Trajectory preserving and lifting maps have been implicitly used in many recursive or hierarchical control design techniques. Well known systems theoretic concepts such as differential flatness or more recent ones such as simulation and bisimulation can be also understood through the trajectory lifting maps they define. In this paper we initiate a study of trajectory preserving and lifting maps...

Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and$Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two$tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplusN_2$ is $tau_M$-lifting. We investigate when homomorphic image of a $tau_M$-lifting moduleis $tau_M$-lifting.

Hensel’s symbolic lifting for a linear system of equations and numerical iterative refinement of its solution have striking similarity. Combining the power of lifting and refinement seems to be a natural resource for further advances, but turns out to be hard to exploit. In this paper, however, we employ iterative refinement to initialize lifting. In the case of Toeplitz, Hankel, and other popu...

Many wavelet shrinkage methods assume that the data are observed on an equally spaced grid of length of the form 2J for some J . These methods require serious modification or preprocessed data to cope with irregularly spaced data. The lifting scheme is a recent mathematical innovation that obtains a multiscale analysis for irregularly spaced data. A key lifting component is the “predict” step w...

Hensel’s symbolic lifting for a linear system of equations and numerical iterative refinement of its solution have striking similarity. Combining the power of lifting and refinement seems to be a natural resource for further advances, but turns out to be hard to exploit. In this paper, however, we employ iterative refinement to initialize lifting. In the case of Toeplitz, Hankel, and other popu...

A compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. Directed Hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. Sets of extrema of Birkhoff polyhedra are mapped to tours ...

a compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. directed hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. sets of extrema of birkhoff polyhedra are mapped to tours ...

The lifting task is the major activity contributing to the risk of lower back injur}. The purpose of this study was to examine the mechanical stresses on the lower back during manual lifting and to analxze how people adapt to the stresses. This purpose was accomplished by approaching the mechanical stresses on the lower back from three different perspectives. The effects of manual lifting tasks...