On the existence of a generalized solution of a nonlinear evolution system of equations in a domain unbounded in time

We consider a mixed problem with Dirichlet homogeneous boundary conditions and nonzero initial conditions for a nonlinear coupled evolution system of equations in a domain unbounded in time. The conditions of existence of a generalized solution are obtained. It is shown that no solution of the problem exists at a negative initial value of the energy integral.     

Alkaloid-like annulated pyrano[4,3-b]pyrroles: antiviral activity and hydrolysis

Chemistry of Heterocyclic Compounds - Alkaloid-like angular 6/6/5/6-annulated pyrano[4,3-b]pyrroles (pretazettine analogs) contain chemically labile groups that can react with water at room...     

Crystal structure variations in the series SrLnCuS3 (Ln = La,Pr, Sm,Gd, Er and Lu)

The crystal structures of the complex sulfides SrLnCuS₃ (Ln = Sm, Gd, Er and Lu) have been determined and refined using powder X‐ray diffraction. The crystals are found to be orthorhombic, with the structure type changing consecutively in the order BaLaCuS₃ → Eu₂CuS₃ → KZrCuS₃ as the Ln³⁺ ionic radius decreases in the order La/Pr → Sm/Gd → Er/Lu. Variations of the structure parameters along the series of compounds studied are analyzed, and an effect caused by crystallochemical contraction on the stabilization of the respective structure types is demonstrated.     

Triplet NOAH supersequences optimised for small molecule structure characterisation

A series of NMR supersequences are presented for the time-efficient structure characterisation of small molecules in the solution state. These triplet sequences provide HMBC, HSQC, and one homonuclear correlation experiment of choice according to the NMR by Ordered Acquisition using ¹H detection principle. The experiments are demonstrated to be compatible with non-uniform sampling schemes and may be acquired and processed under full automation.     

Transverse light guides in microstructured optical fibers

A novel class of microstructured optical fiber coupler is introduced that operates by resonant, rather than proximity, energy transfer by means of transverse light guides built into a fiber cross section. Such a design permits significant spatial separation between interacting fibers, which, in turn, eliminates intercore cross talk owing to proximity coupling. A controllable energy transfer between the cores is then achieved by localized and highly directional transmission through a transverse light guide. The main advantage of this coupling scheme is its inherent scalability, as one can integrate additional fiber cores into the existing fiber cross section simply by placing the cores far enough from the existing optical circuitry to prevent proximity cross talk and then making the necessary intercore connections with transverse light wires, in direct analogy with on-chip electronics integration.     

Surface Tension and Shear Strain Contributions to the Mechanical Behavior of Individual Mg-Ni-Phyllosilicate Nanoscrolls

Some phyllosilicate compounds have the ability of spontaneous scrolling because of the size mismatch between the covalently bounded metal oxide and silica sheets. Their unique structure and high theoretically predicted Young's modulus (around 210–230 GPa) induce phyllosilicates’ application as reinforcing fillers. However, previous nanomechanical experiments with individual phyllosilicate nanoscrolls are in poor agreement with theory. The main reason for this is the low accuracy of experiments, which leads to large measurement errors compared to measured average values. Here, the study of the mechanical properties of synthetic (Mg_1–xNi_x)₃Si₂O₅(OH)₄ phyllosilicates is reported by testing a suspended nanoobject (a nanobridge) with an atomic force microscope (AFM). The Young's modulus of corresponding phyllosilicate model layers is also calculated by means of the density functional theory (DFT). The original AFM approach makes it possible to account for the probe slipping off the nanobridge and determine its boundary conditions. The measured Young's modulus values are considered within the models of surface tension and shear strain contributions. The shear strain appears to have a decisive impact on the measured Young's modulus (from 150 ± 70 GPa to 200 ± 210 GPa) and its spread.     

Copper(I)‐Catalyzed Amination of Halogenopyridines with Polyamines

Cu^I‐Catalyzed amination of 2‐bromo‐, and 2‐, 3‐, and 4‐iodopyridines with tri‐ and tetraamines aimed at the synthesis of N,N′‐diheteroaryl derivatives was studied. A strong dependence of the product yields on the nature of starting compounds and the ligand used was observed. The increase in the number of ethene‐1,2‐diamine fragments in the polyamine structure led to the increase in the yields of polyheteroarylated compounds, whereas propane‐1,3‐diamine fragments favored the formation of monopyridinyl derivatives and promoted the heteroarylation of the secondary amino groups. 2‐Iodopyridine, as a more reactive compound, readily formed N,N‐diarylated products. The best yields of the target N,N′‐dipyridin‐2‐yl derivatives were 76% in the case of the triamine and 68% in the case of the tetraamine. A comparison of Cu^I‐ and Pd⁰‐mediated heteroarylation of polyamines was also presented.