On Fermat Diophantine functional equations,little Picard theorem and beyond

Aequationes mathematicae - We discuss equivalence conditions for the non-existence of non-trivial meromorphic solutions to the Fermat Diophantine equation $$f^m(z)+g^n(z)=1$$ with integers $$m,n\ge...     

Self-Assembly of C3 Symmetric Rigid Macrolactams into Very Polar and Porous Trigonal Crystals

Cyclohexane and cyclotri-β-alanyl have been used as scaffolds for the design of new C₃-symmetric rings incorporating conjugated alkenes and dienes. All three C₃-symmetric lactams share the same triangular shape and their crystal system is trigonal. They all belong to the R3 space group, R3m, R3 and R3c, for the increasingly large 12-, 18- and 24-membered rigid rings, respectively. All lactams stack on top of each other, through H-bonds and van der Waals noncovalent interactions, leading to endless supramolecular cylinders and tubes. The largest member of the family leads to tubes, the central pores of which is wide enough to let water in. A common feature of all the lactams is their very large dipole, of around 9 D, according to DFT calculations. Surprisingly, all the resulting cylinders and tubes pack side by side in the crystals, with all the dipoles pointing to the same direction. As a result, all three crystals are anisotropic and appear to be the first members of a new kind of highly polar crystals.     

Functionalized Silver-Ion-Mediated α-dC/β-dC Hybrid Base Pairs with Exceptional Stability: α-d-5-Iodo-2′-Deoxycytidine and Its Octadiynyl Derivative in Metal DNA

Silver-mediated α-dC–Ag⁺–β-dC hybrid base pairs decorated with 5-iodo- or 5-octadiynyl residues are well accommodated in duplex DNA. A strong T_m increase and favorable thermodynamic data for duplex DNA were observed after addition of silver ions. The phenomenon is particularly obvious when both nucleobases of the base pairs are functionalized. Neither the position of the base pair, nor the type of 5-substituent had a negative influence. On the contrary, functionalization of conventional silver-mediated β-dC–Ag⁺–β-dC homo base pairs showed a negative impact induced by the bulky substituents. To this end, cytosine modified 12-mer oligodeoxynucleotides were prepared by solid-phase synthesis employing new α-anomeric 2′-deoxycytidine phosphoramidites. A multigram scale synthesis was developed for 5-iodo-α-d -2′-deoxycytidine ( 1 ) employing the direct glycosylation of cytosine with Hoffer's α-d -halogenose followed by separation of anomeric DMT nucleosides. Regarding base-pair stability and functionalization silver-mediated α/β-dC hybrid base pairs were found to be superior to β/β-dC homo pairs. According to their extraordinary properties, they might find applications in DNA diagnostics, material science, or nanotechnology.     

Dynamic Interactions in Synthetic Receptors: A Guest Exchange Saturation Transfer Study

The accumulated knowledge regarding molecular architectures is based on established, reliable, and accessible analytical tools that provide robust structural and functional information on assemblies. However, both the dynamicity and low population of noncovalently interacting moieties within studied molecular systems limit the efficiency and accuracy of traditional methods. Herein, the use of a saturation transfer-based NMR approach to study the dynamic binding characteristics of an anion to a series of synthetic receptors derived from bambusuril macrocycles is demonstrated. The exchange rates of BF₄⁻ are mediated by the side chains on the receptor (100 s⁻¹<k_ex<5000 s⁻¹), which play a critical role in receptor-anion binding dynamics. The signal amplification obtained with this approach allows for the identification of different types of intermolecular interactions between the receptor and the anion, something that could not have been detected by techniques hitherto used to study molecular assemblies. These findings, which are supported by a computational molecular dynamic study, demonstrate the uniqueness and added value of this NMR method.     

Transition‐Metal‐Free Trifluoromethylthiolation of N‐Heteroarenes

A general and efficient methodology for the direct transition metal free trifluoromethylthiolation of a broad range of biologically relevant N‐heteroarenes is reported employing abundant sodium chloride as the catalyst. This method is operationally simple, exhibits high functional group tolerance, and does not require protecting groups.     

