This paper deals with the linear canonical wavelet transform. It is a non-trivial generalization of the ordinary wavelet transform in the framework of the linear canonical transform. We first present a direct relationship between the linear canonical wavelet transform and ordinary wavelet transform. Based on the relation, we provide an alternative proof of the orthogonality relation for the linear canonical wavelet transform. Some of its essential properties are also studied in detail. Finally, we explicitly derive several versions of inequalities associated with the linear canonical wavelet transform.
Coterie is a set of quorums which has non-empty intersections and are not part of other quorum. The natural development of the coterie system is k-coterie. The k-coterie consists of 2 types, that are non-dominated k-coterie and dominated k-coterie. The non-dominated k-coterie is more resilient to failure than the dominated k-coterie. Combining two non-dominated k-coterie by applying union operation can result the dominated k-coterie. This study aims to define a combination of the non-dominated k-coterie with non-dominated k-coterie using the expanded union operation. The merger of non-dominated k-coterie with the non-dominated k-coterie produces a non-dominated k-coterie.
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