Optimal estimation of a state based on deterministic and stochastic discrete measurements

A problem of constructing algorithms of optimal estimation of states of a discrete system accounting for deterministic and stochastic measurements is considered. A low order estimation algorithm is proposed in the form of a two-stage procedure for each instant of time obtained by direct application of the Kaiman optimal filtering algorithm.Translated from Dinamicheskie Sistemy, No. 4, pp. 85–89, 1985.     

Synthesis and structure of unsymmetrical cross-conjugated dienones with thienyl substituents

By condensation of thiophenecarbaldehyde and m-nitrobenzaldehyde with furyl-, thienylmethylenecyclohexanones in basic medium 2-(het)arylmethylene-6-thienylmethylenecyclohexanones were prepared. Under the conditions of acid catalysis analogously built dienones were synthesized containing 5-nitrothiophene fragment. Based on the data of IR and ¹H NMR spectroscopy their E,E-configuration was established.     

Catalytic synthesis and stereostructure of 1,2,3-trisubstituted decahydroisoquinolines

Liquid-phase catalytic reduction of 1,2,3-substituted 5,6,7,8-tetrahydroisoquinolinium perchlorates was investigated. The reaction proceeds stereodirectionally affording cis-decahydroisoquinolines. The probable scheme of reaction products formation is suggested. The structure of compounds obtained was established by IR and ¹³C NMR spectroscopy.     

Mössbauer study of the polymorphism in iron and iron-nickel alloys under deformation and high pressure

Structural and phase transitions in iron and binary iron-nickel alloys containing 6–32 at % nickel have been investigated by Mössbauer spectroscopy in situ under quasi-hydrostatic compression and compression shear. It is shown that the deformation decreases the onset pressure of the α-phase transition to the high-pressure ∈ and γ phases. Shear changes the transformation mechanism due to the formation of a large number of structural defects; it is an independent parameter of the phase transition kinetics. Compression shear leads to an irregular change in the hyperfine parameters of the initial and newly formed phases, which is due to the stress relaxation as in the trip effect.     

Application of electric fields uniform in the Euler sense in electron spectrography

A new approach is developed for determining optimal electron-optics media in which the idea of the electron (ion) spectrograph can effectively be implemented. This approach is based on electrostatic fields with the Laplace potential obeying the Euler uniformity condition. The operation principle of the spectrograph with such coupling fields is associated with the special similarity property of constant-energy families of trajectories with different energies under uniformity conditions. For constructing the required fields, we propose a new method of analytic representation, in which the Donkin complex representation apparatus for conical fields plays the leading role. The algorithms developed here make it possible to easily construct the uniform potentials in a wide class in which classical solid spherical harmonics and spherical functions are just special cases. The Cauchy problem is formulated and solved in the general closed analytic form for uniform potentials with a symmetry plane. A number of specific structures of this class are considered.     

Generalized Newton method for linear optimization problems with inequality constraints

A dual problem of linear programming is reduced to the unconstrained maximization of a concave piecewise quadratic function for sufficiently large values of a certain parameter. An estimate is given for the threshold value of the parameter starting from which the projection of a given point to the set of solutions of the dual linear programming problem in dual and auxiliary variables is easily found by means of a single solution of the unconstrained maximization problem. The unconstrained maximization is carried out by the generalized Newton method, which is globally convergent in an a finite number of steps. The results of numerical experiments are presented for randomly generated large-scale linear programming problems.     

Thermochemistry of the silver(I) complexation with 18-crown-6 ether in binary acetonitrile—dimethylsulfoxide solvents

The effect of acetonitrile-dimethylsulfoxide solvents on the enthalpy of silver(I) complexation with 18-crown-6 ether is studied by means of calorimetry. It is found that an increase in the concentration of dimethylsulfoxide leads to an increase in the reaction exothermicity. It is shown that the determining factor in the change in the reaction enthalpy is the solvation effect of the ligand.