On frequency–amplitude dependences for surface and internal standing waves

The analytic approach proposed by Sekerzh-Zenkovich [On the theory of standing waves of finite amplitude, Dokl. Akad. Nauk USSR 58 (1947) 551–554] is developed in the present study of standing waves. Generalizing the solution method, a set of standing wave problems are solved, namely, the infinite- and finite-depth surface standing waves and the infinite- and finite-depth internal standing waves. Two-dimensional wave motion of an irrotational incompressible fluid in a rectangular domain is considered to study weakly nonlinear surface and internal standing waves. The Lagrangian formulation of the problems is used and the fifth-order perturbation solutions are determined. Since most of the approximate analytic solutions to these problems were obtained using the Eulerian formulation, the comparison of the results, as an example the analytic frequency–amplitude dependences, obtained in Lagrangian variables with the corresponding ones known in Eulerian variables has been carried out in the paper. The analytic frequency–amplitude dependences are in complete agreement with previous results known in the literature. Computer algebra procedures were written for the construction of asymptotic solutions. The application of the model constructed in Lagrangian formulation to a set of different problems shows the ability to correctly reproduce and predict a wide range of situations with different characteristics and some advantages of Lagrangian particle models (for example, the bigger radius of convergence of an expansion parameter than in Eulerian variables, simplification of the boundary conditions, parametrization of a free boundary).     

Spontaneous emission rates of a single-impurity molecule in birefringent host crystals for electric quadrupole transitions

In a birefringent host crystal, the spontaneous emission rate of zero-phonon line of a single-impurity molecule depends on the angles between the transition dipole moment and the principal axes of the dielectric (permittivity) tensor and also on the main dielectric constants of a host crystal. In this paper, the spontaneous emission rate of the electric quadrupole transition of a single-impurity molecule is calculated for uniaxial host crystals with the ordinary reflective indices n_o=1.5, 2, 3 and a variable extraordinary reflective index, and for seven biaxial host crystals (anthracene, chrysene, diphenyl, fluorine, naphthalene, phenanthrene, terphenyl). For the above-mentioned biaxial crystals, differences in the values of spontaneous emission rate of the quadrupole transition in the same host crystal are up to 11%.     

Conjugation of the bowman-birk soybean proteinase inhibitor with hydroxyethylstarch

The classical Bowman-Birk soybean proteinase inhibitor was modified by hydroxyethylstarch. The modified inhibitor retained the capacity for simultaneous binding of trypsin and human leukocyte elastase. The inhibition constants,K _i , of bovine trypsin,α-chymotrypsin and human leukocyte elastase (HLE) increased not more than 10-, 1.5-, and 20-fold, respectively, on modification of the inhibitor. The less effective inhibition is presumably due to the steric hindrance brought about by the conjugation with polysaccharide molecules. The results obtained indicate the pronounced structure differences of the binding regions for trypsin and chymotrypsin/leukocyte elastase in the modified preparation.     

Mono- and binuclear ruthenium corroles: synthesis,spectroscopy, electrochemistry,and structural characterization

The aim of this research was to prepare mononuclear ruthenium corroles, because of the well-documented potency of analogous porphyrin complexes in catalysis. The syntheses of the mononuclear nitrosyl complexes [Ru(tpfc)(NO)] and [Ru(tdcc)(NO)] (tpfc=trianion of 5,10,15-tris(pentafluorophenyl)corrole, tdcc=trianion of 5,10,15-tris(2,6-dichlorophenyl)corrole), and of the binuclear [[Ru(tpfc)](2)] were achieved by using [[Ru(cod)Cl(2)](x)] (cod=cyclooctadiene) as the metal source. The NMR spectra of all three complexes clearly demonstrate that they are diamagnetic; this is consistent with a triple bond between the metal ions in [[Ru(tpfc)](2)] and is expected for classical [MNO](6) complexes. These features were further substantiated by the stretching frequencies of the [MNO] moieties, electrochemical measurements on all complexes, and the X-ray crystal structures of [Ru(tpfc)(NO)] and [[Ru(tpfc)](2)]. A comparison of the spectroscopic and structural characteristics of these new complexes with analogous iron corroles, as well as with iron and ruthenium porphyrins, suggests that it will be hard to obtain mononuclear ruthenium corroles without pi-accepting ligands.     

