Steady motion of a rigid disk of finite thickness on a horizontal plane

The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady-state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of ground and it is shown that the possible steady motion of a disk is either on a straight line or in a circle. Oscillations about steady state are discussed and conditions for stable motion established. The bifurcations of steady motions on a smooth surface are also considered.     

Hydrogen‐Bond‐Based Magnetic Exchange Between μ‐Diethylnicotinamide(aqua)bis(X‐salicylato)copper(II) Polymeric Chains

Polymeric salicylatocopper(II) complexes of unusual composition [C u(X‐ sal)₂( μ‐denia)(H₂O)]_n [denia = diethylnicotinamide, and X‐sal = 5‐methylsalicylate ( 1 ), 3‐methylsalicylate ( 2 ), 4‐methoxysalicylate ( 3 ), 3,5‐dichlorosalicylate ( 4 ) and 3,5‐dibromosalicylate ( 5 )] were synthesized and characterized. Magnetic measurements were performed in the temperature range 1.8–300 K. The structural unit of all complexes consists of a Cu^II atom, which is monodentately coordinated by the pair of X‐salicylate anions in trans positions. Water and the diethylnicotinamide ligand occupy the other two basal plane positions of the tetragonal pyramid. The axial positions are occupied by a diethylnicotinamide oxygen atom of neighboring structural units, thus forming a spiral polymeric structure parallel to b axis. Magnetic measurements showed that all complexes 1 – 5 exhibit a susceptibility maximum at about 6–8 K. The obtained data fit to Bleaney–Bowers equation gave singlet‐triplet energy gaps 2J = –8.60 cm^–1 for 1 , 2J = –6.57 cm^–1 for 2 , 2J = –8.57 cm^–1 for 3 , 2J = –6.82 cm^–1 for 4 , and 2J = –6.45 cm^–1 for 5 . The supramolecular structure based on hydrogen bonds [described by supramolecular synthons R₂²(10) and R₂²(12)] is the pathway for antiferromagnetic interactions of the magnetically coupled pairs of copper atoms of neighboring chains within the 2D supramolecular layers. The results of the magnetic measurements suggest involvement of the COO groups in the magnetic interaction pathway for all five complexes.     

Disulfide bond decay during matrix-assisted laser desorption/ionization time-of-flight mass spectrometry experiments

In our laboratory, we have been studying the reductive processes that occur during matrix-assisted laser desorption/ionization (MALDI) experiments. Recently, we have finished an analysis of the DHB matrix effect on the azo group in cyclic peptides. However, deep understanding of disulfide bond behaviour during a mass spectrometry (MS) experiment is much more important in proteomics as its reduction can cause serious errors in protein spectra interpretation. Therefore, we have focused on intra- and intermolecular disulfide bonds as well as disulfide bonds connecting cysteine and 2-thio-5-nitrobenzoic acid (TNB, Ellman's reagent modification) in model peptides during MALDI MS measurements. While the reduction was not observed for intra- and intermolecular cysteine-cysteine disulfide bonds, the disulfide connection between cysteine and TNB was always affected. It was proved that TNB and Ellman's reagent can act as a matrix itself. The results obtained enabled us to propose a reaction mechanism model which is able to describe the phenomena observed during the desorption/ionization process of disulfide-containing molecules.     

Additive-free clicking for polymer functionalization and coupling by tetrazine-norbornene chemistry

Herein we report the use of a tetrazine-norbornene inverse electron demand Diels-Alder conjugation applied to polymer end-functionalization and polymer-polymer coupling. The reaction was found to be applicable to polymer-polymer coupling, as judged by SEC, DOSY NMR, and LCxSEC analyses, giving diblock copolymers by merely mixing the constituent homopolymers together under ambient conditions, using no catalyst, additive, or external stimulus.     

Fast motion in molecular solids at low temperatures: evidence from a pulsed electron paramagnetic resonance study of nitroxyl radical relaxation

We have investigated the electron phase-memory relaxation time of the nitroxyl radical 2,2,6,6-tetramethylpiperidine-1-oxyl at temperatures between 5 and 80 K in crystalline and glassy states of ethanol using pulsed X-band electron paramagnetic resonance spectroscopy. The results indicate that the transition from the slow to fast motion regimes of the paramagnetic center occurs upon further cooling of the sample below ～20 K. We provide experimental evidence that this phenomenon cannot be ascribed to the impact of hyperfine interactions with methyl protons in the system, but it can be instead a signature of the coupling of the electron spin with the boson peak excitations of the lattice.     

Surface plasmon resonance biosensor for determination of tetrodotoxin: prevalidation study

A label-free surface plasmon resonance biosensor method was applied to determine tetrodotoxin (TTX) in pufferfish matrixes using an antibody inhibition assay format. A prevalidation study was conducted to demonstrate the assay performance characteristics, such as selectivity, LOD, LOQ, repeatability, reproducibility, and accuracy. Three participating laboratories reported standard curves in buffer and pufferfish matrix. A set of blind samples with TTX spiked into buffer as well as in 10% pufferfish extract were analyzed. Additionally, three blind naturally contaminated samples were analyzed, and the results were compared to those obtained using a reference method (HPLC/electrospray ionization-selected reaction monitoring-MS). The developed method was demonstrated to be capable of detecting TTX in pufferfish matrix standard samples in a broad concentration range (2-9000 ng/mL) with an LOD of 1.5 ng/mL. Between-laboratory recovery values were in the range of 51-190% with a mean of 107%, and 64-180% with a mean of 103% for TTX-spiked samples in buffer and pufferfish matrix, respectively. Between-laboratory recoveries were in the satisfactory range of 101-119% for naturally contaminated samples. This robust, rapid, and noninvasive method may serve as an attractive alternative to established methods for detection of TTX in pufferfish extracts.     

A filtering method for the interval eigenvalue problem

We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer approximation (superset) of the real eigenvalue set of an interval matrix, we propose a filtering method that iteratively improves the approximation. Even though our method is based on a sufficient regularity condition, it is very efficient in practice and our experimental results suggest that it improves, in general, significantly the initial outer approximation. The proposed method works for general, as well as for symmetric interval matrices.     

Krull’s theory for the double gamma function

The Barnes’ G-function G(x) = 1/Γ₂, satisfies the functional equation logG(x + 1) − logG(x) = logΓ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma functions, a new expansion for the Gamma function and summation formulae with Polygamma functions.