Landau problem for the class of functions that are regular in an annulus

The classical result of Landau, establishing the radius of the largest circle, in which, for any function f(z)R, where R is the class of regular functions w=f(z)=z+c₂z²+..., in¦z¦<1, ¦f(z)¦相似文献   

Luminescence centers in α-Bi<Subscript>2</Subscript>O<Subscript>3</Subscript> ceramics

Luminescence photoexcitation spectra of α-Bi₂O₃ ceramics are investigated. Luminescence spectra were deconvoluted into fundamental components using the Alentsev-Fok method. It is established that the luminescence spectra of α-Bi₂O₃ ceramics consist of three fundamental bands with maxima at 2.75, 2.40, and 1.97 eV. A comparison of the results with those from an investigation of luminescence of various modifications of bismuth oxide and bismuth germanates suggests that luminescence of these compounds is caused by radiation processes that occur in structural complexes that contain the bismuth ion in a nearest oxygen environment. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 5, pp. 672–676, September–October, 2008.     

Dynamic-model reduction for a multimass system with nonideal constraint in a seismic damper

A dynamic model for a multimass system with a seismic damper as a nonlinear inertial component is reduced via balancing. The seismic damper is subject to a nonideal constraint. As an example, the order of the system of differential equations is reduced by one for a dynamic three-mass system. A comparison of the processes in the original and reduced systems confirms that it is possible to use balancing to simplify such models Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 136–144, August 2008.     

Nature of the copper-nitrosyl intermediates of copper nitrite reductases during catalysis

The design and synthesis of copper complexes that can reduce nitrite to NO has attracted considerable interest. They have been guided by the structural information on the catalytic Cu centre of the widespread enzymes Cu nitrite reductases but the chemically novel side-on binding of NO observed in all crystallographic studies of these enzymes has been questioned in terms of its functional relevance. We show conversion of NO₂⁻ to NO in the crystal maintained at 170 K and present ‘molecular movies’ defining events during enzyme turnover including the formation of side-on Cu-NO intermediate. DFT modelling suggests that both true {CuNO}¹¹ and formal {CuNO}¹⁰ states may occur as side-on forms in an enzymatic active site with the stability of the {CuNO}¹⁰ side-on form governed by the protonation state of the histidine ligands. Formation of a copper-nitrosyl intermediate thus needs to be accommodated in future design templates for functional synthetic Cu-NiR complexes.

Observation of side-on copper-nitrosyl intermediate and its confirmation by DFT during catalysis of copper nitrite reductases.     

Nonlinear impurity electron-phonon oscillations

A new type of coupled oscillations has been found for an electron, localized at the impurity, and the lattice. The electron slowly oscillates between a certain pair of levels with corresponding variation in the amplitude of lattice oscillations.     

Nonexplosion and solvability of nonlinear diffusion equations on noncompact manifolds

We find sufficient conditions for the coefficients of a diffusion equation on a noncompact manifold that guarantee the nonexplosion of solutions in finite time. This property leads to the existence and uniqueness of solutions for the corresponding stochastic differential equation with globally non-Lipschitz coefficients. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1454–1472, November, 2007.     

Use of specific polysaccharide‐immobilized monodisperse poly(glycidyl methacrylate) core–silica shell microspheres for affinity purification of lectins

Immobilization of polysaccharides (yeast mannan and gum arabic) on the macroporous poly(glycidyl methacrylate) monodisperse microspheres coated with silica (SiO₂)‐containing amino groups on the surface was used to prepare affinity sorbents for lectin purification. The efficiency of isolating mannose specific Pisum sativum lectin was demonstrated on sorbent with immobilized yeast mannan and that of galactose specific Glycine hispida lectin on sorbent with immobilized gum arabic. The microspheres with immobilized polysaccharides can be used for selecting an affinity sorbent for purification of other mannose‐ and galactose‐specific lectins. In contrast to yeast mannan, the gum arabic immobilized on the microspheres possesses much narrower specificity and is suitable for purification of only those galactose specific lectins which interact well with l ‐rhamnose or l ‐arabinose. The synthesized macroporous particles are capable of immobilizing 50 mg of polysaccharide per 1 g of the matrix, which is 10 times higher than the capacity of epoxy‐activated Sepharose 6B. That makes it possible to obtain the same lectin quantity using a column of 10 times smaller volume. Another advantage of novel affinity sorbents comparing corresponding Sepharose gels is the possibility of sorbent drying after use. Copyright © 2014 John Wiley & Sons, Ltd.