Protective Properties of Zinc-Rich Coatings: An Impedance Method Estimate

The impedance of zinc-rich polymer coatings on steel in a 3-% NaCl solution is studied. The electrochemical behavior of the electrode is satisfactorily described by an equivalent circuit that contains a constant-phase element, which reflects fractal properties of the zinc surface in the binder. From the results of calculations of the circuit elements for metal-rich electrodes with different zinc contents computed are fractions of the active area of the surface of the coating and its fractal dimensionality.     

Pericyclic and Heteroelectrocyclic Mechanisms for the Cyclization of 1,3,5-Hexatrien-1-one and Its 6-Aza Analog

The cyclization of 1,3,5-hexatrien-1-one, 1, and the Z- and E-isomers of 1-aza-1,3-butadienylketene 3 were studied using the semiempirical AM1 and PM3 methods. Cyclizations of compounds 1 and Z-3 are shown to occur via a mono-rotation mechanism with barriers of 15.49 and 32.85 kcal/mol respectively. The reactions proceed via non-planar transition states which result from rotation of the methylene group for compound 1 and the imino group for compound Z-3. Cyclization of E-3 proceeds via a non-rotatory mechanism through a planar transition state. The activation barrier is 4.83 kcal/mol (AM1). The electronic structures of the initial and final states, and of some intermediate structures, including the transition states for the cyclization of compounds 1 and 3, were analyzed by the natural orbital method using HF/6-31G*//AM1 calculations. Energetic, structural, and orbital criteria indicate the heteroelectric mechanism for the cyclization of compound E-3 and the pericyclic mechanism for the cyclization of compounds 1 and Z-3.     

IR Spectroscopic Study of Ethylene Adsorption and Oligomerization on the Hydrogen Form of Mordenite

Diffuse-reflectance IR spectroscopy is used to study adsorption and oligomerization of ethylene on the hydrogen form of mordenite at room temperature. Ethylene adsorbs on bridging acid hydroxyl groups of the zeolite and forms -complexes with a firm hydrogen bond. The interaction with hydroxyl groups most strongly excites composite vibrations in adsorbed molecules. These vibrations are a combination of the stretching vibration of a double bond and the deformational vibrations of the CH₂ group. A conjecture is drawn that these composite vibrations correspond to the reaction coordinate of ethylene transformation to the ethoxy groups. Their further reactions with weakly adsorbed molecules result in ethylene oligomerization. A linear oligomer is formed, grafted on the zeolite surface and filling the pores of zeolites.     

Photometric cyclic-injection trace determination of phosphate ions in natural waters as an ion associate of phosphomolybdate with Astra Phloxine

A procedure for the automatic photometric determination of phosphate ions in natural waters was developed, based on the formation of a colored ion associate of the reduced form of phosphomolybdic heteropoly anion with a polymethine dye, Astra Phloxine. The detection limit was 5 μg P/L at the sample volume of 0.3 mL.     

A Study of the stability of solutions to inverse problems of dynamics of control systems under perturbations of initial data

A novel dual approach to the problem of optimal correction of first-kind improper linear programming problems with respect to their right-hand sides is proposed. It is based on the extension of the traditional Lagrangian by introducing additional regularization and barrier components. Convergence theorems are given for methods based on the augmented Lagrangian, an informal interpretation of the obtained generalized solution is suggested, and results of numerical experiments are presented.     

The value functions of singularly perturbed time-optimal control problems in the framework of Lyapunov functions method

The Dirichlet problems for singularly perturbed Hamilton–Jacobi–Bellman equations are considered. Some impulse variables in the Hamiltonians have coefficients with a small parameter of singularity ε in denominators.The research appeals to the theory of minimax solutions to HJEs. Namely, for any ε>0, it is known that the unique lower semi-continuous minimax solution to the Dirichlet problem for HJBE coincides with the value function u^ε of a time-optimal control problem for a system with fast and slow motions.Effective sufficient conditions based on the fact are suggested for functions u^ε to converge, as ε tends to zero. The key condition is existence of a Lyapunov type function providing a convergence of singularly perturbed characteristics of HJBEs to the origin. Moreover, the convergence implies equivalence of the limit function u⁰ and the value function of an unperturbed time-optimal control problem in the reduced subspace of slow variables.     

Cluster model of defective solid solutionsMe_{c_1 }^{(1)} Me_{c_2 }^{(2)} B_x^{(1)} B_y^{(2)}

In a cluster model of defective solid solutions the cluster components are determined and their concentration is found as a function of the defectiveness for solutions \(Me_{c_1 }^{(1)} Me_{c_2 }^{(2)} B_x^{(1)} B_y^{(2)}\) in the case of limited and unlimited solubility. An interpretation is given of the dependence of the lattice parameter, magnetic moment, and Curie point on the composition in a cluster component model, using the example of oxycarbides, oxynitrides, and solutions of certain metals in Mn₄N.     

On the continuous extension of a generalized solution of the Hamilton–Jacobi equation by characteristics that form a central field of extremals

The Cauchy problem for the Hamilton–Jacobi equation with state constraints is considered. A justification for a construction of a generalized solution with given structure is provided. The construction is based on the method of characteristics and on solutions of problems related to calculus of variations.     

Construction of a generalized solution to an equation that preserves the Bellman type in a given domain of the state space

A Cauchy problem is considered for a Hamilton-Jacobi equation that preserves the Bellman type in a spatially bounded strip. Sufficient conditions are obtained under which there exists a continuous generalized (minimax/viscosity) solution to this problem with a given structure in the strip. A construction of this solution is presented.