Decay estimates for nonlinear nonlocal diffusion problems in the whole space

In this paper, we obtain bounds for the decay rate in the L ^r (? ^d )-norm for the solutions of a nonlocal and nonlinear evolution equation, namely, $$u_t \left( {x,t} \right) = \int_{\mathbb{R}^d } {K\left( {x,y} \right)\left| {u\left( {y,t} \right) - u\left( {x,t} \right)} \right|^{p - 2} \left( {u\left( {y,t} \right) - u\left( {x,t} \right)} \right)dy, x \in \mathbb{R}^d , t > 0.}$$ . We consider a kernel of the form K(x, y) = ψ(y?a(x)) + ψ(x?a(y)), where ψ is a bounded, nonnegative function supported in the unit ball and a is a linear function a(x) = Ax. To obtain the decay rates, we derive lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form $$T\left( u \right) = - \int_{\mathbb{R}^d } {K\left( {x,y} \right)\left| {u\left( y \right) - u\left( x \right)} \right|^{p - 2} \left( {u\left( y \right) - u\left( x \right)} \right)dy, 1 \leqslant p < \infty .}$$ . The upper and lower bounds that we obtain are sharp and provide an explicit expression for the first eigenvalue in the whole space ? ^d : $$\lambda _{1,p} \left( {\mathbb{R}^d } \right) = 2\left( {\int_{\mathbb{R}^d } {\psi \left( z \right)dz} } \right)\left| {\frac{1} {{\left| {\det A} \right|^{1/p} }} - 1} \right|^p .$$ Moreover, we deal with the p = ∞ eigenvalue problem, studying the limit of λ _1,p ^1/p as p→∞.     

Structure and properties of core-shell microparticles in paraffin-ultradispersed polytetrafluoroethylene systems

Microsized spherical core-shell particles consisting of hydrocarbon cores encapsulated into fluoropolymer shells are obtained in supercritical carbon dioxide. Paraffins serve as a core material, while the polymer shell is formed from ultradispersed polytetrafluoroethylene. The morphology and molecular structure in the bulk and on the surface of the particles and the influence of conditions of particle formation on the shell thickness and the thermal properties of the materials are studied. The materials are composites comprised of paraffin cores coated with shells of loosened globular fluoropolymer particles with sizes of 0.2–1.7 μm. The shells is built of low- and high-molecular-mass fractions consisting of CF₃(CF₂)nCF₃ molecular chains with different lengths. The shell thickness is governed by preparation conditions, exposure time, and the percentage of the polymer in the initial dispersion.     

Effect of venous wall immobilization on the thermal degradation of collagen

The results from a comparative study of the thermal denaturation of collagen in the venous walls of reference samples and samples with varicose disease are presented. Changes in the organization of collagen network of the tissue matrix are detected via thermal analysis and multiphoton microscopy with recording of the second harmonic generation (SHG). It is established that the collagen network of venous walls degrades in varicose disease. It is shown that the disordering of the tertiary structure of collagen molecules is reflected in a 40% drop in the enthalpy of protein denaturation compared to reference (ΔH _D = 12.4 ± 4.9 J/g dry residue). The disorganization of fiber structures is recorded on SHG images. It is shown that upon the hydrothermal heating of sequestered samples of venous walls, the complete degradation of the tissue network occurs at 75°C. However, it is noted that upon the mechanical immobilization of samples of both types, the stability of collagen increases and complete denaturation is observed at temperatures above 84°C. It is suggested that the number of available conformations of polypeptide chains in the random coil state falls under tension, lowering ΔS _D and raising the temperature of the denaturation of protein.     

Spectroscopic Study of the Semihydrate of the Dodecahydro-closo-dodecaborate of 2,4,6-Triamino-1,3,5-triazine

Russian Journal of Physical Chemistry A - The presence of directed localized cation–anion interactions in the semihydrate of 2,4,6-triamino-1,3,5-triazine (melamine)...     

