The main purpose of this paper is to find other measurements for constructing optimal duals that minimize the reconstruction errors, when erasures occur. Some known results are investigated with some measurements. Moreover, we investigate extreme points set all 1-erasure by seminorms. Furthermore, examples provided clarification.

We use the theory of quantization to introduce non-commutative versions of metric on state space and Lipschitz seminorm. We show that a lower semicontinuous matrix Lipschitz seminorm is determined by their matrix metrics on the matrix state spaces. A matrix metric comes from a lower semicontinuous matrix Lip-norm if and only if it is convex, midpoint balanced, and midpoint concave. The operator...

We present an operator space version of Rieffel’s theorem on the agreement of the metric topology, on a subset of the Banach space dual of a normed space, from a seminorm with the weak*-topology. As an application we obtain a necessary and sufficient condition for the matrix metric from an unbounded Fredholm module to give the BW-topology on the matrix state space of the C-algebra. Motivated by...

We construct a new version of the dual Gromov–Hausdorff propinquity that is sensitive to strongly Leibniz property. In particular, this distance complete on class quantum compact metric spaces. Then, given an inductive limit C*-algebras for which each C*-algebra equipped with L-seminorm, we provide sufficient conditions placing L-seminorm such sequence converges in propinquity. As application, ...

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an upwind finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by the first author for a simpler, less isotropic, ...

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an “upwind” finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by Chambolle for a simpler, more anisotropic, fin...

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an upwind finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by the first author for a simpler, less isotropic, ...

Abstract We prove residual-type a posteriori error estimates in the maximum norm for linear scalar elliptic convection–diffusion problem that may be singularly perturbed. Similar analysis energy by Verfürth indicates dual of convective derivative must added to natural order residual estimator reliable and efficient. show situation is similar norm. In particular, we define mesh-dependent weighte...

The normal cycle TK associated with a convex body K ⊂ Rn is a current which in principle contains complete information about K. It is known that if a sequence of convex bodies Ki, i ∈ N, converges to a convex body K in the Hausdorff metric, then the associated normal cycles TKi converge to TK in the dual flat seminorm. We give a quantitative improvement of this convergence result by providing a...

In the error analysis of the process of interpolation by translates of a single basis function, certain spaces of functions arise naturally. These spaces are de ned with respect to a seminorm which is given in terms of the Fourier transform of the function. We call this an indirect seminorm. In certain well-understood cases, the seminorm can be rewritten trivially in terms of the function, rath...