This paper explains the implications of a mathematical theory (by the same authors) of holes in fractals and their relation to dimension for measurements. The novelty of our approach is to consider the fractal measure on a set rather than just the support of that measure. This should take into account in a more precise way the distribution of data points in measured sets, such as the distributi...

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...

Storage of newly fixed carbon as starch and sucrose follows a regular daily pattern in exporting sugar beet leaves under constant day length and level of illumination. Up to the final two hours of the light period, when starch storage declines, a nearly constant proportion of newly fixed carbon was allocated to carbohydrate storage, principally starch. Sucrose is stored only early in the light ...

This study was undertaken to determine the effects of storage period and egg weight of hatching eggs of Japanese quails on fertility, hatchability results. Eggs were obtained 150 females quails, all at 15 weeks of age. A total of 1942 hatching eggs were separated into 3 groups as light-weight (9.50-10.50 g), medium-weight (10.5111.50 g), and heavy-weight (11.51-12.50 g). Based on storage period...

In the present study, cryopreservation of common carp (Cyprinus carpio) embryos was studied using a stepwise cooling protocol. Embryos at heartbeat stage were selected, placed in 15- ml plastic tubes and stored at -2 °C for 1, 7, 14, and 21 days in 2 different cryopreservation solutions: S1 (methanol + dimethyl sulfoxide + sucrose) and S2 (methanol + propylene glycol + sucrose). Embryo viabilit...