On the Singularities of the Magnetic Spectral Shift Function at the Landau Levels

We consider the three-dimensional Schrödinger operators and where , A is a magnetic potential generating a constant magnetic field of strength , and where decays fast enough at infinity. Then, A. Pushnitskis representation of the spectral shift function (SSF) for the pair of operators is well defined for energies We study the behaviour of the associated representative of the equivalence class determined by the SSF, in a neighbourhood of the Landau levels Reducing our analysis to the study of the eigenvalue asymptotics for a family of compact operators of Toeplitz type, we establish a relation between the type of the singularities of the SSF at the Landau levels and the decay rate of V at infinity. Communicated by Bernard HelfferSubmitted 23/09/03, accepted 15/01/04     

Adsorption integral equation via complex approximation with constraints: kernel of general form

For the monolayer adsorption on a homogeneous surface, including arbitrary range lateral interactions, the isotherm can be written as a power series of the Langmuir isotherm. If this isotherm is used as the kernel in the adsorption integral equation, this integral equation can be solved in an analytical form. Because the global isotherm is usually known as a set of experimental values, the use of a numerical method is inevitable. A new numerical method for solving the adsorption integral equation with a kernel of general form is developed. It is based on recent results concerning the structure of the local isotherm and on the ideas of complex approximation with constraints, and allows reduction of the problem under consideration to a linear‐quadratic programming problem. Results of numerical experiments are presented. The method can be useful for the evaluation of the adsorption energy distribution from experimental data. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1058–1066, 2001     

Continuous-wave stimulated Raman scattering (cwSRS) microscopy

Stimulated Raman scattering (SRS) microscopy is a powerful tool for chemically sensitive non-invasive optical imaging. However, ultrafast laser sources, which are currently employed, are still expensive and require substantial maintenance to provide temporal overlap and spectral tuning. SRS imaging, which utilizes continuous-wave laser sources, has a major advantage, as it eliminates the cell damage due to exposure to the high-intensity light radiation, while substantially reducing the cost and complexity of the setup. As a proof-of-principle, we demonstrate microscopic imaging of dimethyl sulfoxide using two independent, commonly used lasers, a diode-pumped, intracavity doubled 532-nm laser and a He–Ne laser operating at 632.8-nm.     

Computable Embeddings for Pairs of Linear Orders

Algebra and Logic - We study computable embeddings for pairs of structures, i.e., for classes containing precisely two nonisomorphic structures. Surprisingly, even for some pairs of simple linear...     

The ω-Turing degrees

In this paper we initiate the study of the ω-Turing reducibility between sequences of sets of natural numbers. We shall prove that the induced degree structure is an extension of the structure of the Turing degrees and that the two structures are closely connected, but different enough. Further we shall prove some definability results for the local theory of the newly defined structure.     

Interfacial rheology of mixed layers of food proteins and surfactants

Mixed protein–surfactant adsorption layers at liquid interfaces are described including the thermodynamic basis, the adsorption kinetics and the shear and dilational interfacial rheology. It is shown that due to the protrusion of hydrophobic protein parts into the oil phase the adsorption layers at the water–hexane interface are stronger anchored as compared to the water-air surface. Based on the different adsorption protocols, a sequential and a simultaneous scheme, the peculiarities of complexes between proteins and added surfactants are shown when formed in the solution bulk or at a liquid interface. The picture drawn from adsorption studies is supported by the findings of interfacial rheology.     

Predicting adsorption enthalpies on silicalite and HZSM‐5: A benchmark study on DFT strategies addressing dispersion interactions

We evaluated the accuracy of periodic density functional calculations for adsorption enthalpies of water, alkanes, and alcohols in silicalite and HZSM‐5 zeolites using a gradient‐corrected density functional with empirical dispersion corrections (PBE‐D) as well as a nonlocal correlation functional (vdW‐DF2). Results of both approaches agree in acceptable fashion with experimental adsorption energies of alcohols in silicalite, but the adsorption energies for n‐alkanes in both zeolite models are overestimated, by 21?46 kJ mol^?1. For PBE‐D calculations, the adsorption of alkanes is exclusively determined by the empirical dispersion term, while the generalized gradient approximation‐DFT part is purely repulsive, preventing the molecule to come too close to the zeolite walls. The vdW‐DF2 results are comparable to those of PBE‐D calculations, but the latter values are slightly closer to the experiment in most cases. Thus, both computational approaches are unable to reproduce available experimental adsorption energies of alkanes in silicalite and HZSM‐5 zeolite with chemical accuracy. © 2014 Wiley Periodicals, Inc.