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Journal articles on the topic 'Billard projectif'

Author: Grafiati

Published: 23 June 2021

Last updated: 29 July 2025

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1

Stachel, Hellmuth. "A Triple of Projective Billiards." KoG, no. 26 (2022): 44–51. http://dx.doi.org/10.31896/k.26.4.

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A projective billiard is a polygon in the real projective plane with a circumconic and an inconic. Similar to the classical billiards in conics, the intersection points between the extended sides of a projective billiard are located on a family of conics which form the associated Poncelet grid. We extend the projective billiard by the inner and outer billiard and disclose various relations between the associated grids and the diagonals, in particular other triples of projective billiards.

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2

Glutsyuk, Alexey. "On rationally integrable planar dual multibilliards and piecewise smooth projective billiards." Nonlinearity 37, no. 6 (2024): 065002. http://dx.doi.org/10.1088/1361-6544/ad3606.

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Abstract The billiard flow in a planar domain Ω acts on the tangent bundle T R 2 | Ω as geodesic flow with reflections from the boundary. It has the trivial first integral: squared modulus of the velocity. Bolotin’s conjecture, now a joint theorem of Bialy, Mironov and the author, deals with those billiards whose flow admits an additional integral that is polynomial in the velocity and whose restriction to the unit tangent bundle is non-constant. It states that (1) if the boundary of such a billiard is C 2-smooth, nonlinear and connected, then it is a conic; (2) if it is piecewise C 2-smooth a

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3

Park, Jung-kil, and Jaebyung Park. "Intelligent Carom Billiards Assistive System for automatic solution path generation and actual path prediction with principal component analysis-based ball motion detection." International Journal of Advanced Robotic Systems 19, no. 4 (2022): 172988062211188. http://dx.doi.org/10.1177/17298806221118865.

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This article proposes an Intelligent Carom Billiards Assistive System for a novice at Carom Billiards. Since a novice player is very difficult to find the solution paths of the cue ball, the ICBAS automatically calculates the solution paths for given ball configuration which is detected by a monocular vision and displays them in a guidance monitor. For rapid and systematically calculating the solution paths, the five and half system that is the most representative method in the field of billiard is implemented. In addition, the paths of the cue ball changed by the direction of the cue stick ar

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4

BISWAS, DEBABRATA. "EVOLUTION OF LIOUVILLE DENSITY IN BILLIARDS: THE QUANTUM CONNECTION." Modern Physics Letters B 20, no. 14 (2006): 795–813. http://dx.doi.org/10.1142/s0217984906011232.

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The study of classical Liouville density arises naturally in chaotic systems where a probabilistic treatment is more appropriate. In this review, we show that the evolution of a density projected onto the configuration space has a quantum connection in billiard systems. The eigenvalues and eigenfunctions of the concerned evolution operator have an approximate one-to-one correspondence with the quantum Neumann eigenvalues and eigenfunctions. For exceptional billiard shapes such as the rectangle, this correspondence is even exact. Despite the approximate nature of the correspondence, we demonstr

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5

TABACHNIKOV, SERGE. "Introducing projective billiards." Ergodic Theory and Dynamical Systems 17, no. 4 (1997): 957–76. http://dx.doi.org/10.1017/s0143385797086239.

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We introduce and study a new class of dynamical systems, the projective billiards, associated with a smooth closed convex plane curve equipped with a smooth field of transverse directions. Projective billiards include the usual billiards along with the dual, or outer, billiards.

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6

Dietz, B. "Relativistic Quantum Billiards with Threefold Rotational Symmetry: Exact, Symmetry-Projected Solutions for Equilateral Neutrino Billiard." Acta Physica Polonica A 140, no. 6 (2021): 473–86. http://dx.doi.org/10.12693/aphyspola.140.473.

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7

POPOV, G., and P. TOPALOV. "Discrete analog of the projective equivalence and integrable billiard tables." Ergodic Theory and Dynamical Systems 28, no. 5 (2008): 1657–84. http://dx.doi.org/10.1017/s014338570700096x.

