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Статті в журналах з теми "Arithmetical hyperplanes"
Bergeron, Nicolas, Frédéric Haglund, and Daniel T. Wise. "Hyperplane sections in arithmetic hyperbolic manifolds." Journal of the London Mathematical Society 83, no. 2 (February 11, 2011): 431–48. http://dx.doi.org/10.1112/jlms/jdq082.
Повний текст джерелаWalter, Charles H. "Hyperplane sections of arithmetically Cohen-Macaulay curves." Proceedings of the American Mathematical Society 123, no. 9 (September 1, 1995): 2651. http://dx.doi.org/10.1090/s0002-9939-1995-1260185-2.
Повний текст джерелаRu, Min. "Geometric and Arithmetic Aspects of P n Minus Hyperplanes." American Journal of Mathematics 117, no. 2 (April 1995): 307. http://dx.doi.org/10.2307/2374916.
Повний текст джерелаHanniel, Iddo. "Solving multivariate polynomial systems using hyperplane arithmetic and linear programming." Computer-Aided Design 46 (January 2014): 101–9. http://dx.doi.org/10.1016/j.cad.2013.08.022.
Повний текст джерелаBrowning, Tim, and Shuntaro Yamagishi. "Arithmetic of higher-dimensional orbifolds and a mixed Waring problem." Mathematische Zeitschrift 299, no. 1-2 (March 5, 2021): 1071–101. http://dx.doi.org/10.1007/s00209-021-02695-w.
Повний текст джерелаHoelscher, Zachary. "Semicomplete Arithmetic Sequences, Division of Hypercubes, and the Pell Constant." PUMP Journal of Undergraduate Research 4 (February 25, 2021): 108–16. http://dx.doi.org/10.46787/pump.v4i0.2524.
Повний текст джерелаFraser, Jonathan M., Kota Saito, and Han Yu. "Dimensions of Sets Which Uniformly Avoid Arithmetic Progressions." International Mathematics Research Notices 2019, no. 14 (November 2, 2017): 4419–30. http://dx.doi.org/10.1093/imrn/rnx261.
Повний текст джерелаAmerik, Ekaterina, and Misha Verbitsky. "Collections of Orbits of Hyperplane Type in Homogeneous Spaces, Homogeneous Dynamics, and Hyperkähler Geometry." International Mathematics Research Notices 2020, no. 1 (February 8, 2018): 25–38. http://dx.doi.org/10.1093/imrn/rnx319.
Повний текст джерелаBandyopadhyay, Saptarashmi, Jason Xu, Neel Pawar, and David Touretzky. "Interactive Visualizations of Word Embeddings for K-12 Students." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 11 (June 28, 2022): 12713–20. http://dx.doi.org/10.1609/aaai.v36i11.21548.
Повний текст джерелаKnutsen, Andreas Leopold, Margherita Lelli-Chiesa, and Giovanni Mongardi. "Severi varieties and Brill–Noether theory of curves on abelian surfaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 749 (April 1, 2019): 161–200. http://dx.doi.org/10.1515/crelle-2016-0029.
Повний текст джерелаДисертації з теми "Arithmetical hyperplanes"
Laboureix, Bastien. "Hyperplans arithmétiques : connexité, reconnaissance et transformations." Electronic Thesis or Diss., Université de Lorraine, 2024. http://www.theses.fr/2024LORR0040.
Повний текст джерелаThe digital world is littered with discrete mathematical structures, designed to be easily manipulated by a computer while giving our brains the impression of beautiful continuous real shapes. Digital images can thus be seen as subsets of Z^2. In discrete geometry, we are interested in the structures of Z^d and seek to establish geometric or topological properties on these objects. While the questions we ask are relatively simple in Euclidean geometry, they become much more difficult in discrete geometry: no more division, goodbye to limits, everything is just arithmetic. This thesis is also an opportunity to juggle many elementary notions of mathematics and computer science (linear algebra, rings, automata, real analysis, arithmetic, combinatorics) to solve discrete geometry questions. We are interested in the fundamental structures of this geometry: arithmetic hyperplanes. These have a very simple and purely arithmetical definition: an arithmetical hyperplane is the set of integer points lying between two parallel (real) affine hyperplanes. In this thesis, we discuss three problems involving arithmetic hyperplanes:- connectedness: is an arithmetic hyperplane composed of a single piece or of several pieces? The main contribution of this manuscript is to extend results already known for facewise connectedness for any neighbourhood. While certain phenomena remain in the general case, the combinatorial explosion makes it difficult to adapt known algorithms to solve the problem. We therefore adopt an analytical approach and prove connectivity properties by studying the regularity of a function. - recognition: how can we find out the characteristics of an arithmetic hyperplane? This is a more traditional problem in discrete geometry, with a very rich literature. To solve it, we propose a recognition algorithm based on the generalised Stern-Brocot tree. In particular, we introduce the notion of separating chord, which geometrically characterises the zones to which the parameters of an arithmetic hyperplane belong. - soft transformations: how can an arithmetic hyperplane be continuously transformed using translations or rotations? A discrete approach to homotopic transformations, we characterise the possible pixel movements in a discrete structure while preserving its geometric properties. Beyond the study of these problems and the results we were able to obtain, this thesis shows the interest of using the reals, and in particular real analysis, to better understand arithmetic hyperplanes. Arithmetic hyperplanes are largely characterised by their normal vector, which is often considered integer to obtain periodicity properties. Considering any real normal vectors provides greater flexibility and eliminates the noise induced by the arithmetic relationships of the vector. Finally, opening up to the real again is a way of building bridges to other branches of mathematics, such as word combinatorics or numbering systems
Книги з теми "Arithmetical hyperplanes"
Barg, Alexander, and O. R. Musin. Discrete geometry and algebraic combinatorics. Providence, Rhode Island: American Mathematical Society, 2014.
Знайти повний текст джерелаMathematical Legacy of Richard P. Stanley. American Mathematical Society, 2016.
Знайти повний текст джерелаЧастини книг з теми "Arithmetical hyperplanes"
Jamet, Damien, and Jean-Luc Toutant. "On the Connectedness of Rational Arithmetic Discrete Hyperplanes." In Discrete Geometry for Computer Imagery, 223–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11907350_19.
Повний текст джерелаDomenjoud, Eric, Bastien Laboureix, and Laurent Vuillon. "Facet Connectedness of Arithmetic Discrete Hyperplanes with Non-Zero Shift." In Discrete Geometry for Computer Imagery, 38–50. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14085-4_4.
Повний текст джерелаLaboureix, Bastien, and Isabelle Debled-Rennesson. "Recognition of Arithmetic Line Segments and Hyperplanes Using the Stern-Brocot Tree." In Lecture Notes in Computer Science, 16–28. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57793-2_2.
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