Relevant bibliographies by topics / Polyhedron of arrangements

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Polyhedron of arrangements'

Author: Grafiati
Published: 28 May 2022
Last updated: 31 July 2025

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Journal articles on the topic "Polyhedron of arrangements"

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Yemets, Oleg A., Alexandra O. Yemets, and Ivan M. Polyakov. "Optimization on Arrangements: the Simplex Form of Polyhedron of Arrangements." Journal of Automation and Information Sciences 49, no. 12 (2017): 14–28. http://dx.doi.org/10.1615/jautomatinfscien.v49.i12.20.

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Duan, Jin-Wei, and Tao Deng. "Blueprints of the DNA Archimedean Polyhedra with Minimum Component Number." MATCH – Communications in Mathematical and in Computer Chemistry 92, no. 1 (2024): 5–22. http://dx.doi.org/10.46793/match.92-1.005d.

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DNA has emerged as a versatile material for constructing functional nanostructures with specific topological arrangements, making it highly desirable for synthesizing of DNA nanostructures using minimal components. In this study, we propose a novel approach to fabricate polyhedra using the fewest possible components and investigate the roles played by different components. Our results reveal that even-sided polygon components are composed of subunits distributed contiguously or alternately, while odd-sided polygon components are composed of subunits distributed alternately, which play a crucia
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Iemets, O. Ol, O. Ol Yemets’, and I. M. Polyakov. "Criterion of an Edge of a General Polyhedron of Arrangements." Cybernetics and Systems Analysis 54, no. 5 (2018): 796–805. http://dx.doi.org/10.1007/s10559-018-0081-5.

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Yemets, O. A., and O. A. Chernenko. "A Nonreducible System of Constraints of a Combinatorial Polyhedron in a Linear-Fractional Optimization Problem on Arrangements." Cybernetics and Systems Analysis 41, no. 2 (2005): 246–54. http://dx.doi.org/10.1007/s10559-005-0057-0.

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Babu, Chatla Naga, Paladugu Suresh, Natarajan Sampath, and Ganesan Prabusankar. "Cadmium coordination polymers based on flexible bis(imidazole) ligands: A rare example for doublet of doublet cadmium polyhedron arrangements." Journal of Molecular Structure 1075 (October 2014): 147–53. http://dx.doi.org/10.1016/j.molstruc.2014.06.074.

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Berg, Mark de, Dan Halperin, Mark Overmars, and Marc van Kreveld. "Sparse Arrangements and the Number of Views of Polyhedral Scenes." International Journal of Computational Geometry & Applications 07, no. 03 (1997): 175–95. http://dx.doi.org/10.1142/s0218195997000120.

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In this paper we study several instances of the problem of determining the maximum number of topologically distinct two-dimensional images that three-dimensional scenes can induce. To bound this number, we investigate arrangements of curves and of surfaces that have a certain sparseness property. Given a collection of n algebraic surface patches of constant maximum degree in 3-space with the property that any vertical line stabs at most k of them, we show that the maximum combinatorial complexity of the entire arrangement that they induce is Θ(n2 k). We extend this result to collections of hyp
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Kabešová, Mária, Zlatica Kožíšková, and Michal Dunaj-Jurčo. "The crystal and molecular structure of the bis(thiocyanato)-bis(4-methylpyridine)copper(II) complex at 180 K." Collection of Czechoslovak Chemical Communications 55, no. 5 (1990): 1184–92. http://dx.doi.org/10.1135/cccc19901184.

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At 180 K, [Cu(4-Mepy)2(NCS)2] crystallizes in the monoclinic system, space group P21, Z = 6, with the elementary cell parameters a = 0.963(1), b = 2.653(2), c = 0.984(2) nm, β = 106.40(0.07)°. The central atom possesses the tetragonal bipyramidal coordination; the heterocyclic ligands are bonded in the equatorial plane of the coordination polyhedron in the trans positions, the thiocyanate ligands are bridge ones and are coordinated in both the equatorial and axial positions of the coordination polyhedron. The crystal structure involves three symmetrically independent coordination polyhedra dif
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Siidra, Oleg I., Diana O. Nekrasova, Dmitry O. Charkin, et al. "Anhydrous alkali copper sulfates – a promising playground for new Cu2+ oxide complexes: new Rb-analogues of fumarolic minerals." Mineralogical Magazine 85, no. 6 (2021): 831–45. http://dx.doi.org/10.1180/mgm.2021.73.

