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Journal articles on the topic 'Triangle construction problems'
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Kim, D., A. Bolat, and K. J. Li. "INDOOR SPATIAL DATA CONSTRUCTION FROM TRIANGLE MESH." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W8 (July 11, 2018): 101–8. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w8-101-2018.
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<p><strong>Abstract.</strong> The 3D triangle mesh is widely used to represent indoor space. One of widely used methods of generating 3D triangle mesh data of indoor space is the construction from the point cloud collected using LIDAR. However, there are many problems in using generated triangle mesh data as a geometric representation of the indoor space. First, the number of triangles forming the triangle mesh is very large, which results in a bottleneck of the performance for storage and management. Second, no consideration on the properties of indoor space has been done by the previous work on mesh simplification for indoor geometric representation. Third, there is no research to construct indoor spatial standard data from triangle mesh data. For resolving these problems, we propose the a method for generating triangular mesh data for indoor geometric representation based in the observations mentioned above. First this method removes unnecessary objects and reduces the number of surfaces from the original fine-grained triangular mesh data using the properties of indoor space. Second, it also produces indoor geometric data in IndoorGML &ndash; an OGC standard for indoor spatial data model. In experimental studies, we present a case study of indoor triangle mesh data from real world and compare results with raw data.</p>
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Nirode, Wayne. "Triangles from Three Points." Mathematics Teacher 108, no. 1 (August 2014): 32–38. http://dx.doi.org/10.5951/mathteacher.108.1.0032.
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Ma, Wei. "Technical Risk Assessment of Large-Scale Construction Project Based on Triangle Whitening Weight Function." Advanced Materials Research 989-994 (July 2014): 5294–99. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.5294.
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Technical risk assessment model of large-scale construction project has been established by using triangle whitening weight function of grey theory against the problems of technical risk assessment of large-scale construction project. In the end, through example verification, this model is approved to be feasible and have certain value of reference and utilization in similar problems.
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Reuveni, Shlomi. "CATALAN'S TRAPEZOIDS." Probability in the Engineering and Informational Sciences 28, no. 3 (March 18, 2014): 353–61. http://dx.doi.org/10.1017/s0269964814000047.
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Named after the French–Belgian mathematician Eugène Charles Catalan, Catalan's numbers arise in various combinatorial problems [12]. Catalan's triangle, a triangular array of numbers somewhat similar to Pascal's triangle, extends the combinatorial meaning of Catalan's numbers and generalizes them [1,5,11]. A need for a generalization of Catalan's triangle itself arose while conducting a probabilistic analysis of the Asymmetric Simple Inclusion Process (ASIP) — a model for a tandem array of queues with unlimited batch service [7–10]. In this paper, we introduce Catalan's trapezoids, a countable set of trapezoids whose first element is Catalan's triangle. An iterative scheme for the construction of these trapezoids is presented, and a closed-form formula for the calculation of their entries is derived. We further discuss the combinatorial interpretations and applications of Catalan's trapezoids.
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Chen, Hui Hui, and Cheng Jia. "US-FE-LSPIM TRI3 Element for Free Vibration Analysis." Applied Mechanics and Materials 246-247 (December 2012): 1278–82. http://dx.doi.org/10.4028/www.scientific.net/amm.246-247.1278.
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For the purpose of construction an effective element model, the US- FE-LSPIM TRI3 element formulation, which is based on the concept of unsymmetric finite element formulation, is established. Classical linear triangle shape functions and FE-LSPIM TRI3 element shape functions are used as test and trial functions respectively. Classical linear triangle shape functions fulfill the requirements of continuity in displacement field for test functions. The FE-LSPIM TRI3 element shape functions synthesize the individual strengths of meshfree and finite element methods so they are more proper for trial functions. The element is applied in free vibration analysis of two dimension solids. Typical benchmark problems are solved. The results show that this element is more accurate and capable of good performances under both regular and irregular meshes.
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Zhang, Zhijun. "Two Classes of Nonlinear Singular Dirichlet Problems with Natural Growth: Existence and Asymptotic Behavior." Advanced Nonlinear Studies 20, no. 1 (February 1, 2020): 77–93. http://dx.doi.org/10.1515/ans-2019-2054.
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AbstractThis paper is concerned with the existence, uniqueness and asymptotic behavior of classical solutions to two classes of models {-\triangle u\pm\lambda\frac{|\nabla u|^{2}}{u^{\beta}}=b(x)u^{-\alpha}}, {u>0}, {x\in\Omega}, {u|_{\partial\Omega}=0}, where Ω is a bounded domain with smooth boundary in {\mathbb{R}^{N}}, {\lambda>0}, {\beta>0}, {\alpha>-1}, and {b\in C^{\nu}_{\mathrm{loc}}(\Omega)} for some {\nu\in(0,1)}, and b is positive in Ω but may be vanishing or singular on {\partial\Omega}. Our approach is largely based on nonlinear transformations and the construction of suitable sub- and super-solutions.
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Ma, Li Qiang, Dong Sheng Zhang, Cheng Guo Zhang, Xin Qi Cao, and Yong Shen Li. "Design of Automatic End-Advanced Hydraulic Support in Coal Face with Deep Dip Angle and Large Mining Height." Advanced Materials Research 160-162 (November 2010): 1524–30. http://dx.doi.org/10.4028/www.scientific.net/amr.160-162.1524.
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ZTZL60000/25/45 Automatic End-Advanced Hydraulic Support is developed to meet the needs of the fully mechanized coal face with deep dip angle and large mining height, mechanizing the advanced support of the end and drift, while greatly reducing the construction personnel's labor intensity. Not only the end support strength is enhanced, which improves the safety and reliability of advanced support and generates methods to solve problems related to reserving triangle coal on the face that enhances the support efficiency and reduces support costs, but also more recovered coal resources become available since the height of roadway increases, spawning a certain amount of economic benefits.
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Tymoshenko, Aleksandr Vasil'evich, Rasul Ahmatovich Kochkarov, and Azret Ahmatovich Kochkarov. "Identification Conditions for the Solvability of NP-complete Problems for the Class of Pre-fractal Graphs." Modeling and Analysis of Information Systems 28, no. 2 (June 11, 2021): 126–35. http://dx.doi.org/10.18255/1818-1015-2021-2-126-135.
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Modern network systems (unmanned aerial vehicles groups, social networks, network production chains, transport and logistics networks, communication networks, cryptocurrency networks) are distinguished by their multi-element nature and the dynamics of connections between its elements. A number of discrete problems on the construction of optimal substructures of network systems described in the form of various classes of graphs are NP-complete problems. In this case, the variability and dynamism of the structures of network systems leads to an "additional" complication of the search for solutions to discrete optimization problems. At the same time, for some subclasses of dynamical graphs, which are used to model the structures of network systems, conditions for the solvability of a number of NP-complete problems can be distinguished. This subclass of dynamic graphs includes pre-fractal graphs. The article investigates NP-complete problems on pre-fractal graphs: a Hamiltonian cycle, a skeleton with the maximum number of pendant vertices, a monochromatic triangle, a clique, an independent set. The conditions under which for some problems it is possible to obtain an answer about the existence and to construct polynomial (when fixing the number of seed vertices) algorithms for finding solutions are identified.
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Garanzha, Vladimir A., Lyudmila N. Kudryavtseva, and Aleksei I. Belokrys-Fedotov. "Single and multiple springback technique for construction and control of thick prismatic mesh layers." Russian Journal of Numerical Analysis and Mathematical Modelling 36, no. 1 (February 1, 2021): 1–15. http://dx.doi.org/10.1515/rnam-2021-0001.
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Abstract We suggest an algorithm for construction of semi-structured thick prismatic mesh layers which guarantees an absence of inverted prismatic cells in resulting layer and allows one to control near-surface mesh orthogonality. Initial mesh is modelled as a thin layer of highly compressed prisms made of hyperelastic material glued to the triangulated surface. In order to compute robust normals at the vertices of the surface mesh we use quadratic programming algorithm based on the nearest ball concept. This pre-stressed material expands, possibly with self-penetration and extrusion to exterior of computational domain until target layer thickness is attained. Special preconditioned relaxation procedure is proposed based on the solution of stationary springback problem. It is shown that preconditioner can handle very stiff problems. Once an offset prismatic mesh is constructed, self-intersections are eliminated using iterative prism cutting procedure.Next, variational advancing front procedure is applied for refinement and precise orthogonalization of prismatic layer near boundaries. We demonstrate that resulting mesh layer is ‘almost mesh-independent’ in a sense that the dependence of thickness and shape of the layer on mesh resolution and triangle quality is weak. It is possible to apply elastic springback technique sequentially layer by layer. We compare single springback technique with multiple springback technique in terms of mesh quality, stiffness of local variational problems and mesh orthogonality or/and layer thickness balance.
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Banihashemi, Sayyid Ali, Mohammad Khalilzadeh, Jurgita Antucheviciene, and Jonas Šaparauskas. "Trading off Time–Cost–Quality in Construction Project Scheduling Problems with Fuzzy SWARA–TOPSIS Approach." Buildings 11, no. 9 (August 31, 2021): 387. http://dx.doi.org/10.3390/buildings11090387.
