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In this paper, we generalize Theorem D to a weighted setting.
The main result generalizes the Sawano, Sugano, and Tanaka result to a weighted setting.
Five years later in 1999 Kedlaya [23] improved his result to a weighted setting.
In this way, we can simply obtain quasi-arithmetic means, Gini means, Bajraktarević means etc. (cf. [24] for definitions) in their weighted setting.
Our purpose is to derive some new generalizations of Heinz operator inequalities by refining the ordering relations among Heinz means with different parameters, and of the geometric mean by investigating geometric means of several operator variables in a weighted setting.
Namely, the following generalized Hölder inequality in the weighted setting frac{1}{w(B)} int_{B}bigl|f(x cdot g(x bigr|w(x),dxleq C |f |_{Llog L w),B} |g |_{exp L w),B} (2.9) is true (see [17] for instance).
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Given a sequence of observed frames, our goal is to generate, at each instant, a properly weighted set of samples (or particles),, with associated weights such that, according to some statistical criterion, as goes to infinity, (17).
3GPP standardized a method to increase the OVSF set size by multiplying the given set with precoding weights and then concatenating the weighted sets of the spreading sequences.
For the MIMO system, which requires a larger signature sequence set, 3GPP standardized the use of a given OVSF set multiplied with the pre-coding weights and then concatenating the weighted set of spreading sequences.
This latter gives an unweighted set of samples reflecting an input's weighted set which allows us to consider the associated weights of the training samples without changing the learning function of the classifier.
Section 4 demonstrates the weighted set cover approach.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com