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AbstractWe report the crystal structures of eight new synthetic multinary Rb–Cu sulfates representing four new structure types: δ-Rb2Cu(SO4)2, γ-RbNaCu(SO4)2, γ-RbKCu(SO4)2, Rb2Cu2(SO4)3, Rb2Cu2(SO4)3(H2O), β-Rb2Cu(SO4)Cl2, β-Rb4Cu4O2(SO4)4⋅(Cu0.83Rb0.17Cl) and Rb2Cu5O(SO4)5. The determination of their crystal structures significantly expands the family of anhydrous copper sulfates. Some of the anhydrous rubidium copper sulfates obtained turned out to be isostructural to known compounds and minerals. Rb2Cu5O(SO4)5 is isostructural to cesiodymite, CsKCu5O(SO4)5 and cryptochalcite, K2Cu5O(SO4)5.
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Boulware, Naomi, Naihuan Jing, and Kailash C. Misra. "On Smith normal forms of q-Varchenko matrices." Algebra and Discrete Mathematics 34, no. 2 (2022): 187–222. http://dx.doi.org/10.12958/adm2006.

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In this paper, we investigate q-Varchenko matrices for some hyperplane arrangements with symmetry in two andthree dimensions, and prove that they have a Smith normal formover Z[q]. In particular, we examine the hyperplane arrangement forthe regular n-gon in the plane and the dihedral model in the spaceand Platonic polyhedra. In each case, we prove that the q-Varchenko matrix associated with the hyperplane arrangement has a Smith normal form over Z[q] and realize their congruent transformation matrices over Z[q] as well.
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Xu, Kai, David Hutchins, and Kunshan Gao. "Coccolith arrangement follows Eulerian mathematics in the coccolithophore Emiliania huxleyi." PeerJ 6 (April 9, 2018): e4608. http://dx.doi.org/10.7717/peerj.4608.

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Background The globally abundant coccolithophore, Emiliania huxleyi, plays an important ecological role in oceanic carbon biogeochemistry by forming a cellular covering of plate-like CaCO3 crystals (coccoliths) and fixing CO2. It is unknown how the cells arrange different-sized coccoliths to maintain full coverage, as the cell surface area of the cell changes during daily cycle. Methods We used Euler’s polyhedron formula and CaGe simulation software, validated with the geometries of coccoliths, to analyze and simulate the coccolith topology of the coccosphere and to explore the arrangement mec
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Dissertations / Theses on the topic "Polyhedron of arrangements"

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Iemets, O. O., O. O. Yemets`, and I. M. Polyakov. "About the Simplex Form of the Polyhedron of Arrangements." Thesis, Sumy State University, 2017. http://essuir.sumdu.edu.ua/handle/123456789/55771.

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The simplex form of the general polyhedron of arrangements, which is used in linear programming problems in combinatorial cutting methods is obtained and it increases the efficiency of cutting methods.
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Kaluzny, Bohdan Lubomyr. "Linear programming : pivoting on polyhedra and arrangements." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=100633.

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Linear programming is perhaps the most useful tool in optimization, much of it's success owed to the efficiency of the simplex method in practice --- its ability to solve problems with millions of variables with relative ease. However, whether there exists a strongly polynomial algorithm to solve linear programming remains an open question. Pivot methods, including the simplex method, remain the best hope for finding such an algorithm, despite the fact that almost all variants have been shown to require exponential time on special instances. Fundamental questions about the path length (number
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Beber, Björn [Verfasser]. "Improving interpolants of non-convex polyhedra with linear arithmetic and probably approximatley correct learning for bounded linear arrangements / Björn Beber." Mainz : Universitätsbibliothek Mainz, 2018. http://d-nb.info/1160111235/34.

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Shokrieh, Farbod. "Divisors on graphs, binomial and monomial ideals, and cellular resolutions." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/52176.

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We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the theory of Delaunay decompositions for lattices to describe their minimal polyhedral cellular free resolutions. We show that the resolutions of all these ideals are closely related and that their Z-graded Betti tables coincide. As corollaries, we give conceptual proofs of conjectures and questions posed by Postnikov and Shapiro, by Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various other results rela
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Books on the topic "Polyhedron of arrangements"

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Mathematical Legacy of Richard P. Stanley. American Mathematical Society, 2016.

