The Discrete Spectrum in the Spectral Gaps of Semibounded Operators with Non-sign-definite Perturbations

Given two self-adjoint operators A and V = V₊  − V₋ , we study the motion of the eigenvalues of the operator A(t) = A − tV as t increases. Let α > 0 and let λ be a regular point for A. We consider the quantities N₊ (V; λ, α), N₋ (V; λ, α), and N₀(V; λ, α) defined as the number of eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right, or change the direction of their motion exactly at point λ, respectively, as t increases from 0 to α > 0. We study asymptotic characteristics of these quantities as α → ∞. In the present paper, the results obtained previously [O. L. Safronov, Comm. Math. Phys.193 (1998), 233–243] are extended and given new applications to differential operators.     

Superconducting Multipole Wigglers for Generating Synchrotron Radiation at the Budker Institute of Nuclear Physics

Physics of Particles and Nuclei Letters - Superconducting multipole insertion devices (wigglers and undulators) used to generate synchrotron radiation significantly increase the photon flux,...     

Mechanism of structural networking in hydrogels based on silicon and titanium glycerolates

Formation of organic/inorganic hydrogels based on silicon- and titanium-glycerol precursors synthesized by transesterification of alkoxy derivatives in excess of glycerol was investigated. The precursors in excess of glycerol and obtained gels were studied by chemical and physical methods including gelation kinetics, IR spectroscopy, XRD, dynamic and electrophoretic light scattering, mechanical deformation, which disclosed the basic difference in the gelation mechanism and structure of network in the hydrogels. Due to this difference, the gelation time of silicon- and titanium-glycerol precursors depended on pH or electrolyte addition in an opposite way. In the wide pH range, silicon-glycerol hydrogel was a polymeric single-phase system formed by the polymeric network homogeneously swollen in liquid water/glycerol medium. Flory-Rehner theory applied to the elastic modulus of these gels gave 40-180 monomer base units in the subchains of the network depending on water content in the gel. The mechanism of networking was three-dimensional polycondensation promoted by the electrically charged functional groups attached to the flexible polymeric chains. Electrolyte solutions provided the gelation according to Hofmeister series. Titanium-glycerol hydrogels were heterogeneous colloid systems at pH>1.5 and single-phase polymeric gels at lower pH. Electrolyte solutions provided the gelation according to Schultze-Hardy rule.     

Magnetic impedance of structured film meanders in the presence of magnetic micro- and nanoparticles

The magnetic impedance (MI) of film elements in the form of meanders with a [Fe19Ni81]/Cu]₄/Fe19Ni81/Cu/[Fe19Ni81/Cu]₄/Fe19Ni81 layered structure and variable geometry is studied. For the best meanders (having a maximal MI of up to 125% and an MI maximal sensitivity of about 30%/Oe), the influence of stray magnetic fields is determined. The stray fields are produced by spherical iron particles 500 μm in diameter and ferrofluids containing iron oxide nanoparticles. The feasibility of detecting intricately configured stray fields from a set of ferromagnetic spheres arranged on the surface of an MI element is demonstrated. The sensitivity of film meander MI elements to nonuniform external magnetic fields is simulated. The results of this work may be helpful in developing special-purpose magnetic sensors intended for micropositioning, nondestructive testing, and biomagnetic detection.     

Phosphorodiamidite derivatives of 1,1′-bi-2-naphthol containing stereogenic phosphorus atoms as ligands in enantioselective catalysis

P*-Mono- and P*,P*-bidentate phosphorodiamidites containing the (S _a )-1,1′-binaphthyl core and 1,3,2-diazaphospholidine rings were synthesized. The use of these compounds in the rhodium-catalyzed asymmetric hydrogenation, as well as in the palladium- and platinum-catalyzed asymmetric alkylation and amination, resulted in the formation of the products with ee of up to 99%.     

(1,3-Diformylindenyl)cyclopentadienyl ruthenium derivatives

The reaction of [CpRu(CH₃CN)₃][PF₆], [Cp*RuCl] _n , and [Cp^FRuCl]n with 1,3-diformylindene results in the predominant formation of zwitter-ionic arene-cyclopentadienyl complexes {η⁶-1,3-(CHO)₂C₉H₅}RuCp (Cp = C₅H₅), {η⁶-1,3-(CHO)₂C₉H₅}RuCp* (Cp* = C₅Me₅), and {η⁶-1,3-(CHO)₂C₉H₅}RuCp^F (Cp^F = C₅Me₄CF₃), respectively. The ruthenocenes {η⁵-1,3-(CHO)₂C₉H₅}RuCp, {η⁵-1,3-(CHO)₂C₉H₅}RuCp*, and {η⁵-1,3-(CHO)₂C₉H₅}RuCpF were synthesized by the reaction of 1,3-diformylindenyl potassium with [CpRu(CH₃CN)₃][PF₆], [Cp*RuCl] _n , and [Cp^FRuCl] _n .     

Formation of conductive layers inside diamond by hydrogen ion implantation and subsequent thermal treatment at low or high pressures

(111) synthetic HPTP diamond plates are irradiated by H ₂ ⁺ 50 keV ions in the range of the fluences of 1?13 × 10¹⁶ sm^?2 and annealed in vacuum at 1 mPa (VPHT, 500?C1600°C) or at high HPHT parameters (4.0?C7.5 GPa, 1200?C1550°C). It is shown by measuring the layer conductivity and Raman light scattering that after VPHT annealing, a buried layer of glassy carbon 10?C100 nm thick with low resistance (??1 kOhm/??) is formed, followed by HPHT with high resistance (??1 MOhm/??) and hopping transport along defects.     

Mutual stabilization of components in composites of polyoxomolybdates of buckyball structure and water-soluble nonionic polymers

Thermal degradation of composites consisting of polyoxomolybdates of the buckyball structure (with acetate and chloroacetate ligands) and water-soluble nonionic polymers was studied. The mutual stabilizing effect of components of the systems with polyvinyl alcohol and polyvinylpyrrolidone under UV irradiation was subjected to comparative analysis. The methods of differential scanning calorimetry, mass spectrometry, and ESR spectroscopy were used.     

Copolymers based on products of base hydrolysis of tetraethoxysilane in the presence of poly-<Emphasis Type="Italic">N</Emphasis>-vinylazoles and polyvinylpyridines

The products of base hydrolysis of tetraethoxysilane in the presence of polymeric nitrogen bases poly-1-vinylpyrazole, poly-1-vinylimidazole, poly-4-vinylpyridine, and poly-2-methyl-5-vinylpyridine were isolated. The conditions of their formation, chemical composition, structural characteristics, and sorption properties with respect to noble metals (Ag, Au, Pt, and Pd) were studied. These products are highly dispersed thermally stable interpenetrating copolymers poorly soluble in water and organic solvents. Their composition and properties are governed by the kind of the polymeric nitrogen base.