Extragradient-type method for optimal control problem with linear constraints and convex objective function

The paper presents a method for solving optimal control problem with free right end and linear differential equations constraints. The proposed iterative process of extragradient-type is formulated in the functional subspace of piecewise continuous controls of L ₂. The convergence of the method is proved.     

Structures and Stability of Complexes of E(C6F5)3 (E = B,Al, Ga,In) with Acetonitrile

Complexes formed by interaction of E(C₆F₅)₃ (E = B, Al, Ga, In) with excess of acetonitrile (AN) were structurally characterized. Quantum chemical computations indicate that for Al(C₆F₅)₃ and In(C₆F₅)₃ the formation of a complex of 1:2 composition is more advantageous than for B(C₆F₅)₃ and Ga(C₆F₅)₃, in line with experimental observations. Formation of the solvate [Al(C₆F₅)₃ · 2AN] · AN is in agreement with predicted thermodynamic instability of [Al(C₆F₅)₃ · 3AN]. Tensimetry study of B(C₆F₅)₃ · CH₃CN reveals its stability in the solid state up to 197 °C. With the temperature increase, the complex undergoes irreversible thermal decomposition with pentafluorobenzene formation.     

Dynamics,Phase Constraints,and Linear Programming

Computational Mathematics and Mathematical Physics - A new approach to solving terminal control problems with phase constraints, using sufficient optimality conditions, is considered. The approach...     

Regularized filtering of spectrometric observations

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostiki, pp. 13–18, Izd. Moskovskogo Universiteta, Moscow, 1990.     

The Structure of 2-Methylphenylcyanamide in the Solid State

The structure of 2-methylphenylcyanamide NCNH(C₆H₄Me-2) is established in the solid state using single crystal X-ray diffraction data. The contribution of various intermolecular contacts to the crystal packing is studied using the Hirshfeld surface analysis and quantum chemical calculations within the density functional (DFT) M06-2X/6-311++G(d,p) level of theory.     

Supramolecular Associates of Nickel(II) Complexes with Nitro-Substituted Tetradentate Schiff Bases

Crystal structures of N,N'-ethylenebis(3-nitrosalicylideneiminato)nickel(II) [Ni(3-NO2SalEn)] and N,N'-(2,3-dimethylbutane-2,3-diyl)bis(3-nitrosalicylideneiminato)nickel(II) [Ni(3-NO2SaltmEn)] were determined by single crystal X-ray diffraction analysis. The [Ni(3-NO2SalEn)] complex forms supramolecular associates in the crystal phase, which affects its solubility, thermogravimetric, and spectral characteristics.     

An extragradient method for finding the saddle point in an optimal control problem

We propose an extragradient method for finding the saddle point of a convex-concave functional defined on solutions of controlled systems of linear ordinary differential equations. We prove the convergence of the method.     

Structure and ring-chain tautomerism of oxoalkyl dithiocarbamates and 4-hydroxy-1,3-thiazin-2-thiones

The structures of the reaction products of some , -unsaturated ketones with dithiocarbamic acids have been investigated by IR spectroscopic methods. It has been shown that the adducts, in the crystalline state, may be either the acyclic oxoalkyl dithiocarbamates or the cyclic 4-hydroxytetrahydro-1, 3-thiazin-2-thiones, depending on the number and positions of the substituents in the parent ketones. The existence of prototropic ring-chain tautomerism in solutions of 4-hydroxytetrahydro-1, 3-thiazin-2-thiones has been established.     

Sensitivity function: Properties and applications

The sensitivity function induced by a convex programming problem is examined. Its monotonicity, subdifferentiability, and closure properties are analyzed. A relation to the Pareto optimal solution set of the multicriteria convex optimization problem is established. The role of the sensitivity function in systems describing optimization problems is clarified. It is shown that the solution of these systems can often be reduced to the minimization of the sensitivity function on a convex set. Numerical methods for solving such problems are proposed, and their convergence is proved.     

UV picosecond laser-induced formation of amino acids from aqueous solutions of ammonic salts of dicarboxylic acids

It is shown for the first time that the irradiation of the ammonic-salt aqueous solutions of the dicarboxylic acids by powerful ultrashort uv pulses provokes the formation of the related amino acids. The amino-acid quantum yield depends on the intensity and for the aspartic acid, in particular, it reaches 40% at the intensity of about 1 GW/cm².