The purpose of this paper is to prove some classical estimates for fractional derivatives of functions defined on a Coifman-Weiss space of homogeneous type. In particular the Product Rule and Chain Rule estimates in [KP] and [CW]. The fractional calculus of M. Riesz was extended to these spaces in [GSV]. Our main tools are fractional difference quotients and the square fractional derivative of ...

In spite of its massively parallel architecture [1], the human brain is fundamentally limited if required to perform two tasks at the same time [2, 3]. This limitation can be studied with the psychological refractory period (PRP) paradigm, where two stimuli that require speeded responses occur in close succession [4]. Interference generally takes the form of a delay in the time to respond to th...

We establish that there are bounded Jordan domains Ω ⊂ R (n ≥ 2) that do not carry a (nontrivial) doubling measure with respect to the Euclidean distance. More generally, it is shown that every nonempty metric space (X, d) without isolated points has an open and dense subset A such that (A, d) does not carry a doubling measure.

2014 A simple mechanical system consisting of a bouncing ball subject to repeated impacts with a vibrating table is studied in the period doubling regime. Two control parameters (the table’s forcing frequency and amplitude) are varied to discover the curves in parameter space that separate periodic orbits. Experimental results for the period doubling boundaries agree with calculations from a si...

Let μ be a Radon measure on R, which may be non doubling. The only condition that μ must satisfy is the size condition μ(B(x, r)) ≤ C r, for some fixed 0 < n ≤ d. Recently, the author introduced spaces of type BMO(μ) and H(μ) with properties similar to ones of the classical spaces BMO and H defined for doubling measures. These new spaces proved to be useful to study the L(μ) boundedness of Cald...

Can elderly adults automatize a new task? To address this question, 10 older adults each performed 10,080 training trials over 12 sessions on an easy but novel task. The psychological refractory period (PRP) procedure was then used to evaluate whether this highly practiced task, when presented as task 2 along with an unpracticed task 1, could proceed automatically. If automatic, task 2 processi...

We report the laparoscopic use of a novel perforator-grinder-aspirator apparatus, specifically designed for the evacuation of hydatid cysts. Eleven hepatic hydatid cysts in six patients were treated by laparoscopic technique using this tool, which penetrates the cyst mainly by opening a hole in the cyst wall, grinds the particulate, and sucks it all out; classic surgical aspirators are almost a...

Ascertaining the relationships between sediment transport processes and vegetation cover is essential for watershed soil and water conservation. However, it is not easy to realize this target on a large scale. In this study, the location-weighted landscape contrast index (LCI) based on the “source-sink” theory of ecological processes was introduced to unravel the response of sediment yield to v...

Water meadows in river valleys are a source of very valuable forage. Due to their specificity, an appropriate approach water management is required. This study assessed the impact reclamation traditional gravity irrigation system, aimed at saving and reducing loss from through controlled drainage. The main purpose this was evaluate investment drainage system restoration context improving yield ...

BACKGROUND To present a protocol of a prospective, cohort study in which four groups of spinal cord injury (SCI) patients will participate. (Patients with indwelling urethral catheter; patients who perform intermittent catheterisation without wearing a penile sheath; patients who perform intermittent catheterisation and wear penile sheath as well; and patients with penile sheath drainage). OB...