Consider a class of skew product transformations consisting of an ergodic or a periodic transformation on a probability space (M,B, μ) in the base and a semigroup of transformations on another probability space (Ω,F , P ) in the fibre. Under suitable mixing conditions for the fibre transformation, we show that the properties ergodicity, weakly mixing, and strongly mixing are passed on from the ...

Through the introduction of an aryl chloride substituent, the selectivity of palladium-catalyzed direct arylation may be diverted to provide alternative regioisomeric products in high yields. In cases where low reactivity is typically observed, the presence of the carbon-chlorine bond can serve to enhance reactivity and provide superior outcomes. From a strategic perspective, the C-Cl bond is e...

Since 1915, statisticians have been applying Fisher’s Z-transformation to Pearson product-moment correlation coefficients. We offer new geometric interpretations of this transformation.

This paper introduces the effective speckle reduction of synthetic aperture radar (SAR) images using inner product spaces in undecimated wavelet domain. There are two major areas in projection onto span algorithm where improvement can be made. First is the use of undecimated wavelet transformation instead of discrete wavelet transformation. And second area is the use of smoothing filter namely ...

New product development (NPD) is described in the literature as the transformation of a market opportunity into a product available for sale. In the automotive industry, within the context of ISO/TS16949:2002 (the automotive quality management system international standard),  these related to the product realization process (PRP) which consists of Three main phases such as planning, Implem...

We study birational monomial transformations of the form φ(x : y : z) = (ε1x1y1z1 : ε2x2y2z2 : xα3yβ3zγ3), where ε1,ε2 ∈ {−1,1}. These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation φ, we prove a formula, which represents the transformationφ as a product of generators of the group. To prove this formula, we use birati...