This paper shows that the solutions to various 1-norm minimization problems are unique, if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as certain other 1-norm related models. This condition is previously known to be sufficient for the basis pursuit model to have a unique solutio...

This paper presents a new family of meshless methods for the solution of boundary-value problems. In the h-p cloud method, the solution space is composed of radial basis functions associated with a set of nodes arbitrarily placed in the domain. The paper describes the construction of the h-p cloud functions using a signed partition of unity and how h, p or h-p reenements can be implemented with...

This paper proposes a new design method to determine the feasible set of parameters of translational or position/orientation decoupled parallel robots for a prescribed singularity-free workspace of regular shape. The suggested method uses Groebner bases to define the singularities and the cylindrical algebraic decomposition to characterize the set of parameters. It makes it possible to generate...

We provide a natural characterization of the type two Mehlhorn-CookUrquhart basic feasible functionals as the provably total type two functionals of our (classical) applicative theory PT introduced in [30], thus providing a proof of a result claimed in the conclusion of [30]. This further characterization of the basic feasible functionals underpins their importance as a key candidate for the no...

In this section, we consider a convex optimization problem p * := min x f 0 are affine. We denote by D the domain of the problem (which is the intersection of the domains of all the functions involved), and by X ⊆ D its feasible set.

Introduction: Total hip arthroplasty (THA) after proximal femoral fixation is a challenging procedure due to possible hardware-related complications. Case presentation: A 78-year-old female with hip osteoarthritis had a proximal femoral osteotomy fixed using a blade plate in the same femur 41 years ago. A two-step approach was planned. After a challenging...