The Experts below are selected from a list of 14166 Experts worldwide ranked by ideXlab platform
Martin Vyska - One of the best experts on this subject based on the ideXlab platform.
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the application of Weierstrass elliptic functions to schwarzschild null geodesics
Classical and Quantum Gravity, 2012Co-Authors: G W Gibbons, Martin VyskaAbstract:In this paper, we focus on analytical calculations involving null geodesics in some spherically symmetric spacetimes. We use Weierstrass elliptic functions to fully describe null geodesics in Schwarzschild spacetime and to derive analytical formulae connecting the values of radial distance at different points along the geodesic. We then study the properties of light triangles in Schwarzschild spacetime and give the expansion of the deflection angle to the second order in both M/r0 and M/b where M is the mass of the black hole, r0 the distance of the closest approach of the light ray and b the impact parameter. We also use the Weierstrass function formalism to analyze other more exotic cases such as Reissner–Nordstrom null geodesics and Schwarzschild null geodesics in four and six spatial dimensions. Finally we apply Weierstrass functions to describe the null geodesics in the Ellis wormhole spacetime and give an analytic expansion of the deflection angle in M/b.
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the application of Weierstrass elliptic functions to schwarzschild null geodesics
arXiv: General Relativity and Quantum Cosmology, 2011Co-Authors: G W Gibbons, Martin VyskaAbstract:In this paper we focus on analytical calculations involving null geodesics in some spherically symmetric spacetimes. We use Weierstrass elliptic functions to fully describe null geodesics in Schwarzschild spacetime and to derive analytical formulae connecting the values of radial distance at different points along the geodesic. We then study the properties of light triangles in Schwarzschild spacetime and give the expansion of the deflection angle to the second order in both $M/r_0$ and $M/b$ where $M$ is the mass of the black hole, $r_0$ the distance of closest approach of the light ray and $b$ the impact parameter. We also use the Weierstrass function formalism to analyze other more exotic cases such as Reissner-Nordstr\om null geodesics and Schwarzschild null geodesics in 4 and 6 spatial dimensions. Finally we apply Weierstrass functions to describe the null geodesics in the Ellis wormhole spacetime and give an analytic expansion of the deflection angle in $M/b$.
Gretchen L Matthews - One of the best experts on this subject based on the ideXlab platform.
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triples of rational points on the hermitian curve and their Weierstrass semigroups
Journal of Pure and Applied Algebra, 2021Co-Authors: Gretchen L Matthews, Dane Skabelund, Michael WillsAbstract:Abstract In this paper, we study configurations of three rational points on the Hermitian curve over F q 2 and classify them according to their Weierstrass semigroups. For q > 3 , we show that the number of distinct semigroups of this form is equal to the number of positive divisors of q + 1 and give an explicit description of the Weierstrass semigroup for each triple of points studied. To do so, we make use of two-point discrepancies and derive a criterion which applies to arbitrary curves over a finite field.
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the Weierstrass semigroup of an m tuple of collinear points on a hermitian curve
Lecture Notes in Computer Science, 2003Co-Authors: Gretchen L MatthewsAbstract:We examine the structure of the Weierstrass semigroup of an m-tuple of points on a smooth, projective, absolutely irreducible curve X over a finite field \(\mathbb{F}\). A criteria is given for determining a minimal subset of semigroup elements which generate such a semigroup where 2 \( \leq m \leq |\mathbb{F}|\). For all 2 mq + 1, we determine the Weierstrass semigroup of any m-tuple of collinear \(\mathbb{F}_{q^2}\)-rational points on a Hermitian curve y q + y = x q + 1.
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Weierstrass pairs and minimum distance of goppa codes
Designs Codes and Cryptography, 2001Co-Authors: Gretchen L MatthewsAbstract:We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code which has minimum distance greater than the usual lower bound. We determine the Weierstrass gap set of a pair of any two Weierstrass points on a Hermitian curve and use this to increase the lower bound on the minimum distance of particular codes defined using a linear combination of the two points.
G W Gibbons - One of the best experts on this subject based on the ideXlab platform.
