By direct interpolation of a family of smooth energy estimates for solutions near Maxwellian equilibrium and in a periodic box to several Boltzmann type equations in [7–9, 11], we show convergence to Maxwellian with any polynomial rate in time. Our results not only resolve the important open problem for both the Vlasov-Maxwell-Boltzmann system and the relativistic Landau-Maxwell system for char...

Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of 14C can be calibrated over a period of 12,550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that rad...

First of all: disregard all of so called “preliminary physical expectations”, because all these expectations are just a pseudonym for prejudices elaborated by the older generation. These words belong to Dirac, not to me. The right way of creating new physics is different: one should begin with a beautiful mathematical idea. But it should be really beautiful! No special relations to physics is c...

The volume of social interactions like migration and commuting between two locations depends significantly on the distance between them. In the paper, we analysed the shape and parameters of several distance-decay functions for commuting and for migration flows, respectively. The analysis was performed for inter-municipal interactions in Slovenia in 2010–2011. The functions considered were powe...

We provide a characterization of the Gelfand–Shilov-type spaces test functions and their dual tempered ultradistributions by means Wilson bases exponential decay. offer two different proofs extend known results to Roumieu case.

The recirculation fraction of intramyocardial Ca(2+) (RF) has conventionally been obtained from the monotonic decay of postextrasystolic potentiation (PESP). The used assumption is that the decay is exponential. However, we have found that PESP usually decays in alternans even at spontaneous heart rates (>100 beats/min) in excised, cross-circulated canine heart preparations under normal coronar...

Conventional analyses of fluorescence lifetime measurements resolve the fluorescence decay profile in terms of discrete exponential components with distinct lifetimes. In complex, heterogeneous biological samples such as tissue, multi-exponential decay functions can appear to provide a better fit to fluorescence decay data than the assumption of a mono-exponential decay, but the assumption of m...

The role of the Lambert-Beer law in ocean optics is critically examined. The Lambert-Beer law and the three-parameter model of the submarine light field are used to construct an optical energy budget for any hydrosol. It is further applied to the analytical exponential decay coefficient of the light field and used to estimate the optical properties and effects of the dissolved/suspended compone...

Spectral theory and classical approximation theory are used to give a new proof of the exponential decay of the entries of the inverse of band matrices. The rate of decay oí A'1 can be bounded in terms of the (essential) spectrum of A A* for general A and in terms of the (essential) spectrum of A for positive definite A. In the positive definite case the bound can be attained. These results are...