In this paper, the boundedness properties of vector-valued intrinsic square functions and their commutators with \(BMO(\mathbb {R}^{n})\) are discussed. We first show weighted strong-type weak-type estimates in Morrey-type spaces. Then, we obtain analogues endpoint case, establish weak \(L\log L\)-type for these setting Lebesgue Furthermore, prove commutator operators particular, can Morrey spa...

We continue the study of the efficiency of black-box reductions in cryptography. We focus on the question of constructing strong one-way functions (respectively, permutations) from weak one-way functions (respectively, permutations). To make our impossibility results stronger, we focus on the weakest type of constructions: those that start from a weak one-way permutation and define a strong one...

We calculate the leading divergences at NNLO for the octet part of the nonleptonic weak sector of chiral perturbation theory, using renormalization group methods. The role of counterterms which vanish at the equation of motion and their use to simplify the calculation is shown explicitly. The obtained counterterm Lagrangian can be employed to calculate the chiral double log contributions of qua...

5 A closed curve in the plane is weakly simple if it is the limit (in the Fréchet metric) 6 of a sequence of simple closed curves. We describe an algorithm to determine whether 7 a closed walk of length n in a simple plane graph is weakly simple in O(n log n) time, 8 improving an earlier O(n3)-time algorithm of Cortese et al. [Discrete Math. 2009]. As 9 an immediate corollary, we obtain the fir...

We analyze how to efficiently maintain and update the visibility polygons for a segment observer moving in a polygonal domain. The space and time requirements for preprocessing are O(n) and after preprocessing, visibility change events for weak and strong visibility can be handled in O(log |VP|) and O(log(|VP1| + |VP2|)) respectively, or O(log n) in which |VP| is the size of the line segment’s ...

Let the summatory function of the Möbius function be denoted M(x). We deduce in this article conditional results concerning M(x) assuming the Riemann Hypothesis and a conjecture of Gonek and Hejhal on the negative moments of the Riemann zeta function. The main results shown are that the weak Mertens conjecture and the existence of a limiting distribution of e−y/2M(ey) are consequences of the af...

A weak e-net for a set of points M, is a set of points W (not necessarily in M) where every convex set containing eiMI points in M must contain at least one point in W. Weak e-nets have applications in diverse areas such as computational geometry, learning theory, optimization and statistics. Here we show that, if M is a set of points quasi-uniformly distributed on a unit sphere sd-l, then ther...