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Journal articles on the topic 'Geometrical abstraction'
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Burov, Andrey Mikhailovich. "The Line in Neo-Modernism Geometrical Abstraction." Journal of Flm Arts and Film Studies 3, no. 3 (2011): 54–63. http://dx.doi.org/10.17816/vgik3354-63.
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The article overviews the development of the line as a pictorial element in Neo-Modernism. It refers to different variants of linear strategy in geometric abstractions and the tendency of the line to become the leading element of the work of art up to pure linear constructions, such as a two-or three- dimensional grid. This grid is the key structure of the new forms of modern art built on repetition.
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Hauser, J., and A. Brümmer. "Geometrical abstraction of screw compressors for thermodynamic optimization." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 6 (2011): 1399–406. http://dx.doi.org/10.1177/0954406210395884.
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The construction and development of different rotor profiles is an important area in connection with the development of screw compressors for specific applications. Geometrical performance figures (using criteria to describe interdependencies of geometrical parameters for screw compressors) for profile optimization are used in order to achieve specific improvements in performance. During this process, rotor profiles and spatial parameters are the main factors. Compared to data derived from the front section of rotor profiles, these figures which also take spatial parameters into account provide a better evaluation of gap conditions and operating efficiency of the compressors under examination.
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Dietler, G., W. Känzig, A. Häberli, and P. W. Straub. "Experimental tests of a geometrical abstraction of fibrin polymerization." Biopolymers 25, no. 5 (1986): 905–29. http://dx.doi.org/10.1002/bip.360250511.
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Skordialos, Emmanouil, and Georgios Baralis. "A teaching approach of geometric shapes’ properties with the use of online educational tools in Greek primary school." New Trends and Issues Proceedings on Humanities and Social Sciences 4, no. 9 (2018): 101–9. http://dx.doi.org/10.18844/prosoc.v4i9.3044.
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A number of researchers have shown concern at the difficulties that primary school pupils cope with in learning geometry, and have tried to explain why this happens and what can be done to make the subject more understandable to young learners. Van Hiele’s theoretical model postulates five levels of geometric thinking as visualisation, analysis, abstraction, formal deduction and rigour. Each level uses its own language and symbols. Pupils pass through the levels ‘step by step’. This hierarchical order helps them to achieve better understanding and results. In this research the teacher taught geometry in the 2nd class in a primary Greek school with the use of information and communication technologies. The aim is to find out the level of geometrical thought of the pupils and how geometrical activities – based on online tools – concerning the geometrical shapes and their properties, help students improve their mathematical knowledge in the class. Keywords: Geometric thinking, online tools, shapes, geometrical activities
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Gadh, R., and F. B. Prinz. "A Computationally Efficient Approach to Feature Abstraction in Design-Manufacturing Integration." Journal of Engineering for Industry 117, no. 1 (1995): 16–27. http://dx.doi.org/10.1115/1.2803272.
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Design-for-Manufacturing (DFM) analysis saves time and reduces production costs by anticipating manufacturing problems at a product’s design stage. Performing manufacturing analysis of a design created by Computer Aided Design (CAD) systems requires a higher level of geometrical abstraction of its component features. For complicated parts, such as those found in injection molding, this problem becomes very difficult. The current approach presents a computationally efficient approach to converting the basic topological elements used in CAD systems into more abstract geometrical features necessary for DFM analysis. Very large computer models of parts have been subjected to feature recognition using the current system, ManuFEATURE, with significant success.
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Jamali, Ali, Alias Abdul Rahman, and Pawel Boguslawski. "A Hybrid 3D Indoor Space Model." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W1 (October 26, 2016): 75–80. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w1-75-2016.
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GIS integrates spatial information and spatial analysis. An important example of such integration is for emergency response which requires route planning inside and outside of a building. Route planning requires detailed information related to indoor and outdoor environment. Indoor navigation network models including Geometric Network Model (GNM), Navigable Space Model, sub-division model and regular-grid model lack indoor data sources and abstraction methods. In this paper, a hybrid indoor space model is proposed. In the proposed method, 3D modeling of indoor navigation network is based on surveying control points and it is less dependent on the 3D geometrical building model. This research proposes a method of indoor space modeling for the buildings which do not have proper 2D/3D geometrical models or they lack semantic or topological information. The proposed hybrid model consists of topological, geometrical and semantical space.
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Verburgt, Lukas M. "Duncan F. Gregory, William Walton and the development of British algebra: ‘algebraical geometry’, ‘geometrical algebra’, abstraction." Annals of Science 73, no. 1 (2015): 40–67. http://dx.doi.org/10.1080/00033790.2015.1025844.
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Lathioor, Edward C., William J. Leigh та Michael J. St. Pierre. "Geometrical Effects on Intramolecular Quenching of Aromatic Ketone (π,π*) Triplets by Remote Phenolic Hydrogen Abstraction". Journal of the American Chemical Society 121, № 51 (1999): 11984–92. http://dx.doi.org/10.1021/ja991207z.
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Ramlan, Andi Mariani, and Fitriyani Hali. "Analysis of the Difficulty of Mathematical Education Students in Completing the Geometric Running Problem Based on Van Hiele Theory in Geometry Transformation." Journal of Mathematics Education 3, no. 2 (2018): 65–70. http://dx.doi.org/10.31327/jomedu.v3i2.834.
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The purpose of this study was to: (1) finding out the difficulties experienced by mathematics education students in solving geometric reasoning problems based on van Hiele's theory; (2) identifying the factors causing difficulties experienced by students in solving geometric problems based on van Hiele’s theory; and (3) determining the steps that need to be taken to overcome the students' difficulties in solving geometric reasoning problems based on van Hiele's theory in the Transformation Geometry Course. The students' difficulties in solving geometric reasoning problems based on van Hiele's levels will give an idea of the indicators of geometrical reasoning abilities that are still low, so that the right alternative solutions are obtained. This type of research is descriptive research with a qualitative approach. The research subjects were 28 students who programed geometry transformation courses. The instrument in this study was a test instrument, namely geometric reasoning abilities of students as many as 5 questions consisting of 5 levels of ability, namely visualization, analysis, abstraction, formal deduction, and rigor. While the data analysis techniques in this study used descriptive analysis. Collecting data in this study used interview techniques and written tests. The results showed that from the five indicators of geometric reasoning ability, for the visualization level, there were 26 people who achieved the optimal score with a percentage of 92.9. Seen at the level of analysis still not reached optimally with a percentage of 21.4 or only 6 people who achieved the optimal score, while the level of abstraction, formal deduction, and rigor has not been achieved. Difficulties experienced by students at the level of analysis, abstraction, formal deduction, and rigor. The causal factors experienced by students based on the results of interviews obtained information that students have difficulty answering questions due to several things including; students have forgotten about the material being taught, when they learn they understand but are less interested in developing, feel unsatisfied so they expect concrete media, need to be trained in many questions, and follow up to students. From this information, an appropriate alternative is needed, for example using van Hiele's theory to familiarize students with reasoning skills.