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The increasing number of construction projects together with the limited resources of organizations led to tough competition for achieving project goals. Time, cost, and quality have been known as the project iron triangle. Project managers attempt to allocate the appropriate resources and make the best decisions for accomplishing projects with the shortest durations, lowest costs, and the highest quality. No study has examined the time–cost–quality trade-off problem with decision-making approaches. In this study, the fuzzy multi-criteria decision-making (MCDM) methods are exploited to choose the best mode for performing each activity. For this purpose, the SWARA method is applied to determine the importance weights of time, cost, and quality. In addition, the TOPSIS (Technique for the Order Preference by Similarity to Ideal Solution) technique is used to rank and select the best activity execution modes. The proposed model is implemented on two medium- and large-size construction projects to evaluate its efficiency. Several execution modes with fuzzy duration, cost, and quality are considered for each project activity. Finally, sensitivity analysis is conducted taking three different conditions into account: the shortest duration of the execution modes, the lowest cost of the execution modes, and the highest quality of execution modes for each activity. The solution of each trade-off is compared with the solution obtained from the fuzzy SWARA–TOPSIS method. The schedule is developed according to the best execution mode for each project activity. The obtained results in two different construction projects show significant improvements in the overall project objectives so that the projects can be completed in fewer durations and costs along with higher quality. Because of the higher importance of cost, the cost of each activity is closer to the lowest cost. The activity duration is also closer to the most likely duration, and quality is closer to the high-quality level. The application of this approach can create new opportunities for research and knowledge development in the field of construction project scheduling.
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Zhan, Ming-Sheng, Jin Wang, Wei-Tou Ni, Dong-Feng Gao, Gang Wang, Ling-Xiang He, Run-Bing Li, et al. "ZAIGA: Zhaoshan long-baseline atom interferometer gravitation antenna." International Journal of Modern Physics D 29, no. 04 (July 2, 2019): 1940005. http://dx.doi.org/10.1142/s0218271819400054.
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The Zhaoshan long-baseline Atom Interferometer Gravitation Antenna (ZAIGA) is a new type of underground laser-linked interferometer facility, and is currently under construction. It is in the 200-m-on-average underground of a mountain named Zhaoshan which is about 80[Formula: see text]km southeast to Wuhan. ZAIGA will be equipped with long-baseline atom interferometers, high-precision atom clocks, and large-scale gyros. ZAIGA facility will take an equilateral triangle configuration with two 1-km-apart atom interferometers in each arm, a 300-m vertical tunnel with atom fountain and atom clocks mounted, and a tracking-and-ranging 1-km-arm-length prototype with lattice optical clocks linked by locked lasers. The ZAIGA facility will be used for experimental research on gravitation and related problems including gravitational wave detection, high-precision test of the equivalence principle of micro-particles, clock-based gravitational red-shift measurement, rotation measurement and gravitomagnetic effect.
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Awang, Noorehan, Rahmita Wirza Rahmat, Puteri Suhaiza Sulaiman, Azmi Jaafar, and Ng Seng Beng. "Filling Simple Holes of Triangular Mesh by using Enhanced Advancing Front Mesh (EAFM) method." International Journal of Engineering & Technology 7, no. 2.15 (April 6, 2018): 81. http://dx.doi.org/10.14419/ijet.v7i2.15.11219.
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Triangular meshes are extensively used to represent 3D models. Some surfaces cannot be digitised due to various reasons such as inadequacy of the scanner, and this generally occurs for glossy, hollow surfaces and dark-coloured surfaces. This cause triangular meshes to contain holes and it becomes difficult for numerous successive operations such as model prototyping, model rebuilding, and finite element analysis. Hence, it is necessary to fill these holes in a practical manner. In this paper, the Enhanced Advancing Front Mesh (EAFM) method was introduced for recovering missing simple holes in an object. The first step in this research was to extract the feature vertices around a hole on a 3D test data function. Then the Advancing Front Mesh (AFM) method was used to fill the holes. When conflicts occurred during construction of the triangle, the EAFM method was introduced to enhance the method. The results of the study show that the enhanced method is simple, efficient and suitable for dealing with simple hole problems.
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Gowers, W. T., and J. Long. "The length of an s-increasing sequence of r-tuples." Combinatorics, Probability and Computing 30, no. 5 (January 8, 2021): 686–721. http://dx.doi.org/10.1017/s0963548320000371.
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AbstractWe prove a number of results related to a problem of Po-Shen Loh [9], which is equivalent to a problem in Ramsey theory. Let a = (a1, a2, a3) and b = (b1, b2, b3) be two triples of integers. Define a to be 2-less than b if ai < bi for at least two values of i, and define a sequence a1, …, am of triples to be 2-increasing if ar is 2-less than as whenever r < s. Loh asks how long a 2-increasing sequence can be if all the triples take values in {1, 2, …, n}, and gives a log* improvement over the trivial upper bound of n2 by using the triangle removal lemma. In the other direction, a simple construction gives a lower bound of n3/2. We look at this problem and a collection of generalizations, improving some of the known bounds, pointing out connections to other well-known problems in extremal combinatorics, and asking a number of further questions.
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Ariseno, Nur Muhammad, Afri Medika Utama, Bambang Setiawan, and Noegroho Djarwanti. "PENGARUH POLA PADA SISTEM CAM MENGGUNAKAN METODE ELEMEN HINGGA." Jurnal Riset Rekayasa Sipil 2, no. 2 (March 12, 2019): 59. http://dx.doi.org/10.20961/jrrs.v2i2.28626.
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<em>Cakar Ayam Modification System (CAM) has been widely used as one of the solutions to road pavement problems in soft subgrade, although construction costs were initially high, the total costs incurred were smaller due to small maintenance costs. This research analyzes the deflection produced in a triangle patterned CAM system and quadrilateral with variations in the distance between claws of 2.25 m. Loading uses truck loads based on SNI 1725 2016 with three different position variations each in the middle and edge of the pavement. The analysis was carried out using Finite Element Method-based software which has been proven to be able to approach the original conditions in the field. The results of the analysis show that the CAM pattern with triangular pattern is better at reducing deflection that occurs compared to quadrilateral CAM systems. The deflection difference produced by the triangular CAM system against the clawless pavement system reached 36.97% while on the quadrilateral CAM system the difference was only 28.56%.</em>
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Rusanova, Inna Aleksandrovna. "Integration of interdisciplinary directions in the study of fractal geometry elements." Samara Journal of Science 6, no. 4 (December 1, 2017): 246–51. http://dx.doi.org/10.17816/snv201764311.
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This paper deals with the problem of integrating interdisciplinary areas in research activities that underlie developmental learning. In the conditions of new educational standards introduction deep system transformations of the whole educational process are supposed. The search for solutions to the problems of individualizing the educational route, polar motivation, increasing interest in physics and mathematics lead to the need to design individual methods of pedagogical activity, to implement new approaches and technologies in the natural science cycle of consistent development of holistic research activities, mastering the stages and methods of scientific knowledge. One of the opportunities for the formation of educational and cognitive activity and creative potential in the study of Physics and Mathematics is to study the elements of fractal geometry for analyzing the complex structure of processes of various physical nature, in view of the fact that today there is a large number of problems in Physics, Chemistry, Biology, Geology and Economics, where the fractal structure is the main characteristic of the system. Practical tasks on the construction of fractal sets with the identification of the main signs of self-similarity and the possibility of their computer modeling are considered. Students of grades 9-11 and students of the university are given the task of creating their own images of fractals, investigating the fractality of coastal river lines, constructing self-similar figures according to the algorithm Games in chaos and studying the contracting affine transformations with obtaining various modifications (attractors) of the Serpinsky triangle. The results obtained enable them to conclude that simple mathematical rules can generate self-similar formations with respect to nonlinear transformations, and argue that simple rules can be at the heart of complex structures and processes.
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Crilly, Tony, and Colin R. Fletcher. "Triangles meeting triangles." Mathematical Gazette 98, no. 543 (November 2014): 432–51. http://dx.doi.org/10.1017/s0025557200008135.
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We consider two connected problems: •For a given but otherwise arbitrary triangle in the plane, to construct similar triangles which ‘meet’ this triangle.•To find the triangle so formed which has least area.1. Constructing a triangle which meets anotherThese problems beg the question of what is meant by ‘meet’ and we now aim to make this precise: Definition: A triangle XYZ will meet a given triangle ABC if on the triangle ABC, the vertex X lies on a line through AB, the vertex Y lies on a line through BC, and the vertex Z lies on a line through CA.When triangle XYZ is actually ‘in’ the triangle ABC, ‘meet’ is synonymous with the traditional ‘inscribe’ (such as in case (1) below). For ‘inscribe’ we understand that some of X, Y, Z may coincide with the vertices of ABC (such as case (2) below).More generally we use ‘meet’ to extend these possibilities by allowing XYZ to meet triangle ABC with its sides produced externally (such as case (3) below).
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Hu, Yanhua, Guodong Meng, Jianyu Lv, Hang Jin, and Linlin Lu. "A Study on the Theoretical Model of Port Safety Resilience under Major Emergencies and Its Quantitative Evaluation." E3S Web of Conferences 257 (2021): 03053. http://dx.doi.org/10.1051/e3sconf/202125703053.
