In this article we discuss some general results on the covariant Picard groupoid in the context of differential geometry and interpret the problem of lifting Lie algebra actions to line bundles in the Picard groupoid approach.

A time-variant analogue of an interpolation problem equivalent to the relaxed commutant lifting problem is introduced and studied. In a somewhat less general form the problem already appears in the analysis of the set of all solutions to the three chain completion problem. The interpolants are upper triangular operator matrices of which the columns induce contractive operators. The set of all s...

In this article, we prove some weighted pointwise estimates for three discontinuous Galerkin methods with lifting operators appearing in their corresponding bilinear forms. We consider a Dirichlet problem with a general second order elliptic operator.

this study involved 154 anesthetized patients requiring endotracheal intubation, in whom the epiglottis was visible but not lifted, which restricted the view of the glottis. a simple stylet was used to lift the epiglottis, thus improving the view of the glottis with the glide scope®, allowing tracheal tubes to be inserted into the patients. the stylet easily resolved the difficulty of lifting t...

The xedni calculus attack on the elliptic curve discrete logarithm problem (ECDLP) involves lifting points from the finite field Fp to the rational numbersQ and then constructing an elliptic curve overQ that passes through them. If the lifted points are linearly dependent, then the ECDLP is solved. Our purpose is to analyze the practicality of this algorithm. We find that asymptotically the alg...

In this study, the three-dimensional (3D) asymmetric maximum weight lifting is predicted using an inverse-dynamics-based optimization method considering dynamic joint torque limits. The limits are functions of angles and angular velocities, imposed on hip, knee, ankle, wrist, elbow, shoulder, lumbar spine joints. 3D model has 40 degrees freedom (DOFs) including 34 physical revolute joints 6 glo...

We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting n-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal 2-variable weighted shifts, we then fin...

Mathematicians routinely lift operators to structures. For instance, almost every textbook on calculus lifts addition pointwise to functions: ( f + g)(x) = f (x)+ g(x). In this particular example, the lifted operator inherits the properties of the base-level operator. Does this hold in general? In order to approach this problem, one has to make the concept of lifting precise. I argue that lifti...

Given a valid inequality for the mixed integer infinite group relaxation, a lifting based approach is presented that can be used to strengthen this inequality. Bounds on the solution of the corresponding lifting problem and some necessary conditions for the lifted inequality to be minimal for the mixed integer infinite group relaxation are presented. Finally, these results are applied to genera...

Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...