The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ ℬ s

2021 ◽  
Vol 16 (1) ◽  
pp. 71-92
Author(s):  
Tsvetelina Petrova
Keyword(s):  
Upper Bounds ◽  
Function System ◽  
Trigonometric Sum ◽  
Star Discrepancy

Abstract In the present paper the author uses the function system Γ ℬ s constructed in Cantor bases to show upper bounds of the extreme and star discrepancy of an arbitrary net in the terms of the trigonometric sum of this net with respect to the functions of this system. The obtained estimations are inequalities of the type of Erdős-Turán-Koksma. These inequalities are very suitable for studying of nets constructed in the same Cantor system.

scholarly journals Improved upper bounds for the star discrepancy of digital nets in dimension 3

2003 ◽  
Vol 108 (2) ◽  
pp. 167-189 ◽  
Author(s):  
Friedrich Pillichshammer
Keyword(s):  
Upper Bounds ◽  
Star Discrepancy ◽  
Digital Nets

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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