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With the rapid development of urbanization, China’s security system in ports is facing many problems and challenges, especially after the outbreak of COVID-19 has made a great impact on China. In order to avoid the serious losses caused by safety problems in ports under major emergencies due to the lack of necessary, forward-looking prevention in the increasingly complex system of ports, this paper introduced the theory of safety resilience into the field of ports for the first time and proposed a triangle model of safety resilience in ports, which included three elements: the disaster system, the disaster bearing system and the safety resilience management. Aiming at the quantitative evaluation demands of safety resilience in ports, the system evaluation indexes of safety resilience in ports were established, including 6 secondary indexes and 37 tertiary indexes. The theory of entropy weight based on normalization standard processing was used to calculate and analyze the importance of each index, and the influence weight value of each index on safety resilience and the prediction curve chart of safety resilience in ports were obtained. The research results can provide a reference for the capacity construction and application of safety resilience in ports, which will effectively solve the new challenges faced by port safety at this stage and help to improve the ability of the port not only in disaster prevention and mitigation but also in disaster recovery and continuous improvement.
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Bogomolova, Oksana, and Andrey Zhidelev. "Construction of plastic deformation areas in a homogeneous base of strip foundation." E3S Web of Conferences 281 (2021): 01026. http://dx.doi.org/10.1051/e3sconf/202128101026.
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The article discusses two approaches to the question of plastic deformations constructing areas in a homogeneous baseof a strip foundation: a trivial approach based on the use of the Coulomb plasticity condition, and the approach proposed by the authors based on the approximate analytical solution of the theory of elasticity and the theory of soil plasticity mixed problem. It has been established that the “Coulomb” regions, which originally generated under the edges of the strip load, close under the basement as it increases and form a single crescent-shaped plastic area. Plastic areas built on the basis of a mixed solution develop inward and outward from the foundation. Their closure under the foundation occurs at the beginning of the soil uplift process under the foundation, which is accompanied by the appearance of deep heaving zones (Fig. 8; 9). All other things being equal, the “Coulomb” regions are much larger in size and extend to a greater depth than the regions constructed on the basis of a mixed solution of the theory of elasticity and the theory of soil plasticity problem. The elastic soil core, enveloped by “Coulomb” plastic areas, has a shape close to the shape of a half ellipse or a curved trapezoid, and, alternatively, has the shape of an isosceles triangle with concave lateral sides. If we construct the regions of plastic deformations at the base of a strip foundation using the Coulomb plasticity condition, or apply a solution to a mixed problem, then, all other things being equal, the sizes of the “Coulomb” regions, the “rate” of their development and sensitivity to changes in the value of the lateral pressure coefficient of the soil will always be more than in the alternative case. If the value of the ultimate load is taken as its value corresponding to the closure of the plastic areas under the foundation, then the mixed solution of the theory of elasticity and the theory of plasticity of soils problem gives higher (≥500%) the values of the latter. When finding the value of the bearing capacity of the strip foundation base, it is recommended to apply the solutions of the corresponding problems in the elastoplastic (mixed) formulation, since their results, and this has been shown in the work, are in satisfactory agreement with the experimental data.
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Han, HongJu, JiPing Guo, JiJin Zhang, and Yuan Sun. "Technical Advances of Temporary Facilities for the Failure Prevention of Large-Span Cantilever Casting Construction of Mountainous Concrete Box-Type Arch Bridges." Advances in Civil Engineering 2020 (February 6, 2020): 1–20. http://dx.doi.org/10.1155/2020/6412613.
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In the highways of mountainous areas, the erection of the large-span reinforced concrete box-type arch bridges using the cantilever casting method has unique advantages due to its adaptability to those environments. However, what prevents engineers from choosing this design in practice is that, the efficiency, cost, and safety problems resulting from the defects of the temporary facilities, which are due to the span increase, may immediately make the scheme less attractive. To fully consider the merits of this bridge type, new techniques of the temporary facilities are developed. A new form traveler based on the feathers of such arch rings is invented to promote erection efficacy; this new form further facilitates the technical upgrades of the buckle-anchor system monitoring-control and temporary prestressing design, which together eliminate the difficulties brought by the span increase. The inverted-type triangle traveler composed of tiled main truss structures, with the walking hook and anchor tie rod detached, is used to achieve space adaptability, light weight and modularization. The semiautomatic deviation-rectifying system, which combines the technologies of real-time data collection of the buckle pylon deviations and automatic synchronized tensioning, is developed to ensure the safety of the buckle-anchor system. The temporary short prestressed tendons are designed for control of the arch ring tensile stresses. The effectiveness of the technical upgrades has been demonstrated in the construction application of the Shatuo Bridge in Guizhou, China, which provides a promising alternative for the construction of large-span box-type arch rings of concrete arch bridges with a low cost, high efficiency, and high safety assurance.
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Blanquero, R., and E. Carrizosa. "Continuous location problems and Big Triangle Small Triangle: constructing better bounds." Journal of Global Optimization 45, no. 3 (December 12, 2008): 389–402. http://dx.doi.org/10.1007/s10898-008-9381-z.
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Abu El-Maaty, Ahmed Ebrahim, Amr M. El-Kholy, and Ahmed Yousry Akal. "Modeling schedule overrun and cost escalation percentages of highway projects using fuzzy approach." Engineering, Construction and Architectural Management 24, no. 5 (September 18, 2017): 809–27. http://dx.doi.org/10.1108/ecam-03-2016-0084.
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Purpose Modeling represents the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers and guidance useful for the originating application. The purpose of this paper is to determine the causal causes of schedule overrun and cost escalation of highway projects in Egypt in order to be used as independents variables in mathematical models for predicting the percentages of schedule overrun and cost escalation of such projects in Egypt. Design/methodology/approach A survey of a randomly selected samples yielded responses from 40 owners, 15 consultants and 56 contractors. The survey includes 38 schedule overrun factors and 26 cost escalation factors. The effectiveness degree of the identified factors has been identified by the triangle fuzzy approach. Findings The results of the survey show that “contractor’s technical staff is insufficient and ineligible to accomplish the project” is the most important cause of schedule overrun, while the major cause of cost escalation is inadequate preparation of the project concerning planning and execution. Originality/value The main contribution of this study is predicting the percentages of schedule overrun and cost escalation of highway projects in Egypt. Through the application of the linear regression analysis method and statistical fuzzy theory, four predictive models have been developed and it has been noted that the linear regression-based model shows prediction accuracy better than statistical fuzzy-based model in predicting percentages of schedule overrun and cost escalation.
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Komjáth, Péter, and Saharon Shelah. "Forcing constructions for uncountably chromatic graphs." Journal of Symbolic Logic 53, no. 3 (September 1988): 696–707. http://dx.doi.org/10.2307/2274566.
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In this paper we solve some of Pál Erdős's favorite problems on uncountably chromatic graphs. Generalizing a finite graph theory result of Tutte, Erdős and R. Rado showed that for every infinite cardinal κ there exists a triangle-free, κ-chromatic graph of size κ. For κ = ℵ0, Erdős established the existence of ℵ0-chromatic graphs excluding even C4, C5,…, Cn, i.e. circuits up to a given length. For κ < ℵ0 the situation is different. As shown by Erdős and A. Hajnal, a graph is necessarily countably chromatic if it omits any finite bipartite graph. We can, however, exclude any finite list of nonbipartite graphs (this obviously reduces to excluding finitely many odd circuits). They posed an even stronger conjecture, namely, that similar examples must occur in every uncountably chromatic graph. To be specific, they conjectured that for every infinite κ, every κ-chromatic graph contains a κ-chromatic triangle-free subgraph. Here we show that this may not be true for κ = ℵ1 i.e. we exhibit a model where it is false. We must emphasize that the conjecture is probably false already in ZFC, but we have been unable to show this.
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Burda, Mykhailo. "SOLVING CONSTRUCTION PROBLEMS IN A TEXTBOOK OF PLANIMETRY BY THE AUXILIARY TRIANGLES METHOD." Problems of Modern Textbook, no. 26 (2021): 33–42. http://dx.doi.org/10.32405/2411-1309-2021-26-33-42.
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Swanepoel, Konrad J. "Triangles of nearly equal area." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 62, no. 1 (March 2021): 219–27. http://dx.doi.org/10.1007/s13366-021-00567-2.
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AbstractGiven any n points in the plane, not all on the same line, there exist two non-collinear triples such that the ratio of the areas of the triangles they determine, differs from 1 by at most $$O(\log n/n^2)$$ O ( log n / n 2 ) . If we furthermore insist that the two triangles have a common edge, then there are two with area ratios differing from 1 by at most O(1/n). This improves some results of Ophir and Pinchasi (Discrete Appl. Math. 174 (2014), 122–127). We also give some constructions for these and related problems.
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Vieira, Lygianne Batista, and Geraldo Eustáquio Moreira. "Contribuições da Educação Matemática para a cultura de respeito à dignidade humana." Revista Interdisciplinar de Direitos Humanos 8, no. 2 (November 26, 2020): 173–88. http://dx.doi.org/10.5016/ridh.v8i2.26.