Highly active titanium(IV) dichloride FI catalysts bearing a diallylamino group for the synthesis of disentangled UHMWPE

A family of 16 salicylaldarylimine titanium(IV) dichloride complexes bearing diallylamino group, namely {2‐[3‐ or 4‐(CH₂?CH? CH₂)₂NC₆H₄N?CH]‐6‐R¹‐4‐R²‐C₆H₂O}₂TiCl₂ (R¹ = t‐Bu, CMe₂(Ph); R² = H, Me, OMe, t‐Bu) have been used for polymerization of ethylene in the presence of methylaluminoxane. The effects of reaction conditions on the polymerization were examined in detail. All the pre‐catalyst are highly active (up to 14.0 × 10⁶ g_(PE) mol_(Ti)^{?1 ?1} h^?1) for ethylene polymerization at 30°С to 60°С with the activities and MM correlating with the R¹‐substituent type and position of NAll₂‐group: CMe₂(Ph) > t‐Bu and meta‐NAll₂ > para‐NAll₂ for any R². Highly linear polyethylenes (T_m's as high as 141.0°С) can be obtained with high molecular weights in the range 0.70 to 4.10 × 10⁶ g mol^?1 with disentangled morphology, suitable for technologically more advanced and greeny way to produce high‐modulus high‐strength fibers of ultrahigh molecular weight polyethylene via solid‐state (solvent‐free) deformation processing.     

Comparative characteristics of texture and properties of hybrid organic–inorganic adsorbents functionalized by amine and thiol groups

The structure and texture characteristics of the hybrid organic–inorganic adsorbents, which were obtained by using of two-component systems of “structure-forming agent/trifunctional silane”, are compared as follows: the first component is Si(OC₂H₅)₄ or (C₂H₅O)₃Si–A–Si(OC₂H₅)₃, where A = –(CH₂)₂– or –C₆H₄–; the second one is alkoxysilane with amine (–NH₂, NH, –NH(CH₂)₂NH₂) and thiol (–SH) groups. The adsorbents, derived from TEOS, have more accessible functional groups (2.6–4.2 mmol/g) than xerogels, which are based on bis(triethoxysilanes) (1.0–2.6 mmol/g). On another hand xerogels derived from bis(triethoxysilanes) have a more extended porous structure (S_sp =516–968 m²/g, V_s = 0.418–1.490 cm³/g, d = 2.5–15.0 nm) than those that are based on TEOS (S_sp = 4–631 m²/g, V_s = 0.005–1.382 cm³/g, d = 2.3–17.7 nm). The geometric dimensions of functional groups have a more essential effect on the parameters of porous structure in the case of TEOS-derived xerogels. Using solid-state NMR spectroscopy, it has been shown that in synthesis of xerogels with the use of TEOS, the molecular frame of globules is formed by structural units Qⁿ (n = 2,3,4), and the functional groups exist as structural units of Tⁿ (n = 2,3). The xerogels obtained with using bis(triethoxysilanes) consist only of structural units of Tⁿ-type (n = 1,2,3).     

Design,Cytotoxicity and Antiproliferative Activity of 4-Amino-5-methyl-thieno[2,3-d]pyrimidine-6-carboxylates against MFC-7 and MDA-MB-231 Breast Cancer Cell Lines

Novel 4-amino-thieno[2,3-d]pyrimidine-6-carboxylates substituted at the second position were prepared by cyclocondensation of 2-amino-3-cyano-thiophene and aryl nitriles in an acidic medium. The design of the target compounds was based on structural optimization. The derivatives thus obtained were tested in vitro against human and mouse cell lines. The examination of the compound effects on BLAB 3T3 and MFC-10A cells showed that they are safe, making them suitable for subsequent experiments to establish their antitumor activity. The photoirritancy factor of the compounds was calculated. Using the MTT test, the antiproliferative activity to MCF-10A, MCF-7 and MDA-MB-231 cell lines was estimated. The best antiproliferative effect in respect to the MCF-7 cell line revealed compound 2 with IC₅₀ 4.3 ± 0.11 µg/mL (0.013 µM). The highest selective index with respect to MCF-7 cells was shown by compound 3 (SI = 19.3), and to MDA-MB-231 cells by compound 2 (SI = 3.7). Based on energy analysis, the most stable conformers were selected and optimized by means of density functional theory (DFT). Ligand efficiency, ligand lipophilicity efficiency and the physicochemical parameters of the target 4-amino-thienopyrimidines were determined. The data obtained indicated that the lead compound among the tested substances is compound 2.     

Light-scattering by optically soft randomly oriented spheroids

In the framework of the Rayleigh–Gans–Debye approximation and anomalous diffraction approaches, the light scattering characteristics of randomly oriented spheroids have been investigated. It has been proved that the system of randomly oriented spheroids is equivalent to the system of polydisperse spherical particles that have the same values of volume and surface area as nonspherical particles. The power law size distribution meeting these requirements has been obtained.