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Zhou, Dejian, Alexandru Tatomir, and Martin Sauter. "Thermo-hydro-mechanical modelling study of heat extraction and flow processes in enhanced geothermal systems." Advances in Geosciences 54 (June 8, 2021): 229–40. http://dx.doi.org/10.5194/adgeo-54-229-2021.
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Abstract. Enhanced Geothermal Systems (EGS) are widely used in the development and application of geothermal energy production. They usually consist of two deep boreholes (well doublet) circulation systems, with hot water being abstracted, passed through a heat exchanger, and reinjected into the geothermal reservoir. Recently, simple analytical solutions have been proposed to estimate water pressure at the abstraction borehole. Nevertheless, these methods do not consider the influence of complex geometrical fracture patterns and the effects of the coupled thermal and mechanical processes. In this study, we implemented a coupled thermo-hydro-mechanical (THM) model to simulate the processes of heat extraction, reservoir deformation, and groundwater flow in the fractured rock reservoir. The THM model is validated with analytical solutions and existing published results. The results from the systems of single fracture zone and multi-fracture zones are investigated and compared. It shows that the growth of the number and spacing of fracture zones can effectively decrease the pore pressure difference between injection and abstraction wells; it also increases the production temperature at the abstraction, the service life-spans, and heat production rate of the geothermal reservoirs. Furthermore, the sensitivity analysis on the flow rate is also implemented. It is observed that a larger flow rate leads to a higher abstraction temperature and heat production rate at the end of the simulation, but the pressure difference may become lower.
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Gravel, D., R. Giasson, D. Blanchet, R. W. Yip, and D. K. Sharma. "Photochemistry of the o-nitrobenzyl system in solution: effects of distance and geometrical constraint on the hydrogen transfer mechanism in the excited state." Canadian Journal of Chemistry 69, no. 8 (1991): 1193–200. http://dx.doi.org/10.1139/v91-178.
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Two rigid nitrobenzene derivatives, 5-nitro-1,2,3,4-tetrahydro-1,4-methanonaphthalene (6), and 5-nitro-1,2,3,4-tetra-hydro-1,4-ethanonaphthalene (7), have been synthesized and studied by picosecond flash absorption spectroscopy, steady-state irradiation, and MMX molecular mechanics calculations. Transients with lifetimes of 770 and 410 ps have been detected and assigned to the excited triplet states of 6 and 7, respectively. Consistent with prediction, the o-quinonoid intermediate is not detected in the time domain between the laser excitation and the end of decay of the triplet state. Intramolecular abstraction of the bridgehead benzylic hydrogen by the cited triplet state proceeds with relative rates of 1:125 for 6 and 7, respectively. Since structural constraints prohibit the formation of an orthoquinonoid intermediate in these systems, formation of the usual nitrosoalcohol 13 represents the first substantiation of the biradical route to product (3′ → 4, Scheme 1). Absorption of the intermediate triplet biradical resulting from hydrogen abstraction by the triplet excited state was not observed, and is therefore believed to be either very weak in the 400–700 nm region, or located outside the detection region. The kinetic results together with structural parameters determined by molecular mechanics show good correlation between structure and reactivity. Hydrogen atom transfer can proceed at up to 53° deviation from linearity of the C—H—O nuclei, with transfer rates decreasing sharply as the [Formula: see text] distance increases from 1.3 to 1.6 Å. It is suggested that the conditions of the reaction from the excited triplet state meet those required for a hydrogen tunneling mechanism. Key words: o-nitrotoluene photorearrangement, mechanism of; o-nitrobenzyl systems, mechanism of photorearrangement; [Formula: see text] distance, influence of, in hydrogen abstraction mechanism; picosecond flash absorption spectroscopy study of o-nitrobenzyl photorearrangement; radical pathway to product in o-nitrotoluene photorearrangement.
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Cervantes-Sánchez, J. J., J. M. Rico-Martínez, G. González-Montiel, and E. J. González-Galván. "The differential calculus of screws: Theory, geometrical interpretation, and applications." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 6 (2009): 1449–68. http://dx.doi.org/10.1243/09544062jmes1195.
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This article presents a novel and original formula for the higher-order time derivatives, and also for the partial derivatives of screws, which are successively computed in terms of Lie products, thus leading to the automation of the differentiation process. Through the process and, due to the pure geometric nature of the derivation approach, an enlightening physical interpretation of several screw derivatives is accomplished. Important applications for the proposed formula include higher-order kinematic analysis of open and closed kinematic chains and also the kinematic synthesis of serial and parallel manipulators. More specifically, the existence of a natural relationship is shown between the differential calculus of screws and the Lie subalgebras associated with the expected finite displacements of the end effector of an open kinematic chain. In this regard, a simple and comprehensible methodology is obtained, which considerably reduces the abstraction level frequently required when one resorts to more abstract concepts, such as Lie groups or Lie subalgebras; thus keeping the required mathematical background to the extent that is strictly necessary for kinematic purposes. Furthermore, by following the approach proposed in this article, the elements of Lie subalgebra arise in a natural way — due to the corresponding changes in screws through time — and they also have the typical shape of the so-called ordered Lie products that characterize those screws that are compatible with the feasible joint displacements of an arbitrary serial manipulator. Finally, several application examples — involving typical, serial manipulators — are presented in order to prove the feasibility and validity of the proposed method.
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Balajti, Zsuzsa, and József Ábel. "Applying Projective Geometry in Design of Worm Manufacturing." Key Engineering Materials 581 (October 2013): 77–81. http://dx.doi.org/10.4028/www.scientific.net/kem.581.77.
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The mathematical describing of the production process in mechanical engineer work in the euclidean space model and the base of the analytical describing of the projective space model is practically identical in the form, which makes it reasonable to discuss of the production geometry to approach of the projective geometrical negotiation in the . It is a fact that in one of the cases, using the approach of a projective geometrical connection and the mathematical-kinematical model resulted in expansion in the field of production precision, specifically considering the examination of the production of the conical worm by grinding wheel. The abstraction of the production geometry on projective space model has a few results in case of conical worms. The elliptical errors in production of the conical worm with arched or anything profile by grinding wheel can be eliminated by this method way to achieve the constant pitch, the torsion of profile and others.
