Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schr?dinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves.     

Control of sp2/sp3 carbon ratio and surface chemistry of nanodiamond powders by selective oxidation in air

The presence of large amounts of nondiamond carbon in detonation-synthesized nanodiamond (ND) severely limits applications of this exciting nanomaterial. We report on a simple and environmentally friendly route involving oxidation in air to selectively remove sp(2)-bonded carbon from ND. Thermogravimetric analysis and in situ Raman spectroscopy shows that sp(2) and sp(3) carbon species oxidize with different rates at 375-450 degrees C and reveals a narrow temperature range of 400-430 degrees C in which the oxidation of sp(2)-bonded carbon occurs with no or minimal loss of diamond. X-ray absorption near-edge structure spectroscopy detects an increase of up to 2 orders of magnitude in the sp(3)/sp(2) ratio after oxidation. The content of up to 96% of sp(3)-bonded carbon in the oxidized samples is comparable to that found in microcrystalline diamond and is unprecedented for ND powders. Transmission electron microscopy and Fourier transform infrared spectroscopy studies show high purity 5-nm ND particles covered by oxygen-containing surface functional groups. The surface functionalization can be controlled by subsequent treatments (e.g., hydrogenization). In contrast to current purification techniques, the air oxidation process does not require the use of toxic or aggressive chemicals, catalysts, or inhibitors and opens avenues for numerous new applications of nanodiamond.     

Modeling of ion processes in atmospheric pressure matrix-assisted laser desorption/ionisation

Atmospheric pressure matrix-assisted laser desorption/ionization (AP-MALDI) has proven a convenient and rapid method for ion production in the mass spectrometric analysis of biomolecules. This technique, like other atmospheric pressure ionization methods, suffers from ion loss during ion transmission from the atmosphere into the vacuum of the mass spectrometer. In this work, a simple model describing ion formation and ion motion towards the inlet capillary of the mass spectrometer is described. Both the gas flow and electric field near the MALDI plate were numerically calculated using the boundary element method (BEM). The ions were moving along with the gas flow and drifting in the electric field in accordance with their ion mobility properties. The ion signal dependence on an electric field strength obtained in the proposed model correlates well with experimental results.     

Heat equation with a general stochastic measure on nested fractals

A stochastic heat equation on an unbounded nested fractal driven by a general stochastic measure is investigated. Existence, uniqueness and continuity of the mild solution are proved provided that the spectral dimension of the fractal is less than 4/3.     

Water-Soluble Non-Classical Benzene Mimetics

A new generation of saturated benzene mimetics, 2-oxabicyclo[2.1.1]hexanes, was developed. These compounds were designed as analogues of bicyclo[1.1.1]pentane with an improved water solubility. Crystallographic analysis of 2-oxabicyclo[2.1.1]hexanes revealed that they occupy a novel chemical space, but, at the same time, resemble the motif of meta-disubstituted benzenes.     

Approximation of Fractional Brownian Motion by Martingales

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.     

Local moment problem

The work is devoted to the local moment problem, which consists in finding of non-decreasing functions on the real axis having given first 2n + 1, n ≥ 0, power moments on the whole axis and also 2m + 1 first power moments on a certain finite axis interval. Considering the local moment problem as a combination of the Hausdorff and Hamburger truncated moment problems we obtain the conditions of its solvability and describe the class of its solutions with minimal number of growth points if the problem is solvable. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Potentiometric Electronic Tongue for Taste Assessment of Ibuprofen Based Pharmaceuticals

The flavor aspect of pharmaceutical formulations is very important in terms of their acceptability for the patient. This work is aimed at using of a novel promising type of electronic tongue (ET), consisting of a potentiometric sensor array, for the discrimination and assessment the taste of commercial pharmaceuticals based on ibuprofen (Ibuflam 4 %). The sensor array was formed by six ion‐selective membranes (ISMs) based on both specific and non‐specific active components. Analysis of potentiometric signal outputs including statistical data processing utilizing the principal component analysis (PCA) method allowed evaluating the role of individual active components of the ISMs in the sense of taste control of the pharmaceutical preparation Ibuflam 4 % before and after flavoring. The sensing array can be used to identify differences in flavor within individual batches from the same producer, since ISMs provide a different response to all components present in the analyzed pharmaceutical. The ET contains ISMs which are able to recognize the bitter taste in the framework of the batches of ibuprofen based pharmaceuticals. To recognize bitter taste, it was essential to include ISMs, providing a response to a particular type of taste, namely, specific and non‐specific ISMs. The experimental findings show that taste‐sensing potentiometric sensor system can be a good alternative to the human panel and is able to detect the slight changes in taste.