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Este texto tem o propósito de apresentar as contribuições da Educação Matemática no desafio de construir uma cultura de respeito à dignidade humana, excepcionalmente, em tempo de pandemia e, permanentemente, no pós-pandemia. Utilizamos as produções de Ubiratan D’Ambrosio, de Ole Skovsmose e de Eric Gutstein com o argumento de que a Educação Matemática também deve se responsabilizar pela formação sociopolítica dos estudantes. Para tanto, iniciamos o texto, discorrendo sobre a concepção de dignidade humana como construção intersubjetiva, tendo como principal interlocutor Boaventura de Sousa Santos. Em nossa reflexão, enfatizamos que a falta de consciência sociopolítica dos direitos, bem como, de dignidade humana, resulta na banalização das situações de injustiças e de opressões vividas pela sociedade brasileira. E que as desigualdades sociais são problemas que impedem o enfrentamento da Covid-19. Na busca do lugar de fala da Educação Matemática diante deste cenário, reforçamos o Triângulo Primordial de Ubiratan D’Ambrosio compreendido como: um indivíduo, um outro indivíduo e, portanto, a sociedade, e a natureza como possibilidade filosófica e metodológica de atuação. Aliado a isso, o poder de formatação da sociedade de Skovsmose e o “ler” e “escrever” o mundo de Gutstein representam uma forma de inserção da matemática no desafio de construir uma sociedade que respeita a dignidade humana. Ciente deste papel, é preciso que a Educação Matemática reconheça seu potencial transformador primando pela formação de jovens amparada pelos princípios da humanização, da sustentabilidade e da paz. Contributions of Mathematics Education to the culture of respect for human dignity This text aims to present the contributions of Mathematics Education in the challenge of building a culture of respect for human dignity, exceptionally, in a time of pandemic and, permanently, in the post-pandemic. We use the productions of Ubiratan D’Ambrosio, Ole Skovsmose and Eric Gutstein with the argument that Mathematics Education should also be responsible for the socio-political formation of students. To this end, we begin the text, discussing the conception of human dignity as an intersubjective construction, having as main interlocutor Boa Ventura de Sousa Santos. In our reflection, we emphasize the lack of socio-political awareness of rights, as well as human dignity, results in trivialization of situations of injustice and oppression experienced by Brazilian society. And that social inequalities are problems that prevent Covid-19 from being faced. In the search for the place to speak of Mathematical Education in this scenario, we reinforce the Primordial Triangle of Ubiratan D’Ambrosio understood as: an individual, another individual and, therefore, society, and nature as a philosophical and methodological possibility of action. Allied to this, the formatting power of Skovsmose’s society and the “read” and “write” of Gutstein’s world represent a form of insertion of mathematics in the challenge of building a society that respects human dignity. Aware of this role, it is necessary that Mathematics Education recognizes its transforming potential, excelling in the formation of young people supported by the principles of humanization, sustainability and peace. Keywords: Mathematics Education. Human dignity. Pandemic. Post-pandemic. Socio-political formation.
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Voloshinov, Denis. "Algorithmic Complex for Solving of Problems with Quadrics Using Imaginary Geometric Images." Geometry & Graphics 8, no. 2 (August 17, 2020): 3–32. http://dx.doi.org/10.12737/2308-4898-2020-3-32.
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The paper is devoted to the consideration of a number of issues related to the creation of an algorithmic complex designed to solve positional and metric problems with quadrics on a projection model . A feature of the complex is the active use of geometric schemes and algorithms involving imaginary geometric images. In the paper has been presented a detailed description of constructive geometric algorithms for constructing of conics, quadrics and associated geometric images in a system of constructive geometric modeling – Simplex. All the discussed algorithms are available for independent repetition by the reader. In the paper have been presented and implemented algorithms for constructing conic from a point, a polar, and three points; constructing conic from two pairs of complex conjugate points and one real point; determination of a point on a quadric’s surface; setting a quadric by nine points in three-dimensional space. A new alternative frame of the quadric has been considered, based on which have been solved problems of constructing a tangent and a normal to the quadric, finding an intersection line of an arbitrary plane with the quadric, and performing polar and inverse transformations with respect to the quadric. Have been proposed algorithms for constructing an autopolar tetrahedron with respect to the quadric, and for constructing a conic from an autopolar triangle and two points. Have been considered problems of determining a collinear transformation in three-dimensional space and control the quadric through it. The implementation of the algorithms considered in the paper allowed conclude that there is an urgent need to develop tools for modeling imaginary conics, without which the complex of solving problems with quadrics cannot be taken for the complete one.
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Hanks, Thomas C., and A. Gerald Brady. "The Loma Prieta earthquake, ground motion, and damage in Oakland, Treasure Island, and San Francisco." Bulletin of the Seismological Society of America 81, no. 5 (October 1, 1991): 2019–47. http://dx.doi.org/10.1785/bssa0810052019.
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Abstract The basis of this study is the acceleration, velocity, and displacement wave-forms of the Loma Prieta earthquake (18 October 1989; M = 7.0) at two rock sites in San Francisco, a rock site on Yerba Buena Island, an artificial-fill site on Treasure Island, and three sites in Oakland underlain by thick sections of poorly consolidated Pleistocene sediments. The waveforms at the three rock sites display a strong coherence, as do the three sedimentary sites in Oakland. The duration of strong motion at the rock sites is very brief, suggestive of an unusually short source duration for an earthquake of this size, while the records in Oakland show strong amplification effects due to site geology. The S-wave group at Treasure Island is phase coherent with the Oakland records, but at somewhat diminished amplitudes, until the steps in acceleration at approximately 15 sec, apparently signaling the onset of liquefaction. All seven records clearly show shear-wave first motion opposite to that expected for the mainshock radiation pattern and peak amplitudes greater than expected for sites at these distances (95 ± 3 km) from an earthquake of this magnitude. While the association between these ground motion records and related damage patterns in nearby areas has been easily and eagerly accepted by seismological and engineering observers of them, we have had some difficulty in making such relationships quantitative or even just clear. The three Oakland records, from sites that form a nearly equilateral triangle about the Cypress Street viaduct collapse, are dominated by a long-period resonance (≃ 1 1/2-sec period) far removed from the natural frequency of the structure to transverse motion (2.5 Hz) or from high-frequency amplification bands observed in aftershock studies. A spectral ratio arbiter of this discrepancy confuses it further. The failure of the East Bay crossing of the San Francisco-Oakland Bay Bridge cannot be attributed to relative displacements of the abutments in Oakland and Yerba Buena Island, but the motions of the Bay Bridge causing failure remain unknown. The steps in acceleration at Treasure Island present unusual strong-motion accelerogram processing problems, and modeling suggests that the velocity and displacement waveforms are contaminated by a spurious response of the filtering operations to the acceleration steps. A variety of coincidences suggests that the Treasure island accelerogram is the most likely strong-motion surrogate for the filled areas of the Marina District, for which no mainshock records are available, but the relative contributions of bad ground, poor construction and truly strong ground motion to damage in the Marina District will never by known in any quantitative way. The principal lesson of all of this is that until a concerted effort is mounted to instrument ground and structures that are likely to fail during earthquakes, our understanding of the very complex relationships between strong ground motion and earthquake damage will, in general, remain rudimentary, imprecise, and vague.
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Belyi, Alexander B., Stanislav L. Sobolevsky, Alexander N. Kurbatski, and Carlo Ratti. "Improved upper bounds in clique partitioning problem." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (November 29, 2019): 93–104. http://dx.doi.org/10.33581/2520-6508-2019-3-93-104.
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In this work, a problem of partitioning a complete weighted graph into cliques in such a way that sum of edge weights between vertices belonging to the same clique is maximal is considered. This problem is known as a clique partitioning problem. It arises in many applications and is a varian of classical clustering problem. However, since the problem, as well as many other combinatorial optimization problems, is NP-hard, finding its exact solution often appears hard. In this work, a new method for constructing upper bounds of partition quality function values is proposed, and it is shown how to use these upper bounds in branch and bound technique for finding an exact solution. Proposed method is based on the usage of triangles constraining maximal possible quality of partition. Novelty of the method lies in possibility of using triangles overlapping by edges, which allows to find much tighter bounds than when using only non-overlapping subgraphs. Apart from constructing initial estimate, a method of its recalculation, when fixing edges on each step of branch and bound method, is described. Test results of proposed algorithm on generated sets of random graphs are provided. It is shown, that version that uses new bounds works several times faster than previously known methods.
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Yu, Kai-Ming, Yu Wang, and Charlie C. L. Wang. "Smooth geometry generation in additive manufacturing file format: problem study and new formulation." Rapid Prototyping Journal 23, no. 1 (January 16, 2017): 34–43. http://dx.doi.org/10.1108/rpj-06-2015-0067.
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Purpose In the newly released ASTM standard specification for additive manufacturing file (AMF) format – version 1.1 – Hermite curve-based interpolation is used to refine input triangles to generate denser mesh with smoother geometry. This paper aims to study the problems of constructing smooth geometry based on Hermite interpolation on curves and proposes a solution to overcome these problems. Design/methodology/approach A formulation using triangular Bézier patch is proposed to generate smooth geometry from input polygonal models. Different configurations on the boundary curves in the formulation are analyzed to further enrich this formulation. Findings The study shows that the formulation given in the AMF format (version 1.1) can lead to the problems of inconsistent normals and undefined end-tangents. Research limitations/implications The scheme has requirements on the input normals of a model, only C0 interpolation can be generated on those cases with less-proper input. Originality/value To overcome the problems of smooth geometry generation in the AMF format, the authors propose an enriched scheme for computing smooth geometry by using triangular Bézier patch. For the configurations with less-proper input, the authors adopt the Boolean sum and the Nielson’s point-opposite edge interpolation for triangular Coons patch to generate the smooth geometry as a C0 interpolant.
