We identify some classes $$\mathcal {C}$$ of mixed groups such that if $$G\in \mathcal has the cancellation property then Walk-endomorphism ring G unit lifting property. In particular, is a self-small group torsion-free rank at most 4 with it decomposition $$G=F\oplus H$$ F free and H

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

The description of filter banks using lifting structures does not only benefit low-complexity implementation in software or hardware, but is also advantageous for the design of filter banks because of the guaranteed perfect reconstruction property. This paper proposes a new design method for wavelet filter banks, which is explained based on a single lifting structure suitable for 9/7 filter pai...

In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinear wavelet transforms has been given by the introduction of the lifting scheme by Sweldens. The aim of this paper, which is a sequel of a previous paper devoted exclusively to the pyramid transform, is to ...

In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinear wavelet transforms has been given by the introduction of the lifting scheme by Sweldens (1995, 1996, 1998). The aim of this paper, which is a sequel to a previous paper devoted exclusively to the pyrami...

The description of filter banks using lifting structures does not only benefit low-complexity implementation in software or hardware, but is also advantageous for the design of filter banks because of the guaranteed perfect reconstruction property. This paper proposes a new design method for wavelet filter banks, which is explained based on a single lifting structure suitable for 9/7 filter pai...

The lifting scheme provides a general and flexible tool for the construction of wavelet decompositions and perfect reconstruction filter banks. In this paper we propose an adaptive version of this scheme which has the intriguing property that it allows perfect reconstruction without any overhead cost. We restrict ourselves to the update lifting step which affects the approximation signal only. ...

We prove that the Kawamata-Viehweg vanishing theorem holds on rational surfaces in positive characteristic by means of the lifting property to W2(k) of certain log pairs on smooth rational surfaces. As a corollary, the Kawamata-Viehweg vanishing theorem holds on log del Pezzo surfaces in positive characteristic.