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...

background: the use of feed withdrawal for molt induction can negatively affected the structure and microbial environment of intestine and lead to greater intestinal colonization by salmonella infection. objectives: the aim of the present experiment was to determine the effects of alfalfa as a high fiber ingredient for molt induction on intestinal morphometric characteristics and performance of...

The effect of ketamine (1-100 µM), which has NMDA receptor antagonist properties, on synaptic transmission and long-term potentiation (LTP) in CAl area of rat hippocampus was examined in vitro. Field potentials were recorded in pyramidal cell layer following Schaffer collateral stimulation. Primed-burst stimulation (PEs) was used for induction of LTP. The amplitude of population spiks (PS) was ...

Background & Aims: Change in visual experience impairs circadian rhythms. In this study, The effects of visual deprivation during critical period of brain development and melatonin intake on synaptic plasticity of hippocampal CA1 neurons were evaluated. Methods: This experimental study was done on male rats kept in standard 12 hour light/dark condition (L...

We used functional magnetic resonance imaging (fMRI) to investigate the psychological refractory period (PRP), the delay in the response to the second of two tasks occurring in immediate succession. Our results were consistent with prior work on the PRP in that when two visual-manual tasks were presented within 100 ms of each other, the second response was delayed on the order of 500 ms, compar...