Support Theorems for the Radon Transform and Cramér-Wold Theorems

This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distribution theory and Fourier analysis we show that the presented injectivity results for the Radon transform lead to Cramér-Wold type results for measures. One purpose of this article is to contribute to making known to probabilists interesting results for the Radon transform that have been developed essentially during the 1980s and 1990s.     

HCSE method for detection of small carbon–carbon couplings and their signs,comparison with SLAP pulse sequence

Performance of homonuclear coupling sign edited (HCSE) experiment applied to detection of signed carbon–carbon couplings is discussed using a set of already measured samples of nine monosubstituted benzenes. It is shown that coupling sign detection is insensitive to the settings of carbon–carbon polarization transfer delays. The HCSE spectra of ten from the total of 43 measured carbon–carbon couplings were considerably influenced by relaxations and proton–proton strong couplings. These effects are quantitatively discussed. The results of HCSE and SLAP experiments are compared. It is shown that the two methods may complement each other in detection of signed carbon–carbon couplings. Copyright © 2013 John Wiley & Sons, Ltd.     

1,2,4‐Triazole‐based N‐heterocyclic carbene complexes of gold(I): synthesis,characterization and biological activity

Two gold(I) complexes of the (NHC)AuX type bearing a triazole‐based N‐heterocyclic carbene (NHC) ligand (1‐tert‐butyl‐4‐(4‐methylphenyl)‐3‐phenyl‐1H‐1,2,4‐triazol‐4‐ium‐5‐ylidene) and various halide ligands (X = Br, I) were synthesized and characterized in solution using NMR spectroscopy as well as in the solid state using X‐ray diffraction techniques. The cytotoxic properties of both compounds and the precursor, (NHC)AuCl, were screened against a panel of human tumour cell lines including liver cancer (HepG2), cervical cancer (HeLa S3) and leukaemia (CCRF‐CEM, HL‐60) and compared to cisplatin and auranofin. It was found that the activities of the chloro and bromo derivatives were generally superior to that of cisplatin and slightly less effective compared to auranofin, except for HepG2 cells where auranofin was not as effective. In addition, the ability to induce membrane phosphatidyl serine externalization as a hallmark of apoptosis in CCRF‐CEM leukaemic cells was investigated. Copyright © 2016 John Wiley & Sons, Ltd.     

Insider Trading in Convergent Markets

Optimal trading strategies are found for an insider who is trading in two convergent stocks and is bound by margin constraints.     

A generalization of effect algebras and ortholattices

A common generalization of effect algebras and ortholattices that allows to represent ortholattices in a similar way in which orthomodular lattices are represented in the setting of effect algebras is introduced.     

7‐Methoxy‐2,3‐dioxo‐1,4‐dihydroquinoxalin‐6‐aminium chloride monohydrate

Single crystals of the title compound, C₉H₁₀N₃O₃⁺·Cl⁻·H₂O, were obtained by recrystallization from hydrochloric acid. The cations stack along the crystallographic a direction. The 2,3‐dioxo‐1,4‐dihydroquinoxaline group shows a significant deviation from planarity [r.m.s. deviation from the best plane = 0.063 (2) Å]. Hydrogen bonding links the cations, chloride anions and water molecules to form an extended three‐dimensional architecture.