Sperner extensions of affine spaces

In this paper Sperner spaces are constructed in which the affine space can be embedded in a certain sense.     

Cost allocation in a bank ATM network

We consider a situation in which a group of banks consider connecting their Automated Teller Machines (ATMs) in a network, so that the banks customers may use ATMs of any bank in the network. The problem studied is that of allocating the total transaction costs arising in the network, among the participating banks. The situation is modeled as a cooperative game with transferable utility. We propose two allocations, and discuss their relation to the core and other well-known solution concepts, as well as to population monotonicity.Endre Bjørndal has enjoyed the hospitality of Tilburg University, and has also received financial support from Telenor AS and the Norwegian School of Economics and Business Administration.     

Long Excursions of a Random Walk

In Csáki et al. ⁽¹⁾ and Révész and Willekens⁽⁹⁾ it was proved that the length of the longest excursion among the first n excursions of a plane random walk is nearly equal to the total sum of the lenghts of these excursions. In this paper several results are proved in the same spirit, for plane random walks and for random walks in higher dimensions.     

Offset‐compensated and zero‐quantum suppressed ROESY provides accurate 1H–1H distances in small to medium‐sized molecules

A robust version of the off‐resonance ROESY pulse scheme is suggested for the measurement of proton–proton distances or slow chemical exchange in small to medium‐sized molecules. The method implements adiabatic ramps to establish a pair of opposite frequency off‐resonance spin lock fields – with optionally randomized duration – and adiabatic inversion pulses with simultaneous gradients for efficient zero‐quantum suppression. The amended pulse sequence yields pure absorption cross‐peaks and works safely for small to medium‐sized molecules. The applicability of the method has been demonstrated using small, rigid molecules (strychnine and codeine) and was also applied for a cyclic peptide and a small protein. We found that the pure phase cross‐peaks of the new ROESY version are beneficial for distance measurements. The one‐dimensional (selective) version of the new method is also powerful for measuring selected pair‐wise interactions and distance determination. Copyright © 2016 John Wiley & Sons, Ltd.     

In-situ mechanical characterization of wurtzite InAs nanowires

High aspect ratio vertical InAs nanowires were mechanically characterized in a scanning electron microscope equipped with two micromanipulators. One, equipped with a calibrated atomic force microscope probe, was used for in-situ static bending of single nanowires along the 〈11–20〉 crystallographic direction. The other one was equipped with a tungsten tip for dynamic resonance excitation of the same nanowires. This setup enabled a direct comparison between the two techniques. The crystal structure was analyzed using transmission electron microscopy, and for InAs nanowires with a hexagonal wutzite crystal structure, the bending modulus value was found to BM=43.5 GPa. This value is significantly lower than previously reported for both cubic zinc blende InAs bulk crystals and InAs nanowires. Besides, due to their high resonance quality factor (Q>1200), the wurtzite InAs nanowires are shown to be a promising candidate for sub-femtogram mass detectors.     

Validated HPLC Method for Simultaneous Quantitation of Bergenin,Arbutin, and Gallic Acid in Leaves of Different Bergenia Species

Bergenia species (Saxifragaceae) are important sources of herbal medicines in Asia, mainly in Russia. Various plant parts are valued for their antibacterial, anti-inflammatory, antioxidant sand adaptogenic effect, and used for the dissolution of kidney and bladder stones. In this study a rapid reversed phase liquid chromatography (RP-HPLC) method has been developed for rapid screening and identifying of the main active components in leaf samples of Bergenia accessions. The main goal of this study was to develop an efficient method for the simultaneous identification and detection of arbutin, bergenin and gallic acid from Bergenia leaf samples, which were extracted with a methanolic solvent mixture [methanol:water = 1:1 (v/v)]. Chromatographic separations were performed on a reversed phase Luna C18(2)-HST HPLC column. This chromatographic system provided increased speed and efficiency for separations, without the need for ultra-high pressures. Reversed phase HPLC coupled with diode array detector method was used for the analysis. The method was validated using ICH guidelines. The level of gallic acid was significantly higher in Bergenia crassifolia samples compared to Bergenia cordifolia. However, the samples of the two Bergenia species did not differ substantially regarding the concentrations of arbutin and bergenin. The novel method proved to be fast and allowed sufficient separation and quantification of arbutin, bergenin and gallic acid, the most important bioactive compounds of Bergenia leaves; thus facilitating rapid screening and quality assessment of Bergenia samples of various botanical and geographical origins.     

Studies in the Field of Pyridazine Compounds. X1. A Method for the Synthesis of 6-(Substituted Amino)-3-Pyridazinyl-Hydrazines

Recently, the 6-(substituted amino)-3-pyridazinyl-hydrazines^2–4 and their hydrazones¹ became important as peripheral antihypertensive agents. These compounds have been synthesized from 3,6-dichloropyridazine (1) by introducing to the molecule firstly the substituted amine and then the hydrazine moiety^2–4. This process has some disadvantages. It is known that one chlorine atom of 1 can be easily replaced by nucleophilic substitution. The subsequent replacement of the other chlorine atom in 1 is, however, rather difficult⁵. For example, 2 silosequent substitution with hydrazine should be uarried out with agreat excess of hydrazine at elevated temperatures and the product formed is liable to decompose in this basic medium. As a consequence, overail yield of this process is low ana in general, the final product nas to be purifiea tnroilgh its benzylidene derivative. Tnerefore, according to our experiments, this process does not seem to be useful for large-scale operations.     

Planar S-systems: Permanence

We characterize permanence of planar S-systems. Further, we construct a planar S-system with three limit cycles.