A tight criterion under which the abstract version Lovász Local Lemma (abstract-LLL) holds was given by Shearer [43] decades ago. However, little is known about that of the variable version LLL (variable-LLL) where events are generated by independent random variables, though this model of events is applicable to almost all applications of LLL. We introduce a necessary and sufficient criterion f...

We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entry-wise `p-approximation error, for any p ≥ 1; the case p = 2 is the classical SVD problem. We obtain the first provably good approximation algorithms for this version of lowrank approximation that work for every value of p ≥ 1, including p =∞. Our algorithms are simple, easy to implement, work...

We study contributions from color-octet quarkonium formation mechanisms to p ⊥-integrated ψ ′ production cross sections in pion-nucleon reactions. The observed polarization of the ψ ′ is not reproduced by the lowest-order leading-twist color-singlet and color-octet mechanisms. This suggests that there are important quarkonium production mechanisms beyond leading twist.

We describe a new method of constructing Kobayashi-hyperbolic surfaces in complex projective 3-space based on deforming surfaces with a “hyperbolic non-percolation” property. We use this method to show that general small deformations of certain singular abelian surfaces of degree 8 are hyperbolic. We also show that a union of 15 planes in general position in projective 3-space admits hyperbolic...

Low energy availability, defined as low caloric intake relative to exercise energy expenditure, has been linked to endocrine alterations frequently observed in chronically energy-deficient exercising women. Our goal was to determine the endocrine effects of low energy availability in exercising men. Six exercising men (VO2peak: 49.3 ± 2.4 ml · kg(-1) · min(-1)) underwent two conditions of low e...

Phosphorus (P) is an important element for crop productivity and is widely applied in fertilizers. Most P fertilizers applied to land are sorbed onto soil particles, so research on improving plant uptake of less easily available P is important. In the current study, we investigated the responses in root morphology and root-exuded organic acids (OAs) to low available P (1 μM P) and sufficient P ...

BACKGROUND In forest ecosystems with phosphorus (P) deficiency, the impact of atmospheric nitrogen (N) deposition on nutritional traits related to P uptake and P use potentially determines plant growth and vegetation productivity. METHODOLOGY/PRINCIPAL FINDINGS Two N deposition simulations were combined with three soil P conditions (homogeneous P deficiency with evenly low P; heterogeneous P ...

in this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-laplacian fractional order differential equations. we use schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. we include some examples to show the applicability of our results.