in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

A new distance norm [5] is used with the LBG algorithm and its eectiveness in achieving minimum distortion is studied with respect to Euclidean and L 1 norms. Partial Sum and Nearest Neighbouring Distance (NND) approaches are used with this new norm to reduce vector quantization (VQ) codebook design time. The mean square error (MSE) achieved with this new norm is similar to that of the conventi...

We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for co-dimension one boundaries. While this observation alone is very useful, other important implications for image analysis and shape statistics include a method for denoising sets which are not boundaries or which have higher co-dimension and the fact that using the flat norm to compute dista...

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

In this paper, we study shape matching under the current distance, a distance measure on shapes proposed by Vaillant and Glaunès [4]. This measure has four attractive properties. Firstly, it is global in nature, and thus does not require the determination of correspondences between features. Computing correspondences is often the most expensive part of computing distance between shapes. Secondl...

The main results of this paper are derived by using only simple Gröbner basis techniques. We present a new construction of evaluation codes from MiuraKamiya curves Cab. We estimate the minimum distance of the codes and estimate the minimum distance of a class of related one-point geometric Goppa codes. With respect to these estimates the new codes perform at least as well as the related geometr...

Controllability is a fundamental concept in control theory. Given a linear control system, we present new algorithms for estimating its distance to uncontrollability, i.e., the norm of the norm-wise smallest perturbation that makes the given system uncontrollable. Many algorithms have been previously proposed to estimate this distance. Our new algorithms are the rst that correctly estimate this...

The isotropic elastic moduli closest to a given anisotropic elasticity tensor are defined using three definitions of elastic distance, the standard Frobenius (Euclidean) norm, the Riemannian distance for tensors, and the log-Euclidean norm. The closest moduli are unique for the Riemannian and the log-Euclidean norms, independent of whether the difference in stiffness or compliance is considered...