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Rectifiable pencils of conics
 Mosc. Math. J
, 2007
"... Abstract. We describe analytic pencils of conics passing through the origin in C 2 that can be mapped to straight lines locally near the origin by an analytic diffeomorphism. Under a minor nondegeneracy assumption, we prove that in a pencil with this property, almost all conics have 3 points of tan ..."
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Cited by 1 (0 self)
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Abstract. We describe analytic pencils of conics passing through the origin in C 2 that can be mapped to straight lines locally near the origin by an analytic diffeomorphism. Under a minor nondegeneracy assumption, we prove that in a pencil with this property, almost all conics have 3 points
Geometry of YangBaxter maps: pencils of conics and quadrirational mappings
 Comm. Anal. and Geom
"... Birational YangBaxter maps (‘settheoretical solutions of the YangBaxter equation’) are considered. A birational map (x,y) ↦ → (u,v) is called quadrirational, if its graph is also a graph of a birational map (x,v) ↦ → (u,y). We obtain a classification of quadrirational maps on CP 1 × CP 1, and sho ..."
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Cited by 19 (5 self)
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, and show that all of them satisfy the YangBaxter equation. These maps possess a nice geometric interpretation in terms of linear pencil of conics, the YangBaxter property being interpreted as a new incidence theorem of the projective geometry of conics. Keywords: YangBaxter map, YangBaxter equation
Discrete Conics
"... In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise naturally from several constructions, including the discrete negative pedal construction and an action of a group acti ..."
RATIONAL POINTS ON PENCILS OF CONICS AND QUADRICS WITH MANY DEGENERATE FIBRES
"... Abstract. For any pencil of conics or higherdimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer–Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics over ..."
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Cited by 11 (5 self)
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Abstract. For any pencil of conics or higherdimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer–Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics
CONICS, (q + 1)ARCS, PENCIL CONCEPT OF TIME AND PSYCHOPATHOLOGY
, 2003
"... Abstract: – It is demonstrated that in the (projective plane over) Galois fields GF(q) with q = 2 n and n ≥ 3 (n being a positive integer) we can define, in addition to the temporal dimensions generated by pencils of conics, also time coordinates represented by aggregates of (q + 1)arcs that are n ..."
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Abstract: – It is demonstrated that in the (projective plane over) Galois fields GF(q) with q = 2 n and n ≥ 3 (n being a positive integer) we can define, in addition to the temporal dimensions generated by pencils of conics, also time coordinates represented by aggregates of (q + 1)arcs
PENCILS OF THE MAUTUALLY SUPER OSCULATING CONICS P21=2=3=4
"... Abstract. The E transformation is a quadratic transformation in the projective 2D space for which the base constitute the circle n2 and the center W which lies on this circle. Specifically, the authors present the results of the further discussion on the properties of the pencils of super osculatin ..."
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osculating conics. The theorem on projective relation between the elements of the pencil of super osculating conics and the range (of the second order) of the conics ’ centers has been proved.
Classification of Conic Sections in PE2(R)
"... Abstract: This paper gives a complete classification of conics in PE2(R). The classification has been made earlier (Reveruk [5]), but it showed to be incomplete and not possible to cite and use in further studies of properties of conics, pencil of conics, and of quadratic forms in pseudoEuclidean ..."
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Abstract: This paper gives a complete classification of conics in PE2(R). The classification has been made earlier (Reveruk [5]), but it showed to be incomplete and not possible to cite and use in further studies of properties of conics, pencil of conics, and of quadratic forms in pseudo
Camera Autocalibration and the Calibration Pencil
, 2003
"... We study the geometric object given by the set of lines incident with the absolute conic. We see that this object is given by a pencil of quadrics of P^5, which is characterized. We describe some of its most relevant properties for the camera autocalibration problem. Finally we illustrate the app ..."
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Cited by 4 (2 self)
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We study the geometric object given by the set of lines incident with the absolute conic. We see that this object is given by a pencil of quadrics of P^5, which is characterized. We describe some of its most relevant properties for the camera autocalibration problem. Finally we illustrate
Tangency of Conics and Quadrics
"... Abstract: Our paper discusses a simple way of determining tangency of conics using the concept of pencils of conics and the polepolar relationship. We discuss the method, analyze the different situations of tangency for conics, and extend it to find the tangency of quadrics in 3d space. Although t ..."
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Abstract: Our paper discusses a simple way of determining tangency of conics using the concept of pencils of conics and the polepolar relationship. We discuss the method, analyze the different situations of tangency for conics, and extend it to find the tangency of quadrics in 3d space. Although
Results 1  10
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