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AbstractA class of discrete dynamical systems called projectively (or geodesically) equivalent Lagrangian systems is defined. We prove that these systems admit families of integrals. In the case of geodesically equivalent billiard tables, these integrals are pairwise commuting. We describe a family of geodesically equivalent billiard tables on surfaces of constant curvature. This is a special case of the so-called ‘Liouville billiard tables’.

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8

Takeuchi, Airi, and Lei Zhao. "Projective integrable mechanical billiards." Nonlinearity 37, no. 1 (2023): 015011. http://dx.doi.org/10.1088/1361-6544/ad0d6f.

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Abstract In this paper, we use the projective dynamical approach to integrable mechanical billiards as in (Zhao 2021 Commun. Contemp. Math. 24 2150085) to establish the integrability of natural mechanical billiards with the Lagrange problem, which is the superposition of two Kepler problems and a Hooke problem, with the Hooke center at the middle of the Kepler centers, as the underlying mechanical systems, and with any finite combinations of confocal conic sections with foci at the Kepler centers as the reflection wall, in the plane, on the sphere, and in the hyperbolic plane. This covers many

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9

Tabachnikov, Serge. "On cusps of caustics by reflection in two dimensional projective Finsler metrics." Theoretical and Applied Mechanics, no. 00 (2025): 4. https://doi.org/10.2298/tam250109004t.

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Given a projective Finsler metric in a convex domain in the projective plane, that is, a metric in which geodesics are straight lines, consider the respective Finsler billiard system. Choose a generic point inside the table and consider the billiard trajectories that start at this point and undergo N reflection off the boundary. The envelope of the resulting 1-parameter family of straight lines is the Nth caustic by reflection. We prove that, for every N, it has at least four cusps, generalizing a similar result for Euclidean metric, obtained recently jointly with G. Bor.

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10

JULIEN, ANTOINE. "Complexity and cohomology for cut-and-projection tilings." Ergodic Theory and Dynamical Systems 30, no. 2 (2009): 489–523. http://dx.doi.org/10.1017/s0143385709000194.

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AbstractWe consider a subclass of tilings: the tilings obtained by cut-and-projection. Under somewhat standard assumptions, we show that the natural complexity function has polynomial growth. We compute its exponentαin terms of the ranks of certain groups which appear in the construction. We give bounds forα. These computations apply to some well-known tilings, such as the octagonal tilings, or tilings associated with billiard sequences. A link is made between the exponent of the complexity, and the fact that the cohomology of the associated tiling space is finitely generated over ℚ. We show t

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11

Coleman, Joyce, and Elisabeth Sekyi-Whyte. "MANIPULATION AS A MARKETING STRATEGY: A CRITICAL DISCOURSE ANALYSIS OF BILLBOARDS IN GHANA." MALAYSIAN E COMMERCE JOURNAL 6, no. 2 (2022): 96–100. http://dx.doi.org/10.26480/mecj.02.2022.96.100.

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The discourse of advertising has provided a fertile ground for scholars with keen interest in the effects persuasive rhetoric has on both the emotional and the psychological dispositions of people. This study focused on one particular type of advertisement, the billboard advertisement. The aim of the study is two-fold: first, to explore the linguistic and nonlinguistic devices used as persuasive artifacts in billboard advertisements; and second, to find out how ideology was projected by the billboard advertisements. The study is qualitative research. Data collection was done in the Cape Coast

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12

Biswas, Debabrata. "Evolution of classical projected phase space density in billiards." Pramana 64, no. 4 (2005): 563–75. http://dx.doi.org/10.1007/bf02706204.

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13

Tabachnikov, S. "Exact Transverse Line Fields and Projective Billiards in a Ball." Geometric And Functional Analysis 7, no. 3 (1997): 594–608. http://dx.doi.org/10.1007/s000390050020.