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Piu, Angela, Cesare Fregola, and Barbara Barbieri. "Geometry Classrooms With Simulation/Games. Research Results and Future Developments." Simulation & Gaming 47, no. 6 (2016): 796–817. http://dx.doi.org/10.1177/1046878116665464.
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Background. As revealed by national surveys and comparisons with other countries, Italian students may have difficulties in learning mathematical content, and geometry in particular. Aim. This research aimed at ascertaining if, with respect to traditional methods, the structural characteristics of simulation games designed on the basis of specific theoretical and methodological choices can: (a) facilitate comprehension and improve the retention of geometric concepts; (b) increase pupils’ motivation to learn geometry; (c) affect perceived social and scholastic self-efficacy. Method. This mixed method research included an experimental and a control group and a qualitative analysis of an open-ended examination. Results. Our research with Y4 primary pupils (n=104) indicates that students who learned geometrical concepts via the simulation game had a higher level of both content retention and level of abstraction compared with those in the control group. Conclusions. The results of this study highlight the didactic effectiveness of simulation games with reference to the cognitive aspects of the learning process and indicate the need to develop design models for geometry-based simulations.
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Buongiorno Nardelli, Marco. "Topology of Networks in Generalized Musical Spaces." Leonardo Music Journal 30 (December 2020): 38–43. http://dx.doi.org/10.1162/lmj_a_01079.
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The abstraction of musical structures as mathematical objects in a geometrical space is one of the major accomplishments of contemporary music theory. The author generalizes the concept of musical spaces as networks and derives compositional design principles via network topology analysis. This approach provides a framework for analysis and quantification of similarity of musical objects and structures and suggests a way to relate such measures to human perception of different musical entities. Finally, network analysis provides alternative ways of interpreting the compositional process by quantifying emergent behaviors with well-established statistical mechanics. Interpreting the latter as probabilistic randomness in the network, the author develops novel compositional design frameworks.
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Kaufmann, Manuel, Ira Effenberger, and Marco F. Huber. "Measurement uncertainty assessment for virtual assembly." Journal of Sensors and Sensor Systems 10, no. 1 (2021): 101–8. http://dx.doi.org/10.5194/jsss-10-101-2021.
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Abstract. Virtual assembly (VA) is a method for datum definition and quality prediction of assemblies considering local form deviations of relevant geometries. Point clouds of measured objects are registered in order to recreate the objects' hypothetical physical assembly state. By VA, the geometrical verification becomes more accurate and, thus, increasingly function oriented. The VA algorithm is a nonlinear, constrained derivate of the Gaussian best fit algorithm, where outlier points strongly influence the registration result. In order to assess the robustness of the developed algorithm, the propagation of measurement uncertainties through the nonlinear transformation due to VA is studied. The work compares selected propagation methods distinguished from their levels of abstraction. The results reveal larger propagated uncertainties by VA compared to the unconstrained Gaussian best fit.
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Molina-Carmona, R., A. Jimeno, and R. Rizo-Aldeguer. "Morphological Offset Computing for Contour Pocketing." Journal of Manufacturing Science and Engineering 129, no. 2 (2006): 400–406. http://dx.doi.org/10.1115/1.2540741.
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Background. Tool path generation problem is one of the most complexes in computer aided manufacturing. Although some efficient algorithms have been developed to solve it, their technological dependency makes them efficient in only a limited number of cases. Method of Approach. Our aim is to propose a model that will set apart the geometrical issues involved in the manufacturing process from the purely technology-dependent physical issues by means of a topological system. This system applies methods and concepts used in mathematical morphology paradigms. Thus, we will obtain a geometrical abstraction which will not only provide solutions to typically complex problems but also the possibility of applying these solutions to any machining environment regardless of the technology. Presented in the paper is a method for offsetting any kind of curve. Specifically, we use parametric cubic curves, which is one of the most general and popular models in computer aided design (CAD)/computer aided manufacturing (CAM) applications. Results. The resulting method avoids any constraint in object or tool shape and obtains valid and optimal trajectories, with a low temporal cost of O(n∙m), which is corroborated by the experiments. It also avoids some precision errors that are present in the most popular commercial CAD/CAM libraries. Conclusions. The use of morphology as the base of the formulation avoids self-intersections and discontinuities and allows the system to machine free-form shapes using any tool without constraints. Most numerical and geometrical problems are also avoided. Obtaining a practical algorithm from the theoretical formulation is straightforward. The resulting procedure is simple and efficient.
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Dahiya, Deepak, Ashok Kumar, and V. K. Tripathi. "Influence of target curvature on ion acceleration in radiation pressure acceleration regime." Laser and Particle Beams 33, no. 2 (2015): 143–49. http://dx.doi.org/10.1017/s0263034615000026.
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AbstractIon acceleration from submicron thick foil target irradiated by a circularly polarized laser is studied using multidimensional particle-in-cell simulations. Convex, flat, and concave target shapes are considered. Radius of curvature of curved target is of the order of laser width in transverse direction. Accelerated ion beam of highest peak energy and least energy spread is obtained from concave target, whereas total accelerated charge is highest in convex target. It is attributed to the change in the growth of transverse instabilities and geometrical effects due to target curvature in initial stages of acceleration process. The variation in the radius of curvature of the foil depends on the ratio of initial spot size to the radius of curvature. Faster reduction in curvature is achieved for tightly focused Gaussian pulses as conjectured by the model.
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Corish, Denis. "Could Time be Change?" Philosophy 84, no. 2 (2009): 219–32. http://dx.doi.org/10.1017/s0031819109000199.
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AbstractSydney Shoemaker argues that time without change is possible, but begs the question by assuming an, in effect, Newtonian absolute time, that ‘flows equably’ in a region in which there is no change and in one in which there is. An equally possible, relativist, assumption, consistent, it seems, with relativity theory, is that where nothing changes there is no time flow, though there may be elsewhere, where there is change. Such an assumption would require some revision of uncritical common thought about time. Aristotle argues that there is no time without change but that time is not change. His arguments for the latter can be faulted both internally and again in terms of the same relativist assumption. From the Physics we can derive, though Aristotle himself did not, an argument that time is to change as geometrical space is to body: the thing itself in abstraction.
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Tylén, Kristian, Riccardo Fusaroli, Johanne Stege Bjørndahl, Joanna Raczaszek-Leonardi, Svend Østergaard, and Frederik Stjernfelt. "Diagrammatic reasoning." Diagrammatic Reasoning 22, no. 2 (2014): 264–83. http://dx.doi.org/10.1075/pc.22.2.06tyl.
