Differential equations with set-valued solutions

We consider a special space of convex compact sets and introduce the notions of derivative and integral for a set-valued mapping that differ from those already known. We also consider a differential equation with set-valued right-hand side satisfying the Carathéodory conditions and prove theorems on the existence and uniqueness of its solutions. This approach, in contrast to the Kaleva approach, enables one to consider fuzzy differential equations as ordinary differential equations with set-valued solutions. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1326–1337, October, 2008.     

Conditions for the Existence of Basic Solutions of Linear Multivalued Differential Equations

Ukrainian Mathematical Journal - We discuss various definitions and properties of the derivatives of set-valued mappings. We also consider a linear set-valued differential equation and investigate...     

Comparative analysis of cytotoxic effects and intracellular accumulation of platinum(IV) nitroxyl complexes

Russian Chemical Bulletin - The relationship between the lipophilicity, cytotoxic effects, and intracellular accumulation for potential antitumor agents, viz., amino complexes of platinum(IV) with...     

The Effect of MoS x Nanocoatings on the Water Electrolysis Performance Using a Nickel-Foam-Based Bifunctional Catalyst

The ability to increase the efficiency of electrochemical H2 and O2 evolution reactions in an alkaline solution using nickel-foam-based electrodes has been studied. To improve the catalytic properties of the foam, it was subjected to complex modification via sulfurizing in sulfur-containing gaseous media and the additional formation of amorphous or crystalline MoSx nanolayers. The foam was sulfidized in hydrogen sulfide or sulfur vapor at a temperature of 400°C. Amorphous MoSx films were produced via pulsed laser deposition from a MoS2 target in an H2S atmosphere. To obtain nanocrystalline catalytic MoSx layers, thin-film Mo precursors were preliminarily applied to the foam pre-sulfurized in sulfur vapor at 400°C. The deposition of precursors was carried out in vacuum at 22°C. After deposition, the foam with precursors was oxidized in air at 600°C. The modified samples were probed via scanning electron microscopy involving microanalysis and Raman spectroscopy. The effect of the precursor layer thickness on the sulfurizing efficiency and phase composition of the modified layers was established. The amorphous layer deposition was found to have a strong impact on only the O2 evolution. The crystalline layers obtained via sulfidizing of Mo-containing precursors exerted influence on both the cathodic and anodic reactions. The hydrogen overvoltage at a current density of 10 mA/cm2 was −160 mV, and the oxygen overvoltage was below 150 mV, which corresponded to the best electrocatalysts on the nickel foam after the volume modification via conventional chemical treatment (hydro- and solvothermal synthesis).     

On some properties of bundles of trajectories of a controlled bilinear inclusion

We consider a differential bilinear inclusion with control and present conditions under which the reachability set for this inclusion is compact.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 484–494, April, 2004.     

On the Time of Completion of Pursuit in One Nonlinear Differential Game

For a nonlinear antagonistic two-person differential game on a manifold, we propose a method for the solution of the pursuit problem and determine the time of guaranteed capture.     

Perspectives in the development of the theory of spark-source and laser-plasma source mass-spectrometry

The processes of substance evaporation and atom ionization under different conditions of spark discharge or laser radiation are considered. It is shown that the dependence of the relative sensitivity coefficients on the properties of an element can be presented as the product of two exponents with parameters proportional to the atomization energies and first ionization potentials of the element. Differences in matrix composition and conditions influencing a sample in the ion source are considered by means of introducing two fitting parameters-atomization and ionization "temperatures"-into these exponents. Experiments carried out with the help of mass-spectrometers with spark and laser ion sources have corroborated the validity of the suggested quasi-equilibrium model and shown the possibility of its application for the improvement of the accuracy of analysis without use of standards as well as for checking the stability of experimental conditions in the process of analysis with standard samples.     

Differential inclusions with Hukuhara derivative

We introduce two types of differential inclusions with Hukuhara derivative and consider properties of these inclusions. For differential inclusions of the second type, we give different definitions of a solution, prove theorems on the existence of an ordinary solution, and establish the compactness of the set of these solutions. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 229–246, April–June, 2007.