, no. 3-4 (1996): 1–6. http://dx.doi.org/10.1615/jautomatinfscien.v28.i3-4.10.

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Yudianto, Erfan, Sunardi Sunardi, Titik Sugiarti, and Feny Rita Fiantika. "Student’s Anticipation Profile at Rigor Level in Determining Papaya Tree Root Dimensions." Jurnal Didaktik Matematika 8, no. 1 (May 8, 2021): 59–74. http://dx.doi.org/10.24815/jdm.v8i1.19954.

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Students with a rigor level of geometric thinking can analytically solve problems, yet the ability may not be readily observable. Thus, an example of how students solve problems merits explorations. Inspired by student’s problem solving, this study aimed to examine the student’s anticipatory profile in determining Papaya tree roots' dimensions. This qualitative research utilized tests and interview. Two tests were carried out: van Hiele geometric level grouping test for selecting the research participants and the report-based test for the actual project. Seventeen students took the van Hiele test, and one of them, who achieved the rigor level, was selected for the interview. Data obtained from the interview were then analyzed qualitatively. The study showed that students with a rigor level of geometric thinking anticipated analytically. The subject was able to explain a geometric problem systematically, starting from analyzing problems, clarifying detailss, to presenting arguments clearly and precisely. The findings in this study generate useful information for teachers who train their students to analyze a geometric problem correctly and adequately.

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Zhang, Jianchen, and Heying Li. "Incremental Updating Information Extraction and Topology Conflict Detection Method for Updating Road Network." Abstracts of the ICA 1 (July 15, 2019): 1. http://dx.doi.org/10.5194/ica-abs-1-429-2019.

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Abstract. In recent years, Located Based Service (LBS) has become one of the hotspots on the application of geographic information to the government and the public. Providing a good performance map to the users is an important part of the location service system. Compared with the traditional web spatial information service system, service system of map information also put forward higher requirements of real time and veracity. The problem of updating electronic map in real-time cannot be effectively solved, hindering the updating of multi-scale electronic map and restricting the development of location service market. As a very important branch for the updating data field of geographic information science, incremental update has become a hot issue in the current international GIS research field. The extraction of incremental information includes two key technologies, namely road network matching and road network selection. After incremental updating roads were inserted into the database, coordinating topological conflicts caused by these inserted roads was the mainly task. However, the accuracy and algorithm efficiency of each technology need further improvement to provide the users with the latest and the most accurate basic geographic data. As the "skeleton" element of a map, the road network rapidly changes, carrying out more urgent requires for the incremental road update. Aiming at key technology problems of the updated road network, the paper focused on the following three parts:(1) To address the problems that the traditional probabilistic relaxation method only adopted geometric constraints as one of road matching criterions and could not respond to M: N matching pattern, an improved probabilistic relaxation method was proposed from the combined views of local optimization and global one, integrating geometric indicators with topology ones to achieve an effect with local optimization, as well as identifying M: N matching pattern by inserting virtual nodes to achieve a globally optimal effect. Then the matching strategies and corresponding implement algorisms were designed for different matching patterns. The case test showed that the overall matching accuracy of each evaluation indictor reached over 90%, increasing by 6%&ndash;12%; the evaluation indicators on both spatial and attribute properties increased by 4%&ndash;6%; the proper buffer threshold could be defined as twice the average value of the closest distances from all nodes in the candidate matching dataset.(2) Aiming at the low accuracy and irrational structural selection caused by only using linear pattern or areal pattern, an improved method was proposed combining linear method as well as areal ones. The proposed method improves the Stroke generation algorithm of linear pattern using OLS model taking the overall information from the roads to be connected. Meanwhile, it partitioned road network by weighted Voronoi diagrams. The roads were selected under the process of calculating the importance of Stroke and its road density threshold. The test demonstrated that the improved method added the accuracy of Stroke generation results, and the results of road selection could maintain the overall characteristics of the road network as well as its spatial distribution information. Compared with method only using one pattern, the combined method had a better accuracy of road selection.(3) According to the characteristics of detection topology for an updated road network, this paper proposed a topology conflict detection algorithm considering the incremental update of multi-scale network. The algorithm designed K-level topological neighbourhood to identify incremental neighbourhood road segments, built a topological refinement model based on geometric metrics, proposed checking rules based on comprehensive operation operator, and detected the conflict topology by using improved topological distance. The experimental results showed that 1) the accuracy and recall of the proposed method were more than 90%; 2) considering conflict topology caused by the generalization, the accuracy increased by 29.2%; 3) the average path length of a road network could be used as the reference of the best K-value in the K order incremental neighbourhood method.

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Fisher, Linda C. "Strategies Used by Secondary Mathematics Teachers to Solve Proportion Problems." Journal for Research in Mathematics Education 19, no. 2 (March 1988): 157–68. http://dx.doi.org/10.5951/jresematheduc.19.2.0157.

