The influence of solvation on the stability constants of Ag<Superscript>+</Superscript>-18-crown-6 complexes in acetonitrile-dimethylsulfoxide mixtures at 298.15 K

The influence of the composition of acetonitrile-dimethylsulfoxide solvents on the stability of silver(I) complexes with 18-crown-6 ether was studied potentiometrically. An increase in the concentration of dimethylsulfoxide decreased the stability of the coordination compound. It was shown on the basis of the thermodynamic characteristics of solvation of the reagents that a determining factor of complex formation equilibrium shifts was the solvation effect of the Ag⁺ ion. An equation was suggested for predicting the stability of silver(I) coordination compounds with crown ethers and pyridine-type ligands in binary mixtures of aprotic solvents from changes in the solvation state of the central ion.     

Reactions of ethyl 1-benzylidene-7a-hydroxy-4-phenyl-6-oxooctahydro-1H-indene-5-carboxylate and ethyl 5-benzylidene-4a-hydroxy-1-phenyl-3-oxodecahydronaphthalene-2-carboxylate with 1,2,4-triazol-3-amine. Synthesis of substituted triazoloquinazolines

Russian Journal of Organic Chemistry -     

Homogeneity region of erbium manganite Er<Subscript>2 − <Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3 ± δ</Subscript> in air

The solubility ranges of Er₂O₃ and Mn₃O₄ oxides and ErMn₂O₅ manganite in ErMnO_{3 ± δ} are determined for the temperature range 900–1400°C.     

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton’s method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton’s method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.     

Application of the method of nonstationary waveguide equations to simulating pulsed processes in irregular transmission lines

The potentialities of the model of nonstationary waveguide equations for describing pulsed processes in irregular transmission lines are studied using planar lines as an example. The problem of high-accuracy controllable-error numerical simulation is discussed. Typical examples of simulating ultra-wide-band electromagnetic pulses with an initial TEM structure in terms of time-domain representation are presented with emphasis on the interaction of the pulses with irregularities, including their transformation into longitudinal waves. Both lumped and distributed irregularities are addressed: deep corrugations that cover 90% of the transmission line’s aperture (distributed irregularities) and these corrugations in combination with sharp kinks at the boundary surfaces and permittivity steps at the boundaries of the dielectric filling (lumped irregularities). It is shown that a relative rms error involved in the calculated field intensity of no higher than 10⁻⁴ is easy to achieve.     

Molecular and crystal structures of 3-(4-bromphenyl)-7-furfurylidene-3,3a,4,5,6,7-hexahydro(2H)indazole

As determined by single crystal X-ray diffraction, 3-(4-bromphenyl)-7-furfurylidene-3,3a, 4,5,6,7-hexahydro(2H)indazole has the trans-position of protons at C(3) and C(3a), s-cis-conformation of the furfurylidene fragment, and exists in the 2H-form.     

Three-dimensional Laplace’s potentials in a complex representation

A new analytic method for constructing wide classes of three-dimensional Laplace’s potentials that admit a closed representation in terms of elementary functions is developed. These classes are especially useful in designing electron-optics devices on the basis of inverse problems of particle dynamics, in which case there arises an ill-posed Cauchy problem for Laplace’s equation, this problem involving an analytic continuation of the sought potential from a plane to three-dimensional space.     

Parallel implementation of Newton’s method for solving large-scale linear programs

Parallel versions of a method based on reducing a linear program (LP) to an unconstrained maximization of a concave differentiable piecewise quadratic function are proposed. The maximization problem is solved using the generalized Newton method. The parallel method is implemented in C using the MPI library for interprocessor data exchange. Computations were performed on the parallel cluster MVC-6000IM. Large-scale LPs with several millions of variables and several hundreds of thousands of constraints were solved. Results of uniprocessor and multiprocessor computations are presented.