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14

Azizian, Parnian, Mahbod Mohammadrashidi, Ali Abbas Azimi, Mohamad Ali Bijarchi, Mohammad Behshad Shafii, and Rohollah Nasiri. "Magnetically Driven Manipulation of Nonmagnetic Liquid Marbles: Billiards with Liquid Marbles." Micromachines 14, no. 1 (2022): 49. http://dx.doi.org/10.3390/mi14010049.

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Liquid marbles are droplets encapsulated by a layer of hydrophobic nanoparticles and have been extensively employed in digital microfluidics and lab-on-a-chip systems in recent years. In this study, magnetic liquid marbles were used to manipulate nonmagnetic liquid marbles. To achieve this purpose, a ferrofluid liquid marble (FLM) was employed and attracted toward an electromagnet, resulting in an impulse to a water liquid marble (WLM) on its way to the electromagnet. It was observed that the manipulation of the WLM by the FLM was similar to the collision of billiard balls except that the liqu

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15

Dietz, Barbara. "Semi-Poisson Statistics in Relativistic Quantum Billiards with Shapes of Rectangles." Entropy 25, no. 5 (2023): 762. http://dx.doi.org/10.3390/e25050762.

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Rectangular billiards have two mirror symmetries with respect to perpendicular axes and a twofold (fourfold) rotational symmetry for differing (equal) side lengths. The eigenstates of rectangular neutrino billiards (NBs), which consist of a spin-1/2 particle confined through boundary conditions to a planar domain, can be classified according to their transformation properties under rotation by π (π/2) but not under reflection at mirror-symmetry axes. We analyze the properties of these symmetry-projected eigenstates and of the corresponding symmetry-reduced NBs which are obtained by cutting the

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16

López-Pumarejo, Tomás. "Urban Consumers on Two Wheels." Transfers 1, no. 3 (2011): 90–112. http://dx.doi.org/10.3167/trans.2011.010306.

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Large-scale public bicycle rental programs represent the latest grand venture for outdoor advertising corporations. By supporting these programs, advertisers gain unfettered access to street furniture and municipal billboard space and thus acquire the power to transform the city dwellers' experience of the urban landscape both visually and kinetically. These public-private bike rental programs have mushroomed around the world due in part to the impact of Paris' Vélib, which is the world's largest. This paper discusses the role of outdoor advertising in this trend, and focuses on two existing a

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17

Glutsyuk, Alexey A. "On Hamiltonian Projective Billiards on Boundaries of Products of Convex Bodies." Proceedings of the Steklov Institute of Mathematics 327, no. 1 (2024): 37–54. https://doi.org/10.1134/s008154382406004x.

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18

Jairo, Dávalos, Amaya Edwin, and Martínez Fredy. "Optimizing Outdoor Advertising: A Case Study on the Economic and Technical Viability of Solar-Powered Billboards." Engineering and Technology Journal 9, no. 06 (2024): 4194–201. https://doi.org/10.5281/zenodo.11503999.

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This paper presents a comprehensive analysis of implementing solar photovoltaic (PV) systems for billboard lighting, with a focus on technical design, economic feasibility, and sustainability. Traditional billboard lighting methods largely depend on conventional power sources, which not only contribute to environmental pollution but also incur significant energy costs. To address these challenges, we propose a solar PV system specifically designed for dual-sided billboards typically found in urban and rural settings across Colombia. The study covers detailed system design, including the select

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19

Kazakov, A. L., A. A. Lempert, and D. M. Nguyen. "On the method of packing geodesic circles into a spherical segment using a plane projection." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 65, no. - (2025): 36–53. https://doi.org/10.35634/2226-3594-2025-65-03.

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The article discusses the problem of finding the optimal location for a given number of equal geodesic circles without overlapping on a spherical segment. The optimality criterion is to maximize the radius of the circles. This formulation is known as the Tammes problem, and it is a variant of the classical densest packing problem of equal objects in a specified container. We propose a new two-stage numerical method to solve the issue under consideration. The first stage is the construction of an initial approximation using the best-of-known optimal packings of equal circles into a circle of a

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20

Mehta, Varshil, Kavya Bhatt, Nimit Desai, and Mansi Naik. "Probiotics: An Adjuvant therapy for D-Galactose induced Alzheimer's disease." Journal of Medical Research and Innovation 1, no. 1 (2017): 30–33. https://doi.org/10.5281/zenodo.345753.