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Twenty secondary mathematics teachers described their thinking as they solved four proportion problems (Task 1), explained how they would teach two of the problems (Task 2), and solved four similar problems after being asked to use proportion strategies (Task 3). Their solution strategies were classified using a nine-category scheme. Overall, the teachers were more successful with direct proportion than with inverse proportion. On Task 1 proportion strategies were used on only half the problems. On Task 3 three fourths of the responses depended upon proportion strategies. On Task 2 most teachers said they would use the same strategies in teaching the problems that they used in solving them.

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Fisher, Linda C. "Strategies Used by Secondary Mathematics Teachers to Solve Proportion Problems." Journal for Research in Mathematics Education 19, no. 2 (March 1988): 157. http://dx.doi.org/10.2307/749409.

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Giordano, Gerard. "Strategies That Help Learning-Disabled Students Solve Verbal Mathematical Problems." Preventing School Failure: Alternative Education for Children and Youth 35, no. 1 (October 1990): 24–28. http://dx.doi.org/10.1080/1045988x.1990.9944245.

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Vondrová, Naďa, and Barbora Divišová. "Strategies for a Certain Type of Geometric Problems Solvable without Calculations." Procedia - Social and Behavioral Sciences 93 (October 2013): 400–404. http://dx.doi.org/10.1016/j.sbspro.2013.09.211.

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ZHANG, GUI-FANG, and XIAO-SHAN GAO. "WELL-CONSTRAINED COMPLETION AND DECOMPOSITION FOR UNDER-CONSTRAINED GEOMETRIC CONSTRAINT PROBLEMS." International Journal of Computational Geometry & Applications 16, no. 05n06 (December 2006): 461–78. http://dx.doi.org/10.1142/s0218195906002142.

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In this paper, we consider the optimal well-constrained completion problem, that is, for an under-constrained geometric constraint problem, add automatically new constraints in such a way that the new constraint problem G is well-constrained and the set of equations to be solved simultaneously in order to solve G has the smallest size. We propose a polynomial time algorithm which gives a partial solution to the above problem.

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Hamzić, Dina Kamber, and Zenan Šabanac. "Two plane geometry problems approached through analytic geometry." Mathematical Gazette 104, no. 560 (June 18, 2020): 255–61. http://dx.doi.org/10.1017/mag.2020.48.

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Geometry is a very interesting, applicable and beautiful part of mathematics. However, geometry is often difficult for students to understand and demanding for teachers to teach [1]. Constructing proofs in geometric problems turns out to be particularly difficult, even for high attaining students [2]. Sometimes, students do not even know where to start when trying to solve these [3].

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White, C. Stephen, and Patricia A. Alexander. "Effects of Training on Four-Year-Ols' Ability to Solve Geometric Analogy Problems." Cognition and Instruction 3, no. 3 (September 1986): 261–68. http://dx.doi.org/10.1207/s1532690xci0303_6.

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Mahmassani, Hani S., Yongjin Kim, and Patrick Jaillet. "Local Optimization Approaches to Solve Dynamic Commercial Fleet Management Problems." Transportation Research Record: Journal of the Transportation Research Board 1733, no. 1 (January 2000): 71–79. http://dx.doi.org/10.3141/1733-10.

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Strategies are presented that a dispatcher may use to take advantage of real-time information to manage a fleet of trucks to provide truckload pickup-and-delivery service under time windows for service and computing time constraints. These strategies are hybrid in that they combine very efficient dynamic local heuristic rules for quick initial assignment, with formal optimization-based procedures for subsequent load reassignment decisions within the time requirements of the dynamic problem. Simulation experiments were performed to test these strategies under alternative specifications and parameter values. In the first stage, the acceptance decision and initial schedule of trucks were determined so as to respond rapidly to incoming customer requests for service. Then, some time is allowed to improve the schedule of trucks by swapping the assigned loads using local optimization at the reassignment stage. Two strategies are described to control the computation time of the reassignment optimization problem by controlling the problem size. The simulation results confirm the significant potential for reassignment strategies under real-time information to improve system performance and suggest that considerable improvement is attainable even under restricted problem formulations.

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BURAGO, D., S. FERLEGER, and A. KONONENKO. "A geometric approach to semi-dispersing billiards (Survey)." Ergodic Theory and Dynamical Systems 18, no. 2 (April 1998): 303–19. http://dx.doi.org/10.1017/s014338579811564x.

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We summarize the results of several recent papers, together with a few new results, which rely on a connection between semi-dispersing billiards and non-regular Riemannian geometry. We use this connection to solve several open problems about the existence of uniform estimates on the number of collisions, topological entropy and periodic trajectories of such billiards.

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Thompson, Frances M. "Geometric Patterns for Exponents." Mathematics Teacher 85, no. 9 (December 1992): 746–49. http://dx.doi.org/10.5951/mt.85.9.0746.

