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.     

Regularity of nonlinear flows on noncompact Riemannian manifolds: Differential geometry versus stochastic geometry or what kind of variations is natural?

It is shown that the geometrically correct investigation of regularity of nonlinear differential flows on manifolds and related parabolic equations requires the introduction of a new type of variations with respect to the initial data. These variations are defined via a certain generalization of a covariant Riemannian derivative to the case of diffeomorphisms. The appearance of curvature in the structure of high-order variational equations is discussed and a family of a priori nonlinear estimates of regularity of any order is obtained. By using the relationship between the differential equations on manifolds and semigroups, we study C ^∞-regular properties of solutions of the parabolic Cauchy problems with coefficients increasing at infinity. The obtained conditions of regularity generalize the classical coercivity and dissipation conditions to the case of a manifold and correlate (in a unified way) the behavior of diffusion and drift coefficients with the geometric properties of the manifold without traditional separation of curvature. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1011–1034, August, 2006.     

Conformations of highly hindered aryl ethers: IX. Dipole moment evidence for an intramolecular donor-acceptor complex

In a search for evidence that a π cloud proximal halogen interaction is of importance to the mode of action of the thyroid hormones, the dipole moments of the 1'-naphthyl (I), (4.29 D), 4'-carboxymethylphenyl (II), (2.90 D), 2'-bromo4'-carboxymethylphenyl (III), (3.56 D), and methyl (IV), (3.24 D) ethers of 2,4dinitro-6-bromophenol were determined in benzene at 25 °C. The moments of (I), (II) and (III) are approximated best by those calculated for the twisted conformation in which the bromine closely approaches the face of the other ring. That of the naphthyl ether (I) can, however, be explained only by inclusion of an intramolecular electron donor-acceptor charge-transfer moment of 1.6 D directed from the π cloud of the naphthyl ring to the proximal nitro group of the other ring, or of 2.8 D to the proximal bromine of that ring. In the preferred conformation of the methyl ether (IV), the methoxy group is coplanar with the ring while the 2-nitro group is twisted 90° from coplanarity to accomodate it. A mesomeric moment of 2.3 D is estimated from this for the 2,4-dinitro-6-bromophenoxy moiety and is used in calculating the expected moments of the other ethers.     

Synthesis of a program trajectory for a wheeled vehicle to bypass side obstacles

A method of practical synthesis of a program trajectory for a mobile robot moving along an L-shaped holding alley with a 90°-turn is developed. The geometric parameters of the possible maneuvers are given. Software is developed. Examples of the robot's moving along such alleys are considered Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 133–143, September 2008.     

Excitation of nonlinear impurity electron-phonon oscillations. Raman scattering

The impurity is shown to transit into the state of non-linear electron-phonon oscillation upon the passage of a resonance electromagnetic wave pulse. In this case some lines appear in the Raman spectrum at frequencies characteristic for the oscillations.     

ACTIVATION ENERGY OF DESORPTION OF DIBENZOFURAN ON ACTIVATED CARBONS

1. INTRODUCTION With the development of municipalization in China, more and more cities are challenged by the problem of how to dispose of the dramatically increased municipal waste. Generally, most of municipal solid waste is landfilled or dumped openly in the suburbs. It causes not only land waste, but also serious environment pollution. In order to solve efficiently the environment pollution caused by municipal solid waste, incineration technique was introduced in some big cities such…     

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.     

Obtaining biologically active substances from Amaranthus caudatus L. seeds in one technological cycle

Nowadays, amaranth is a valuable multipurpose crop and a source of a number of very important biologically active substances. The aim of this study was to develop a comprehensive scheme for obtaining fatty oil, triterpenoids and lectin from the seeds of Amaranthus caudatus L. in one technological cycle. Two variants of the lectin and triterpene compound purification method from amaranth seeds were tested. It was determined that the extraction of triterpene compounds should be carried out after purification of the lectin from degreased seeds. The rationality of this sequence of technological operations is explained by the lability of the lectin and the insolubility in water of triterpene compounds from amaranth seeds. The study also presents a scheme for obtaining squalene from amaranth oil by chromatography on silica gel and proposes a more effective affinity sorbent for purification of the lectin. The use of such a sorbent also opens up the possibility of preserving other water-soluble substances from amaranth seeds. The physicochemical characteristics and carbohydrate specificity of the lectin are described and new data on the results of the interaction of lectin with human and animal erythrocytes are given. The obtained results are discussed in the light of the complex use of raw materials.