Department of Mathematics

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Browsing Department of Mathematics by Author "Herbert, Mukalazi"

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    Calculation algorithm for electromagnetic wave processes in multi-wire intersystem ETL
    (Discover Electronics, 2024-06-10) Rashad, Huseyn; Arif, Hashimov; Ali, Shokri; Herbert, Mukalazi
    The nature of the transient process and the magnitude of the overvoltages are determined by a large number of factors in the HV/EHV AC transmission networks. The paper presents the study of mathematical modelling of electromagnetic wave processes in long-distance electric transmission line (ETL). The mathematical model is based on electromagnetic processes occurring on distributed parameter lines that are characterized by specific derivatives of the system of differential equations. The application of a spline-interpolation technique enables the calculation of currents and voltages at the nodes of the scheme, which obtains the unknown coordinates of the overhead line mode at the beginning of the ETL to solve the transmission line equation. The following results are derived from computer simulations of transients during switching on. With a simulation model, the importance of intelligent control of shunt reactor (SR) and ungrounded reactor (UR) was demonstrated and considered for a 500 kV power networks.
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    Exact solutions for the Cahn–Hilliard equation in terms of Weierstrass‑elliptic and Jacobi‑elliptic functions
    (Scientific Reports, 2024-05) Akhtar, Hussain; Tarek, F. Ibrahim; Osman, Birkea F. M.; Abeer, M. Alotaibi; Bushra, R. Al‑Sinan; Herbert, Mukalazi
    Despite the historical position of the F‑expansion method as a method for acquiring exact solutions to nonlinear partial differential equations (PDEs), this study highlights its superiority over alternative auxiliary equation methods. The efficacy of this method is demonstrated through its application to solve the convective–diffusive Cahn–Hilliard (cdCH) equation, describing the dynamic of the separation phase for ternary iron alloys (Fe–Cr–Mo) and (Fe–X–Cu). Significantly, this research introduces an extensive collection of exact solutions by the auxiliary equation, comprising fifty‑ two distinct types. Six of these are associated with Weierstrass‑elliptic function solutions, while the remaining solutions are expressed in Jacobi‑elliptic functions. I think it is important to emphasize that, exercising caution regarding the statement of the term ’new,’ the solutions presented in this context are not entirely unprecedented. The paper examines numerous examples to substantiate this perspective. Furthermore, the study broadens its scope to include soliton‑like and trigonometric‑ function solutions as special cases. This underscores that the antecedently obtained outcomes through the recently specific cases encompassed within the more comprehensive scope of the present findings.
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    Parametrized multiplicative integral inequalities
    (Advances in Continuous and Discrete Models, 2024-04) Herbert, Mukalazi; Abdelghani, Lakhdari; Ali, Shokri; Meftah, Badreddine; Assia, Frioui
    In this paper, we introduce a biparametrized multiplicative integral identity and employ it to establish a collection of inequalities for multiplicatively convex mappings. These inequalities encompass several novel findings and refinements of established results. To enhance readers’ comprehension, we offer illustrative examples that highlight appropriate choices of multiplicatively convex mappings along with graphical representations.