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Many types of everyday and specialized reasoning depend on diagrams: we use maps to find our way, we draw graphs and sketches to communicate concepts and prove geometrical theorems, and we manipulate diagrams to explore new creative solutions to problems. The active involvement and manipulation of representational artifacts for purposes of thinking and communicating is discussed in relation to C.S. Peirce’s notion of diagrammatical reasoning. We propose to extend Peirce’s original ideas and sketch a conceptual framework that delineates different kinds of diagram manipulation: Sometimes diagrams are manipulated in order to profile known information in an optimal fashion. At other times diagrams are explored in order to gain new insights, solve problems or discover hidden meaning potentials. The latter cases often entail manipulations that either generate additional information or extract information by means of abstraction. Ideas are substantiated by reference to ethnographic, experimental and historical examples.
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Mandasari, Novianti. "Model Elaborasi Kognitif Siswa dalam Proses Abstraksi Prinsip dan Konsep Matematika Ruang Dimensi Dua di Kelas XI Teknik Las SMKN 1 Curup." Jurnal Pendidikan Matematika (JUDIKA EDUCATION) 1, no. 1 (2018): 21–32. http://dx.doi.org/10.31539/judika.v1i1.235.
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This study aimed to describe the Cognitive Elaboration Model Students In The Process Of Abstraction Concepts And Principles Of Mathematics Two-Dimensional Space In Class Xi Technique Las SMKN1 Curup. This study used a qualitative approach. The subjects were students of class XI Technique Las SMK 1 Curup. The main instrument is the researcher guided the students' abilities test sheets and sheets interview guide. Data were analyzed through three stages of data reduction, data presentation and conclusion. Decryption of students in the process of elaboration of the model abstraction mathematical concept of two-dimensional space:Model Recognizing; Students clearly recognize the shapes of two-dimensional space, students can understand the definition of a two-dimensional geometrical objects of a given two-dimensional space, and based on the information that the student has previously obtained. students can determine the objects that constitute the two-dimensional geometry and not the two-dimensional geometry. Students can find the principle of the wake - wake up a two-dimensional space and linking these results with the information stored in the memory of the student. Model Building With; Students can find the relationships of concepts and principles of two-dimensional geometry by analyzing the images of objects are two-dimensional geometry. Model Contracting; Concepts students know what to use, and to know the students visualize concepts, and sketched a two-dimensional object space of the existing problems, in solving the problems associated with the incorporation of mathematical principles contained in the concept, and the students' knowledge according to students' ability to recall concepts that have been held so mengasilkan an idea to solve the existing problems. Students are able to use the concepts and principles of mathematics in solving the problems that students are able to make conclusions from the results of the settlement. Students are able to explain or memperesentasikan his work.
 Keywords: Cognitive elaboration Model, Process Abstraction, Mathematics Concepts, Principles of Mathematics,.
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Verenich, Igor Vasilievich. "Criminalistic Studies about Overcoming the Counteraction to the Crimes of Investigation." Юридические исследования, no. 11 (November 2019): 40–45. http://dx.doi.org/10.25136/2409-7136.2019.11.31368.
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The subject of the research is the mechanism of overcoming the counteraction to the crimes of investigation and mechanism of marking formation, patterns of overcoming the counteraction to the crimes of investigation, their technological and criminalistic support, tactical and criminalistic support, methodological and criminalistic support of activities performed by law enforcement agencies and court. This is the first research to create a criminalistic teaching about overcoming the counteraction to the crimes of investigation and to develop an integral concept of such study as a combination of interrelated ideas and concepts. The methodology of the research includes general research methods (observation, description, comparison, experiment and modelling as sense-based research methods, analysis, synthesis, induction, deduction, analogy, hypothesis and abstraction as logical research methods, measurement, calculation and geometrical construction as mathematical methods). The author has also used special criminalistics methods (criminalistic identification, dactyloscopy, odorology, planning of investigative activities and organisation of investigation) as well as special methods from other branches of science such as physical, chemical and physical-chemical methods, anthropological and anthropometric methods, sociological methods and psychological methods. The scientific novelty of the research is caused by the fact that the author offers a new branch of criminalistics, criminalistic teaching about overcoming the counteraction to the crimes of investigation and development of the integral concept thereof based on rules and patterns of criminal procedure. 
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Boeré, René T., and Yuankui Zhang. "A study of the pyramidality index in tris(2,4,6-triisopropylphenyl)phosphonium perchlorate." Acta Crystallographica Section C Crystal Structure Communications 69, no. 9 (2013): 1051–54. http://dx.doi.org/10.1107/s0108270113020647.
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The title compound, C45H70P+·ClO4−or [Tripp3PH+][ClO4−], was produced from the perchlorate salt of the corresponding radical cation Tripp3P·+through very slow H-atom abstraction reactions in a solution of 1,2-dimethoxyethane (Tripp is 2,4,6-triisopropylphenyl). The H atom on the P atom was located in a difference map and was freely refined with an isotropic displacement consistent with full occupancy [P—H = 1.37 (3) Å]. It is the most sterically congested triarylphosphonium salt yet to be reported and has a `propeller' arrangement of the three Tripp groups around the P atom, with the protonation site located along the molecular threefold axis. There are short contacts between the flanking isopropyl methine H atoms and the P atom [P...H = 1.99 (2)–2.17 (2) Å]. The sum of the angles around the P atom [Σ(C—P—C) = 349.9 (6)°] is a convenient index of pyramidality for tricoordinate centres. This value is significantly larger than in analogous Mes3PH+salts (Mes is mesityl or 2,4,6-trimethylphenyl), for which the average of the three reported structures in the literature is Σ(C—P—C) = 345.3 (6)°. For comparison, in the ubiquitous Ph3PH+salts, this parameter has a typical average value of only 333.3 (9)°. The value of Σ(C—P—C) in the title compound is midway between that of the neutral phosphane Tripp3P [334.4 (6)°] and the phosphoniumyl radical cation Tripp3P·+[359.8 (2)°]. This geometrical feature provides additional support for the assignment as a phosphonium salt.
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Mozgot, Svetlana. "Phenomenon of Spatial Representations in Music: Psychophysiological Aspects." Scientific and analytical journal Burganov House. The space of culture 16, no. 1 (2020): 144–56. http://dx.doi.org/10.36340/2071-6818-2020-16-1-144-156.
