scholarly journals Computational Aspects of the Colorful Carathéodory Theorem

2018 ◽  
Vol 60 (3) ◽  
pp. 720-755
Author(s):  
Wolfgang Mulzer ◽  
Yannik Stein
2016 ◽  
Vol 339 (4) ◽  
pp. 1300-1305 ◽  
Author(s):  
Nabil H. Mustafa ◽  
Saurabh Ray

Author(s):  
Abdulkarim Magomedov ◽  
S.A. Lavrenchenko

New laconic proofs of two classical statements of combinatorics are proposed, computational aspects of binomial coefficients are considered, and examples of their application to problems of elementary mathematics are given.


1987 ◽  
Vol 19 (5-6) ◽  
pp. 721-727 ◽  
Author(s):  
J. Pintér ◽  
L. Somlyódy

A conceptual framework is presented for optimizing the operation of regional monitoring networks which assist water quality management. The primary objective of the studied network is to determine the annual nutrient load carried into a lake by its tributaries. Following the description of the basic (single time–period, single water quality indicator) model, several extension possibilities and computational aspects are highlighted. The suggested methodology is illustrated by a numerical example, concerning the surveillance system on the tributaries of Lake Balaton (Hungary).


Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1108
Author(s):  
Olga Kudryavtseva ◽  
Aleksei Solodov

The class of holomorphic self-maps of a disk with a boundary fixed point is studied. For this class of functions, the famous Julia–Carathéodory theorem gives a sharp estimate of the angular derivative at the boundary fixed point in terms of the image of the interior point. In the case when additional information about the value of the derivative at the interior point is known, a sharp estimate of the angular derivative at the boundary fixed point is obtained. As a consequence, the sharpness of the boundary Dieudonné–Pick lemma is established and the class of the extremal functions is identified. An unimprovable strengthening of the Osserman general boundary lemma is also obtained.


PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Ritukesh Bharali ◽  
Fredrik Larsson ◽  
Ralf Jänicke

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