On the projectors FF and FF

A particular version of the singular value decomposition is exploited for an extensive analysis of two orthogonal projectors, namely FF^† and F^†F, determined by a complex square matrix F and its Moore-Penrose inverse F^†. Various functions of the projectors are considered from the point of view of their nonsingularity, idempotency, nilpotency, or their relation to the known classes of matrices, such as EP, bi-EP, GP, DR, or SR. This part of the paper was inspired by Benítez and Rako?evi? [J. Benítez, V. Rako?evi?, Matrices A such that AA^† − A^†A are nonsingular, Appl. Math. Comput. 217 (2010) 3493-3503]. Further characteristics of FF^† and F^†F, with a particular attention paid on the results dealing with column and null spaces of the functions and their eigenvalues, are derived as well. Besides establishing selected exemplary results dealing with FF^† and F^†F, the paper develops a general approach whose applicability extends far beyond the characteristics provided therein.     

Simulations of lipid vesicle rupture induced by an adjacent supported lipid bilayer patch

Using a simple phenomenological model of a lipid bilayer and a surface, simulations were performed to study the bilayer-induced vesicle rupture probability as a vesicle adsorbs adjacently to a bilayer patch already adsorbed on the surface. The vesicle rupture probability was studied as a function of temperature, vesicle size, and surface-bilayer interaction strength. From the simulation data, estimates of the apparent activation energy for bilayer-induced vesicle rupture were calculated, both for different vesicle sizes and for different surface-bilayer interaction strengths.     

COLTRAP: a 22-pole ion trapping machine for spectroscopy at 4 K

Two similar 4 K 22-pole trapping machines have been recently completed in our laboratory. As a first experimental test in one of them, CH ₅ ⁺ and H₃O⁺ ions have been trapped in the presence of helium gas at 3.8 K and the kinetics and temperature dependence of He tagging investigated. A first shell closure with 5 and (3 + 2) attached He atoms, respectively, is observed for both species. Applying IR radiation in the 3 μm region, helium attachment to CH ₅ ⁺ is hindered by exciting CH-stretches of CH ₅ ⁺ prior to attachment. The resulting spectroscopic signal shows that the kinetic temperature of the stored CH ₅ ⁺ ensemble is below 12 K.     

Evaluation of human plasma sample preparation protocols for untargeted metabolic profiles analyzed by UHPLC-ESI-TOF-MS

Eight human plasma preparation protocols were evaluated for their suitability for metabolomic studies by ultra-high-performance liquid chromatography coupled with electrospray ionization time-of-flight mass spectrometry: organic solvent protein precipitation (PPT) with either methanol or acetonitrile in 2:1 and 3:1 (v/v) ratios with plasma; solid-phase extraction (SPE) using C₁₈ or HybridSPE cartridges; and a combination of PPT and SPE C₁₈ cartridges and microextraction by packed sorbent. A study design in which the order of injection of the samples was not randomized is presented. The analyses were conducted in a BEH C₁₈ column (1.7 μm, 2.1 mm?×?100 mm) using a linear gradient from 100 % water to 100 % methanol, both with 0.1 % formic acid, in 21 min. The most reproducible protocol considering both the univariate and the multivariate analysis results was PPT with acetonitrile in a 2:1 (v/v) ratio with plasma, offering a mean coefficient of variation of the area of all the detected features of 0.15 and one of the best clusterings in the principal component analysis plots. On the other hand, the highest number of extracted features was achieved using methanol in a 2:1 (v/v) ratio with plasma as the PPT solvent, closely followed by the same protocol with acetonitrile in a 2:1 (v/v) ratio with plasma, which offered only 1.2 % fewer repeatable features. In terms of concentration of remaining protein, protocols based on PPT with acetonitrile provided cleaner extracts than protocols based on PPT with methanol. Finally, pairwise comparison showed that the use of PPT- and SPE-based protocols offers a different coverage of the metabolome. Graphical Abstract

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Structure-property relationships in redox-gated single molecule junctions--a comparison of pyrrolo-tetrathiafulvalene and viologen redox groups

We demonstrate that the electrical "switching" behavior of single molecules connected between two electrode contacts can be controlled by altering their structure and electrochemical characteristics. The electrical properties of gold|molecule|gold single molecule junctions incorporating HS(CH2)6-X-(CH2)6SH, where X = viologen (4,4'-bipyridinium) or pyrrolotetrathiafulvalene, are determined using a scanning tunneling microscopy based technique. The switching behavior, controlled through a tuneable electrochemical gate, changes from an on-off response (viologen) to an off-on-off response (pyrrolotetrathiafulvalene) on changing the central redox group. In contrast, the electrical properties of junctions incorporating redox-inactive HS(CH2)6-1,4-C6H4-(CH2)6SH do not alter significantly as a function of applied potential.     

Modern Trends in Organic Light-Emitting Devices (OLEDs)

Summary. Synthesis of crosslinkable small and large organic molecules having OLED properties will be presented. Three strategies for the construction of multilayer devices will be described. In the first case small, well-defined OLED-molecules are functionalized with oxetanes as crosslinker. The second case deals with polymers having OLED active units in the main chain and pendant crosslinkers and finally it was shown that styrene polymers with pendant OLED functions and crosslinkers can be applied for the construction of such multilayer and multicolour devices.     

On angles and distances between subspaces

The angles and distances between two given subspaces of are investigated on the basis of a joint decomposition of the corresponding orthogonal projectors. Several new results are established, with the particular attention paid to the notions of inclinedness and minimal angle. To demonstrate the usefulness of the approach utilized, some results known to be valid in Hilbert space are reestablished in , either in generalized form or with considerably shorter proofs than in the original sources.     

New aspects of pseudostationary polymerization and their application

Contrary to the stationary state little thought has been given so far to the general principles of the pseudostationary state. In this discourse an attempt is made to demonstrate that — within wide limits — arbitrary initiation profiles may be used to determine k_p/k_t (k_p = rate constant of chain propagation, k_t = rate constant of chain termination) from the frequency dependence of rate of polymerization (in analogy to the rotating-sector technique) as well as to evaluate k_p from the chain-length distribution (CLD) of samples prepared under pseudostationary conditions. Adverse factors like nonspontaneous transformation of absorbed photons into primary radicals do not invalidate this result. The existence of a universal relationship (independent of the initiation profile) is proved to exist for the second moment of the CLD of samples prepared under pseudostationary initiation conditions for constant (chain-length independent) k_t. Pseudostationarity, however, might be also achieved if not the initiation but the termination is periodically varied. In this case the CLD has a completely different shape but allows determination of k_p likewise. Finally, the case of chain-length dependent k_t is shortly discussed in connection with pulsed-laser initiation. Although the general equation for the second moment of the CLD does not apply any longer for this case some generality appears to exist under these conditions, too.