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<strong>Abstract</strong> Alzheimer's disease (AD) is a chronic and slowly progressing neurodegenerative disorder which has become a major health concern worldwide. The literature has shown that oxidative stress is one of the most important risk factors behind the cause of AD. Oxidative stress often leads to the production of Reactive Oxygen Species (ROS). D-Galactose, a physiological nutrient and reducing sugar, non-enzymatically reacts with amines of amino acids in proteins and peptides to form Advanced Glycation End products which activate its receptors coupled to Biochemical pathways that

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21

De Luca, R. "Numerical evaluation of the escape time of a classical point particle from an annular billiard." Revista Brasileira de Ensino de Física 32, no. 3 (2010). http://dx.doi.org/10.1590/s1806-11172010000300006.

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A two-dimensional annular billiard consisting of a region confined within two concentric circumferences, the outer of radius R and the inner of radius r, is considered. The escape time of a point particle projected at a given angle within this billiard is numerically evaluated in terms of the size of the opening in the billiard. The problem is solved by means of classical mechanics and can be of interest for advanced high school physics students or undergraduate college physics students

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22

De, Luca R. "Numerical evaluation of the escape time of a classical point particle from an annular billiard." April 8, 2011. https://doi.org/10.1590/s1806-11172010000300006.

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A two-dimensional annular billiard consisting of a region confined within two concentric circumferences, the outer of radius R and the inner of radius r, is considered. The escape time of a point particle projected at a given angle within this billiard is numerically evaluated in terms of the size of the opening in the billiard. The problem is solved by means of classical mechanics and can be of interest for advanced high school physics students or undergraduate college physics students

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23

Zhao, Lei. "Projective dynamics and an integrable Boltzmann billiard model." Communications in Contemporary Mathematics, September 17, 2021, 2150085. http://dx.doi.org/10.1142/s0219199721500851.

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The aim of this note is to explain the integrability of an integrable Boltzmann billiard model, previously established by Gallavotti and Jauslin [G. Gallavotti and I. Jauslin, A theorem on Ellipses, an integrable system and a theorem of Boltzmann, preprint (2020); arXiv:2008.01955], alternatively via the viewpoint of projective dynamics. We show that the energy of a corresponding spherical problem leads to an additional first integral of the system equivalent to Gallavotti–Jauslin’s first integral. The approach also leads to a family of integrable billiard models in the plane and on the sphere

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24

Demers, Mark F., and Carlangelo Liverani. "Projective Cones for Sequential Dispersing Billiards." Communications in Mathematical Physics, February 23, 2023. http://dx.doi.org/10.1007/s00220-023-04657-1.

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25

Fierobe, Corentin. "On projective billiards with open subsets of triangular orbits." Israel Journal of Mathematics, December 18, 2024. https://doi.org/10.1007/s11856-024-2712-z.

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26

Fierobe, Corentin. "Examples of projective billiards with open sets of periodic orbits." Discrete and Continuous Dynamical Systems, 2024, 0. http://dx.doi.org/10.3934/dcds.2024059.

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27

Faifman, Dmitry. "A Funk perspective on billiards, projective geometry and Mahler volume." Journal of Differential Geometry 127, no. 1 (2024). http://dx.doi.org/10.4310/jdg/1717356157.

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28

Dávalos, Jairo, Edwin Amaya, and Fredy Martínez. "Optimizing Outdoor Advertising: A Case Study on the Economic and Technical Viability of Solar-Powered Billboards." Engineering and Technology Journal 09, no. 06 (2024). http://dx.doi.org/10.47191/etj/v9i06.04.

