Let $\Omega$ be an open set in a metric measure space $X$. Our main result gives equivalence between the validity of weighted Hardy–Sobolev inequality and quasiadditivity capacity with respect to Whitney covers $\Omega$. Important ingredients proof include use discrete convolution as test function Maz'ya type characterization inequalities.

In this paper, we present a new approach to obtain trapezoidal approximation of fuzzy numbers with respect to weighted distance proposed by Nasibov [5] which the main property of this metric is flexibility in the decision maker’s choice. Also, we prove some properties of the proposed method such as translation invariance, scale invariance and identity. Finally, we illustrate the efficiency of p...

A method is presented for identifying individuals by shape, given a sequence of noisy silhouettes segmented from video. A spectral partitioning framework is used to cluster similar poses and automatically extract gait shapes. The method uses a variance-weighted similarity metric to induce clusters that cover disparate stages in the gait cycle. This technique is applied to the HumanID Gait Chall...

The algorithm of fingerprint constructing for still images based on weighted image structure model is proposed. The error correcting codes that are perfect in weighted Hamming metric are used as a base for fingerprint constructing.

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...

We present a pseudo-metric for weighted point sets. There are numerous situations, for example in the shape description domain, where the individual points in a feature point set have an associated attribute, a weight. A distance function that incorporates this extra information apart from the points' position can be very useful for matching and retrieval purposes. There are two main approaches...

Polymorphism is one of the main pillars of objectoriented paradigm. It induces hidden forms of class dependencies which may impact software quality, resulting in higher cost factor for comprehending, debugging, testing, and maintaining the software. In this paper, a new cognitive complexity metric called Cognitive Weighted Polymorphism Factor (CWPF) is proposed. Apart from the software structur...