An Existence Theorem for Wave‐Type Hyperbolic Hemivariational Inequalities

In this paper we prove the existence of solutions for a hyperbolic hemivariationalinequality of the form u″ + Bu + ∂j (u) ∋ f where B is a linear elliptic operator and ∂j is the Clarke subdifferential of a locally Lipschitz function j. Our result is based on the parabolic regularization method.     

Preliminary studies on the surface layer of starch

Characterization of the surface layer of starch powder, originated from potato or maize, was carried out applying various experimental techniques: Fourier-transformed infrared internal reflection spectroscopy (FTIR-IRS), inverse gas chromatography (IGC) and scanning electron microscopy (SEM). The main kinds of starch were studied as potential fillers for rubber and results discussed in terms of factors requiring modification to improve starch miscibility and activity towards rubber. Starch of high amylopectine content shows surface enrichment with amylose what makes crystallinity of the surface layer higher than in bulk of the material. Particles of the both kinds of starch have very smooth surface (morphological index, I_m = 0.995), highly resistant to its geometrical development. Dispersive component of the surface energy of starch was found to be similar to that of low energy polymers (γ_s^d = 32.5 mJ/m² at 23°C) and its surface to be of electron-donor character.     

Shaping a Porphyrinoid Frame by Heteroatoms Extrusion: Formation of an Expanded [22]Triphyrin(6.6.0)

An aromatic expanded triphyrin, [22]triphyrin(6.6.0) 2 , containing a pyrrole unit, a bipyrrole moiety, and annulene links, was obtained from a tellurium-containing precursor meso-tetraaryl-26,28-ditellurasapphyrin 1 . The reaction path proceeds through an acid-promoted tellurium extrusion from 1 yielding directly 2 , characterized in a dicationic form by X-ray crystallography. In solution the neutral macrocycle 2 reveals flexibility typical for annulenes and it exists as a mixture of conformers that differ by the configuration of the annulene fragments, as proven by ¹H NMR studies and analyzed by DFT methods. The conformation is controlled by protonation state, the nature of an interacting anion, solvent identity, and by interaction with water.     

Electroactive Organic Building Blocks for the Chemical Design of Functional Porous Frameworks (MOFs and COFs) in Electronics

Electroactive organic molecules have received a lot of attention in the field of electronics because of their fascinating electronic properties, easy functionalization and potential low cost towards their implementation in electronic devices. In recent years, electroactive organic molecules have also emerged as promising building blocks for the design and construction of crystalline porous frameworks such as metal–organic frameworks (MOFs) and covalent-organic frameworks (COFs) for applications in electronics. Such porous materials present certain additional advantages such as, for example, an immense structural and functional versatility, combination of porosity with multiple electronic properties and the possibility of tuning their physical properties by post-synthetic modifications. In this Review, we summarize the main electroactive organic building blocks used in the past few years for the design and construction of functional porous materials (MOFs and COFs) for electronics with special emphasis on their electronic structure and function relationships. The different building blocks have been classified based on the electronic nature and main function of the resulting porous frameworks. The design and synthesis of novel electroactive organic molecules is encouraged towards the construction of functional porous frameworks exhibiting new functions and applications in electronics.     

Interpolating between Positive and Completely Positive Maps: A New Hierarchy of Entangled States

A new class of positive maps is introduced. It interpolates between positive and completely positive maps. It is shown that this class gives rise to a new characterization of entangled states. Additionally, it provides a refinement of the well-known classes of entangled states characterized in terms of the Schmidt number. The analysis is illustrated with examples of qubit maps.     

Structural Characterization of a High-Nuclearity Niobium(V) Carboxylate Cluster Based on Pivalic Acid

We report a novel Nb(V)−carboxylate cluster obtained from reaction of niobium(V) ethoxide and pivalic (trimethylacetic) acid. Single crystal X-ray diffraction data reveal a structure composed of 16 Nb(V) ions featuring oxo-, ethoxy- and pivalate moieties. The new cluster exhibits the highest nuclearity among structurally characterized niobium carboxylates reported to date.     

