On the uniqueness of the solution of nonlinear differential-algebraic systems

We consider the Cauchy problem for a system of nonlinear ordinary differential equations unsolved for the derivative of the unknown vector function and identically degenerate in the domain. We prove a theorem on the coincidence of two smooth solutions of the considered problem. We show that, under some additional assumptions, the above-mentioned problem cannot have classical solutions with less smoothness. We obtain conditions under which the problem has a fixed finite number of solutions.     

On the nonresonance property of linear differential-algebraic systems

We consider a system of linear ordinary differential equations in which the coefficient matrix multiplying the derivative of the unknown vector function is identically singular. For systems with constant and variable coefficients, we obtain nonresonance criteria (criteria for bounded-input bounded-output stability). For single-input control systems, we consider the problem of synthesizing a nonresonant system in the stationary and nonstationary cases. An arbitrarily high unsolvability index is admitted. The analysis is carried out under assumptions providing the existence of a so-called “equivalent form” with separated “algebraic” and “differential” components.     

NMR spectra of a hydrocarbon-soluble organosodium compound and its lithium analogs

¹H,²³Na, and⁷Li NMR spectra of 2-ethyl hexylsodiurn, 2-ethylhexyllithium, and isobutyllithium obtained in the reaction of the corresponding alkyl chlorides and metals have been recorded. The¹H N MR signal for the protons of the CH₂Na group is shifted upheld compared with that for the protons of the CH₂Li group (doublets at -0.88 and -0.83, respectively). The composition of the products of reaction of 2-ethylhexyl chloride with sodium depends on the form of the metal reagent employed. The use of sodium balls with diameter up to 2 mm results in the formation of products containing ionic chlorine (30–50 % with respect to Na); the reaction with the dispersion proceeds faster and the reaction product is chlorine-free. The²³Na NMR spectra of these substances are also different, which is explained by the formation of 2-ethylhexylsodium complexes with NaCl in the former case.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 883–885, April, 1996.     

The Neumann boundary value problem for a semilinear elliptic equation in a thin cylinder. The least energy solutions

It is proved that the least energy solution of the BVP

Solution of the center-focus problem for a nine-parameter cubic system

We present a solution of the center-focus problem for a nine-parameter cubic system that can be reduced to a Lienard type system.     

To the question of the minimal number of inputs for linear differential algebraic systems

We examine a control linear system of ordinary differential equations with an identically degenerate matrix coefficient of the derivative of the unknown vector function. We study the question of the minimal dimension of the control vector when the system could be fully controllable on any segment in the domain of definition. The problem is investigated in the cases of stationary systems and the systems with real analytic and smooth coefficients for which some structural forms can be defined.     

Index for linear systems of differential-algebraic equations with partial derivatives

We investigate time-varying linear differential algebraic equations with partial derivatives. We introduce concept of insolubility index as the least possible order of the differential operator which transforms the initial system into a structural form with separated the “algebraic” and “differential” subsystems. The approach does not assume the existence of differential indexes with respect to independent variables.     

Solvent Extraction–Photometric Determination of Palladium Using Complexation with 1-(2-Pyridylazo)-2-Naphthol

Palladium(II) complexation with 1-(2-pyridylazo)-2-naphthol (PAN) in aqueous solutions followed by extraction with chloroform and photometric detection was studied. The best conditions were found for the formation of the complex in an aqueous solution and for its extraction with chloroform that provided a sufficient degree of binding palladium ions. The stability constant of the complex cation PdX⁺, which is extracted by chloroform as an ion pair [PdX]⁺[An^–] (An^–– CH₃COO^–), was calculated using the methods proposed by Rossotti (log K _stab= 18.73) and Komar' (log K _stab= 18.82). The equilibrium constant of the complexation reaction was also calculated (5.45 × 10⁴). It was shown that components of nonferrous alloys affect the determination of palladium by photometry as its complex or ion pair with PAN in chloroform.     

Effect of silicon carbide coatings on the strength of carbon fibers

Conclusion The character of the effect of silicon carbide coatings on the strength of carbon fibers is a function of the strength of the coating, which decreases with an increase in its thickness. The results obtained permit hoping for a significant increase in the strength of fibers by application of high-modulus coatings. It can be attained as a result of increasing the critical value of the coating thickness due to optimization of the conditions of preparation, which will improve the structure of the articles.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 604–608, July–August, 1988.