For each k = 0, 1, 2, . . . we define an equivalence relation called k-quasi-isotopy on the set of classical links in R3 up to isotopy in the sense of Milnor (1957), such that all sufficiently close approximations of a topological link are k-quasi-isotopic. Whereas 0-quasi-isotopy coincides with link homotopy, 1-quasi-isotopy is not implied by concordance, with aid of the generalized (lk 6= 0) ...

A forest is the clique complex of a strongly chordal graph and a quasiforest is the clique complex of a chordal graph. Kruskal–Katona type theorems for forests, quasi-forests, pure forests and pure quasi-forests will be presented. Introduction Recently, in commutative algebra, the forest ([5]) and the quasi-forest ([17] and [9]) have been extensively studied. Each of these concepts is, however,...

This paper follows the recent discussion on the sparse solution recovery with quasi-norms `q, q ∈ (0, 1) when the sensing matrix possesses a Restricted Isometry Constant δ2k (RIC). Our key tool is an improvement on a version of “the converse of a generalized Cauchy-Schwarz inequality” extended to the setting of quasi-norm. We show that, if δ2k ≤ 1/2, any minimizer of the lq minimization, at lea...

Let 0 < p < 1 and 0 < 2 . We prove that for n 1 and trigonometric polynomials sn of degree n, we have Z sn ( ) p 6664 sin 2 sin 2 + n 2 cos + 2 2 2 + 1 n 2 7775 p=2 d cn Z jsn ( )j d ; where c is independent of ; ; n; sn. The essential feature is the uniformity in [ ; ] of the estimate, and the fact that as [ ; ] approaches [0; 2 ], we recover the Lp Markov inequality. The result may be viewed ...

In this paper, we consider the modified quasi-geostrophic equation ∂tθ + (u · ∇) θ + κΛ θ = 0 u = ΛRθ. with κ > 0, α ∈ (0, 1] and θ0 ∈ L(R). We remark that the extra Λ is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence and regula...

A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (xn) statistically quasiCauchy if st − limn→∞ d(xn+1, xn) = 0, and lacunary statistically quasi-Cauchy if Sθ − limn→∞ d(xn+1, xn) = 0.Weprove that a subset E of ametric space is totally bounded if and only if any sequence of points in E has a subsequence...

We apply a method developed by one of the authors, see [1], to localize the numerical range of quasi-sectorial contractions semigroups. Our main theorem establishes a relation between the numerical range of quasi-sectorial contraction semigroups {exp(−tS)}t≥0, and the maximal sectorial generators S. We also give a new prove of the rate O(1/n) for the operator-norm Euler formula approximation: e...

A quasi Riemann surface is defined to be a certain kind of complete metric space Q whose integral currents are analogous to the integral currents of a Riemann surface. In particular, they have properties sufficient to express Cauchy-Riemann equations on Q. The prototypes are the spaces D 0 (Σ)m of integral 0-currents of total mass m in a Riemann surface Σ (usually called the integral 0-cycles o...

We consider stable signal recovery in `q quasi-norm for 0 < q ≤ 1. In this problem, given a measurement vector y = Ax for some unknown signal vector x ∈ R and a known matrix A ∈ Rm×n, we want to recover z ∈ R with ‖x − z‖q = O(‖x − x‖q) from a measurement vector, where x∗ is the s-sparse vector closest to x in `q quasi-norm. Although a small value of q is favorable for measuring the distance to...