Asymptotic bounds for the eigenvalues and eigenvectors of a perturbed linear non-self-conjugate operator

We obtain asymptotic bounds for the perturbed eigenvalues and eigenvectors of a perturbed linear bounded operator A(), in a Hilbert space under the assumption that A() is holomorphic at the point =₀ and the eigenvalue ₀= gl(₀) of the operator A(₀) is isolated and of finite multiplicity. We study certain cases of high degeneracy in the limiting problem, i.e., the case when there are generalized associated vectors.Translated from Matematicheskie Zametki, Vol. 12, No. 4, pp. 403–412, October, 1972.The author wishes to express his sincere gratitude to his scientific director T. Sabirov for valuable observations and advice.     

The search for narrow resonances in the reactione + e −→hardrons at centre-of-mass energy range between 7.23 and 10.34 GeV

The results of a search for narrow resonances ine ⁺ e ^? annihilation at centre-of-mass energies between 7.23 and 10.34 GeV are presented. The experiment was performed using the MD-1 detector at the VEPP-4 storage ring. The total luminosity integral of 16 pb^?1 was taken. There is no evidence that new states exist. The upper limits on the leptonic widthΓ _ee of possible resonances are less, by a factor of 10–80, than theΓ _ee for the ?(1S) meson.     

Multiplicity of supercritical fronts for reaction–diffusion equations in cylinders

We study multiplicity of the supercritical traveling front solutions for scalar reaction–diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions connecting an unstable equilibrium to the closest stable equilibrium for all speeds exceeding a critical value. We show that these are, in fact, the only traveling front solutions in the considered problems for sufficiently large speeds. In addition, we show that other traveling fronts connecting to the unstable equilibrium may exist in a certain range of the wave speed. These results are obtained with the help of a variational characterization of such solutions.     

Domain Structure of Bulk Ferromagnetic Crystals in Applied Fields Near Saturation

We investigate the ground state of a uniaxial ferromagnetic plate with perpendicular easy axis and subject to an applied magnetic field normal to the plate. Our interest is in the asymptotic behavior of the energy in macroscopically large samples near the saturation field. We establish the scaling of the critical value of the applied field strength below saturation at which the ground state changes from the uniform to a multidomain magnetization pattern and the leading order scaling behavior of the minimal energy. Furthermore, we derive a reduced sharp interface energy, giving the precise asymptotic behavior of the minimal energy in macroscopically large plates under a physically reasonable assumption of small deviations of the magnetization from the easy axis away from domain walls. On the basis of the reduced energy and by a formal asymptotic analysis near the transition, we derive the precise asymptotic values of the critical field strength at which non-trivial minimizers (either local or global) emerge. The non-trivial minimal energy scaling is achieved by magnetization patterns consisting of long slender needle-like domains of magnetization opposing the applied field.     

On an Isoperimetric Problem with a Competing Nonlocal Term II: The General Case

This paper is the continuation of a previous paper (H. Knüpfer and C. B. Muratov, Comm. Pure Appl. Math. 66 (2013), 1129–1162). We investigate the classical isoperimetric problem modified by an addition of a nonlocal repulsive term generated by a kernel given by an inverse power of the distance. In this work, we treat the case of a general space dimension. We obtain basic existence results for minimizers with sufficiently small masses. For certain ranges of the exponent in the kernel, we also obtain nonexistence results for sufficiently large masses, as well as a characterization of minimizers as balls for sufficiently small masses and low spatial dimensionality. The physically important special case of three space dimensions and Coulombic repulsion is included in all the results mentioned above. In particular, our work yields a negative answer to the question if stable atomic nuclei at arbitrarily high atomic numbers can exist in the framework of the classical liquid drop model of nuclear matter. In all cases the minimal energy scales linearly with mass for large masses, even if the infimum of energy cannot be attained. © 2014 Wiley Periodicals, Inc.     

Synthesis of dicationic μ-diborolyl triple-decker complexes [CpCo(μ-1,3-C<Subscript>3</Subscript>B<Subscript>2</Subscript>Me<Subscript>5</Subscript>)M(C<Subscript>6</Subscript>H<Subscript>6</Subscript>)]<Superscript>2+</Superscript> (M = Rh,Ir)

Dicationic triple-decker complexes [CpCo(μ-1,3-C₃B₂Me₅)M(C₆H₆)]²⁺ (M = Rh (3), Ir (4)) were synthesized by the reaction of [CpCo(μ-C₃B₂Me₅)MBr₂]₂ (M = Rh, Ir) with benzene in the presence of AgBF₄. The structure of 3(BF₄)₂ was determined by X-ray diffraction analysis.     

Magnetoactive Humic-Based Nanocomposites

Summary: We have elaborated several approaches for the preparation of magneto-active nano-hybrid composites, including i) ex situ method, which consists of the precipitation of magnetic particles from Fe(II) and Fe(III) salts followed by their incorporation into the humic acids matrix and ii) a chemical precipitation method in situ where the magnetic particles are grown within the humic acids matrix. It was proven that adsorption of humic acids on the magnetic particle surface leads to an enhanced electrostatic and steric stabilization of particles, due to the absorbed layer of highly charged macromolecular compounds. The sorbents under study were found to reveal a high sorption capacity towards uranyl ions. Using the adsorption isotherm, in the linear form of the Langmuir equation, the adsorption parameters were estimated. The results obtained show that the adsorption of uranyl ions by the magneto-active nanocomposite is enhanced in comparison with the free HA.