New upper bounds on the smallest size of a saturating set in a projective plane

2016 ◽  
Author(s):  
Daniele Bartoli ◽  
Alexander A. Davydov ◽  
Massimo Giulietti ◽  
Stefano Marcugini ◽  
Fernanda Pambianco
Keyword(s):  
Projective Plane ◽  
Upper Bounds ◽  
Saturating Set

New upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane

2013 ◽  
Vol 104 (1) ◽  
pp. 11-43 ◽  
Author(s):  
Daniele Bartoli ◽  
Alexander A. Davydov ◽  
Giorgio Faina ◽  
Stefano Marcugini ◽  
Fernanda Pambianco
Keyword(s):  
Projective Plane ◽  
Upper Bounds ◽  
Desarguesian Projective Plane ◽  
Complete Arc ◽  
Finite Desarguesian Projective Plane

Upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane based on computer search

2015 ◽  
Vol 107 (1) ◽  
pp. 89-117 ◽  
Author(s):  
Daniele Bartoli ◽  
Alexander A. Davydov ◽  
Giorgio Faina ◽  
Alexey A. Kreshchuk ◽  
Stefano Marcugini ◽  
...  
Keyword(s):  
Projective Plane ◽  
Upper Bounds ◽  
Computer Search ◽  
Desarguesian Projective Plane ◽  
Complete Arc ◽  
Finite Desarguesian Projective Plane

scholarly journals Improved Bounds on mr(2,q) q=19,25,27

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rumen Daskalov ◽  
Elena Metodieva
Keyword(s):  
Projective Plane ◽  
Maximum Size ◽  
Upper Bounds ◽  
Computer Search ◽  
Lower And Upper Bounds ◽  
Local Computer

An (n,r)-arc is a set of n points of a projective plane such that some r, but no r+1 of them, are collinear. The maximum size of an (n,r)-arc in PG(2, q) is denoted by mr(2, q). In this paper, a new (286, 16)-arc in PG(2,19), a new (341, 15)-arc, and a (388, 17)-arc in PG(2,25) are constructed, as well as a (394, 16)-arc, a (501, 20)-arc, and a (532, 21)-arc in PG(2,27). Tables with lower and upper bounds on mr(2, 25) and mr(2, 27) are presented as well. The results are obtained by nonexhaustive local computer search.

scholarly journals Genera of knots in the complex projective plane

2020 ◽  
Vol 29 (12) ◽  
pp. 2050081
Author(s):  
Jake Pichelmeyer
Keyword(s):  
Projective Plane ◽  
Lower Bounds ◽  
Infinite Family ◽  
Upper Bounds ◽  
Complex Projective Plane ◽  
Low Dimensional Topology ◽  
Low Dimensional ◽  
Complex Projective

Our goal is to systematically compute the [Formula: see text]-genus of as many prime knots up to 8-crossings as possible. We obtain upper bounds on the [Formula: see text]-genus via coherent band surgery. We obtain lower bounds by obstructing homological degrees of potential slice discs. The obstructions are pulled from a variety of sources in low-dimensional topology and adapted to [Formula: see text]. There are 27 prime knots and distinct mirrors up to 7-crossings. We now know the [Formula: see text]-genus of all of these knots. There are 64 prime knots and distinct mirrors up to 8-crossings. We now know the [Formula: see text]-genus of all but 6 of these knots, where the [Formula: see text]-genus was not determined explicitly, it was narrowed down to 2 possibilities. As a consequence of this work, we show an infinite family of knots such that the [Formula: see text]-genus of each knot differs from that of its mirror.

Gilles Deleuze's Luminous Philosophy

2020 ◽  
Author(s):  
Hanjo Berressem
Keyword(s):  
Projective Plane ◽  
Visual Arts ◽  
Whole Body ◽  
Literary Studies ◽  
Chronological Order ◽  
Real Projective Plane ◽  
Cinema Studies ◽  
The Real

Providing a comprehensive reading of Deleuzian philosophy, Gilles Deleuze’s Luminous Philosophy argues that this philosophy’s most consistent conceptual spine and figure of thought is its inherent luminism. When Deleuze notes in Cinema 1 that ‘the plane of immanence is entirely made up of light’, he ties this philosophical luminism directly to the notion of the complementarity of the photon in its aspects of both particle and wave. Engaging, in chronological order, the whole body and range of Deleuze’s and Deleuze and Guattari’s writing, the book traces the ‘line of light’ that runs through Deleuze’s work, and it considers the implications of Deleuze’s luminism for the fields of literary studies, historical studies, the visual arts and cinema studies. It contours Deleuze’s luminism both against recent studies that promote a ‘dark Deleuze’ and against the prevalent view that Deleuzian philosophy is a philosophy of difference. Instead, it argues, it is a philosophy of the complementarity of difference and diversity, considered as two reciprocally determining fields that are, in Deleuze’s view, formally distinct but ontologically one. The book, which is the companion volume toFélix Guattari’s Schizoanalytic Ecology, argues that the ‘real projective plane’ is the ‘surface of thought’ of Deleuze’s philosophical luminism.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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