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Titlebook: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan; Josef Dick,Frances Y. Kuo,Henryk Woźniakowski Bo

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Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness,ion of a truncated power function . (which assumes 0 if . ≤ 0 and is the power . if . > 0) that reduces to ., ., and . if . > 0. These types of trial functions have as support the whole sphere, a spherical cap centered at ., a bi-cap centered at the antipodes ., −., or an equatorial belt. We give in
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Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere: The Exceptional Case,oblem are confined to this support. For . − 2 ≤ . < ., we show that for point sources on the sphere, the equilibrium measure has support in the complement of the union of specified spherical caps about the sources. Numerical examples are provided to illustrate our results.
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Multilevel QMC with Product Weights for Affine-Parametric, Elliptic PDEs,tain input data. In particular, we show that locally supported basis functions allow for multilevel QMC quadrature with product weights, and prove new error vs. work estimates superior to those in these references (albeit at stronger, mixed regularity assumptions on the parametric integrand function
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Book 2018nd friend, who has been an inspiration to many of us. The reader may especially enjoy thestory from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in scien
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,Die Stellung der Webschäfte zur Kette,non-standard integro-differential equations type that arise as mathematical models in applications. We shall see that in addition to numerous open problems in the numerical analysis of such equations, many challenges in the computational solution of non-standard Volterra and Fredholm integro-differential equations are waiting to be addressed.
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