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Book chapters on the topic "Polyhedron of arrangements"

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Nishio, Kengo, and Takehide Miyazaki. "Polyhedron and Polychoron Codes for Describing Atomic Arrangements." In Nanoinformatics. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-7617-6_6.

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Deza, Antoine, and Feng Xie. "Hyperplane arrangements with large average diameter." In Polyhedral Computation. American Mathematical Society, 2009. http://dx.doi.org/10.1090/crmp/048/05.

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Brass, Peter. "On Lattice Polyhedra and Pseudocircle Arrangements." In Karl der Grosse und sein Nachwirken. 1200 Jahre Kultur und Wissenschaft in Europa. Brepols Publishers, 1998. http://dx.doi.org/10.1484/m.sths-eb.4.2017046.

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Bezdek, Károly. "Ball-Polyhedra and Spindle Convex Bodies." In Lectures on Sphere Arrangements – the Discrete Geometric Side. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8118-8_5.

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Karpinski, Marek. "Randomized complexity of linear arrangements and polyhedra?" In Fundamentals of Computation Theory. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48321-7_1.

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Bezdek, Károly. "Proofs on Ball-Polyhedra and Spindle Convex Bodies." In Lectures on Sphere Arrangements – the Discrete Geometric Side. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8118-8_6.

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Read, Ronald C., and Robin J. Wilson. "Special Graphs." In An Atlas Of Graphs. Oxford University PressOxford, 1998. http://dx.doi.org/10.1093/oso/9780198532897.003.0006.

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Abstract In this chapter we depict a number of sped.al graphs: Platonic graphs: these are the graphs formed by the vertices and edges of the Platonic solids—the polyhedra in which all the faces are identical regular polygons and where the arrangement of polygons at each vertex is the same. There are five Platonic graphs, corresponding to the tetrahedron, octahedron, cube, icosahedron and dodecahedron. Archimedean graphs: these are the graphs formed by the vertices and edges of the Archimedean solids—the polyhedra in which each face is a regular polygon (but not all faces are of the same type)
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Mee, Nicholas. "Interstellar Overdrive." In Celestial Tapestry. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851950.003.0007.

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Kepler sought patterns and symmetry in the laws of nature. In 1611 he wrote a booklet, De Niva Sexangular (The Six-Cornered Snowflake), in which he attempted to explain the structure of familiar symmetrical objects. Almost 300 years before the existence of atoms was definitively established, he concluded that the symmetrical shape of crystals is due to the regular arrangement of the atoms of which they are formed. He also investigated the structure of geometrical objects such as the Platonic solids and the regular stellated polyhedra, known today as the Kepler–Poinsot polyhedra. Like Kepler, t
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Mingos, D. M. P. "Periodic table to polyhedral cage geometries." In Essentials of Inorganic Chemistry 1. Oxford University Press, 1995. http://dx.doi.org/10.1093/hesc/9780198558484.003.0013.

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This chapter evaluates the periodic table before looking at periodic trends. Although historically the periodic table can be traced back to Mendeleev in 1871, its modern interpretation depends on the quantum mechanical solution of the wavefunctions of the hydrogen atom and its extension to polyelectronic atoms. The arrangement of elements in order of increasing atomic number with the elements showing similarities placed in vertical columns formed the basis of the original periodic table. We now realize that the fundamental basis of this periodicity is the repeating character of electron config
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Glazer, A. M. "1. A long history." In Crystallography: A Very Short Introduction. Oxford University Press, 2016. http://dx.doi.org/10.1093/actrade/9780198717591.003.0001.

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‘A long history’ explains that it was during the 17th-century Enlightenment that saw the systematic study of crystals or ‘crystallography’ by key scientists including Johannes Kepler, Robert Hooke, Christian Huygens, Nicolas Steno, and Abbé René-Just Haüy—the true father of crystallography, who postulated that crystals must be made up of regular arrangements of polyhedral units. The 19th century saw new theories of crystals with the identification of thirty-two crystal classes, fourteen Bravais lattices, and 230 possible space groups. A new era of crystallography emerged with the discovery of
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Conference papers on the topic "Polyhedron of arrangements"

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Hobbs, Linn W. "What Can Topological Models Tell Us About Glass Structure and Properties?" In Bragg Gratings, Photosensitivity, and Poling in Glass Fibers and Waveguides. Optica Publishing Group, 1997. http://dx.doi.org/10.1364/bgppf.1997.jsua.2.