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Siniuta, K. O. "COORDINATE METHOD FOR DETERMINING THE GROUND SPEED OF THE VESSEL BY VECTORS AND DISPLACEMENT OF RELATIVE SPEEDS." Shipping & Navigation 30, no. 1 (December 1, 2020): 117–23. http://dx.doi.org/10.31653/2306-5761.30.2020.117-123.
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During the movement of the vessel along the route there is a problem of observation of natural and man-made obstacles, which is solved by modernizing the management using enavigation. Intensification of the movement process is provided by increasing the number and frequency of observations according to static criteria. In this case, the methods of graphical and analytical calculation of the path are the basis of navigation, forcing a return to the local criterion, which reflects the full physical nature of the process. The calculation of the vessel's path on the route is carried out according to the rule of the polygon, the sides of which are the vectors of the speed of the path, the vessel and perturbations (wind, waves, current). The main problem is the accuracy of determining the magnitude of the perturbation vector. The inaccuracy of the definition leads to the extension of the vessel's path, which contributes to energy and financial losses for transport support and maintenance of the vessel. The aim of the study is to create a reliable, fast and accurate (innovative) way to determine the characteristics of rectilinear gradual uniform motion of the vessel, which features three speed vectors: perturbation, relative and absolute velocities. The object of study was the process of ship movement, and the subject - the elements (parameters) of movement. The article determines the forecast parameters with a minimum of a priori information at the beginning of the vessel: the sequence of determining the angles of the speed triangle is determined, the sides (modules) of the speed triangle are determined, the order of determining the coordinates of the vertices of the velocity triangle is established. This allows to solve more complex problems of graph-analytical and mechatronic calculus and observation of translational and rotational motion of the vessel along the route and to improve control to reduce risk on the course of disturbances in "big" real time, with variable intervals of observations, approaching invariant and robust control. The advantage of the coordinate method is to solve the problem of determining the parameters of vectors by methods of analytical geometry more accurate, proven and simple in comparison with empirical dependencies, as well as geometric constructions
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Chekmarev, D. T., M. H. Abuziarov, and Cheng Wang. "ABOUT SMOOTH INTERPOLATION OF A TRIANGULATED SURFACE." Problems of strenght and plasticity 82, no. 2 (2020): 147–55. http://dx.doi.org/10.32326/1814-9146-2020-82-2-147-155.
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A method and algorithm for rebuilding a surface triangulation in three-dimensional space defined by an STL file is proposed. An initial surface in 3D space (STL file) is represented as a polyhedron composed of triangular faces. The method is based on the analytical representation of the surface as a piecewise polynomial function. This function is built on a polyhedral surface composed of triangles and satisfies the following requirements: 1) within one face, the function is an algebraic polynomial of the third degree; 2) the function is continuous on the entire surface and preserves the continuity of the first partial derivatives; 3) the surface determined by the function passes through the vertices of the initial triangulated surface. The restructuring of computational meshes is required in cases of distortion of the shape of cells when solving problems of mathematical physics using mesh methods (finite-difference, FEM, etc.). Cell distortion can be due to various reasons. These can be large distortions of moving Lagrangian meshes in the calculations in the current configuration, with instability of the hourglass type, with distortion of the faces of the interface between interacting gaseous, liquid and elastoplastic bodies. The rebuilding of the mesh reduces to solving the problem of constructing a smooth surface passing through the nodes of an existing triangulated surface or part of it. Later the nodes of the new mesh are placed on the constructed smooth surface with existing requirements for the size and shape of the cells. The construction of a smooth piecewise polynomial surface is based on the ideas of spline approximation and reduces to the building of a cubic polynomial on each triangular face, taking into account the smooth conjugation of polynomial pieces of the surface constructed on adjacent faces. The proposed method for rebuilding surface triangulation can be useful for calculating the motion of deformable bodies when solving problems of the dynamics of continuous media on immovable Euler grids.
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Omidi, Mahdi, Qingfei Min, Vahab Moradinaftchali, and Muhammad Piri. "The Efficacy of Predictive Methods in Financial Statement Fraud." Discrete Dynamics in Nature and Society 2019 (May 2, 2019): 1–12. http://dx.doi.org/10.1155/2019/4989140.
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The existence and persistence of financial statement fraud (FSF) are detrimental to the financial health of global capital markets. A number of detective and predictive methods have been used to prevent, detect, and correct FSF, but their practicability has always been a big challenge for researchers and auditors, as they do not address real-world problems. In this paper, both supervised and unsupervised approaches are employed for analysing the financial data obtained from China’s stock market in detecting FSF. The variables used in this paper are 18 financial datasets, representing a fraud triangle. Additionally, this study examined the properties of five widely used supervised approaches, namely, multi-layer feed forward neural network (MFFNN), probabilistic neural network (PNN), support vector machine (SVM), multinomial log-linear model (MLM), and discriminant analysis (DA), applied in different real-life situations. The empirical results show that MFFNN yields the best classification results in detection of fraudulent data presented in financial statement. The outcomes of this study can be applied to different types of financial statement datasets, as they present a practical way for constructing predictive models using a combination of supervised and unsupervised approaches.
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Huang, Guanxin, Hu Wang, and Guangyao Li. "Some modifications for ES-FEM and its application for vehicle design." Engineering Computations 32, no. 5 (July 6, 2015): 1432–59. http://dx.doi.org/10.1108/ec-11-2013-0268.
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Purpose – The purpose of this paper is to enhance the feasibility of the edge-based smoothed triangular (EST) element, some modifications are made in this study. Design/methodology/approach – First, an efficient strategy based on graph theory is proposed to construct the edge system. Second, the stress is smoothed in global coordinate system based on edge instead of strain, which makes the theory of EST more rigorous and can be easily extended to the situation of multi elements sharing the same edge. Third, the singular degree of freedoms (DOFs) of the nodes linked by edges are restrained in edge local coordinate system, which makes the global stiffness matrix non-singular and can be decomposed successfully. Findings – First, an efficient edge constructing strategy can make EST element more standout. Second, some modifications should be made to EST element to extend it to the situation with multi elements sharing the same edge, so that EST element can deal with the geometrical models with this kind of features. Third, the way to restrain the singular DOFs of EST element must be different from normal isoparametric triangle element, because the stiffness matrix of the smoothing domain is not computed in local coordinate system. Originality/value – The modified EST element performs stably in engineering analysis including large scale problems and the situation with multi elements sharing the same edge, and the efficiency of edge system constructing is no longer the bottleneck.
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Ghasemi, Farid. "Clean Energy Efficiency of Vernacular-Traditional Architectural Indicators for the Development of Sustainable Tourism." Journal of Sustainable Development 10, no. 3 (May 31, 2017): 250. http://dx.doi.org/10.5539/jsd.v10n3p250.
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Over the decades, due to the different crises, in which people are involved, they are trying to remove these big challenges with their dynamic mind. The consecutive changes in climatic conditions on one hand and energy crises on the other hand have affected human life every moment. It seems that through considering the attitudes to clean energies and their efficiency through inspiring past experiences in a combination of past and present time can not only show response to the coming problems, but also it can cover some parts of economic considerations. Tourism industry that has been considered for many years as one of the sustainable economic aspects can be valuable base for the said combination. This study tends to introduce a triangle of sustainable origins of tourism based on 3 mentioned factors including decline of energy resources, vernacular-traditional architecture experiences and tourism industry. According to the mentioned, it is necessary to implement some plans in way of use of nature of clean energies with approach of sustainable development and create some powerful foundations for this purpose through an overview of Iran's traditional architecture, which has paid specific attention to climate and the designations and constructions have been based on climatic approaches.
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Yurkov, V. "Images of Linear Conditions on a Manhattan Plane." Geometry & Graphics 8, no. 1 (April 20, 2020): 3–14. http://dx.doi.org/10.12737/2308-4898-2020-3-14.
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In this paper are considered planar point sets generated by linear conditions, which are realized in rectangular or Manhattan metric. Linear conditions are those expressed by the finite sum of the products of distances by numerical coefficients. Finite sets of points and lines are considered as figures defining linear conditions. It has been shown that linear conditions can be defined relative to other planar figures: lines, polygons, etc. The design solutions of the following general geometric problem are considered: for a finite set of figures (points, line segments, polygons...) specified on a plane with a rectangular metric, which are in a common position, it is necessary to construct sets that satisfy any linear condition. The problems in which the given sets are point and segment ones have been considered in detail, and linear conditions are represented as a sum or as relations of distances. It is proved that solution result can be isolated points, broken lines, and areas on the plane. Sets of broken lines satisfying the given conditions form families of isolines for the given condition. An algorithm for building isoline families is presented. The algorithm is based on the Hanan lattice construction and the isolines behavior in each node and each sub-region of the lattice. For isoline families defined by conditions for relation of distances, some of their properties allowing accelerate their construction process are proved. As an example for application of the described theory, the problem of plane partition into regions corresponding to a given set of points, lines and other figures is considered. The problem is generalized problem of Voronoi diagram construction, and considered in general formulation. It means the next: 1) the problem is considered in rectangular metric; 2) all given points may be integrated in various figures – separate points, line segments, triangles, quadrangles etc.; 3) the Voronoi diagram’s property of proximity is changed for property of proportionality. Have been represented examples for plane partition into regions, determined by two-point sets.