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This paper presents a comprehensive analysis of implementing solar photovoltaic (PV) systems for billboard lighting, with a focus on technical design, economic feasibility, and sustainability. Traditional billboard lighting methods largely depend on conventional power sources, which not only contribute to environmental pollution but also incur significant energy costs. To address these challenges, we propose a solar PV system specifically designed for dual-sided billboards typically found in urban and rural settings across Colombia. The study covers detailed system design, including the select

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29

Biswas, Debabrata. "Classical Projected Phase Space Density of Billiards and Its Relation to the Quantum Neumann Spectrum." Physical Review Letters 93, no. 20 (2004). http://dx.doi.org/10.1103/physrevlett.93.204102.

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30

Roll Jakobsen, Peter, Erik Skovbjerg Rasmussen, Karen Dybkjær, and Jacob Kidmose. "Miocene deposits at Silkeborg, Jylland, and their influence on hydrology." Geological Survey of Denmark and Greenland Bulletin, July 15, 2016, 9–12. http://dx.doi.org/10.34194/geusb.v35.4399.

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A motorway was constructed in 2010–2016 through the suburbs of the city of Silkeborg (Fig. 1). The Danish Road Directorate wished to climate-proof the motorway against adverse future climate changes. The directorate collaborated with the Geological Survey of Denmark and Greenland (GEUS) to study the hydrological conditions. Studies of historical and projected climate-change-driven variations in groundwater levels in relation to urbanised hydrological fluxes were conducted by Kidmose et al. (2013, 2015). During the construction of the motorway, Miocene and Quaternary deposits were exposed in th

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31

Mules, Warwick. "That Obstinate Yet Elastic Natural Barrier." M/C Journal 4, no. 5 (2001). http://dx.doi.org/10.5204/mcj.1936.

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Introduction It used to be the case that for the mass of workers, work was something that was done in order to get by. A working class was simply the sum total of all those workers and their dependents whose wages paid for the necessities of life, providing the bare minimum for family reproduction, to secure a place and a lineage within the social order. However, work has now become something else. Work has become the privileged sign of a new kind of class, whose existence is guaranteed not so much by work, but by the very fact of holding a job. Society no longer divides itself between a rulin

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32

Murray, Simone. "Harry Potter, Inc." M/C Journal 5, no. 4 (2002). http://dx.doi.org/10.5204/mcj.1971.

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Engagement in any capacity with mainstream media since mid-2001 has meant immersion in the cross-platform, multimedia phenomenon of Harry Potter: Muggle outcast; boy wizard; corporate franchise. Consumers even casually perusing contemporary popular culture could be forgiven for suspecting they have entered a MÃbius loop in which Harry Potter-related media products and merchandise are ubiquitous: books; magazine cover stories; newspaper articles; websites; television specials; hastily assembled author biographies; advertisements on broadcast and pay television; children's merchandising; and the

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33

Kolff, Louise Moana. "New Nordic Mythologies." M/C Journal 20, no. 6 (2017). http://dx.doi.org/10.5204/mcj.1328.

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IntroductionNordic mythology, also known as Norse mythology, is a term used to describe Medieval creation myths and tales of Gods and otherworldly realms, told and retold by Northern Germanic and Scandinavian tribes of the ninth century AD (see for example Gaiman).I discuss a new type of Nordic mythology that is being created through popular culture, social media, books, and television shows. I am interested in how contemporary portrayals of the Nordic countries has created a kind of mythological place called Scandinavia, where things, people, and ideas are better than in other places.Whereas

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34

Harley, Ross. "Light-Air-Portals: Visual Notes on Differential Mobility." M/C Journal 12, no. 1 (2009). http://dx.doi.org/10.5204/mcj.132.

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0. IntroductionIf we follow the line of much literature surrounding airports and urban mobility, the emphasis often falls on the fact that these spaces are designed to handle the mega-scale and super-human pace of mass transit. Airports have rightly been associated with velocity, as zones of rapid movement managed by enormous processing systems that guide bodies and things in transit (Pascoe; Pearman; Koolhaas; Gordon; Fuller & Harley). Yet this emphasis tends to ignore the spectrum of tempos and flows that are at play in airport terminals — from stillness to the much exalted hyper-rapidit

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