Using some known lifting theorems we present three-space property type and permanence results; some of them seem to be new, whereas other are improvements of known facts.

The polyphase-with-advance matrix representations of whole-sample symmetric (WS) unimodular filter banks form a multiplicative matrix Laurent polynomial group. Elements of this group can always be factored into lifting matrices with half-sample symmetric (HS) off-diagonal lifting filters; such linear phase lifting factorizations are specified in the ISO/IEC JPEG 2000 image coding standard. Half...

Abstract We prove a version of the Lebesgue differentiation theorem for mappings that are defined on measure space and take values into metric space, with respect to basis induced by von Neumann lifting. As consequence, we obtain lifting sections measurable Banach bundle disintegration vector measures whose target is Radon–Nikodým property.

We investigate combinatorial commutation properties for reordering a sequence consisting of two kinds of steps and for separating the well-foundedness of their combination into well-foundedness of each. A weakened version of the lifting property—requiring only an eventual lifting, is used for proving wellfoundedness of such unions of relations. In particular, it is used to show the well-founded...

A new algorithm is introduced which computes the multivariate leading coefficients of polynomial factors from their univariate images. This algorithm is incorporated into a sparse Hensel lifting scheme and only requires the factorization of a single univariate image. The algorithm also provides the content of the input polynomial in the main variable as a by-product. We show how we can take adv...

Motivated by the Lipschitz-lifting property of Banach spaces introduced Godefroy and Kalton, we consider lattice-lifting property, which is an analogous notion within category lattices lattice homomorphisms. Namely, a X satisfies if every homomorphism to having bounded linear right-inverse must have right-inverse. In terms free lattices, this can be rephrased into following question: embed they...

The role of the compression is to reduce bandwidth requirements for transmission requirements for storage of all forms of data as it would not be practical to put images, audio, video alone on websites without compression. The medical community has many applications in image compression often involving various types of diagnost due to its multi resolution and scaling property. Among the various...