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Summary: The article is devoted to exploration of the functions of visual thinking in the formation of spatial representations in human knowledge, which help to recognize the meanings of musical compositions. The purpose of this work is to study “visual” ways of spatial perception of musiсal works, in which eye-mindedness of the composer is implemented in specific operation by expressive means of music. Methods of hermeneutics, comparativistics, musicological analysis and interdisciplinary approach are used to realize this purpose. Principles of visual perception – simplicity and influence of geometric form on emotional properties of the object in music – are regarded as an example to show how they act. Principle of simplicity is evident in the organization of the form of “second plan” which unites multiple-part structures in music, tonal development, according to the type of “the highest order functions”. Influence of geometric form on emotional properties of the object in music is defined by the correlation of statics and dynamics in the development of a musical work; in semantics of geometrical figures “visualizing” in the graphic of melodic line or form of texture, which is supported by musical examples. We draw the conclusions that the existence of these principles in music helps to structure and store information about music in simple mental models, which are easy to recall. Interaction of means of musical expression gradually forms an in the consciousness of the listener, which contains certain spatial and visual characteristics, helping to recognize its real prototype, its artistic sense and meanings. Finally, the ontology of the category of space itself causes availability of a number of universal laws that ensure the convergence of different types of art in the act of artistic creativity and perception. It can be stated that the process of musical perception is dependent on the proceeding and results of different kinds of thinking, which are based on the already available knowledge about the reality and specifics of its reflection. Important components in perception are the nature of the organization of thought processes – attention, imagination, memory; the pace at which thought operations are performed – analysis, synthesis, comparison, generalization, concretization and abstraction, and a variety of other internal human properties and qualities. Understanding these patterns is possible not only based on the study of human psychophysiology, but also, on the contrary, through the study of the principles of the impact of art on man in an interdisciplinary aspect.
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Cheng, Xiufeng, Jinqing Yang, Ling Jiang, and Anlei Hu. "Interpreting and semantically describing Chinese traditional brocade: Xilankapu." Electronic Library 37, no. 3 (2019): 474–89. http://dx.doi.org/10.1108/el-09-2018-0193.
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Purpose The purpose of this paper is to introduce an interpreting schema and semantic description framework for a collection of images of Xilankapu, a traditional Chinese form of embroidered fabric and brocade artwork. Design/methodology/approach First, the authors interpret the artwork of Xilankapu through Gillian Rose’s “four site” theory by presenting how the brocades were made, how the patterns of Xilankapu are classified and the geometrical abstraction of visual images. To further describe the images of this type of brocade, this paper presents semantic descriptions that include objective–non-objective relations and a multi-layered semantic framework. Furthermore, the authors developed corresponding methods for scanning, storage and indexing images for retrieval. Findings As exploratory research on describing, preserving and indexing images of Xilankapu in the context of the preservation of cultural heritage, the authors collected 1,000+ images of traditional Xilankapu, classifying and storing some of the images in a database. They developed an index schema that combines concept- and content-based approaches according to the proposed semantic description framework. They found that the framework can describe, store and preserve semantic and non-semantic information of the same image. They relate the findings of this paper to future research directions for the digital preservation of traditional cultural heritages. Research limitations/implications The framework has been designed especially for brocade, and it needs to be extended to other types of cultural image. Originality/value The semantic description framework can describe connotative semantic information on Xilankapu. It can also assist the later information retrieval work in organizing implicit information about culturally related visual materials.
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Amor, Monica. "Displaced Boundaries: Geometric Abstraction from Pictures to Objects." ARTMargins 3, no. 2 (2014): 101–17. http://dx.doi.org/10.1162/artm_r_00083.
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This review concerns Osbel Suarez, Cold America: Geometric Abstraction in Latin America (1934–1973), an exhibition presented by the Fundación Juan March in Madrid, Feb 11–May 15, 2011 and Alejandro Crispiani's book Objetos para transformar el mundo: Trayectorias del arte concreto-invención, Argentina y Chile, 1940–1970 [Objects to Transform the World: Trajectories of Concrete-Invention Art, Argentina and Chile, 1940–1970] (Buenos Aires: Universidad Nacional de Quilmes, 2011). The review briefly assesses the state of the literature on Latin American Geometric Abstractio and analyzes these two publications from 2011, which stand precisely for traditional approaches and new developments in the field.
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Pal, Janos, and Dana Schlomiuk. "Summing up the Dynamics of Quadratic Hamiltonian Systems With a Center." Canadian Journal of Mathematics 49, no. 3 (1997): 582–99. http://dx.doi.org/10.4153/cjm-1997-027-0.
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AbstractIn this work we study the global geometry of planar quadratic Hamiltonian systems with a center and we sum up the dynamics of these systems in geometrical terms. For this we use the algebro-geometric concept of multiplicity of intersection Ip(P,Q) of two complex projective curves P(x, y, z) = 0, Q(x,y,z) = 0 at a point p of the plane. This is a convenient concept when studying polynomial systems and it could be applied for the analysis of other classes of nonlinear systems.
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Liang, Meng, Yuhang Fu, Ruibo Gao, Qiaoqiao Wang, and Junlan Nie. "Ellipsoidal Abstract and Illustrative Representations of Molecular Surfaces." International Journal of Molecular Sciences 20, no. 20 (2019): 5158. http://dx.doi.org/10.3390/ijms20205158.
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Molecular visualization is often challenged with rendering of large molecular structures in real time. The key to LOD (level-of-detail), a classical technology, lies in designing a series of hierarchical abstractions of protein. In the paper, we improved the smoothness of transition for these abstractions by constructing a complete binary tree of a protein. In order to reduce the degree of expansion of the geometric model corresponding to the high level of abstraction, we introduced minimum ellipsoidal enveloping and some post-processing techniques. At the same time, a simple, ellipsoid drawing method based on graphics processing unit (GPU) is used that can guarantee that the drawing speed is not lower than the existing sphere-drawing method. Finally, we evaluated the rendering performance and effect on series of molecules with different scales. The post-processing techniques applied, diffuse shading and contours, further conceal the expansion problem and highlight the surface details.
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Wright, Geoff, and Patrick Weltevrede. "Tilted Pulsar Beams." Proceedings of the International Astronomical Union 13, S337 (2017): 426–27. http://dx.doi.org/10.1017/s1743921317009255.
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AbstractIn 1975 the carousel model was proposed by Ruderman & Sutherland to explain the beautiful phenomenon of drifting subpulses. However the simultaneous appearance of subpulse bands which drift in opposing directions - a feature now found in two pulsars - is difficult to reconcile with this model, both geometrically and physically. Here we propose a geometric resolution of this problem which also may shed light on a range of previously baffling phenomena. The model places significant constraints on the underlying physics of pulsar emission.
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Yamba Yamba, André, Krister Ålander, and Malin Ljungberg. "Designing for Geometrical Symmetry Exploitation." Scientific Programming 14, no. 2 (2006): 61–80. http://dx.doi.org/10.1155/2006/764609.
