This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups. An asymptotic formula is also presented.

Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase space. A recent numerical study of spatially extended systems has revealed that the diffusion coefficient D of the Lyapunov exponents (LEs) exhibits a nontrivial scaling behavior, D(L)~L(-γ), with the system size L. He...

Recent studies of correlations of intensity in databases of natural images revealed a remarkable property. The two point correlations are described in terms of power law behavior, with an exponent which seems to be robust. In the present Letter we consider the statistical meaning of that result. We study many individual images of one of the databases considered. We find that the same law charac...

In this article we study atomic and molecular decompositions in 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spac...

In this Letter, we derive exponent inequalities relating the dynamic exponent z to the steady state exponent Γ for a general class of stochastically driven dynamical systems. We begin by deriving a general exact inequality, relating the response function and the correlation function, from which the various exponent inequalities emanate. We then distinguish between two classes of dynamical syste...

It has been found that after pulmonary valvotomy for pulmonary valvular stenosis with an intact interventricular septum a satisfactory fall in right ventricular pressure is not always achieved immediately. In order to explain this, Kirklin, Connolly, Ellis, Burchell, Edwards, and Wood (1953) concluded that before the development of open heart surgery there were two main reasons: (1) failure to ...

The Swan-Ganz balloon flotation catheter was introduced in 1970. It can be placed at the bedside within a few minutes even in critically ill patients. Although placement of these catheters is not difficult, some training and experience are required to avoid complications and for proper interpretation of the hemodynamic data that can be obtained by pulmonary artery catheterization. Because of th...

While the development of land for residential housing along the Swan and Canning Rivers in Perth, WA, Australia has reduced natural mosquito breeding sites, the role of backyard container breeding remains a relatively unknown factor. Local Governments responsible for these areas focus management and control efforts on low lying, tidally driven mosquito habitats to control Aedes vigilax (Skuse) ...