Odd subgraphs and matchings

Let G be a graph and f : V(G)→{1,3,5,…}. Then a subgraph H of G is called a (1,f)-odd subgraph if deg_H(x){1,3,…,f(x)} for all xV(H). If f(x)=1 for all xV(G), then a (1,f)-odd subgraph is nothing but a matching. A (1,f)-odd subgraph H of G is said to be maximum if G has no (1,f)-odd subgraph K such that |K|>|H|. We show that (1,f)-odd subgraphs have some properties similar to those of matchings, in particular, we give a formula for the order of a maximum (1,f)-odd subgraph, which is similar to that for the order of a maximum matching.     

Synthesis and stereochemical studies of 6-substituted 1H,3H,6H,7aH-3,3-dimethylimidazo-[1,5-c]thiazol-5-one-7-thiones

The reaction of (4S)-5,5-dimethyl-4-thiazolidine-carboxylic acid 1 with alkyl and aryl isothiocyanates 2 gave bicyclic thiohydantoins 3 . The (2R,4S)- and (2S,4S)-mixtures of 2-substituted 5,5-dimethyl-4-thiazolidine-carboxylic acids 4 and 8 containing two centers of chirality in the analogous reaction afforded thiohydantoins 7 and 10 , respectively, with (1R)-configuration. In some cases we managed to isolate the thioureido acid intermediates 6 and 9 or their triethylamine salts which afforded the corresponding bicycles 7 and 10 under thermal cyclization or acidification. The stereochemistry has been elucidated by high resolution ram studies, optical rotation measurements and X-ray crystallography.     

Quality-by-Design-Based Development of n-Propyl-Gallate-Loaded Hyaluronic-Acid-Coated Liposomes for Intranasal Administration

The present study aimed to develop n-propyl gallate (PG)-encapsulated liposomes through a novel direct pouring method using the quality-by-design (QbD) approach. A further aim was to coat liposomes with hyaluronic acid (HA) to improve the stability of the formulation in nasal mucosa. The QbD method was used for the determination of critical quality attributes in the formulation of PG-loaded liposomes coated with HA. The optimized formulation was determined by applying the Box–Behnken design to investigate the effect of composition and process variables on particle size, polydispersity index (PDI), and zeta potential. Physiochemical characterization, in vitro release, and permeability tests, as well as accelerated stability studies, were performed with the optimized liposomal formulation. The optimized formulation resulted in 90 ± 3.6% encapsulation efficiency, 167.9 ± 3.5 nm average hydrodynamic diameter, 0.129 ± 0.002 PDI, and −33.9 ± 4.5 zeta potential. Coated liposomes showed significantly improved properties in 24 h in an in vitro release test (>60%), in vitro permeability measurement (420 μg/cm²) within 60 min, and also in accelerated stability studies compared to uncoated liposomes. A hydrogen-peroxide-scavenging assay showed improved stability of PG-containing liposomes. It can be concluded that the optimization of PG-encapsulated liposomes coated with HA has great potential for targeting several brain diseases.     

Investigation of solid-state reaction in Ag/Sn nanostructured thin films at room temperature

Diffusion intermixing processes in nanostructured Ag/Sn thin-film system at room temperature were investigated by means of secondary neutral mass Spectrometry depth profiling technique. As it was confirmed by X-ray diffraction too, the reaction started already in the as-deposited sample. Since the bulk diffusion was frozen at room temperature, the Ag₃Sn phase was formed along the grain boundaries (GBs), gradually consuming the interior of grains, and was grown perpendicular to the GBs. At the same time, formation and growth of a small compact reaction layer near the interface were observed and the shift of the bordering parallel interfaces was controlled by GB diffusion. From the kinetics of the diffusion process in the above two mechanisms, both the interface velocity in the diffusion-induced grain boundary motion regime as well as the coefficient of parabolic growth in the planar growth regime were determined.     

Effects of Sucrose Palmitate on the Physico-Chemical and Mucoadhesive Properties of Buccal Films

In our current research, sucrose palmitate (SP) was applied as a possible permeation enhancer for buccal use. This route of administration is a novelty as there is no literature on the use of SP in buccal mucoadhesive films. Films containing SP were prepared at different temperatures, with different concentrations of SP and different lengths of hydroxypropyl methylcellulose (HPMC) chains. The mechanical, structural, and in vitro mucoadhesive properties of films containing SP were investigated. Tensile strength and mucoadhesive force were measured with a device and software developed in our Institute. Positron annihilation lifetime spectroscopy (PALS) and X-ray powder diffractometry (XRPD) were applied for the structure analysis of the films. Mucoadhesive work was calculated in two ways: from the measured contact angle and compared with direct mucoadhesive work, which measured mucoadhesive force, which is direct mucoadhesion work. These results correlate linearly with a correlation coefficient of 0.98. It is also novel because it is a new method for the determination of mucoadhesive work.     

Numerical approximation of AR‐XPS spectra for rough surfaces considering the effect of electron shadowing

A computational scheme is presented that takes into account the topography, i.e. the shadowing and hence the local emission angle of the electrons when evaluating AR‐XPS data of macroscopic rough surfaces. The topography of the sample surface is supposed to be recorded by atomic force microscopy and/or optical microscopy. The emitted photoelectrons are simulated based on an extension of the Beer–Lambert law that includes the shadowing, the current local emission angle, and the geometrical instrument setup. The obtained angle‐resolved XPS spectra are optimized in accordance with experimental ones via a self‐consistent minimization algorithm that also allows one to determine the layer thicknesses of the corrugated sample. In order to validate the proposed numerical scheme, the simulation program simulation of electron spectra for surface analysis is used. An additional analysis is then performed considering only experimental data. The numerical scheme gives good agreement in simulation–simulation as well as simulation–experiment comparisons and permits a comprehensible interpretation of the measured data. Copyright © 2014 John Wiley & Sons, Ltd.