Current Issue : April-June Volume : 2026 Issue Number : 2 Articles : 5 Articles
The problem of nonlinear elastic transverse oscillations of a beam moving along its axis and subjected to an axial compressive or tensile force is considered. A theoretical study is carried out using the asymptotic method of nonlinear mechanics KBM (Krylov–Bogolyubov– Mitropolsky). Using this methods, differential equations were obtained in a standard form, determining the law of variation in amplitude and frequency as functions of kinematic, force, and physico-mechanical parameters in both resonant and non-resonant regimes. The fourth-order Runge–Kutta method was applied for the oscillatory system numerical analysis. The computation of complex mathematical expressions and graphical representation of the results were implemented in the mathematical software Maple 15. The results obtained can be applied for engineering calculations of structures containing moving beams subjected to compressive or tensile forces....
An overview on the study of nonlinear evolution equations of soliton type is provided. In addition, 5th-order nonlinear evolution equations are shown to be connected to the Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation via Bäcklund transformations. The links are depicted in a wide net of links which we term a Bäcklund Chart. The links obtained previously by Rogers and Carillo and by Carillo and Fuchssteiner are revisited, and new results are obtained. A 5th-order nonlinear evolution equation, which does not seem to appear in any list of integrable equations, is provided. All the connected equations exhibit a very interesting symmetry structure enjoyed by the corresponding full hierarchies. Indeed, they all admit a hereditary recursion operator. Hence, each one of the mentioned equations represents the base member of a corresponding hierarchy of equations. These hierarchies are constructed via the recursive application of the respective recursion operators. The symmetry properties of such equations are recalled. Finally, we compare the net of links, derived via Bäcklund transformations, in the case of the fifth-order nonlinear evolution equations with an analog net of links connecting third-order Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. Analogies and discrepancies between the connections established in the case of fifth-order equations with respect to those established in the case of third-order equations are analyzed. This study aims to open the way for the construction of corresponding non-Abelian equations of the fifth order....
The aim of this paper is to find formulas for the solutions of the nonlinear system of difference equations related to symmetry Pn+1 = TnTn−2 −Pn−3−Tn , Tn+1 = PnPn−2 ±Tn−3±Pn , where the initial conditions P−3, P−2, P−1, P0, T−3, T−2, T−1, and T0 are arbitrary real numbers. Moreover, the theoretical results are verified through several numerical examples, which are simulated and graphically illustrated using mathematical programs....
This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit systems undergoing pure dephasing, considering the effects of squeezing parameter, phase difference, and coupling strength within an Ohmic spectral density model. The decoherence factor shows how reservoir engineering influences coherence loss. Numerical results demonstrate that optimal squeezing and local bath configurations enhance QFI preservation, while collective couplings accelerate decay. We also examine the interplay with von Neumann entropy, highlighting their inverse correlation, where increased mixedness reduces metrological sensitivity....
Engineering education for sustainability extends beyond environmental awareness. It is aimed at the cultivation of resilient and self-regulated learners capable of continuous growth. The present work draws upon empirical data from three complementary investigations on first-year engineering students’ affective behavior, mathematical difficulties and the use of online quizzes as self-assessment tools. By integrating these findings, the paper proposes a framework for sustainable learning practices in engineering mathematics. The results highlight that affective factors, such as confidence, self-efficacy and motivation, interact significantly with students’ self-regulatory strategies and performance outcomes. Digital self-assessment tools, when purposefully designed, can promote metacognitive reflection and foster a sustainable cycle of feedback and self-improvement. The study argues that sustainable education in engineering must include pedagogical approaches that empower students with interindividual differences to manage their own learning, overcome affective barriers and develop adaptive resilience in demanding quantitative subjects. The proposed model offers practical implications for designing assessment systems that support long-term learner autonomy and well-being, aligning engineering mathematics education with the broader goals of sustainable development. In alignment with SDG 4.7 and the European Skills Agenda, which both emphasize lifelong learning, learner autonomy and the cultivation of adaptive competences for sustainable futures, the proposed framework positions self-regulation and resilience as core sustainability-oriented outcomes in engineering mathematics education....
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