Topic
Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
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TL;DR: In this paper, the authors show that Hadamard was not the first to discover the inequalities, but C. Hermite who obtained them in 1883, ten years before J.Hadamard.
246 citations
TL;DR: In this article, a general method for constructing supersaturated 2 N-1 designs with a large number of interaction columns was proposed, and the efficiency of the constructed designs was studied by using three criteria.
Abstract: SUMMARY An N x N Hadamard matrix can be used to construct a saturated 2 N-1 design with N runs. Furthermore, if an interaction column for two of the columns of the matrix is not fully aliased with any column of the matrix, this interaction column can be used as a supplementary column for studying an additional factor. For some small Hadamard matrices studied by Plackett & Burman (1946), the number of such interaction columns is very large, thus allowing the construction of supersaturated designs whose number of factors far exceeds the number of runs. A general method of construction along these lines is proposed. The efficiency of the constructed designs is studied by using three criteria.
245 citations
TL;DR: A Hadamard product induced bias matrix model is proposed, which only requires the use of the data in the original matrix to identify and adjust the cardinally inconsistent element(s) in a PCM and significantly enhances matrix consistency and improves the reliability of PCM decision making.
240 citations
TL;DR: In this article, it was shown that if a scalar field has the Hadamard singularity structure in an open neighborhood of a Cauchy surface, then it does so everywhere.
Abstract: In the point-splitting prescription for renormalizing the stress-energy tensor of a scalar field in curved spacetime, it is assumed that the anticommutator expectation valueG(x, x′)=〈o(x)o(x′)+o(x′)o(x)〉 has a singularity of the Hadamard form asx→x′. We prove here that ifG(x,x′) has the Hadamard singularity structure in an open neighborhood of a Cauchy surface, then it does so everywhere, i.e., Cauchy evolution preserves the Hadamard singularity structure. In particular, in a spacetime which is flat below a Cauchy surface, for the “in” vacuum stateG(x,x′) is of the Hadamard form everywhere, and thus the point-splitting prescription in this case has been rigorously shown to give meaningful, finite answers.
239 citations
TL;DR: Several Hadamard-type inequalities for products of two convex and s-convex functions are proved and some new inequalities for differentiable functions based on concavity and s -conveXity are established.
239 citations