Theorem on integral inequalities with functional argument

A theorem on the integral Volterra-Fredholm inequalities with a functional limit is proved. By using this theorem, the theorem on integral inequalities with retarded argument is established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 136–139, January, 1993.     

D2-symmetric dirhodium catalyst derived from a 1,2,2-triarylcyclopropanecarboxylate ligand: design, synthesis and application

Dirhodium tetrakis-(R)-(1-(4-bromophenyl)-2,2-diphenylcyclopropanecarboxylate) (Rh(2)(R-BTPCP)(4)) was found to be an effective chiral catalyst for enantioselective reactions of aryl- and styryldiazoacetates. Highly enantioselective cyclopropanations, tandem cyclopropanation/Cope rearrangements and a combined C-H functionalization/Cope rearrangement were achieved using Rh(2)(R-BTPCP)(4) as catalyst. The advantages of Rh(2)(R-BTPCP)(4) include its ease of synthesis, its tolerance to the size of the ester group in the styryldiazoacetates, and its compatibility with dichloromethane as solvent. Computational studies suggest that the catalyst adopts a D(2)-symmetric arrangement, but when the carbenoid binds to the catalyst, two of the p-bromophenyl groups on the ligands rotate outward to make room for the carbenoid and the approach of the substrate to the carbenoid.     

Accounting for the local surface geometry in the classical theory of spin waves

The effect of the surface energy on the formation of the spin spectrum is considered. Different aspects are examined of the effect of the surface on the energy spectrum of the system associated with structural features of the surface structure. The calculations are carried out for the spectrum of elementary excitations of a ferromagnetic system that is bounded by a surface. Calculations are conducted following the standard method of the Hamiltonian diagonalization. Relationships are obtained that completely determine the surface spectrum in the zero approximation in the spin-spin interaction.     

Influence of the liquid environment on the products formed from the laser ablation of tin

Tin targets immersed in ethanol and distilled water were ablated using a UV pulsed laser. The ablated products were investigated with transmission and scanning electron microscopy, X-ray photoelectron spectroscopy, and energy dispersive spectroscopy. For ablation in both liquids, the size distribution of the produced particles was bimodal, with particles having diameters of ～10 nm and ～1 μm. Formation mechanisms that caused the bimodal distribution are suggested. Ablation in ethanol resulted in nanoparticles that were found to be single crystals of tin coated with tin hydroxide (Sn(OH)₂) while ablation in water yielded nanoparticles that were polycrystalline tin dioxide (SnO₂) throughout.     

Ni nanoparticles fabricated by laser ablation in water

Nickel nanoparticles were fabricated by ablating a bulk Ni target with pulsed 337-nm laser radiation in distilled water. Transmission electron microscope images of the removed material show spherical particles with two size scales: tens of nm and hundreds of nm. Phase explosion and Rayleigh–Plateau hydrodynamic instability are suggested as being responsible for this distribution. An X-ray diffraction pattern of the ablated material demonstrates the presence of both nickel and nickel oxide.     

Vicinal Dinitridoruthenium‐Substituted Polyoxometalates γ‐[XW10O38{RuN}2]6− (X=Si or Ge)

Reaction of the divacant polyoxometalate K₈[γ‐XW₁₀O₃₆] (X=Si, Ge) with two equivalents of the metal‐nitrido precursor Cs₂[Ru^VINCl₅], at room temperature in water, produces K₂(Me₂NH₂)₂H₂[γ‐XW₁₀O₃₈{RuN}₂], X=Si ( DMA ‐ 1 a ) or Ge ( DMA ‐ 1 b ). The X‐ray crystal structures of both complexes show monomeric complexes with highly unusual vicinal terminal metal‐nitrido units. The Ru?N bond lengths are 1.594(10) and 1.612(11) Å in 1 a and 1 b , respectively. EXAFS studies confirmed the key structural assignments from X‐ray crystallography. The XANES spectrum of DMA‐1 a , diamagnetism, NMR (²⁹Si and ¹⁸³W) chemical shifts, voltammetric behavior, reductive titrations with [PW₁₂O₄₀]^4?, and computational data are all consistent with d² Ru^VI centers in these complexes. The FT‐IR and Raman spectra show the expected vibrational modes of the {γ‐XW₁₀} unit and the Ru?N stretch at 1080 cm^?1, respectively. Interestingly, reduction of DMA‐1 a by 4 equivalents of [PW₁₂O₄₀]^4? produces NH₃ in nearly quantitative yield. Cyclic voltammetry versus pH and calculations provide the energetics for the possible two‐electron reduction and two‐proton addition processes in this reaction.     

Methods for obtaining solid dispersions of drugs and their properties

The possibility of improving the solubility of drugs by obtaining solid dispersions (SDs) with polymers is demonstrated. The solubility of these SDs is dependent both on the nature of drug and polymer and on the conditions of their preparation. IR spectroscopy of the obtained SDs and the analysis of results found in literature indicate that inclusion complexes are formed within them.

     

Stability of a noncircular cylinder in a matrix with small strains

Institute of Mathematics and Mechanics, Academy of Sciences of the Azerbaidzhan SSR, Baku. Translated from Prikladnaya Mekhanika, Vol. 25, No. 6, pp. 27–31, June, 1989.