An inverse problem for infinitely divisible moving average random fields

Statistical Inference for Stochastic Processes - Given a low frequency sample of an infinitely divisible moving average random field $$\{\int _{\mathbb {R}^d} f(x-t)\varLambda (dx); \ t \in \mathbb...     

Lattice embeddings and array noncomputable degrees

We focus on a particular class of computably enumerable (c. e.) degrees, the array noncomputable degrees defined by Downey, Jockusch, and Stob, to answer questions related to lattice embeddings and definability in the partial ordering (??, ≤) of c. e. degrees under Turing reducibility. We demonstrate that the latticeM₅ cannot be embedded into the c. e. degrees below every array noncomputable degree, or even below every nonlow array noncomputable degree. As Downey and Shore have proved that M₅ can be embedded below every nonlow₂ degree, our result is the best possible in terms of array noncomputable degrees and jump classes. Further, this result shows that the array noncomputable degrees are definably different from the nonlow₂ degrees. We note also that there are embeddings of M₅ in which all five degrees are array noncomputable, and in which the bottom degree is the computable degree 0 but the other four are array noncomputable. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Randeigenschaften zufälliger Potenzreihen und eine damit zusammenhängende Verallgemeinerung des Satzes von Fatou und Nevanlinna

Ohne Zusammenfassung     

Some remarks on computer-aided design of optical lens systems

Computer-aided design of optical lens systems implies the solution of an optimization problem of large dimension. To apply a local algorithm, we want to know a starting point within a small neighborhood of the desired system. For a given task, the designer is not able to define a suitable starting point. In this paper, we describe a global optimization algorithm which uses the principles of biological evolution with the aim of locating an adequate starting point for a local correction routine.This work was supported by the Department of Mathematics, Friedrich Schiller University, Jena, GDR, in cooperation with the research center of VEB Kombinat Carl Zeiss, Jena, GDR. The authors are indebted to Dr. L. C. W. Dixon for discussions of the topic.     

The Averaged Robbins – Monro Method for Linear Problems in a Banach Space

We consider a recursive method of Robbins–Monro type to solve the linear problem Ax=V in a Banach space. The bounded linear operator A and the vector V are assumed to be observable with some noise only. According to Polyak and Ruppert we use gains converging to zero slower than 1/n and take the average of the iterates as an estimator for the solution of the linear problem. Under weak conditions on the noise processes almost sure and distributional invariance principles are shown.     

Behaviour of wetting films of sodium hyaluronate saline solutions

The behaviour of wetting films of sodium hyaluronate (NaHA) saline solutions, at physiological conditions, is investigated using interferometry. Concentrations in the range of dilute and semi-dilute regimes were chosen to assess the role of bulk molecular interactions on the surface forces. The transition from dilute to semi-dilute solutions is known to occur at c*=0.59 mg mL(-1). Dilute solutions form stable films whose behaviour is explained by van der Waals interactions. For semi-dilute solutions, the disjoining pressure vs film thickness isotherms show branches attributed to stepwise thinning or film stratification, which is interpreted in terms of a network as predicted by the theory of semi-dilute polyelectrolyte solutions. The distance between branches is 16 nm for the NaHA concentration of 2 mg mL(-1) and 12 nm for the concentration of 3.5 mg mL(-1), in agreement with the calculated correlation lengths of the polymeric network. Since no experimental evidence exists for the presence of a stable network in the bulk, this tendency for self-association should be the result of the liquid confinement. To our knowledge, the existence of oscillatory disjoining pressure isotherms in the presence of excess salt was never observed for other polyelectrolyte solutions.     

FT-IR Mapping—A New Tool for Spatially Resolved Characterization of Polymer-Bound Combinatorial Compound Libraries with IR Microscopy

In the search for selective receptors , a promising approach is provided by immobilization of cyclopeptides on sensor surfaces (see picture) and subsequent detection of low molecular weight analytes with reflectometric interference spectroscopy (RIfS). Together with combinatorial chemistry, this innovative method offers a great potential for applications as sensors.