A detailed study of the generation of optically detectable watermarks using the logistic map

A digital watermark is a visible, or preferably invisible, identification code that is permanently embedded in digital media, to prove owner authentication and provide protection for documents. Given the interest in watermark generation using chaotic functions a detailed study of one chaotic function for this purpose is performed. In this paper, we present an approach for the generation of watermarks using the logistic map. Using this function, in conjunction with seed management, it is possible to generate chaotic sequences that may be used to create highpass or lowpass digital watermarks. In this paper we provide a detailed study on the generation of optically detectable watermarks and we provide some guidelines on successful chaotic watermark generation using the logistic map, and show using a recently published scheme, how care must be taken in the selection of the function seed.     

The dependence of critical parameter bounds on the monotonicity of a Newton sequence

Summary A new method is proposed for the inclusion of the critical parameter ^* of some convex operator equationu=Tu (appearing e.g. in thermal explosion theory). It is based on the fact that for a fixed Newton's method starting with a suitable subsolution is not monotonically if and only if >^*. Several numerical examples arising from nonlinear boundary value problems illustrate the efficiency of the method.     

Observation of columnar microstructure in step-graded Si1-xGex/Si films using high-resolution X-ray microdiffraction

Columnar microstructure in step-graded Si(1-x)Ge(x)/Si(001) structures with low threading dislocation densities has been determined using high angular resolution (approximately 0.005 degrees ) x-ray microdiffraction. X-ray rocking curves of a 3-microm-thick strain-relaxed Si(0.83)Ge(0.17) film show many sharp peaks and can be simulated with a model having a set of Gaussians having narrow angular widths (0.013 degrees -0.02 degrees ) and local ranges of tilt angles varying from 0.05 degrees to 0.2 degrees. These peaks correspond to individual tilted rectangular columnar micrograins having similar (001) lattice spacings and average areas of 0.8 to 2.0 microm(2).