Synthesis and characterization of new ammonium-containing niobium fluoro complexes of composition NH<Subscript>4</Subscript>NaNbF<Subscript>7</Subscript> and NH<Subscript>4</Subscript>MNbOF<Subscript>5</Subscript> (M = Li and Na)

Ammonium-containing mixed-alkali-metal fluoro complexes NH₄NaNbF₇ and NH₄MNbOF₅ (M = Li and Na) crystallizing in orthorhombic system were synthesized and characterized for the first time. Unit cell parameters for these complexes were determined. Their IR absorption spectra were measured and characterized in the range 4000-350 cm⁻¹.     

CaL-B a highly selective biocatalyst for the kinetic resolution of furylbenzthiazole-2-yl-ethanols and acetates

A highly stereoselective enzymatic kinetic resolution of novel various substituted racemic furylbenzthiazole-2-yl-ethanols and their acetates has been developed. Both processes, the enzymatic acylation of the racemic alcohols and the enzymatic methanolysis of racemic acetates yielded highly enantiomerically enriched (ee >98%) resolution product, when CaL-B was used as a biocatalyst in acetonitrile. The absolute configuration of the obtained (R)-(+)-1-(5-(4-chlorobenzo[d]thiazol-2-yl)furan-2-yl)ethanol was determined by a detailed ¹H NMR study of rac- and (+)-1-(5-(4-chlorobenzo[d]thiazol-2-yl)furan-2-yl)ethanol Mosher derivatives.     

A method for determining argon isotopes in a continuous helium flow for K/Ar geochronology

A new method for the measurement of the argon isotope composition in a continuous helium flow using isotope mass spectrometers is described for potassium-argon geochronology. Argon was extracted from the samples in a chamber with a multiple-sample holder by successively heating the samples with a continuous infrared laser. Argon extracted in the chamber was preconcentrated in a capillary, separated on a chromatographic capillary column in a helium flow, and then injected into the ion source of a mass spectrometer through an open splitter. Measurements of the ³⁶Ar, ³⁸Ar, and ⁴⁰Ar isotopes were carried out on isotope mass spectrometers in a dynamic mode using a triple-collector ion detector and three electrometric amplifiers. Preliminary experiments on the developed device for measuring argon isotopes in a continuous helium flow have shown that the proposed method can be used for the determination of radiogenic argon in an amount of n × 10^?12 g with the accuracy satisfying the solution of many geochronological problems. In sensitivity and reproducibility, the proposed method is highly competitive to the isotope dilution method for measuring argon and simpler than the conventional methods for measuring radiogenic argon.     

Integration of the equations of gas dynamics for 2.5-dimensional solutions

We integrate the equations of gas dynamics in finite form for the solutions in which the thermodynamic parameters depend only on one spatial variable. The corresponding motion of gas represents the nonlinear superposition of the one-dimensional gas motion corresponding to the invariant system and the two-dimensional motion determined by noninvariant functions. These motions are called 2.5-dimensional. We reduce the invariant system to a first-order implicit ordinary differential equation. We study various solutions of the latter. We construct some continuous and discontinuous solutions to the equations of gas dynamics and give their physical interpretation.     

Synthesis and Antimicrobial Evaluation of Some New 4,5′‐Bisthiazoles

Thiazole and bisthiazole derivatives represent a prevalent scaffold in the antimicrobial drug discovery. Therefore, we have decided to synthesize some new series of 4,5′‐bisthiazoles. A total of 17 compounds were synthesized, their structural elucidation being based on elemental analysis (C,H,N,S) and spectroscopic data (MS and ¹H NMR). Their in vitro antimicrobial activities were assessed against several Gram‐positive and Gram‐negative bacteria strains and also against one fungal strain (Candida albicans) using the difusimetric method. Some of the compounds showed modest to good antibacterial activity against Gram‐negative Escherichia coli and Salmonella typhimurium and Gram‐positive Staphylococcus aureus and Bacillus cereus bacterial strains. All of the synthesized compounds showed moderate to very good antifungal activity against C. albicans.