منابع مشابه
Illumination by Taylor Polynomials
Let f(x) be a differentiable function on the real line R, and let P be a point not on the graph of f(x). Define the illumination index of P to be the number of distinct tangents to the graph of f which pass through P . We prove that if f ′′ is continuous and nonnegative on R, f ′′ ≥ m > 0 outside a closed interval of R, and f ′′ has finitely many zeros onR, then any point P below the graph of f...
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The expansion of complicated functions of many variables in Taylor polynomials is an important problem for many applications, and in practice can be performed rather conveniently (even to high orders) using polynomial algebras. An important application of these methods is the eld of beam physics, where often expansions in about six variables to orders between ve and ten are used. However, often...
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We propose a general study of the convergence of a Hermite subdivision scheme H of degree d > 0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme S. The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of S is contractive, then S is C...
متن کاملIllumination by floodlights
We consider three problems about the illumination of planar regions with oodlights of prescribed angles. Problem 1 is the decision problem: given a wedge W of angle , n points p 1 ; ; p n in the plane and n angles 1 ; ; n summing up to , decide whether W can be illuminated by oodlights of angles 1 ; ; n placed in some order at the points p 1 ; ; p n and then rotated appropriately. We show that ...
متن کاملSolving singular integral equations by using orthogonal polynomials
In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2001
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171201004173