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 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...

It has been argued that the psychological refractory period (PRP) effect is eliminated with two ideomotor compatible tasks when instructions stress fast and simultaneous responding. Three experiments were conducted to test this hypothesis. In all experiments, Task 1 required spatially compatible manual responses (left or right) to the direction of an arrow, and Task 2 required saying the name o...

In this paper we discuss general properties of geodesic surfaces that are (locally) biLipschitz homogeneous. In particular, we prove that they are locally doubling and there exists a special doubling measure analogous to the Haar measure for locally compact groups.

We show that the string bit model suffers from doubling in the fermionic sector. The doubling leads to strong violation of supersymmetry in the limit N → ∞. Since there is an exact correspondence between string bits and the algebra of BMN operators even at finite N , doubling is expected also on the side of super-Yang–Mills theory. We discuss the origin of the doubling in the BMN sector.

We conducted 2 multitasking experiments to examine the finding that first-task reaction times (RTs) are slower in the psychological refractory period (PRP) paradigm than in the prioritized processing (PP) paradigm. To see whether this difference between the 2 paradigms could be explained entirely by differences in first-task preparation, which would be consistent with the standard response sele...

People often have trouble performing 2 relatively simple tasks concurrently. The causes of this interference and its implications for the nature of attentional limitations have been controversial for 40 years, but recent experimental findings are beginning to provide some answers. Studies of the psychological refractory period effect indicate a stubborn bottleneck encompassing the process of ch...