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PADILLA, JENNIFER E., MATTHEW J. PATITZ, ROBERT T. SCHWELLER, NADRIAN C. SEEMAN, SCOTT M. SUMMERS, and XINGSI ZHONG. "ASYNCHRONOUS SIGNAL PASSING FOR TILE SELF-ASSEMBLY: FUEL EFFICIENT COMPUTATION AND EFFICIENT ASSEMBLY OF SHAPES." International Journal of Foundations of Computer Science 25, no. 04 (June 2014): 459–88. http://dx.doi.org/10.1142/s0129054114400061.
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In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla et al. [24] to be asynchronous, allowing any action of turning a glue on or off, attaching a new tile, or breaking apart an assembly to happen in any order. Within this highly generalized model we provide three new solutions to tile self-assembly problems that have been addressed within the abstract Tile Assembly Model and its variants, showing that signal passing tiles allow for substantial improvement across multiple complexity metrics. Our first result utilizes a recursive assembly process to achieve tile-type efficient assembly of linear structures, using provably fewer tile types than what is possible in standard tile assembly models. Our second system of signal-passing tiles simulates any Turing machine with high fuel efficiency by using only a constant number of tiles per computation step. Our third system assembles the discrete Sierpinski triangle, demonstrating that this pattern can be strictly self-assembled within the STAM. This result is of particular interest in that it is known that this pattern cannot self-assemble within a number of well studied tile self-assembly models. Notably, all of our constructions are at temperature 1, further demonstrating that signal-passing confers the power to bypass many restrictions found in standard tile assembly models.
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BALOGH, JÓZSEF, JANE BUTTERFIELD, PING HU, JOHN LENZ, and DHRUV MUBAYI. "On the Chromatic Thresholds of Hypergraphs." Combinatorics, Probability and Computing 25, no. 2 (March 6, 2015): 172–212. http://dx.doi.org/10.1017/s0963548315000061.
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Let $\mathcal{F}$ be a family of r-uniform hypergraphs. The chromatic threshold of $\mathcal{F}$ is the infimum of all non-negative reals c such that the subfamily of $\mathcal{F}$ comprising hypergraphs H with minimum degree at least $c \binom{| V(H) |}{r-1}$ has bounded chromatic number. This parameter has a long history for graphs (r = 2), and in this paper we begin its systematic study for hypergraphs.Łuczak and Thomassé recently proved that the chromatic threshold of the so-called near bipartite graphs is zero, and our main contribution is to generalize this result to r-uniform hypergraphs. For this class of hypergraphs, we also show that the exact Turán number is achieved uniquely by the complete (r + 1)-partite hypergraph with nearly equal part sizes. This is one of very few infinite families of non-degenerate hypergraphs whose Turán number is determined exactly. In an attempt to generalize Thomassen's result that the chromatic threshold of triangle-free graphs is 1/3, we prove bounds for the chromatic threshold of the family of 3-uniform hypergraphs not containing {abc, abd, cde}, the so-called generalized triangle.In order to prove upper bounds we introduce the concept of fibre bundles, which can be thought of as a hypergraph analogue of directed graphs. This leads to the notion of fibre bundle dimension, a structural property of fibre bundles that is based on the idea of Vapnik–Chervonenkis dimension in hypergraphs. Our lower bounds follow from explicit constructions, many of which use a hypergraph analogue of the Kneser graph. Using methods from extremal set theory, we prove that these Kneser hypergraphs have unbounded chromatic number. This generalizes a result of Szemerédi for graphs and might be of independent interest. Many open problems remain.
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Aboulnaga, Mohsen, and Mona Mostafa. "Mitigating Heat Islands Effect in Mega Cities through Districts' Prioritisation for Urban Green Coverage Applications: Cairo – Egypt as a Case Study." Renewable Energy and Environmental Sustainability 4 (2019): 5. http://dx.doi.org/10.1051/rees/2019002.
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Heat-related problems have become a global issue resulted from climate change. Prolonged exposure to extreme high temperatures increased the percentage of mortality and morbidity in cities worldwide. Urbanization and population contribute to urban heat islands effect (UHIE). The purpose of this paper is to prioritize urban areas at high risk for heat related incidents in mega cities and to propose the implementation of urban green coverage (UGC) strategies which contribute to mitigating UHIE. The methodology includes a review on the UHI problems, along with the cooling benefits the UGC can produce. Then, the study's application is mainly focused on Cairo Governorate, Egypt as an example of a developing country. Cairo Governorate, Egypt lacks well maintained vegetation in almost all districts as results indicated that it has a mean normalized difference vegetation index (NDVI) ranging from 0.08 to 0.25. The study adopts the Australian model developed by Norton et al. [Landsc. Urban Plan. 134, 127 (2015)], which includes the intersection of three factors (heat exposure, vulnerability, and behavioural exposure) to identify a high priority area. It was difficult to assess the behaviour of population in outdoor public spaces in a city like Cairo; hence, the study follows “Crichton's Risk Triangle” conducted by Morabito et al. [PLoS One 10, e0127277 (2015)], to identify high risk areas based on the intersection of three layers: (a) high day-time/night-time surface temperatures − hazard; (b) total exposed population in a city − exposure; and (c) sub-populations at risk of being harmed during extreme heat − vulnerability. In the simulation, the risk assessment method simplifies the process of constructing the GIS database as it is composed of layering system. The development of a Heat-related Vulnerability Index (HVI) map for Cairo districts was conducted by over layering the natural hazard layer (land surface temperature) with spatial demographic data using GIS Software. Results of risk maps of Cairo were presented and showed normalized HVI values ranging between 0.0 and 1.0, which can be categorized into five risk levels (very low to very high). Results also indicated that 13 out of the 46 districts in Cairo are at very high/high risk, while only 5 districts have a very low risk. Finally, a tool was established to map the population vulnerability to extreme heat events by identifying high priority risk areas that requires urgent intervention by applying more UGC to mitigate UHIE and climate action and adaptation.
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Li, Gaoyang, Yuxiang Hong, Jiapeng Gao, Bo Hong, and Xiangwen Li. "Welding Seam Trajectory Recognition for Automated Skip Welding Guidance of a Spatially Intermittent Welding Seam Based on Laser Vision Sensor." Sensors 20, no. 13 (June 29, 2020): 3657. http://dx.doi.org/10.3390/s20133657.
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To solve the problems of low teaching programming efficiency and poor flexibility in robot welding of complex box girder structures, a method of seam trajectory recognition based on laser scanning displacement sensing was proposed for automated guidance of a welding torch in the skip welding of a spatially intermittent welding seam. Firstly, a laser scanning displacement sensing system for measuring angles adaptively is developed to detect corner features of complex structures. Secondly, a weld trajectory recognition algorithm based on Euclidean distance discrimination is proposed. The algorithm extracts the shape features by constructing the characteristic triangle of the weld trajectory, and then processes the set of shape features by discrete Fourier analysis to solve the feature vector used to describe the shape. Finally, based on the Euclidean distance between the feature vector of the test sample and the class matching library, the class to which the sample belongs is identified to distinguish the weld trajectory. The experimental results show that the classification accuracy rate of four typical spatial discontinuous welds in complex box girder structure is 100%. The overall processing time for weld trajectory detection and classification does not exceed 65 ms. Based on this method, the field test was completed in the folding special container production line. The results show that the system proposed in this paper can accurately identify discontinuous welds during high-speed metal active gas arc welding (MAG) welding with a welding speed of 1.2 m/min, and guide the welding torch to automatically complete the skip welding, which greatly improves the welding manufacturing efficiency and quality stability in the processing of complex box girder components. This method does not require a time-consuming pre-welding teaching programming and visual inspection system calibration, and provides a new technical approach for highly efficient and flexible welding manufacturing of discontinuous welding seams of complex structures, which is expected to be applied to the welding manufacturing of core components in heavy and large industries such as port cranes, large logistics transportation equipment, and rail transit.
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Aspara, Wimpie Agoeng Noegroho, and Eka Nur Fitriani. "PENGARUH JARAK DAN POLA PREFABRICATED VERTICAL DRAIN (PVD) PADA PERBAIKAN TANAH LEMPUNG LUNAK = EFFECT OF DISTANCE AND PATTERN OF PREFABRICATED VERTICAL DRAIN FOR IMPROVEMENT OF SOFT CLAY SOIL." Majalah Ilmiah Pengkajian Industri 10, no. 1 (April 1, 2016): 41–50. http://dx.doi.org/10.29122/mipi.v10i1.102.
