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Bounds for even moments of sums of strong mixing random variables are given which extend existing bounds. The method of __Cheap Nike Air Max 1__ proof uses simple facts about strong mixing random variables and combinatorial methods. The bound is particularly useful for triangular arrays with entries decreasing in size. To illustrate this, applications are being discussed to nonparametric kernel estimation with dependent observations.
The atom-bond connectivity index is a useful topological index in studying the stability of alkanes and the strain energy of cycloalkanes. In this paper some inequalities for the atom-bond connectivity index of a series of graph operations are presented. We also prove our bounds are tight. As an application, the ABCABC indices of C4C4 nanotubes and nanotori are computed.
Here we prove that every real quadratic irrational α can be expressed as a periodic non-simple continued fraction having period length one. Moreover, we show that the sequence of rational numbers generated by successive truncations of this expansion is a sequence of convergents of α. We close with an application relating the structure of a quadratic α to its conjugate.
Traveling wave solutions are obtained by Air Max 2013 Cheap using the sine–cosine method for KdVs. Solution procedure and the obtained results re-confirm the efficiency of the proposed scheme.