scholarly journals Cell Decompositions of the Projective Plane with Petrie Polygons of Constant Length

1997 ◽  
Vol 17 (4) ◽  
pp. 377-392 ◽  
Author(s):  
J. Bokowski ◽  
J.-P. Roudneff ◽  
T.-K. Strempel
Keyword(s):  
Projective Plane ◽  
Constant Length ◽  
Cell Decompositions

Introductory Remarks

1980 ◽  
Vol 38 ◽  
pp. 598-599
Author(s):  
H. Mohri
Keyword(s):  
Muscle Contraction ◽  
Experimental Evidence ◽  
Sea Urchin ◽  
Constant Length ◽  
Thin Filaments ◽  
Bridge Formation ◽  
Thick Filaments ◽  
Sliding Mechanism ◽  
Radial Spokes ◽  
Cilia And Flagella

In 1959, Afzelius observed the presence of two rows of arms projecting from each outer doublet microtubule of the so-called 9 + 2 pattern of cilia and flagella, and suggested a possibility that the outer doublet microtubules slide with respect to each other with the aid of these arms during ciliary and flagellar movement. The identification of the arms as an ATPase, dynein, by Gibbons (1963)strengthened this hypothesis, since the ATPase-bearing heads of myosin molecules projecting from the thick filaments pull the thin filaments by cross-bridge formation during muscle contraction. The first experimental evidence for the sliding mechanism in cilia and flagella was obtained by examining the tip patterns of molluscan gill cilia by Satir (1965) who observed constant length of the microtubules during ciliary bending. Further evidence for the sliding-tubule mechanism was given by Summers and Gibbons (1971), using trypsin-treated axonemal fragments of sea urchin spermatozoa. Upon the addition of ATP, the outer doublets telescoped out from these fragments and the total length reached up to seven or more times that of the original fragment. Thus, the arms on a certain doublet microtubule can walk along the adjacent doublet when the doublet microtubules are disconnected by digestion of the interdoublet links which connect them with each other, or the radial spokes which connect them with the central pair-central sheath complex as illustrated in Fig. 1. On the basis of these pioneer works, the sliding-tubule mechanism has been established as one of the basic mechanisms for ciliary and flagellar movement.

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.

scholarly journals Group-labeled light dual multinets in the projective plane

2018 ◽  
Vol 341 (8) ◽  
pp. 2121-2130 ◽  
Author(s):  
Gábor Korchmáros ◽  
Gábor P. Nagy
Keyword(s):  
Projective Plane

scholarly journals Cell decompositions and algebraicity of cohomology for quiver Grassmannians

2021 ◽  
Vol 379 ◽  
pp. 107544
Author(s):  
Giovanni Cerulli Irelli ◽  
Francesco Esposito ◽  
Hans Franzen ◽  
Markus Reineke
Keyword(s):  
Quiver Grassmannians ◽  
Cell Decompositions

scholarly journals On 3-syzygy and unexpected plane curves

2021 ◽  
Author(s):  
Grzegorz Malara ◽  
Piotr Pokora ◽  
Halszka Tutaj-Gasińska
Keyword(s):  
Projective Plane ◽  
Plane Curves ◽  
Complex Projective Plane ◽  
Geometric Properties ◽  
Complex Projective

AbstractIn this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties. More generally, we study 3-syzygy curve arrangements and we present examples that admit unexpected curves.

Divisible Semiplanes, Arcs, and Relative Difference Sets

1987 ◽  
Vol 39 (4) ◽  
pp. 1001-1024 ◽  
Author(s):  
Dieter Jungnickel
Keyword(s):  
Projective Plane ◽  
Difference Sets ◽  
Difference Set ◽  
Relative Difference ◽  
List Type ◽  
Relative Difference Set ◽  
Large Collection ◽  
Baer Subplane ◽  
Relative Difference Sets ◽  
Definition Of

In this paper we shall be concerned with arcs of divisible semiplanes. With one exception, all known divisible semiplanes D (also called “elliptic” semiplanes) arise by omitting the empty set or a Baer subset from a projective plane Π, i.e., D = Π\S, where S is one of the following:(i) S is the empty set.(ii) S consists of a line L with all its points and a point p with all the lines through it.(iii) S is a Baer subplane of Π.We will introduce a definition of “arc” in divisible semiplanes; in the examples just mentioned, arcs of D will be arcs of Π that interact in a prescribed manner with the Baer subset S omitted. The precise definition (to be given in Section 2) is chosen in such a way that divisible semiplanes admitting an abelian Singer group (i.e., a group acting regularly on both points and lines) and then a relative difference set D will always contain a large collection of arcs related to D (to be precise, —D and all its translates will be arcs).

scholarly journals Maximal arcs in projective planes of order 16 and related designs

2019 ◽  
Vol 19 (3) ◽  
pp. 345-351 ◽  
Author(s):  
Mustafa Gezek ◽  
Vladimir D. Tonchev ◽  
Tim Wagner
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Maximal Arcs ◽  
Even Order

Abstract The resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising from maximal (120,8)-arcs, and the 2-(52,4,1) designs arising from previously known maximal (52,4)-arcs, as well as some newly discovered maximal (52,4)-arcs in the known projective planes of order 16, are computed. It is shown that each 2-(120,8,1) design associated with a maximal (120,8)-arc is embeddable in a unique way in a projective plane of order 16. This result suggests a possible strengthening of the Bose–Shrikhande theorem about the embeddability of the complement of a hyperoval in a projective plane of even order. The computations of the maximal sets of compatible resolutions of the 2-(52,4,1) designs associated with maximal (52,4)-arcs show that five of the known projective planes of order 16 contain maximal arcs whose associated designs are embeddable in two nonisomorphic planes of order 16.

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