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Symmetry-exploiting software based on the generalized Fourier transform (GFT) is presented from a practical design point of view. The algorithms and data structures map closely to the relevant mathematical abstractions, which primarily are based upon representation theory for groups. Particular care has been taken in the design of the data layout of the performance-sensitive numerical data structures. The use of a vanilla strategy is advocated for the design of flexible mathematical software libraries: An efficient general-purpose routine should be supplied, to obtain a practical and useful system, while the possibility to extend the library and replace the default routine with a special-purpose – even more optimized – routine should be supported. Compared with a direct approach, the performance results show the superiority of the GFT-based approach for so-called dense equivariant systems. The GFT application is found to be well suited for parallelism.
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Goranov, Peter, Desislava Georgieva, and Elena Todorova. "“Top-down” design methodology utilizing abstraction of mechanical interfaces." MATEC Web of Conferences 287 (2019): 01029. http://dx.doi.org/10.1051/matecconf/201928701029.
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CAD systems are a key design tool. As technology evolves, they provide greater functionality and solve tasks that are more complex. Consequently, the question of their effective use is becoming increasingly important. The present paper discusses the "top-down" design method. During the initial stages of a design process, the geometric description of the components is missing or it is not complete which calls into question the use of CAD. The present work proposes a “top-down” methodology that includes CAD in the early stages of the design process. The discussed methodology takes advantage of the object-oriented approach. There is originated a hierarchical scheme of objects, each of which inherits the methods and attributes of its higher class. This allows design information to spread throughout the whole design process as well as its integration. With an implementation of this model, CAD models of an assembly and its parts can be created on the basis of the information available when the product concept is being developed. The geometric description recorded in the CAD model elaborates as the design project evolves. In this way, the formation of the CAD model goes hand in hand with the clarification of the product design.
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Lee, Michael D. "Neural Feature Abstraction from Judgments of Similarity." Neural Computation 10, no. 7 (1998): 1815–30. http://dx.doi.org/10.1162/089976698300017151.
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The common neural network modeling practice of representing the elements of a task domain in terms of a set of features lacks justification if the features are derived through some form of ad hoc preabstraction. By examining a featural similarity model related to established multidimensional scaling techniques, a neural network is developed that generates features from similarity data and attaches weights to these features. The network performs a constrained search of a continuous solution space to determine the features and uses a previously developed regularization technique to minimize the number of features it derives. The network is demonstrated on artificial data, from which it recovers known features and weights, and on two real data sets involving the similarity of a set of geometric shapes and the abstract conceptual similarities of the 10 Arabic numerals. On the basis of these results, the relationship between the multidimensional scaling approach adopted by the network and an alternative additive clustering approach to feature extraction is discussed.
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Jiang, Renjin, Jie Xiao, and Dachun Yang. "Relative ∞-capacity and its affinization." Advances in Calculus of Variations 11, no. 1 (2018): 95–110. http://dx.doi.org/10.1515/acv-2016-0023.
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AbstractIn this paper, the so-called relative {\infty}-capacity is introduced and investigated in a close connection to the viscosity solution of the {\infty}-Laplace equation. We not only show that the relative {\infty}-capacity equals the limit of the p-th root of the relative p-capacity as {p\to\infty} and hence has a simple geometric characterization in terms of the Euclidean distance, but also establish several basic properties for the relative {\infty}-capacity. Consequently, we apply the relative {\infty}-capacity to the embedding theory of the {\infty}-Sobolev space. More geometrically, we affinize the relative {\infty}-capacity and its fundamental features as much as possible.
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González-Varela, José Edgar. "The Platonist Absurd Accumulation of Geometrical Objects: Metaphysics Μ.2". Phronesis 65, № 1 (2020): 76–115. http://dx.doi.org/10.1163/15685284-12342074.
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AbstractIn the first argument of Metaphysics Μ.2 against the Platonist introduction of separate mathematical objects, Aristotle purports to show that positing separate geometrical objects to explain geometrical facts generates an ‘absurd accumulation’ of geometrical objects. Interpretations of the argument have varied widely. I distinguish between two types of interpretation, corrective and non-corrective interpretations. Here I defend a new, and more systematic, non-corrective interpretation that takes the argument as a serious and very interesting challenge to the Platonist.
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Zheng, Jian-Hua. "On transcendental meromorphic functions which are geometrically finite." Journal of the Australian Mathematical Society 72, no. 1 (2002): 93–108. http://dx.doi.org/10.1017/s144678870000361x.
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AbstractIn this paper we give the definition of a meromorphic function which is geometrically finite and investigate some properties of geometrically finite meromorphic functions and the Lebesgue measure of their Julia sets.
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Belbase, Shashidhar. "Beliefs about Teaching Geometric Transformations with Geometers’ Sketchpad: A Reflexive Abstraction." Journal of Education and Research 3, no. 2 (2013): 15–38. http://dx.doi.org/10.3126/jer.v3i2.8396.
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A teacher’s belief plays a significant role in the quality of teaching mathematics. In a fictive way, I changed my role from a researcher to a research participant in an imaginative interview. My interior other (David) interviewed me as a researcher. A single interview session was held lasting for about three hours. The interview text was used for the analysis and interpretation using the grounded theory method. I invented a substantive theory of my beliefs about teaching geometric transformations with Geometer’s Sketchpad. The theory is “reflexive abstraction of my beliefs about teaching Geometric Transformations with Geometer’s Sketchpad” as a personal theory characterized by some basic categories of - beliefs about the advancement of pedagogy, beliefs about pedagogical environment, beliefs about the role of students’ and teacher, beliefs about self as a future teacher, beliefs about teaching learning activities, and beliefs about transitions in teaching learning. I reconstructed a synthesis of the characteristics of these beliefs. While constructing these layers of interpretive accounts, I used radical constructivist grounded theory as a theoretical base.DOI: http://dx.doi.org/10.3126/jer.v3i2.8396Journal of Education and Research August 2013, Vol. 3, No. 2, pp.15-38
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Nasehi, Mehri, and Mansour Aghasi. "On the geometrical properties of hypercomplex four-dimensional Lie groups." Georgian Mathematical Journal 27, no. 1 (2020): 111–20. http://dx.doi.org/10.1515/gmj-2018-0003.
