Stable iterative Lagrange principle in convex programming as a tool for solving unstable problems

A convex programming problem in a Hilbert space with an operator equality constraint and a finite number of functional inequality constraints is considered. All constraints involve parameters. The close relation of the instability of this problem and, hence, the instability of the classical Lagrange principle for it to its regularity properties and the subdifferentiability of the value function in the problem is discussed. An iterative nondifferential Lagrange principle with a stopping rule is proved for the indicated problem. The principle is stable with respect to errors in the initial data and covers the normal, regular, and abnormal cases of the problem and the case where the classical Lagrange principle does not hold. The possibility of using the stable sequential Lagrange principle for directly solving unstable optimization problems is discussed. The capabilities of this principle are illustrated by numerically solving the classical ill-posed problem of finding the normal solution of a Fredholm integral equation of the first kind.     

Changes in luminescence of semiconductor colloidal quantum dots CdSe@CdS by replacement of hydrophobic ligands with 1-thioglycerol

Luminescent properties of CdSe@CdS colloidal quantum dots upon replacement of hydrophobic stabilizing ligands with water-soluble 1-thioglycerol have been studied. The data obtained have made it possible to optimize the ligand replacement procedure and significantly decrease the loss of the fluorescence quantum yield of the resulting hydrophilic quantum dots.     

Experimental study of gasification of vacuum residue in metal melt by alternating reactor feeding with carbonaceous feedstock and oxidant

Processes occurring in a metal melt during plasma-assisted melt gasification of carbonaceous feedstock have been studied in the mode of alternating feeding the reactor with the carbonaceous feedstock and oxidant. Vacuum residue was used as an oxygen-free carbonaceous material, and air and steam were used as an oxidant. The results of the study show that by alternating the carbonaceous-feedstock pyrolysis step and the step of carbon oxidation in the metal melt, it is possible to produce synthesis gas with any desired H₂/CO ratio.     

Crystal structure of 9-(5,5-dimethyl-2,4,5,6-tetrahydro-1<Emphasis Type="Italic">H</Emphasis>-phenalen-2-yl)-5,5,9-trimethyl-5,6,8,9-tetrahydrocyclopenta[<Emphasis Type="Italic">a</Emphasis>]phenalen-10(4<Emphasis Type="Italic">H</Emphasis>)-one

The structure of 9-(5,5-dimethyl-2,4,5,6-tetrahydro-1H-phenalen-2-yl)-5,5,9-trimethyl-5,6,8,9-tetrahydrocyclopenta[а]phenalen-10(4H)-one was determined by X-ray crystallography. The intermolecular interaction energies were calculated by the atom-atomic approach for the crystal structure. The character of the crystal structure and the structural subclass were established.     

Phase equilibria in the Cu–Cu<Subscript>2</Subscript>Se–As system

Phase equilibria in the Cu–Cu₂Se–As were investigated by differential thermal analysis and X-ray powder diffraction analysis. Informative plots describing this system were constructed, viz., the polythermal sections Cu_0.667Se_0.333–As, Cu_0.667Se_0.333–Cu_0.735As_0.265, and Cu_0.8Se_0.2–As, the isothermal section of the phase diagram at 300 K, and the projection of the liquidus surface. The obtained results differ from the published data in length of fields of primary crystallization of phases and in coordinates of a number of invariant equilibrium points.     

Simulation of equilibria of formation of mono- and polynuclear heteroligand cobalt(II) and nickel(II) complexonates in aqueous solutions

We report the results of our studies of the protolytic and coordination equilibria of formation of mono- and polynuclear heteroligand complexonates containing cobalt(II) and nickel(II) salts and EDTA, as well as monoamine complexons, such as iminodiacetic acid and hydroxyethyliminodiacetic acid. The experimental data obtained by absorption spectrophotometry were processed using the mathematical models that allowed us to assess the probability of existence of a broad range of complex species in the solution and to select the species sufficient for the experimental data to be reconstituted from them. The compositions of the polynuclear heteroligand cobalt(II) and nickel(II) complexonates were determined. The pH ranges of their existence were found; the equilibrium constants of the reactions and the stability constants of the resulting complexes were calculated. An assumption is made about their structure.     

Sequential reactions from catalytic hydroformylation toward the synthesis of amino compounds

Different families of new amino compounds were efficiently synthesized, through optimized sequential processes, involving rhodium catalyzed hydroformylation as the key step. The selection of appropriate hydroformylation catalytic systems and reaction conditions allowed obtaining aldehydes derived from several n-alkyl olefins, cholest-4-ene and 3-vinyl-1H-indole, which were subsequently transformed, in one-pot, in to α-amino acids via hydroformylation/Strecker reaction, and in to tertiary amines via hydroaminomethylation, with excellent yields.     

Mathematical simulation of the formation of liquid products from catalytic cracking gases over a zeolite-containing catalyst modified with Group VI and VIII metals

The kinetics of the formation of liquid products from catalytic cracking gases over a zeolite-containing catalyst in a flow reactor in the temperature range from 260 to 420°C at GHSV = 30–264 h^–1 and an on-stream time of 5–25 s has been investigated. A kinetic model for the process proceeding according to a likely scheme is proposed. The rate constants and activation energies of certain reactions involved in the process have been determined. A mathematical model of the process taking into account the mass and heat balances, as well as hydrodynamic conditions, has been developed. The concentration and temperature fields and the pressure over the catalyst bed height have been calculated. The target product yield on has been plotted as a function of the on-stream time.     

Theoretical investigation of the molecular structure and spectroscopic properties of oxicams

Nonsteroidal anti-inflammatory drugs (NSAIDs) are among the most frequently prescribed drugs and have multiple therapeutic uses. These drugs are predominantly used for the treatment of musculoskeletal diseases because of their analgesic, antipyretic, and antiplatelet activities. Oxicams constitute an interesting class of organic compounds and have been investigated in the search for new analgesic and anti-inflammatory drugs. In the present work, a theoretical investigation of the molecular structure and spectroscopic properties of a series of five oxicams in different solvents was performed using density functional theory (DFT) methods. The geometric optimizations of the oxicams were carried out using the M06 density functional and the CBSB7 basis set. The infrared data were all obtained at the same theoretical level. The UV-Vis absorption and NMR data of some oxicams were calculated using the DFT and CBSB3 basis sets. The analysis of structural parameters, particularly the bond length and spectroscopic data, indicated that interactions occurred between the hydrogen bond types for 4-meloxicam, isoxicam, and normeloxicam. Stereoelectronic interactions caused by the substitution of alkyl groups caused the bond lengths to elongate. Similarly, the substitution of heteroatoms, such as nitrogen, sulfur, or oxygen, increased the bond lengths and angular stresses.