The general methods of finding the sum for all kinds of series
K. Orlov (1981)
Matematički Vesnik
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K. Orlov (1981)
Matematički Vesnik
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Eduardo Rangel-Heras, Pavel Zuniga, Alma Y. Alanis, Esteban A. Hernandez-Vargas, Oscar D. Sanchez (2023)
Kybernetika
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This work presents a new approach for the imputation of missing data in weather time-series from a seasonal pattern; the seasonal time-series imputation of gap missing algorithm (STIGMA). The algorithm takes advantage from a seasonal pattern for the imputation of unknown data by averaging available data. We test the algorithm using data measured every minutes over a period of days during the year 2010; the variables include global irradiance, diffuse irradiance, ultraviolet irradiance,...
Ján Plavka (2016)
Kybernetika
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A vector is said to be an eigenvector of a square max-min matrix if . An eigenvector of is called the greatest -eigenvector of if and for each eigenvector . A max-min matrix is called strongly -robust if the orbit reaches the greatest -eigenvector with any starting vector of . We suggest an algorithm for computing the greatest -eigenvector of and study the strong -robustness. The necessary and sufficient conditions for strong -robustness are introduced...
Murray R. Bremner, Sara Madariaga, Luiz A. Peresi (2016)
Commentationes Mathematicae Universitatis Carolinae
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This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux...
Frédéric Bayart, Yanick Heurteaux (2012)
Annales scientifiques de l'École Normale Supérieure
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A famous theorem of Carleson says that, given any function , , its Fourier series converges for almost every . Beside this property, the series may diverge at some point, without exceeding . We define the divergence index at as the infimum of the positive real numbers such that and we are interested in the size of the exceptional sets , namely the sets of with divergence index equal to . We show that quasi-all functions in have a multifractal behavior with respect to...
Tomoko Hachiro, Takateru Okayasu (2003)
Studia Mathematica
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We take another approach to the well known theorem of Korovkin, in the following situation: X, Y are compact Hausdorff spaces, M is a unital subspace of the Banach space C(X) (respectively, ) of all complex-valued (resp., real-valued) continuous functions on X, S ⊂ M a complex (resp., real) function space on X, ϕₙ a sequence of unital linear contractions from M into C(Y) (resp., ), and a linear isometry from M into C(Y) (resp., ). We show, under the assumption that , where is...
S. V. Konyagin, V. N. Temlyakov (2003)
Studia Mathematica
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We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in...
Daniel C. Mayer (2014)
Journal de Théorie des Nombres de Bordeaux
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For an algebraic number field with -class group of type , the structure of the -class groups of the four unramified cyclic cubic extension fields , , of is calculated with the aid of presentations for the metabelian Galois group of the second Hilbert -class field of . In the case of a quadratic base field it is shown that the structure of the -class groups of the four -fields frequently determines the type of principalization of the -class group of in . This...
Reynaldo Rojas-Hernández (2015)
Commentationes Mathematicae Universitatis Carolinae
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We show that any -product of at most -many -spaces has the -property. This result generalizes some known results about -spaces. On the other hand, we prove that every -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...
Jiří Matoušek, Martin Tancer, Uli Wagner (2011)
Journal of the European Mathematical Society
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Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all...