The β-skeleton {Gβ(V )} for a point set V is a family of geometric graphs, defined by the notion of neighborhoods parameterized by real number 0 < β < ∞. By using the distance-based version definition of β-skeletons we study those graphs for a set of points in R d space with l1 and l∞ metrics. We present algorithms for the entire spectrum of β values and we discuss properties of lens-based and ...

The Group-Lasso is a well-known tool for joint regularization in machine learning methods. While the `1,2 and the `1,∞ version have been studied in detail and efficient algorithms exist, there are still open questions regarding other `1,p variants. We characterize conditions for solutions of the `1,p GroupLasso for all p-norms with 1 ≤ p ≤ ∞, and we present a unified active set algorithm. For a...

Numerical experiments in literature on compressed sensing have indicated that the reweighted l1 minimization performs exceptionally well in recovering sparse signal. In this paper, we develop exact recovery conditions and algorithm for sparse signal via weighted l1 minimization from the insight of the classical NSP (null space property) and RIC (restricted isometry constant) bound. We first int...

Let $\mathscr{C}_n=\{-1,1\}^n$ be the discrete hypercube equipped with uniform probability measure $\sigma_n$. Talagrand's influence inequality (1994) asserts that there exists $C\in(0,\infty)$ such for every $n\in\mathbb{N}$, function $f:\mathscr{C}_n\to\mathbb{C}$ satisfies $$\mathrm{Var}_{\sigma_n}(f) \leq C \sum_{i=1}^n \frac{\|\partial_if\|_{L_2(\sigma_n)}^2}{1+\log\big(\|\partial_if\|_{L_...

We suggest an elementary harmonic analysis approach to canceling and weakly differential operators, which allows us extend these notions the anisotropic setting replace operators with Fourier multiplies mild smoothness regularity. In this more general of multipliers, we prove inequality $$\|f\|_{L_\infty} \lesssim \|Af\|_{L_1}$$ if $$A$$ is a operator order $$d$$ $$\|f\|_{L_2} $$d/2$$ , provide...

We introduce Banach algebras arising from tensor norms. By these Banach algebras we make Arensregular Banach algebras such that tensor product becomes irregular, where is tensor norm. Weillustrate injective tensor product, does not preserve bounded approximate identity and it is notalgebra norm.

organic farming as an approach to sustainable agriculture tries to decrease environmental problems and possible health hazards caused by the residues from pesticides. since the agricultural professionals are responsible to inform the farmers and the public by education and extension efforts, it is necessary to understand their attitudes. the main purpose of this research was to investigate fact...

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.