From Colloidal Dispersions of Zeolite Monolayers to Effective Solid Catalysts in Transformations of Bulky Organic Molecules: Role of Freeze-Drying and Dialysis

We investigated the properties and catalytic activity of zeolites with MWW topology obtained by unprecedented liquid exfoliation of the MCM-56 zeolite into solutions of monolayers and isolation/reassembly of the dispersed layers by various methods, with optional purification by dialysis or ammonium exchange. The layers were recovered by flocculation with alcohol or ammonium nitrate and freeze-drying. Flocculation alone, even with ammonium nitrate, did not ensure removal of residual sodium cations resulting in catalysts with low activity. Dialysis of the solutions with dispersed monolayers proved to be efficient in removing sodium cations and preserving microporosity. The monolayers were also isolated as solids by freeze-drying. The highest BET area and pore volume obtained with the freeze-dried sample confirmed lyophilization efficiency in preserving layer structure. The applied test reaction, Friedel–Crafts alkylation of mesitylene, showed high benzyl alcohol conversion due to increased concentration of accessible acid centers caused by the presence of secondary mesoporosity. The applied treatments did not change the acid strength of the external acid sites, which are the most important ones for converting bulky organic molecules. Zeolite acidity was not degraded in the course of exfoliation into monolayers, showing the potential of such colloid dispersions for the formation of active catalysts.     

The [4+2]-Cycloaddition of α-Nitrosoalkenes with Thiochalcones as a Prototype of Periselective Hetero-Diels–Alder Reactions—Experimental and Computational Studies

The [4+2]-cycloadditions of α-nitrosoalkenes with thiochalcones occur with high selectivity at the thioketone moiety of the dienophile providing styryl-substituted 4H-1,5,2-oxathiazines in moderate to good yields. Of the eight conceivable hetero-Diels–Alder adducts only this isomer was observed, thus a prototype of a highly periselective and regioselective cycloaddition has been identified. Analysis of crude product mixtures revealed that the α-nitrosoalkene also adds competitively to the thioketone moiety of the thiochalcone dimer affording bis-heterocyclic [4+2]-cycloadducts. The experiments are supported by high-level DFT calculations that were also extended to related hetero-Diels–Alder reactions of other nitroso compounds and thioketones. These calculations reveal that the title cycloadditions are kinetically controlled processes confirming the role of thioketones as superdienophiles. The computational study was also applied to the experimentally studied thiochalcone dimerization, and showed that the 1,2-dithiin and 2H-thiopyran isomers are in equilibrium with the monomer. Again, the DFT calculations indicate kinetic control of this process.     

Convergence theorems for adapted sequences of random sets

We consider random sets with values in a separable Banach space. We study set-valued amarts, L¹-amarts, uniform amarts and submartingales. For all these classes of random sets, we prove convergence theorems in all main modes of set convergence (weak, Wijsman, Mosco, and Hausdorff). We also prove new convergence theorems for vector-valued subpramarts and pramarts.     

Scattering of long-wavelength acoustic phonons by isotopic impurities

We consider the problem of the relaxation of an arbitrary initial distribution function of a gas of long-wave acoustic phonons scattered by isotopic impurities embedded in a crystalline medium with cubic symmetry. The spectral decomposition of the collision integral of the suitable Boltzmann-Peierls equation is obtained. The spectrum of the collision operator is purely discrete and in addition to the eigenvalue 0 consists of three other eigenvalues. Explicit analytic expressions for these eigenvalues are obtained. Within the Chapman-Enskog approximation we derive the diffusion equation for the density of phonons and obtain the explicit expression for the diffusion coefficient. The dependency of the eigenvalues of the collision operator and the diffusion coefficient on the elastic constants of the medium is studied.