Random constructions for translates of non-negative functions

Suppose A is a discrete infinite set of nonnegative real numbers. We say that A is type 2 if the series s(x) = Sigma lambda Lambda f (x + lambda) does not satisfy a zero-one law. This means that we can find a non-negative measurable "witness function" f : R -> [0,+ infinity) such that both the convergence set C(f, Lambda) ={x : s(x) < + infinity} and its complement the divergence set D (f, Lambda) = {x : s(x) = +infinity} are of positive Lebesgue measure. If Lambda is not type 2 we say that A is type 1. The main result of our paper answers a question raised by Z. Buczolich, J-P. Kahane, and D. Mauldin. By a random construction we show that one can always choose a witness function which is the characteristic function of a measurable set. We also consider the effect on the type of a set A if we randomly delete its elements. Motivated by results concerning weighted sums Sigma c(n)f(nx)and the Khinchin conjecture, we also discuss some results about weighted sum

Local structure and eddy current loss on the surface of carbon-steels in the vicinity of laser markings

The magnitude of laser beam induced transformations is fitted to the sensitivity of a Fluxset sensor described in this paper. It was found that markers produced in the 100-300 W power range and reparated by 6 ram, can be successfully detected by the applied sensor even under the 0,01 mm thick phosphate layer. The thermal stability of the markers increases due to heat treatment at 150degreesC for 30 hours, so that marking is stable enough to be used as barcode in production logistics

Scanning tunneling microscopy and spectroscopy of nitrogen doped multi-walled carbon nanotubes produced by the pyrolysis of ferrocene and benzylamine.

In this work, carbon nanotube samples were produced by aerosol chemical vapour deposition from a solution of ferrocene in benzylamine. The multi-walled nanotubes produced by this method were investigated by TEM, SEM/EDS, scanning tunneling microscopy (STM) and tunneling spectroscopy (STS). The dl/dV curves obtained from the STS measurements showed asymmetric density of states (DOS) in nanotubes, with higher DOS above the Fermi energy. These STS measurements and the EDS analysis indicate successful doping with nitrogen originating from the decomposition of benzylamine