In this paper, sufficient conditions for compactness of sets in generalized Morrey spaces are given in terms of an averaging function. This result is analogous to the well-known Fréchet-Kolmogorov theorem for the pre-compacting of sets in Lebesgue spaces. Our main result consisted of four conditions on the behavior of the function norm and the norm of its averages in generalised ...

The optimization of recycling processes for waste motor oil (WMO) into diesel fuel is crucial for sustainable waste management and resource recovery. This study explores the application of novel deep eutectic solvents (DES), specifically methyltriphenylphosphonium chloride (MTPPCl) and ethylene glycol (EGL)-based DES, for the efficient removal of naphthalene from WMO. Density ...

In this paper we establish uniqueness of the weak solutions of nonlinear stochastic functional differential equations of neutral type in Hilbert spaces. We also study the continuous dependence of such solutions on the initial data.

The differential equation of fourth-order with variable smooth coefficients, given on the real axis, is investigated. The coefficients of the equation can be unbounded, and the sign of the potential (the lowest coefficient) is not defined. The case is considered that the intermediate term containing the second derivative of the desired function, as an operator, does not obey ...

In this work, a boundary value problems for a system of nonlinear ordinary differential equations that incorporates impulsive actions is considered. This formulation is significant for modeling real-world phenomena in which abrupt changes occur at specific time instants. The study established sufficient conditions for the existence of isolated solutions to the proposed boundary ...

We prove that a finite pointed abelian group generates a finitely axiomatizable variety that has a finite quasivariety lattice. As a consequence, we obtain that a quasivariety generated by a finite pointed abelian group has a finite basis of quasi-identities. The problems arising from the results obtained are also discussed.

In this paper, we study oscillatory properties of a fourth-order differential equation and spectral properties of a corresponding differential operator. These properties are established by first proving a new second-order Hardy-type inequality, where the weights are the coefficients of the equation and the operator. This new inequality, in its turn, is established for ...

Many modern technological objects in practice are characterized by the uncertainty of the initial information necessary for their management. Recently, one of the pressing scientific and practical problems is the development of new optimization methods for controlling the operating modes of such objects in a fuzzy environment. In this regard, the objective of this study is to ...

International transport corridors (ITCs) are intricate logistical networks essential for global trade flows. The effective modeling of these corridors provides invaluable insights into optimizing the transport system. However, existing approaches have significant limitations in dynamically representing the complexities and uncertainties inherent in ITC operations and at the ...

This research is among the most relevant research on the problems of natural gas transportation via pipe networks. The increased demand for natural gas in Kazakhstan is associated with a greater level of environmental friendliness; as a result, many power-generating stations use natural gas as their main source of energy. Modernization of existing thermal power plants is ...