In the field of fisheries, one of the key tasks is to determine the total and commercial stocks of fish resources in a water body, as well as to establish the maximum allowable catch of fish to maintain the sustainability of the ecosystem. Mathematical models play an important role in this process, providing effective resource management and predicting fish population dynamics, ...

This article examines quantum group symmetry using the Potts model. The transformation of the Potts model into a polynomial knot state on Kaufman square brackets is analyzed. It is shown how a dichromatic polynomial for a planar graph can be obtained using Temperley–Lieb operator algebra. The proposed work provides insight into the 74 knot-partition function of Takara Musubi using ...

In this study, the object of the research is low-rank coal during the process of thermal heating of five types: brown, high moisture brown, long-flame, coke weakly sintering and coke fusinite. In the research, when conducting thermal and gas analysis in inert media, the problem of using low-rank coal in the thermal heating process to obtain volatile fuel gases was solved ...

This work is devoted to the study and solution of the problems of modeling complex objects on the example of the atmospheric block of the primary oil refining unit, associated with the deficit and fuzziness of the necessary initial information. Since many real technological objects of oil refining and other industries are often characterized by a deficit and fuzziness of the ...

The Ginzburg-Landau equation with rapidly oscillating terms in the equation and boundary conditions in a perforated domain was considered. Proof was given that the trajectory attractors of this equation converge weakly to the trajectory attractors of the homogenized Ginzburg-Landau equation. To do this, we use the approach from the articles and monographs of V.V. Chepyzhov and ...

Existing cathode electrode materials used in commercially available lithium-ion batteries (LIBs) exhibit inadequate electrochemical performance at low temperatures, significantly constraining their utility in regions with cold climates. Promising in this context, the NASICON-structure Na3V2(PO4)3 (NVP) nanomaterial was successfully synthesized using a modified Pechini method ...

We consider a special class of Galton–Watson theta-processes in a varying environment fully defined by four parameters, with two of them (θ, r) being fixed over time n, and the other two (an , cn) characterizing the altering reproduction laws. We establish a sequence of transparent limit theorems for the theta-processes with possibly defective reproduction laws. These results ...

This investigation focuses on the construction of novel dark and singular soliton solutions for the Hirota equation, which models the propagation of ultrashort light pulses in optical fibers. Initially, we employ a wave variable transformation to convert the physical model into ordinary differential equations. Utilizing extended rational sinh–cosh and sine–cosine techniques, ...

This paper investigates the (2 + 1)-dimensional nonlocal Hirota–Maxwell–Bloch (NH-MB) system under various types of nonlocality. The mathematical consistency of possible nonlocal structures is analyzed, and three types that lead to a well-posed system are identified. The integrability of the system is established through its Lax pair representation, and a Darboux transformation ...

Parameters such as various integral and differential characteristics of functions, smoothness properties of regions and their boundaries, as well as many classes of weight functions cause complex relationships and embedding conditions for multi-weighted anisotropic Sobolev type spaces. The desire not to restrict these parameters leads to the development of new approaches based ...