Fredholm boundary value problems for perturbed systems of dynamic equations on time scales

This paper offers conditions ensuring the existence of solutions of linear boundary value problems for systems of dynamic equations on time scales. Utilizing a method of Moore–Penrose pseudo‐inverse matrices leads to an analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a system of dynamic equations. As an example of an application of the presented results, the problem of bifurcation of solutions of boundary value problems for systems of dynamic equations on time scales with a small parameter is considered.     

Combining ferrocene,thiophene and a boronic acid: a hybrid ligand for reagentless electrochemical sensing of cis-diols

A redox-active affinity ligand suitable for reagentless sensing of cis-diols was synthesised and characterised. 4-[(Ferrocenylamino)methyl]thiophene-3-boronic acid (FcTBA) was allowed to interact with the model cis-diol, sorbitol. A discrete, cathodic shift of the redox potential was observed upon interaction of FcTBA with sorbitol thus providing simultaneous differentiation between the free and bound forms of this sensor molecule. Similar behaviour was observed also for FcTBA co-immobilised with thiophene in a mixed self-assembled monolayer on a gold electrode.     

Using LR-HSQMBC to observe long-range H–N correlations

The recently reported LR-HSQMBC experiment has been optimized for ¹H–¹⁵N long-range heteronuclear couplings. Several previously unreported four-bond correlations, consistent with the predicted by DFT calculations (0.2–0.3 Hz ⁴J_NH couplings), have been observed for strychnine using 2 Hz optimization of the LR-HSQMBC experiment. This experiment offers an advantage over accordion-optimized experiments such as IMPEACH and CIGAR for the observation of long-range ¹H–¹⁵N correlations in that the experiment is refocused and employs a CLIP pulse sequence element to bring the long-range correlations into phase, allowing broadband X-decoupling to be employed during acquisition.     

A new asymmetric Pseudo‐Voigt function for more efficient fitting of XPS lines

Asymmetric peak profiles for the application in spectroscopy can be obtained in a simple way by substituting the usually constant full width at half maximum parameter in Pseudo‐Voigt functions with an energy‐dependent expression, for instance of sigmoidal shape. While this approach has been successfully applied to vibrational spectra, we find that the resulting curves are less suitable for least‐squares fits of X‐ray photoelectron spectroscopy (XPS) data. However, if one additionally allows a variable displacement of the sigmoidal step relative to the peak, excellent fitting results can be obtained. We demonstrate the applicability of our extended approach on several inherently asymmetric XPS lines, i.e. the C 1s signal of graphite and C₂H₂/Pd(100), the 3d_5/2–3d_3/2 doublet of palladium, and the 4f_7/2–4f_5/2 doublet of platinum. Comparison of the corresponding fit results with the results obtained by the application of more elaborate, theory‐based line profiles (Doniach‐?unji? and Mahan functions) shows that the modified Pseudo‐Voigt function gives practically identical results in terms of peak shape and area, while requiring much less computational effort since no convolution procedures are required for its calculation. Thus, this function is most suitable for application in one of the following situations: (i) the peak shape of a given signal is known but cannot be calculated with ease, and (ii) the theoretical peak shape is not (yet) known, however, one wants to perform a first quantitative screening of the data at issue. Copyright © 2014 John Wiley & Sons, Ltd.