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AbstractIn this paper, we first classify Einstein-like metrics on hypercomplex four-dimensional Lie groups. Then we obtain the exact form of all harmonic maps on these spaces. We also calculate the energy of an arbitrary left-invariant vector field X on these spaces and determine all critical points for their energy functional restricted to vector fields of the same length. Furthermore, we give a complete and explicit description of all totally geodesic hypersurfaces of these spaces. The existence of Einstein hypercomplex four-dimensional Lie groups and the non-existence of non-trivial left-invariant Ricci and Yamabe solitons on these spaces are also proved.
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Ameen, Sura Kassim, Ibrahim Jawad Al-yusif, and Ali Musa Hussein. "Abstraction the architectural heritage of contemporary local architecture." Iraqi Journal of Architecture and Planning 19, no. 1 (2020): 1–12. http://dx.doi.org/10.36041/iqjap.v16i1.490.
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Abstraction is used in architectural and interior design and is based on abstraction with formal values, taking into account the functional aspect of architecture. Architectural heritage represents the cultural value that directly affects successive generations, and embodies cultural values to reflect the social, economic and political aspect that contributes to the advancement of human civilization, and architectural heritage is the basis of architectural thought in societies that have unity. Cultural. He found that the concept of the philosophy of abstraction has multiple views, whether Western and local and dependent on the nature of cultural, social and environmental thought, and for this the aim of the research was to activate the role of the philosophy of abstraction in the formal formations of both the vocabulary of heritage architecture and contemporary architecture by architectural elements, Analysis of international, Arab and local architectural productions, to reach a conscious understanding of the philosophy and thought of abstraction in contemporary heritage architecture, and its spiritual values to reach the essence of things.
 The practical study was the analysis of Western and Arab and local projects with heritage architectural values and a practical study compared to them to see which architectural outputs were able to generate heritage values stable from its past in abstract geometric forms reflecting different ideas
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Ameen, Sura Kassim, Ibrahim Jawad Al-yusif, and Ali Musa Hussein. "Abstraction the architectural heritage of contemporary local architecture." Iraqi Journal of Architecture and Planning 19, no. 1 (2020): 1–12. http://dx.doi.org/10.36041/iqjap.v19i1.490.
Full textAbstract:
Abstraction is used in architectural and interior design and is based on abstraction with formal values, taking into account the functional aspect of architecture. Architectural heritage represents the cultural value that directly affects successive generations, and embodies cultural values to reflect the social, economic and political aspect that contributes to the advancement of human civilization, and architectural heritage is the basis of architectural thought in societies that have unity. Cultural. He found that the concept of the philosophy of abstraction has multiple views, whether Western and local and dependent on the nature of cultural, social and environmental thought, and for this the aim of the research was to activate the role of the philosophy of abstraction in the formal formations of both the vocabulary of heritage architecture and contemporary architecture by architectural elements, Analysis of international, Arab and local architectural productions, to reach a conscious understanding of the philosophy and thought of abstraction in contemporary heritage architecture, and its spiritual values to reach the essence of things.
 The practical study was the analysis of Western and Arab and local projects with heritage architectural values and a practical study compared to them to see which architectural outputs were able to generate heritage values stable from its past in abstract geometric forms reflecting different ideas
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Brandl, Flora L. "On a Curious Chance Resemblance: Rudolf von Laban’s Kinetography and the Geometric Abstractions of Sophie Taeuber-Arp." Arts 9, no. 1 (2020): 15. http://dx.doi.org/10.3390/arts9010015.
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This paper investigates a case of historical co-emergence between a modern system of dance notation and the rise of geometric abstraction in the applied arts during the first decades of the 20th century. It does so by bringing together the artistic careers of the choreographer Rudolf von Laban and the visual artist Sophie Taeuber-Arp. Comparing their pedagogical agendas and visual aesthetics, this paper argues that the resemblances between Laban’s Kinetography and Taeuber-Arp’s early geometric compositions cannot be a matter of pure coincidence. The paper therefore presents and supports the hypothesis of a co-constitutive relationship between visual abstraction and the dancing body in the European avant-garde.
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Waterman, Stephanie, and Jonathan M. Lilly. "Geometric Decomposition of Eddy Feedbacks in Barotropic Systems." Journal of Physical Oceanography 45, no. 4 (2015): 1009–24. http://dx.doi.org/10.1175/jpo-d-14-0177.1.
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AbstractIn oceanic and atmospheric flows, the eddy vorticity flux divergence—denoted “F” herein—emerges as a key dynamical quantity, capturing the average effect of fluctuations on the time-mean circulation. For a barotropic system, F is derived from the horizontal velocity covariance matrix, which itself can be represented geometrically in terms of the so-called variance ellipse. This study proves that F may be decomposed into two different components, with distinct geometric interpretations. The first arises from variations in variance ellipse orientation, and the second arises from variations in the kinetic energy of the anisotropic part of the velocity fluctuations, which can be seen as a function of variance ellipse size and shape. Application of the divergence theorem shows that F integrated over a closed region is explained entirely by separate variations in these two quantities around the region periphery. A further decomposition into four terms shows that only four specific spatial patterns of ellipse variability can give rise to a nonzero eddy vorticity flux divergence. The geometric decomposition offers a new tool for the study of eddy–mean flow interactions, as is illustrated with application to an unstable eastward jet on a beta plane.
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Tabar, Roham Sadeghi, Kristina Wärmefjord, and Rikard Söderberg. "A new surrogate model–based method for individualized spot welding sequence optimization with respect to geometrical quality." International Journal of Advanced Manufacturing Technology 106, no. 5-6 (2019): 2333–46. http://dx.doi.org/10.1007/s00170-019-04706-x.
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AbstractIn an individualized shee metal assembly line, form and dimensional variation of the in-going parts and different disturbances from the assembly process result in the final geometrical deviations. Securing the final geometrical requirements in the sheet metal assemblies is of importance for achieving aesthetic and functional quality. Spot welding sequence is one of the influential contributors to the final geometrical deviation. Evaluating spot welding sequences to retrieve lower geometrical deviations is computationally expensive. In a geometry assurance digital twin, where assembly parameters are set to reach an optimal geometrical outcome, a limited time is available for performing this computation. Building a surrogate model based on the physical experiment data for each assembly is time-consuming. Performing heuristic search algorithms, together with the FEM simulation, requires extensive evaluations times. In this paper, a neural network approach is introduced for building surrogate models of the individual assemblies. The surrogate model builds the relationship between the spot welding sequence and geometrical deviation. The approach results in a drastic reduction in evaluation time, up to 90%, compared to the genetic algorithm, while reaching a geometrical deviation with marginal error from the global optimum after welding in a sequence.
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SHARMA, B. S., and N. K. JAIMAN. "Numerical investigations on the effects of geometrical parameters on free electron laser instability." Journal of Plasma Physics 74, no. 6 (2008): 741–47. http://dx.doi.org/10.1017/s0022377808007447.
