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...

Identification and analysis of flow fluctuations in consequences of climate change is one of the most important factors in water resources management planning and this is vital especially in areas where large crowds are engaged in agriculture. Dez watershed, as an agricultural hub in the country, is one of areas that river flow fluctuations caused by climate change can affect a large population...

the round city of ardeshir khwarah, with its concentric layout, can be considered as the first city which established by the founder of the sasanian dynasty as a symbol of the sasanian royal ideology. ardeshir khwarah plays a key role in establishment of sasanian sovereignty and urban planning. however, a little is known about the history of the city. it seems even stranger if we consider the r...