Essential self-adjointness of Dirichlet operators of Gibbs measures on infinite products of manifolds

We obtain the conditions of essential self-adjointness of Dirichlet operators of Gibbs measures with essential domains consisting of smooth cylindrical functions. It is proved that certain spaces of smooth functions are invariant under the action of the semigroup of the Dirichlet operator.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 4–11, January, 1995.This research was partially supported by the Ukrainian State Committee on Science and Technology.     

Noncommutative central limit theorem for Gibbs temperature states

For Gibbs temperature states, the scheme of the proof of the noncommutative central limit theorem is given by using the commutative central limit theorem for corresponding Euclidean measures. Applications are constructed for the model of a temperature-anharmonic crystal and the generalized Ising model with compact continuous configuration space.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 299–306, March, 1995.This work was partially supported by the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology.     

Dynamic chain system with seismic damper: reduction of nonlinear model

The efficiency of model reduction via balancing for a multimass system with a nonlinear inertial link is demonstrated. As an example, a three-mass dynamic system with a seismic damper is examined. The constraints of the seismic damper are assumed to be ideal. The order of the system of differential equations is reduced by one. It is pointed out that the difference between the numerically analyzed dynamic processes in the original and reduced systems is minor, which makes it possible to use the method for justified simplification of nonlinear systems     

Three-dimensional structure of the enzyme dimanganese catalase from Thermus Thermophilus at 1 Å resolution

The crystal structures of two forms of the enzyme dimanganese catalase from Thermus Thermophilus (native and inhibited by chloride) were studied by X-ray diffraction analysis at 1.05 and 0.98 Å resolution, respectively. The atomic models of the molecules were refined to the R factors 9.8 and 10%, respectively. The three-dimensional molecular structures are characterized in detail. The analysis of electron-density distributions in the active centers of the native and inhibited enzyme forms revealed that the most flexible side chains of the amino acid residues Lys162 and Glu36 exist in two interrelated conformations. This allowed us to obtain the structural data necessary for understanding the mechanism of enzymatic activity of the dimanganese catalase.     

Structure of a Bloch domain wall in a cubic crystal

Planar Bloch domain walls with different senses and paths of rotation of the magnetization vector are studied in a cubic crystal with a negative first constant of magnetic anisotropy.     

Trace cobalt speciation in bacteria and at enzymic active sites using emission Mössbauer spectroscopy

57Co emission M?ssbauer spectroscopy (EMS) allows the chemical state of cobalt, as influenced by its coordination environment, to be monitored in biological samples at its physiological (trace) concentrations. To draw attention to EMS as a valuable tool for speciation of cobalt in biocomplexes, the process of cobalt(II) metabolism in cells of the plant growth-promoting rhizobacterium Azospirillum brasilense Sp245 was investigated using EMS of 57CoII-doped bacterial cells. EMS measurements also showed 57CoII-activated glutamine synthetase (GS, a key enzyme of nitrogen metabolism, isolated from this bacterium) to have two different cobalt(II) forms at its active sites, in agreement with data available on other bacterial GSs. Chemical after-effects following electron capture by the nucleus of the parent 57CoII during the 57Co-->57Fe transition, which contribute to the formation of a stabilised daughter 57FeIII component along with the nucleogenic 57FeII forms, are also briefly considered.     

On models of dynamic systems with dry friction

An approach to the design of models of dynamical systems with high dry friction in the kinematic pair is developed. The members of the kinematic pair are represented by parts of rigid bodies. The system as a whole is considered to have a variable structure. According to this assumption, two modes of motion with different dissipative characteristics are possible. The states in which the modes exchange and the motion switches over into critical modes with dynamic self-locking are established. A system with a variable transfer function between members that form a nonideal constraint is described __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 97–105, May 2007.     

Dynamic Processes in a Spheroidal Seismic-Damping Mechanism

A mathematical model of a variable-structure system of solids with rolling friction and unilateral sliding friction bonds is described. The model can be applied to seismic isolation mechanisms. Conditions for transition between the possible structures of the equations of state are formulated. The behavior of the system with kinematically defined motion of the base is analyzed as an example__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 119–127, January 2005.