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AbstractIn this paper we numerically investigate the effects of various geometrical parameters of a backward wave oscillator (BWO), filled with a magnetized plasma of uniform density and driven by a mild relativistic solid electron beam, on the instability growth rate (Γ) of a free electron laser (FEL). The FEL instability is numerically calculated and the result is compared with the instability growth rate of an annular electron beam for the same set of parameters. The instability growth for a solid electron beam scales inversely to the seventh power of relativistic gamma factor γ0 and directly proportional to the corrugation amplitude.
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Blanc, Jérémy, and Frédéric Mangolte. "Geometrically rational real conic bundles and very transitive actions." Compositio Mathematica 147, no. 1 (2010): 161–87. http://dx.doi.org/10.1112/s0010437x10004835.
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AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.
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SCHAPIRA, BARBARA. "Density of half-horocycles on geometrically infinite hyperbolic surfaces." Ergodic Theory and Dynamical Systems 33, no. 4 (2012): 1162–77. http://dx.doi.org/10.1017/s0143385712000156.
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AbstractOn the unit tangent bundle of a hyperbolic surface, we study the density of positive orbits $(h^s v)_{s\ge 0}$ under the horocyclic flow. More precisely, given a full orbit $(h^sv)_{s\in {\mathbb R}}$, we prove that under a weak assumption on the vector $v$, both half-orbits $(h^sv)_{s\ge 0}$ and $(h^s v)_{s\le 0}$ are simultaneously dense or not in the non-wandering set $\mathcal {E}$of the horocyclic flow. We give also a counterexample to this result when this assumption is not satisfied.
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Lamken, E. R., and S. A. Vanstone. "A note on group divisible designs with mutually orthogonal resolutions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 44, no. 3 (1988): 397–401. http://dx.doi.org/10.1017/s1446788700032171.
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Khasanah, Nor, Nurkaidah Nurkaidah, Rosmala Dewi, and Yusuf Arkham Prihandika. "The Process of Student's Mathematic Abstract from Spatial Intelligence." Journal of Mathematics and Mathematics Education 9, no. 2 (2019): 24. http://dx.doi.org/10.20961/jmme.v9i2.48396.
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<p>Every student must have mathematical abstraction skills. Research with a qualitative approach aims to identify the mathematical abstraction process of students when working on geometric material problems in terms of spatial intelligence. By using a descriptive design, apart from the researcher as the main instrument, the mathematical abstraction test, the spatial intelligence test, and the interview reference were used as auxiliary instruments. A total of 6 students from class VIII were selected through purposive sampling technique which was taken from each category of spatial ability which had been classified into high, medium and low criteria. Based on data analysis, students' mathematical abstraction can be grouped into 4 levels, namely: recognition, representation, structural abstraction, and structural awareness. The conclusions of this study are: 1) students with a high level of spatial intelligence can achieve all four levels of mathematical abstraction characteristics and activities, namely recognition, representation, structural abstraction, and structural awareness. 2) students with moderate spatial intelligence can only achieve two levels of mathematical characteristics and abstraction activities, namely recognition and representation. 3) students with low-level spatial intelligence are only able to achieve one level of mathematical abstraction characteristics and activity, namely recognition where students are able to remember previous activities and experiences related to the problems at hand. This shows that students with moderate and low-level spatial intelligence do not have adequate abstraction skills in the concept of geometry.</p>
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Le, Duong, and Erion Plaku. "Cooperative, Dynamics-based, and Abstraction-Guided Multi-robot Motion Planning." Journal of Artificial Intelligence Research 63 (October 31, 2018): 361–90. http://dx.doi.org/10.1613/jair.1.11244.
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This paper presents an effective, cooperative, and probabilistically-complete multi-robot motion planner that enables each robot to move to a desired location while avoiding collisions with obstacles and other robots. The approach takes into account not only the geometric constraints arising from collision avoidance, but also the differential constraints imposed by the motion dynamics of each robot. This makes it possible to generate collision-free and dynamically-feasible trajectories that can be executed in the physical world.The salient aspect of the approach is the coupling of sampling-based motion planning to handle the complexity arising from the obstacles and robot dynamics with multi-agent search to find solutions over a suitable discrete abstraction. The discrete abstraction is obtained by constructing roadmaps to solve a relaxed problem that accounts for the obstacles but not the dynamics. Sampling-based motion planning expands a motion tree in the composite state space of all the robots by adding collision-free and dynamically-feasible trajectories as branches. Efficiency is obtained by using multi-agent search to find non-conflicting routes over the discrete abstraction which serve as heuristics to guide the motion-tree expansion. When little or no progress is made, the routes are penalized and the multi-agent search is invoked again to find alternative routes. This synergistic coupling makes it possible to effectively plan collision-free and dynamically-feasible motions that enable each robot to reach its goal. Experiments using vehicle models with nonlinear dynamics operating in complex environments, where cooperation among robots is required, show significant speedups over related work.
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Weiss, Gunter. "Visualisation - interpretation understanding: Traveling on the royal road to mathematical abstraction in old boots: Descriptive geometry." Filomat 23, no. 2 (2009): 1–11. http://dx.doi.org/10.2298/fil0902001w.
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Sketching and computer visualization are standard communication media in Technology and Natural Science as well as in Mathematics. Of any visualization we demand easy interpretability by the 'educated' viewer not only can 'read' the meaning of the figure but also gains some understanding of the visualized problem. Such a 'visual communication' needs schooling and training. Descriptive Geometry provides some simple but effective rules and techniques for such a visual communication. Using properties classical geometric mappings, e.g. normal projections or cyclography, can give insight to problems, which sometimes are rather hard to tackle purely by mathematical calculation. Sometimes we receive even an easy proof of the problem, a proof 'by looking at the figure', such that one is encouraged to speak of a 'geometric royal road' to the problem. Some special examples of such problems shall illustrate this statement. Most of the shown examples are not new, but they are not at all very well known! What should be shown is that Descriptive Geometry is much more than just an engineering graphics tool for visualizing 3D-objects. It strongly supports mathematicians, too. To emphasize that Descriptive Geometry is an intellectual tool besides for visualization the figures in this work are freehand drawn sketches instead of perhaps more beautiful computer generated drawings.
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Ku, Hsu-Tung, Mei-Chin Ku, and Xin-Min Zhang. "Isoperimetric Inequalities on Surfaces of Constant Curvature." Canadian Journal of Mathematics 49, no. 6 (1997): 1162–87. http://dx.doi.org/10.4153/cjm-1997-057-x.
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