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the application of Weierstrass elliptic functions to schwarzschild null geodesics
Classical and Quantum Gravity, 2012Co-Authors: G W Gibbons, Martin VyskaAbstract:In this paper, we focus on analytical calculations involving null geodesics in some spherically symmetric spacetimes. We use Weierstrass elliptic functions to fully describe null geodesics in Schwarzschild spacetime and to derive analytical formulae connecting the values of radial distance at different points along the geodesic. We then study the properties of light triangles in Schwarzschild spacetime and give the expansion of the deflection angle to the second order in both M/r0 and M/b where M is the mass of the black hole, r0 the distance of the closest approach of the light ray and b the impact parameter. We also use the Weierstrass function formalism to analyze other more exotic cases such as Reissner–Nordstrom null geodesics and Schwarzschild null geodesics in four and six spatial dimensions. Finally we apply Weierstrass functions to describe the null geodesics in the Ellis wormhole spacetime and give an analytic expansion of the deflection angle in M/b.
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the application of Weierstrass elliptic functions to schwarzschild null geodesics
arXiv: General Relativity and Quantum Cosmology, 2011Co-Authors: G W Gibbons, Martin VyskaAbstract:In this paper we focus on analytical calculations involving null geodesics in some spherically symmetric spacetimes. We use Weierstrass elliptic functions to fully describe null geodesics in Schwarzschild spacetime and to derive analytical formulae connecting the values of radial distance at different points along the geodesic. We then study the properties of light triangles in Schwarzschild spacetime and give the expansion of the deflection angle to the second order in both $M/r_0$ and $M/b$ where $M$ is the mass of the black hole, $r_0$ the distance of closest approach of the light ray and $b$ the impact parameter. We also use the Weierstrass function formalism to analyze other more exotic cases such as Reissner-Nordstr\om null geodesics and Schwarzschild null geodesics in 4 and 6 spatial dimensions. Finally we apply Weierstrass functions to describe the null geodesics in the Ellis wormhole spacetime and give an analytic expansion of the deflection angle in $M/b$.
Petko D. Proinov - One of the best experts on this subject based on the ideXlab platform.
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on a family of Weierstrass type root finding methods with accelerated convergence
Applied Mathematics and Computation, 2016Co-Authors: Petko D. Proinov, Maria T VasilevaAbstract:Kyurkchiev and Andreev (1985) constructed an infinite sequence of Weierstrass-type iterative methods for approximating all zeros of a polynomial simultaneously. The first member of this sequence of iterative methods is the famous method of Weierstrass (1891) and the second one is the method of Nourein (1977). For a given integer N ? 1, the Nth method of this family has the order of convergence N + 1 . Currently in the literature, there are only local convergence results for these methods. The main purpose of this paper is to present semilocal convergence results for the Weierstrass-type methods under computationally verifiable initial conditions and with computationally verifiable a posteriori error estimates.
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on a family of Weierstrass type root finding methods with accelerated convergence
arXiv: Numerical Analysis, 2015Co-Authors: Petko D. Proinov, Maria T VasilevaAbstract:Kyurkchiev and Andreev (1985) constructed an infinite sequence of Weierstrass-type iterative methods for approximating all zeros of a polynomial simultaneously. The first member of this sequence of iterative methods is the famous method of Weierstrass (1891) and the second one is the method of Nourein (1977). For a given integer $N \ge 1$, the $N$th method of this family has the order of convergence ${N+1}$. Currently in the literature, there are only local convergence results for these methods. The main purpose of this paper is to present semilocal convergence results for the Weierstrass-type methods under computationally verifiable initial conditions and with computationally verifiable a posteriori error estimates.
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a new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously
Journal of Complexity, 2014Co-Authors: Petko D. Proinov, Milena PetkovaAbstract:Abstract In this paper we study the convergence of the famous Weierstrass method for simultaneous approximation of polynomial zeros over a complete normed field. We present a new semilocal convergence theorem for the Weierstrass method under a new type of initial conditions. Our result is obtained by combining ideas of Weierstrass (1891) and Proinov (2010). A priori and a posteriori error estimates are also provided under the new initial conditions.
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A new semilocal convergence theorem for the Weierstrass method from data at one
2012Co-Authors: Petko D. ProinovAbstract:In this paper we present a new semilocal convergence theorem from data at one point for the Weierstrass iterative method for the simultaneous computation of polynomial zeros. The main result generalizes and improves all previous ones in this area. Key words: polynomial zeros, simultaneous methods, Weierstrass method, convergence theorems, point estimation 2000 Mathematics Subject Classification: 65H05
B. Banaschewski - One of the best experts on this subject based on the ideXlab platform.
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f-Rings and the Stone-Weierstrass Theorem
Order, 2001Co-Authors: B. BanaschewskiAbstract:Using an appropriate notion of separating subring, it is shown that the classical Stone-Weierstrass Theorem for compact Hausdorff spaces is ultimately a result about f -rings. As an application the constructively valid Stone-Weierstrass Theorem for compact completely regular frames is obtained.
