We analyze the orthogonal greedy algorithm when applied to dictionaries $\mathbb {D}$ whose convex hull has small entropy. show that if metric entropy of decays at a rate notation="LaTeX">$O\left({n^{-\frac {1}{2}-\alpha }}\right)$ fo...

We propose a two-parameter family of nonsymmetric dense $n\times n$ matrices $A(\alpha,\beta)$ for which LU factorization without pivoting is numerically stable, and we show how to choose $\alpha$ $\beta$ achieve any value the $\infty$-norm condition number. The matrix can be formed from simple formula in $O(n^2)$ flops. suitable use HPL-AI Mixed-Precision Benchmark, requires an extreme scale t...

We use a novel formation to illustrate the ($\alpha,\beta,\gamma$) modified weighted Wigner-Yanase-Dyson (($\alpha,\beta,\gamma$) MWWYD) skew information of quantum channels. By using operator norm inequalities, we explore sum uncertainty relations for arbitrary $N$ channels and unitary These inequalities are shown be tighter than existing ones by detailed example. Our results also applicable (...

In this paper, we redefine the notion of fuzzy 2-normed linear space using t-norm and fuzzy anti-2-normed linear space using t-conorm and introduced the definition of intuitionistic fuzzy 2-norm on a linear space. Mathematics Subject Classification: 46S40, 03E72

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.

Abstract It is a longstanding conjecture that given subset E of metric space, if has unit $\mathscr {H}^{\alpha }\llcorner E$ -density almost everywhere, then an $\alpha $ -rectifiable set. We prove this under the assumption ambient space homogeneous group with smooth-box norm.