Sentence examples for different indices in different from inspiring English sources

In Section 4, we compare the two different indices in different aspects.

Remark Theorem 2.3 generalizes Theorem 1.2 to the case where different indices have different powers in the normalization.

Recently, the limit theorems for independent random fields such that different indices have different powers in the normalization are investigated.

In this paper we generalize the above results (Theorem 1.2, Corollary 1.3, and Theorem 1.4) to the case where different indices have different powers in the normalization.

In this paper we extend the complete convergence for weighted sums of dependent random fields to the case that different indices have different powers in the normalization.

We are going to generalize the result given by Kuczmaszewska and Lagodowski [[13], Theorem  3.1] to the case that different indices have different powers in the normalization.

The purpose of this paper is to obtain the convergence rates in strong laws of large numbers for nonidentically distributed and independent random fields such that different indices have different powers in the normalization.

The aim of this paper is to extend a complete convergence of weighted sums ∑ i ≤ n a n, i X i to the case that different indices have different powers in the normalization, where { a n, i, n ∈ Z + d, i ≤ n } is an array of real numbers and { X i, i ∈ Z + d } is a field of negatively associated random variables and ρ ∗ -mixing random variables.

From experimental results of this study, useful clues or guidance could be obtained for the structure design of hydrocyclones with different target indices in different applications.

The Land Registry and the ONS have traditionally calculated their indices in different ways, which may explain why their conclusions have often been very different.

How can one compare cost-of-living indices in different periods when new goods are constantly upending traditional consumption models?