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AbstractIf a structure for reasons of technical, economic, social, or startegic is to be built on a soft ground, then there are usually two problems to be solved, namely the low geotechnical bearing capacity and large soil deformation with sometimes differential settlement. Pre-compression is a foundation soil compression process with the provision of temporary loading (preloading) before actually constructing a building. Pre-fabricated vertical drain is a synthetic drainage system installed vertically inside soft soil layers. Soil condition at the project activity is a relatively very soft clay soil with relatively high coefficient of consolidation resulting in very long period of consolidation process. Therefore, it is needed advance soil improvement by prealoding of pre-fabricated vertical drain. Spacings of installed PVD vary, those are 50 cm, 100 cm, 150 cm, and 200 cm with a pattern of triangles and rectangles. Based on the analytical calculation, it is resulted that optimum PVD distance to achieve 90% consolidation is 150 cm with a triangular pattern. The time of consolidation was achieved within four months. AbstrakKetika suatu struktur karena alasan-alasan teknis, ekonomi, sosial, atau strategis terpaksa didirikan di atas tanah lunak, maka biasanya ada dua masalah geoteknik yang harus dipecahkan yaitu daya dukung yang rendah dan penurunan serta beda penurunan yang besar. Prakompresi adalah suatu proses pemampatan tanah pondasi dengan jalan pemberian pembebanan sementara (prabeban/preloading) sebelum konstruksi yang sesungguhnya didirikan. Prefabricated vertical drain (PVD) adalah sistem drainase buatan yang dipasang vertikal di dalam lapisan tanah lunak. Kondisi tanah di lokasi kegiatan relatif sangat lunak dengan koefisien konsolidasi relatif sangat tinggi mengakibatkan proses konsolidasi berjalan relatif sangat lama. Untuk itu diperlukan perbaikan tanah terlebih dahulu dengan prealoading menggunakan PVD. Jarak spasi antar PVD yang dipasang bervaiasi yaitu 50 cm, 100 cm, 150 cm, dan 200 cm dengan pola konfigurasi segitiga dan segiempat. Berdasarkan hasil perhitungan secara analitis didapatkan jarak optimum PVD untuk mencapai konsolidasi 90% adalah 150 cm dengan pola segitiga dengan proses konsolidasi dicapai selama waktu penurunan 4 bulan.
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Schweimer, Christoph, Bernhard C. Geiger, Meizhu Wang, Sergiy Gogolenko, Imran Mahmood, Alireza Jahani, Diana Suleimenova, and Derek Groen. "A route pruning algorithm for an automated geographic location graph construction." Scientific Reports 11, no. 1 (June 2, 2021). http://dx.doi.org/10.1038/s41598-021-90943-8.
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AbstractAutomated construction of location graphs is instrumental but challenging, particularly in logistics optimisation problems and agent-based movement simulations. Hence, we propose an algorithm for automated construction of location graphs, in which vertices correspond to geographic locations of interest and edges to direct travelling routes between them. Our approach involves two steps. In the first step, we use a routing service to compute distances between all pairs of L locations, resulting in a complete graph. In the second step, we prune this graph by removing edges corresponding to indirect routes, identified using the triangle inequality. The computational complexity of this second step is $$\mathscr{O}(L^3)$$ O ( L 3 ) , which enables the computation of location graphs for all towns and cities on the road network of an entire continent. To illustrate the utility of our algorithm in an application, we constructed location graphs for four regions of different size and road infrastructures and compared them to manually created ground truths. Our algorithm simultaneously achieved precision and recall values around 0.9 for a wide range of the single hyperparameter, suggesting that it is a valid approach to create large location graphs for which a manual creation is infeasible.
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Atteh, Evans, Emmanuel Acquandoh, Augustine Boadi, and Emmanuel Appoh Andam. "The Effect of Using Hands-on Materials in Teaching Pythagoras Theorem." Journal of Scientific Research and Reports, July 2, 2020, 106–16. http://dx.doi.org/10.9734/jsrr/2020/v26i530265.
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This study sought to improve students’ performance in solving problems on the application of the Pythagoras Theorem using hands - on materials. It is an action research and the selected sample of the study was mixed gender class of level 200 (2A1 Class) year group, comprising of forty (40) students in Wiawso College of Education. It involved the use of pre –test and post –test as the methods for data collection. The pre-test was conducted after which an intervention period of four weeks, which involved taking the students through the concept of the application of Pythagoras theorem. A post-test was also conducted after the intervention, the scores obtained from the pre-test and post-test were analyzed by the use of statistical package for social sciences (SPSS). The findings revealed that after the intervention, students were able to overcome the challenges they faced when solving story problems and problems on 3-dimensions involving the Pythagoras Theorem. They could also identify shapes depicting the concept of the Pythagoras’ theorem and construction of squares on each side of a right triangle. From the findings it was concluded that the use of hands-on materials in the intervention processes has help improved students understanding and performance.
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Gowers, W. T., and J. Long. "The length of an s-increasing sequence of r-tuples." Combinatorics, Probability and Computing, January 8, 2021, 1–36. http://dx.doi.org/10.1017/s0963548320000371.
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Abstract We prove a number of results related to a problem of Po-Shen Loh [9], which is equivalent to a problem in Ramsey theory. Let a = (a1, a2, a3) and b = (b1, b2, b3) be two triples of integers. Define a to be 2-less than b if a i < b i for at least two values of i, and define a sequence a1, …, a m of triples to be 2-increasing if a r is 2-less than a s whenever r < s. Loh asks how long a 2-increasing sequence can be if all the triples take values in {1, 2, …, n}, and gives a log* improvement over the trivial upper bound of n2 by using the triangle removal lemma. In the other direction, a simple construction gives a lower bound of n3/2. We look at this problem and a collection of generalizations, improving some of the known bounds, pointing out connections to other well-known problems in extremal combinatorics, and asking a number of further questions.
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Steffen, Vibeke. "TIL KONSULTATION HOS ÅNDERNE: Om klarsyn, energier og magi i Danmark." Tidsskriftet Antropologi, no. 61 (July 1, 2010). http://dx.doi.org/10.7146/ta.v0i61.106863.
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There is a long-standing anthropological tradition of studies where the concept
of magic is related to crisis and the re-establishment of order, whether on a
social or an individual level. The risk of this approach, however, is that we may
mistake the intention with magic for its result, and thus overestimate the role of
crisis, the management of problems and the construction of meaning. This article
demonstrates that instead of providing answers and solutions, the engagement with
magic may just as well open up for new questions and new problems. The subject
of the study is spiritualism and second sight as practised in contemporary Danish
society primarily by women. In this context, magic is not necessarily something
extraordinary that people turn to when facing severe trouble, but rather a way of
dealing with social relations in everyday life. My approach is inspired by Evans-
Pritchard’s classic work on witchcraft, oracles and magic among the Azande in
the sense that the concept of magic forms only one leg in a triangle with energies
and second sight as the other two. Second sight is provided by mediums passing
on messages from deceased relatives or other spirits at platform demonstrations
or in private consultations. The messages often deal with distance and proximity
in social relations and how to protect yourself against feelings of being drained of
energy or invaded by other human or spiritual beings. The term energy provides a
sense of physical reality to these otherwise subtle feelings and makes it possible
to deal with them in concrete situations through spells, invocations, and other
kinds of magic manipulation.
Keywords: Spiritism, social relations, the boundaries of self , women.
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Shang, Yan, and Huanpu Wu. "Couple stress-based unsymmetric 8-node planar membrane elements with good tolerances to mesh distortion." Engineering Computations ahead-of-print, ahead-of-print (August 18, 2021). http://dx.doi.org/10.1108/ec-03-2021-0145.
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PurposeThe paper aims to propose two new 8-node quadrilateral membrane elements with good distortion tolerance for the modified couple stress elasticity based on the unsymmetric finite element method (FEM).Design/methodology/approachThe nodal rotation degrees of freedom (DOFs) are introduced into the virtual work principle and constrained by the penalty function for approximating the test functions of the physical rotation and curvature. Therefore, only the C0 continuity instead of C1 continuity is required for the displacement during the element construction. The first unsymmetric element assumes the test functions of the displacement and strain using the standard 8-node isoparametric interpolations, while these test functions in the second model are further enhanced by the nodal rotation DOFs. Besides, the trial functions in these two elements are constructed based on the stress functions that can a priori satisfy related governing equations.FindingsThe benchmark tests show that both the two elements can efficiently simulate the size-dependent plane problems, exhibiting good numerical accuracies and high distortion tolerances. In particular, they can still exactly reproduce the constant couple stress state when the element shape deteriorates severely into the degenerated triangle. Moreover, it can also be observed that the second element model, in which the linked interpolation technique is used, has better performance than the first one, especially in capturing the steep gradients of the physical rotations.Originality/valueAs the proposed new elements use only three DOFs per node, they can be readily incorporated into the existing finite element (FE) programs. Thus, they are of great benefit to analysis of size-dependent membrane behaviors of micro/nano structures.
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Asmiani, Asmiani, and Hayari Hayari. "SEJARAH BANDARA MATAHORA DI PULAU WANGI-WANGI KABUPATEN WAKATOBI (2007-2017)." Jurnal Penelitian Pendidikan Sejarah UHO 3, no. 3 (July 12, 2020). http://dx.doi.org/10.36709/jpps.v3i3.12820.
