Results 21 to 30 of about 2,867,834 (292)
On Rational Points on Conics [PDF]
Proceedings of the American Mathematical Society, 1977 The purpose of this paper is to prove the following result: let K be a finitely, separably generated extension field of transcendence degree one and genus zero over the exact constant field k .
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Game interrupted: The rationality of considering the future [PDF]
Judgment and Decision Making, 2013 The “problem of points”, introduced by Paccioli in 1494 and solved by Pascal and Fermat 160 years later, inspired the modern concept of probability. Incidentally, the problem also shows that rational decision-making requires the consideration of future ...
Brandon Almy, Joachim I. Krueger
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The Interval Rational- Interpolation Method
Fuzzy Optimization and Modeling, 2022 The rational interpolation sometimes gives better approximations than polynomial interpolation particularly for large sequence of points. In this paper, for the first time we provide a combination of rational interpolation and interval data.
Hajar Rasekhinezhad +4 more
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Counting rational points on algebraic varieties [PDF]
, 2006 For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is concerned with the number Nz(B) of ℚ-rational points on Z which have height at most B. For any ε > 0, we establish the estimate NZ(B) = O d,ε,N(Bdim Z+ε),
Heath-Brown, D. R. +9 more
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Counting rational points on quadric surfaces
Discrete Analysis, 2018 Counting rational points on quadric surfaces, Discrete Analysis 2018:15, 29 pp. A _quadric hypersurface_ of dimension $D$ is the zero set of a quadratic form $Q$ in $D+2$ variables. If $Q(x_1,\dots,x_{D+2})=0$, then $Q(\lambda x_1,\dots,\lambda x_{D+2})=
Tim Browning, Roger Heath-Brown
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All rational one-loop Einstein-Yang-Mills amplitudes at four points
Journal of High Energy Physics, 2018 All four-point mixed gluon-graviton amplitudes in pure Einstein-Yang-Mills theory with at most one state of negative helicity are computed at one-loop order and maximal powers of the gauge coupling, using D-dimensional generalized unitarity.
Dhritiman Nandan +2 more
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Thurston equivalence for rational maps with clusters [PDF]
, 2013 We investigate rational maps with period-one and period-two cluster cycles. Given the definition of a cluster, we show that, in the case where the degree is d and the cluster is fixed, the Thurston class of a rational map is fixed by the combinatorial ...
Thomas Sharland, Sharland, Thomas Joseph
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Covering Rational Surfaces with Rational Parametrization Images
Mathematics, 2021 Let S be a rational projective surface given by means of a projective rational parametrization whose base locus satisfies a mild assumption. In this paper we present an algorithm that provides three rational maps f,g,h:A2⇢S⊂Pn such that the union of the ...
Jorge Caravantes +3 more
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Curves with rational chord-length parametrization [PDF]
, 2008 It has been recently proved that rational quadratic circles in standard Bezier form are parameterized by chord-length. If we consider that standard circles coincide with the isoparametric curves in a system of bipolar coordinates, this property comes as ...
Fernández Jambrina, Leonardo +1 more
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Counting algebraic numbers in short intervals with rational points
Журнал Белорусского государственного университета: Математика, информатика, 2019 In 2012 it was proved that real algebraic numbers follow a nonuniform but regular distribution, where the respective definitions go back to H. Weyl (1916) and A. Baker and W. Schmidt (1970).
Vasily I. Bernik +2 more
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