On the “function” and “lattice” definitions of a narrow operator

We prove that the function and lattice definitions of a narrow operator defined on a Köthe Banach space E on a finite atomless measure space \((\Omega , \Sigma , \mu )\) are equivalent if and only if the set of all simple functions is dense in E. This answers Problem 10.3 from Popov and Randrianantoanina (Narrow operators on function spaces and vector lattices, De Gruyter studies in mathematics 45, De Gruyter, Berlin, 2013).     

Ergodicity of non-equilibrium Glauber dynamics in continuum

We study asymptotic properties of the continuous Glauber dynamics with unbounded death and constant birth rates. In particular, an information about the location of the spectrum for the symbol of the Markov generator is obtained. The latter fact is used for the proof of the ergodicity of this process. We show that the speed of convergence to the equilibrium is exponential.     

Oscillation of solutions of second-order linear differential equations and corresponding difference equations

In this paper, we present conditions ensuring that solutions of linear second-order differential equations oscillate, provided solutions of corresponding difference equations oscillate. We also establish the converse result, namely, when oscillation of solutions of difference equations implies oscillation of solutions of corresponding differential equations.     

Transverse conductivity in Pr_yY_{1-y}Ba_2Cu_3O_{7-\delta } single crystals in a wide range of praseodymium concentrations

A single-sized dielectric cylinder-based metamaterial is fabricated from TiO₂ nanoparticles, using a bottom-up approach. The sub-elements constituting the metalayer are embedded in a nonmagnetic transparent host matrix in the microwave regime and arranged in a square lattice. We demonstrate numerically and experimentally a broadband magnetic activity. The key feature to achieve this performance remains in the high aspect ratio of the metamaterial building blocks. This is a very promising step towards complex electromagnetic functions, involving low-cost metamaterials with simple fabrication.     

Synthesis of azachromones and azachromanones

Chemistry of Heterocyclic Compounds - This minireview highlights known methods for the synthesis of azachromones and azachromanones, including the earliest and the latest examples of their...     

Multicomponent Self‐Assembly with a Shape‐Persistent N‐Heterotriangulene Macrocycle on Au(111)

Multicomponent network formation by using a shape‐persistent macrocycle ( MC6 ) at the interface between an organic liquid and Au(111) surface is demonstrated. MC6 serves as a versatile building block that can be coadsorbed with a variety of organic molecules based on different types of noncovalent interactions at the liquid–solid interface. Scanning tunneling microscopy (STM) reveals the formation of crystalline bicomponent networks upon codeposition of MC6 with aromatic molecules, such as fullerene (C₆₀) and coronene. Tetracyanoquinodimethane, on the other hand, was found to induce disorder into the MC6 networks by adsorbing on the rim of the macrocycle. Immobilization of MC6 itself was studied in two different noncovalently assembled host networks. MC6 assumed a rather passive role as a guest and simply occupied the host cavities in one network, whereas it induced a structural transition in the other. Finally, the central cavity of MC6 was used to capture C₆₀ in a complex three‐component system. Precise immobilization of organic molecules at discrete locations within multicomponent networks, as demonstrated here, constitutes an important step towards bottom‐up fabrication of functional surface‐based nanostructures.     

3-Fluoroalkyl (CF3, CHF2, CH2F) Cyclobutane-Derived Building Blocks for Medicinal Chemistry: Synthesis and Physicochemical Properties

Synthesis and physicochemical characterization of all possible cis- and trans-1,3-disubstituted cyclobutane-derived amines and carboxylic acids bearing mono-, di- and trifluoromethyl groups at the C-3 position is disclosed. Tetramethylammonium fluoride (TMAF)- or morpholinosulfur trifluoride (Morph-DAST)-mediated nucleophilic fluorination of appropriate cis- and trans-diastereomeric substrates was used as the key step for the preparation of CH₂F- and CHF₂-substituted derivatives. To obtain the corresponding cis- and trans-isomeric CF₃-substituted derivatives, resolution of known 3-(trifluoromethyl)cyclobutanecarboxylic acid (obtained as a mixture of diastereomers) was applied. The proposed procedures were suitable for the preparation of corresponding fluoroalkyl-substituted cyclobutane-derived amines and carboxylic acids on up to 50 g scale. All 12 building blocks obtained were characterized by measuring dissociation constants (pK_a) and lipophilicities (LogP, for model derivatives) to evaluate the effect of the fluoroalkyl substituents on their physicochemical properties relevant to further drug discovery applications.