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The first integral gives us (3.15).
Quantum mechanics shows that large hopping integral gives a large energy dispersion in most cases.
From the above properties, it is clear that the singular Cauchy integral gives rise to two important operators, that is, (3.8).
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where is the Hermitean Cauchy integral given by (5.9).
Noting that and dividing the integral give (A3).
where F ( z ) is Libera integral given in (1.1).
Inequality (14) is achieved by applying (15 - 18 15 - 18e definition of definite integrand(given in Secthen 2 above) to (19).
The non-linear condition is in the form of a double integral giving the specification of mass in the solution domain.
We will use the sinc quadrature rule given with equation (2.13) to compute it because the integral given in (3.9) is divergent on the interval [ x, 1 ].
One should note that in the case of strongly C -linearly convex domains, the Cauchy Leray integral given here requires no correction.
The distortion integral given by (2) allows the minimization of the overall distortion by optimizing the choice of the Voronoi shape and the point density function.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com