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ABSTRAK: Permasalahan pokok dalam penelitian ini adalah: (1) Apa latar belakang pembangunan Bandara Matahora di Pulau Wangi-Wangi Kabupaten Wakatobi, (2) Apa kendala yang dihadapi dalam pembangunan Bandara Matahora di Pulau Wangi-Wangi Kabupaten Wakatobi? (3) Apa dampak yang ditimbulkan terhadap pembangunan Bandara Matahora di Pulau Wangi-Wangi Kabupaten Wakatobi? dan (4) Bagaimana Perkembangan pembangunan Bandara Matahora di Pulau Wangi-Wangi Kabupaten Wakatobi? Penelitian ini menggunakan metode sejarah yang dikemukakan oleh Helius Sjamsuddin, yang terdiri atas 3 tahap yaitu: (1) Heuristik yakni mencari sumber melalui wawancara, studi kepustakaan, dan penelitian lapangan, (2) Kritik Sumber terdiri atas kritik eksternal dan kritik internal guna mendapat data yang akurat, (3) Historiografi yang dimaksudkan dalam bentuk karya tulis kronologis, sistematis dan ilmiah. Penelitian ini menunjukan bahwa latar belakang perkembangan Bandara Matahora berawal dari pemikiran atau ide bupati wakatobi Ir. Hugua yang yang tergambar dalam visi misinya membangun dan menjadikan Kabupaten Wakatobi menjadi daerah yang digemari oleh banyak orang dengan visi “Terwujudnya Surga Nyta Bawah Laut di Pusat Segitiga Karang Dunia” (2) Kendala yang dihadapi dalam pembangunan Bandara Matahora dapat dilihat dari pandangan masyarakat yang diwujudkan dalam bentuk respon dari masyarakat berkaitan dengan pembangunan Bandara Matahora serta kecenderungan rencana yang dilakukan pasca Bandara terbangun. Respon yang dimaksud adalah respon mengenai pembangunan Bandara Matahora. Misalnya dari satu pihak menerima adanya Bandara Matahora dipihak lain ada yang menolak pembangunan Bandara Matahora. (3) Dampak dari pembangunan Bandara Matahora ialah terdapat dampak yang bersifat positif dan yang bersifat negatif bagi masyarakat dan daerah. (4) Perkembangan pembangunan Bandara Matahora dari tahun ke tahun semakin bagus, dimana Bandara yang menjadi kebanggaan masyarakat tersebut digunakan dengan semaksimal mungkin dan pembangunan tambahan Bandara terus berkelanjutan hingga saat ini. Disamping itu, banyak wisatawan dalam dan luar negeri yang menggunakan Bandara Matahora tersebut sebagai alternatif yang memungkinkan perjalanan masyarakat bisa dijangkau dengan cepat. Kata Kunci: Sejarah, Bandara Matahora, Pulau Wangi-Wangi, dan Wakatobi ABSTRACT: The main problems in this study are: (1) What is the background of the development of Matahora Airport on Wangi-Wangi Island, Wakatobi Regency, (2) What are the obstacles faced in the construction of Matahora Airport on Wangi-Wangi Island, Wakatobi Regency? (3) What are the impacts on the construction of Matahora Airport on Wangi-Wangi Island, Wakatobi Regency? and (4) How is the development of Matahora Airport development on Wangi-Wangi Island, Wakatobi Regency? This research uses the historical method proposed by Helius Sjamsuddin, which consists of 3 stages, namely: (1) Heuristics which is looking for sources through interviews, library research, and field research, (2) Source Criticism consists of external criticism and internal criticism in order to obtain data accurate, (3) Historiography intended in the form of chronological, systematic and scientific writing. This research shows that the background of the development of Matahora Airport originated from the thoughts or ideas of the Regent of Wakatobi, Ir. Hugua, who is depicted in his vision and mission to build and make Wakatobi Regency a favorite area for many people with the vision of "Realizing the Underwater Paradise of the Sea at the Center of the World Coral Triangle" (2) Constraints faced in the construction of Matahora Airport can be seen from the view of the community that is realized in the form of response from the public relating to the construction of Matahora Airport and the tendency of plans to be carried out after the Airport was built. The response in question is the response regarding the construction of Matahora Airport. For example, from one party accepting the existence of Matahora Airport, on the other hand there are those who reject the construction of Matahora Airport. (3) The impact of Matahora Airport development is that there are positive and negative impacts on the community and the region. (4) The development of the Matahora Airport development from year to year is getting better, where the Airport which is the pride of the community is used to the maximum extent possible and the construction of additional airports continues to the present. In addition, many domestic and foreign tourists who use the Matahora Airport as an alternative that allows people's trips can be reached quickly. Keywords: History, Matahora Airport, Wangi-Wangi Island, and Wakatobi
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"Triangular Relationships and Most Beautiful Bodies: On the Significance of απειρα at Timaeus 57d5, and on the Number of Plato's Elementary Triangles." Mnemosyne 62, no. 1 (2009): 11–29. http://dx.doi.org/10.1163/156852508x252867.
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AbstractAccording to an interpretation first proposed by Cornford (1937), Plato intends that the many different triangles or squares required for the construction of 'elements' in the Timaeus are all built up using multiples of two elemental triangles, the στοιχεια. An alternative view, which also has wide acceptance, is that there are many elemental triangles, of different sizes; in an extreme form of this there is an unlimited or even infinite variety of the triangles. These views are analysed, and it is concluded that Cornford's interpretation, despite some problems, is still the best currently available.
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ÇEZIKTÜRK, ÖZLEM, SINEM İNCE, GÜLAY YALIM, KÜBRA KARADENIZ, and ZÜLAL KENAR. "Making a Rhombicosidodecahedron: Mathematical Thinking Revisited." Indonesian Research Journal in Education |IRJE|, May 17, 2019, 120–40. http://dx.doi.org/10.22437/irje.v3i1.4865.
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A rhombicosidodecahedron (an Archimedean solid with 30 square, 20 triangles, and 12 pentagon faces) was redeemed from 60 pieces by modular origami. This study used a qualitative research case study as it asked about how participants experienced this construction process of rhombicosidodecahedron. Preservice primary mathematics teachers from a mathematics and art course were participants of the study. Additionally, one student; the first student who came out with the totally symmetric and no damaged object was interviewed for the assembly process. Mathematical thinking throughout the process was noted. Student brought her/his previous experiences as much as specific aptıtudes. Student took this project as a creative writing piece so that the process gone through similar phases as intro, progress, and artifact. Deformations and sinking occurred but student investigated the specifics of the real mathematical object did it without a fault. To deal with problems occurred in the phases; students used a creative insight as using paperclips to attach modules and assembly of half spheres. Two main processes; organizational and structural took place in the creative model formation and assembly. Suggestions and future studies are also discussed.
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Bayoumi, Mohamed A., Tarek M. Salem, and Samir M. Koriem. "Improving the Mechanism of Detecting and Measuring Holes in Ad hoc Wireless Sensor Network." Computer Journal, August 15, 2019. http://dx.doi.org/10.1093/comjnl/bxz054.
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Abstract Area detection and measuring is one of the most important problems in wireless sensor network because it mainly relates to the continuity and functionality of most routing protocols applied to the region of interest (ROI). Electronics failure, random deployment of nodes, software errors or some phenomena such as fire spreading or water flood could lead to wide death of sensor nodes. The damage on ROI can be controlled by detecting and calculating the area of the holes, resulting from the damaged sensor networks. In this paper, a new mathematical algorithm, wireless sensor hole detection algorithm (WHD), is developed to detect and calculate the holes area in ROI where the sensor nodes are spread randomly. WHD is developed for achieving quality of service in terms of power consumption and average hole detection time. The dynamic behavior of the proposed WHD depends on executing the following steps. Firstly, WHD algorithm divides down the ROI into many cells using the advantage of the grid construction to physically partition the ROI into many small individual cells. Secondly, WHD algorithm works on each cell individually by allocating the nearest three sensor nodes to each of the cell’s coordinates by comparing their positions, WHD connects each cell’s coordinate points with the selected sensor nodes by lines that construct a group of triangles, then WHD calculates the area of upcoming triangles. Repeating the previous step on all the cells, WHD can calculate and locate each hole in the ROI. The performance evaluation depends on the NS-2 simulator as a simulation technique to study and analyze the performance of WHD algorithm. Results show that WHD outperforms, in terms of average energy consumption and average hole discovery time, path density algorithm, novel coverage hole discovery algorithm and distriputed coverage hole Detection.
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Butler, Richard J. "Econometrics Illustrated, with Applications from Insurance-Research Awards." Asia-Pacific Journal of Risk and Insurance 11, no. 2 (January 1, 2017). http://dx.doi.org/10.1515/apjri-2017-0002.
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AbstractThe linear regression model is the dominant tool employed in applied risk and insurance research. Based on my 2016 APRIA lecture at Chengdu, China, I illustrate the simple geometry of the linear regression model, as well as some standard results from it: omitted variable bias (OVB), classical measurement error (CME), simultaneous equation models (SEM), and instrumental variable estimation. Instrumental variable estimation solves OVB, CME, and SEM problems by constructing similar triangles to retrieve consistent estimates. I apply these tools by estimating the determinants of the Witt and Mehr awards given annually for Journal of Risk and Insurance articles, as two examples. The Witt vs. Mehr awards also contrasts short-term scholarly recognition (Witt) versus long-term scholarly recognition (Mehr). The comments made here apply to other paper awards, such as those presented by the Asian Pacific Journal of Risk and Insurance. I also present a simple index function based on the classical Gini index (hence, this new index is denoted as the regression gini index, RGI) useful for comparing two regression models, and apply this to explain the empirical difference between the determinants of the Witt and Mehr awards.