D3h‐Symmetric Porphyrin‐Based Rigid Macrocyclic Ligands for Multicofacial Multinuclear Complexes in a One‐Nanometer‐Sized Cavity

The one‐step synthesis of D_3h‐symmetric cyclic porphyrin trimers 1 composed of three 2,2′‐[4,4′‐bis(methoxycarbonyl)]bipyridyl moieties and three porphyrinatozinc moieties was achieved from a nickel‐mediated reductive coupling of meso‐5,15‐bis(6‐chloro‐4‐methoxycarbonylpyrid‐2‐yl)porphyrinatozinc. Although cyclic trimers 1 were obtained as a mixture that included other cyclic and acyclic porphyrin oligomers, an extremely specific separation was observed only for cyclic trimers 1 when using columns of silica gel modified with pyrenylethyl, cyanopropyl, and other groups. Structural analysis of cyclic trimers 1 was carried out by means of NMR spectroscopy and X‐ray crystallography. Treatment of an η³‐allylpalladium complex with a cyclic trimer gave a tris(palladium) complex containing three η³‐allylpalladium groups inside the space, which indicated that the bipyridyl moieties inside the ring could work as bidentate metalloligands.     

Metabolic profiles of dioscin in rats revealed by ultra‐performance liquid chromatography quadrupole time‐of‐flight mass spectrometry

Dioscin (DIS), one of the most abundant bioactive steroidal saponins in Dioscorea sp., is used as a complementary medicine to treat coronary disease and angina pectoris in China. Although the pharmacological activities and pharmacokinetics of DIS have been well demonstrated, information regarding the final metabolic fates is very limited. This study investigated the in vivo metabolic profiles of DIS after oral administration by ultra‐performance liquid chromatography quadrupole time‐of‐flight mass spectrometry method. The structures of the metabolites were identified and tentatively characterized by means of comparing the molecular mass, retention time and fragmentation pattern of the analytes with those of the parent compound. A total of eight metabolites, including seven phase I and one phase II metabolites, were detected and tentatively identified for the first time. Oxidation, deglycosylation and glucuronidation were found to be the major metabolic processes of the compound in rats. In addition, a possible metabolic pathway on the biotransformation of DIS in vivo was proposed. This study provides valuable and new information on the metabolism of DIS, which will be helpful for further understanding its mechanism of action. Copyright © 2015 John Wiley & Sons, Ltd.     

New Phenomena in Organometallic‐Mediated Radical Polymerization (OMRP) and Perspectives for Control of Less Active Monomers

The impact of reversible bond formation between a growing radical chain and a metal complex (organometallic‐mediated radical polymerization (OMRP) equilibrium) to generate an organometallic intermediate/dormant species is analyzed with emphasis on the interplay between this and other one‐electron processes involving the metal complex, which include halogen transfer in atom transfer radical polymerization (ATRP), hydrogen‐atom transfer in catalytic chain transfer (CCT), and catalytic radical termination (CRT). The challenges facing the controlled polymerization of “less active monomers” (LAMs) are outlined and, after reviewing the recent achievements of OMRP in this area, the perspectives of this technique are analyzed.     

Photoisomerisation in Aminoazobenzene‐Substituted Ruthenium(II) Tris(bipyridine) Complexes: Influence of the Conjugation Pathway

Transition‐metal complexes containing stimuli‐responsive systems are attractive for applications in optical devices, photonic memory, photosensing, as well as luminescence imaging. Amongst them, photochromic metal complexes offer the possibility of combining the specific properties of the metal centre and the optical response of the photochromic group. The synthesis, the electrochemical properties and the photophysical characterisation of a series of donor–acceptor azobenzene derivatives that possess bipyridine groups connected to a 4‐dialkylaminoazobenzene moiety through various linkers are presented. DFT and TD‐DFT calculations were performed to complement the experimental findings and contribute to their interpretation. The position and nature of the linker (ethynyl, triazolyl, none) were engineered and shown to induce different electronic coupling between donor and acceptor in ligands and complexes. This in turn led to strong modulations in terms of photoisomerisation of the ligands and complexes.