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NCTM's Professional Standards for Teaching Mathematics suggests that “tasks that require students to reason and to communicate mathematically are more likely to promote their ability to solve problems and to make connections” with other mathematical ideas (1991, 24). Yet too frequently our classroom introductions to mathematics concepts and theorems demand little reasoning from students, leaving them unconvinced or with minimal understanding. Concrete, visual, or geometric models are seldom offered as aids, particularly when studying new numerical relations (Suydam 1984, 27; Bennett 1989, 130), even though many people depend heavily on visual stimuli for their learning, The challenge to the teacher is to select appropriate tasks and materials that will stimulate students to visualize and think about new mathematical concepts, thereby allowing them to develop their own understanding.

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Fu, Xiao-Ming, Jian-Ping Su, Zheng-Yu Zhao, Qing Fang, Chunyang Ye, and Ligang Liu. "Inversion-free geometric mapping construction: A survey." Computational Visual Media 7, no. 3 (July 27, 2021): 289–318. http://dx.doi.org/10.1007/s41095-021-0233-9.

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AbstractA geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free. Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others. This task is usually formulated as a non-convex, nonlinear, constrained optimization problem. Various methods have been developed to solve this optimization problem. As well as being inversion-free, different applications have various further requirements. We expand the discussion in two directions to (i) problems imposing specific constraints and (ii) combinatorial problems. This report provides a systematic overview of inversion-free mapping construction, a detailed discussion of the construction methods, including their strengths and weaknesses, and a description of open problems in this research field.

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Benito, Yolanda. "Metacognitive Ability and Cognitive Strategies to Solve Maths and Transformation Problems." Gifted Education International 14, no. 2 (January 2000): 151–59. http://dx.doi.org/10.1177/026142940001400205.

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Anamuah-Mensah, J. "Cognitive strategies used by chemistry students to solve volumetric analysis problems." Journal of Research in Science Teaching 23, no. 9 (December 1986): 759–69. http://dx.doi.org/10.1002/tea.3660230902.

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Sanyasiraju, Y. V. S. S., and Chirala Satyanarayana. "Upwind strategies for local RBF scheme to solve convection dominated problems." Engineering Analysis with Boundary Elements 48 (November 2014): 1–13. http://dx.doi.org/10.1016/j.enganabound.2014.06.008.

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Budiaman, Budiaman, and Nadiroh Nadiroh. "THE INFLUENCE OF LEARNING STRATEGIES AND STYLES OF THOUGHT ON THE ABILITY OF STUDENTS TO SOLVE ENVIRONMENTAL PROBLEMS." Jurnal Ilmiah Pendidikan Lingkungan dan Pembangunan 16, no. 02 (August 30, 2017): 85–100. http://dx.doi.org/10.21009/plpb.162.02.

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This study aims to determine the effect of learning models and styles of thought on the ability of students to solve environmental problems. The study was conducted in SMP 21 Bekasi during August 2012 to May 2013 academic year 2012/2013. This study used an experimental method, with 2 x 2 factorial designs. Variable research include learning model as an independent variable, style of thinking as a control variable, and the ability of students to solve environmental problems as the dependent variable. Sampling techniques using multistage random sampling, a class VIII-2 obtained as an experimental class and class as the control class VIII-1. The results showed that: First, the ability of students to solve environmental problems learning with instructional strategies ekperiensial higher than students using expository. Second, the ability of students to think accommodative style in solving environmental problems is higher than students think assimilative style. Third, the ability of students to solve environmental problems that have accommodative learning style with experiential learning strategies are higher than students who learned with expository learning strategies. Fourth, the ability of students to solve environmental problems that have assimilative learning style with instructional strategies expository higher than students who study with experiential learning strategies.Fifth, the interaction between learning strategy and thinking styles affect students' ability to solve environmental problems. This means that the effect of the interaction between learning strategy and thinking styles affect the level of students' abilities to solve environmental problems. The conclusion of this study is that students are given learning with experiential learning model has the ability to solve environmental problems is higher compared with the gain ekpositori learning.

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Feng, Xiao Hua, Yu Yao He, and Juan Yu. "Economic Load Dispatch Using Bacterial Foraging Optimization Algorithm Based on Evolution Strategies." Advanced Materials Research 860-863 (December 2013): 2040–45. http://dx.doi.org/10.4028/www.scientific.net/amr.860-863.2040.

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This paper presents a novel modiﬁed bacterial foraging optimization(BFO) to solve economic loaddispatch (ELD) problems. BFO isalready successfully employed to solve variousoptimization problems. However original BFOfor small problems with moderate dimensionand searching space is satisfactory. As searchspace and complexity growexponentially in scalable ELD problems, it shows poorconvergence properties. To tackle this complex problem considering itshigh-dimensioned search space, the Evolution Strategies is introduced to thebasic BFO. The chemotactic step is adjusted to have a dynamic non-linearbehavior in order to improve balancing the global and local search. Theproposed algorithm is validated using several thermal generation test systems.The results are compared with those obtained by other algorithms previouslyapplied to solve the problem considering valve-point effects and power losses.

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Waseem, Neha, Muhammad Akram, and José Carlos R. Alcantud. "Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators." Symmetry 11, no. 12 (December 10, 2019): 1498. http://dx.doi.org/10.3390/sym11121498.

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In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis.

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Journal articles on the topic 'Strategies to solve geometric problems'

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