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Atomic arrangements in condensed matter partition three-dimensional space into polyhedra whose edges are interatomic vectors. These polyhedra, formally known as void polytopes, fill (tesselate) space, and their identity and arrangement can provide one description of a given atomic arrangement (Figure 1a) [1]. Other tessellations associated with space-filling of random structures are Voronoi polyhedral cells [2] and their dual the Delauney network [3]. These tessellations are relatively intuitive in two dimensions, but considerably more complex in three-dimensions—for example in tetrahedral net
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Raab, Sigal. "Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes." In the fifteenth annual symposium. ACM Press, 1999. http://dx.doi.org/10.1145/304893.304965.

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Avis, David, and Komei Fukuda. "A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra." In the seventh annual symposium. ACM Press, 1991. http://dx.doi.org/10.1145/109648.109659.

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Malikov, German, Vladimir Lisienko, Roman Koptelov, Jakov Kalugin, and Raymond Viskanta. "A Numerical Investigation of Ray Tracing Method in a View Factor Calculation Procedure for Zonal Radiation Heat Transfer in Complex Systems." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10429.

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In this paper a variety of well known computer graphics algorithms (Binary Spatial Partitioning-BSP, Bounding Box-BB, and direct method of sequential search) for ray tracing are studied numerically in the context of the view factor calculations for the zonal method of radiation heat transfer analysis in complex industrial furnace geometries. The paper reports on a modified BSP algorithm which takes into account the specific types of obstructions and their arrangement in different types of metallurgical furnaces. The modified algorithm enhances the ray tracing calculations by two to three order
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Ezra, Esther. "Almost tight bound for a single cell in an arrangement of convex polyhedra in R3." In the twenty-first annual symposium. ACM Press, 2005. http://dx.doi.org/10.1145/1064092.1064099.

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Wei, Guowu, and Jian S. Dai. "Linkages That Transfer Rotations to Radially Reciprocating Motion." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28678.

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Stemming from study of polyhedral and spheroidal linkages and investigation of reciprocating motion of the PRRP chain, this paper presents four overconstrained linkages that are capable of transferring rotations to radially reciprocating motion. The linkages connected by revolute joints are of symmetrical arrangement and mobility one and are analysed by using the screw-loop equation method. The paper further investigates geometry and kinematics of the linkages and reveals their kinematic characteristics, leading to the constraint equation.
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Yasuda, Hiromi, Mia Lee, and Jinkyu Yang. "Tunable Wave Dynamics in Origami-Based Mechanical Metamaterials." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59592.

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We investigate unique wave dynamics in origami-based mechanical metamaterials composed of volumetric 3D origami unit cells. Specifically, we assemble a chain of lattice structures, in which the Tachi-Miura Polyhedron (TMP) is employed as a building block. We conduct two types of theoretical/computational analysis on this origami-based system. One is the dynamic analysis on the TMP unit cell under harmonic excitations. We find that the system transits from linear to nonlinear regimes or vice versa, depending on the amplitude of the excitation and the initial configurations of the given geometry
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Bober, Waldemar, and Przemyslaw Stobiecki. "Experimental geodesic dome with a sandwich panels structure." In Human Interaction and Emerging Technologies (IHIET-AI 2022) Artificial Intelligence and Future Applications. AHFE International, 2022. http://dx.doi.org/10.54941/ahfe100895.

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The popularization of geodesic domes as a living space was one of R. B. Fuller's challenges for modern mankind. The search for a technology that can optimally satisfy this desire in a society living in a temperate climate has become the goal of the structural studies described in this study. The technological solution for the layer of sandwich panels depends on the adopted discrete division of the polyhedron surface. Due to the relatively simple shape of this element, the dodecahedron was adopted as the basis form. The designated triangular elements constitute the initial shape of the basic el
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Mahyawansi, Pratik, and Cheng-Xian Lin. "An Investigation of the Effects of Volume Fraction on Drag Coefficient of Non-Spherical Particles Using PR-DNS." In ASME 2021 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/fedsm2021-65809.

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Abstract Prediction of the drag coefficient is required in gas-particle multiphase flow modeling and simulation. Experimental data and correlations on the fixed-bed system of spherical particles with high volume fractions for various possible arrangements are available in the literature. However, the effect of volume fraction on the drag coefficient of non-spherical particles is not well studied. In solving the momentum equation, the volume fraction plays a vital role in determining the flow resistances. In this paper, we study the impact of volume fraction in the range of 0.069 to 0.65 on the
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