Journal of Experiential Education

<p>Let $ \left(u_n\right)_{n\geq0} $ be the special Lucas $ u $-sequence defined by</p><p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{n+2} = Au_{n+1}-Bu_n,\quad u_0 = 0,\, u_1 = 1, $\end{document} </tex-math></disp-formula></p><p>where $ n\geq0 $, $ B = \pm1 $, and $ A $ is an integer such that $ A^2-4B > 0 $. Let</p><p><disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ a_k = \frac{1}{u_{mk}^s},\,\frac{1}{u_{mk}+u_{mk+l}},\,\frac{1}{\sum\nolimits_{i = 0}^l u_{mk+i}},\,\frac{1}{u_{mk}u_{mk+2l}},\,\frac{1}{u_{mk}u_{mk+2l-1}},\,\frac{1}{u_{mk}+C}, $\end{document} </tex-math></disp-formula></p><p>where $ m, \, l $ are positive integers, $ s = 1, 2, 3, 4 $, and $ C $ is any constant. The aim of this paper is to find a form $ g_n $ such that</p><p><disp-formula> <label/> <tex-math id="FE3"> \begin{document}$ \underset{n\to\infty}{\lim}\left(\left(\sum\limits_{k = n}^\infty a_k\right)^{-1}-g_n\right) = 0. $\end{document} </tex-math></disp-formula></p><p>For example, we show that</p><p><disp-formula> <label/> <tex-math id="FE4"> \begin{document}$ \underset{n\to\infty}{\lim}\left(\left( \sum\limits_{k = n}^\infty \frac{1}{u_{mk}}\right)^{-1}-\left(u_{mn}-u_{m(n-1)}\right)\right) = 0. $\end{document} </tex-math></disp-formula></p>

<p>Considering the influence of population heterogeneity, media coverage and spatial diffusion on disease transmission, this paper investigated an acquired immunodeficiency syndrome (AIDS) reaction-diffusion model with nonlinear incidence rates and media coverage. First, we discussed the positivity and boundedness of system solutions. Then, the basic reproduction number $ \mathcal{R}_0 $ was calculated, and the disease-free equilibrium (DFE), denoted as $ E^0 $, was locally and globally asymptotically stable when $ \mathcal{R}_0 < 1 $. Further, there existed a unique endemic equilibrium (EE), denoted as $ E^* $, which was locally and globally asymptotically stable when $ \mathcal{R}_0 > 1 $ and certain additional conditions were satisfied. In addition, we showed that the disease was uniformly persistent. Finally, the visualization results of the numerical simulations illustrated that: The media coverage was shown to mitigate the AIDS transmission burden in the population by lowering the infection peak and the time required to reach it; a higher awareness conversion rate can effectively reduce the basic reproduction number $ \mathcal{R}_0 $ to curb the spread of AIDS.</p>

<p>An improved metaheuristic algorithm called the Crossover strategy integrated Secretary Bird Optimization Algorithm (CSBOA) is proposed in this work for solving real optimization problems. This improved algorithm integrated logistic-tent chaotic mapping initialization, an improved differential mutation operator, and crossover strategies with the Secretary Bird Optimization Algorithm (SBOA) for a better quality solution and faster convergence. To evaluate the performance of CSBOA, two sets of a standard benchmark set, CEC2017 and CEC2022, were applied first. The Wilcoxon rank sum test and Friedman test were also used to statistically compare the proposed CSBOA algorithm with seven common metaheuristics. The comparisons demonstrated that CSBOA is more competitive than other metaheuristic algorithms on most benchmark functions. Additionally, the performance of CSBOA was validated for two challenging engineering design case studies. Comparative results showed that CSBOA provides more accurate solutions than the SBOA and the other seven algorithms, suggesting viability in dealing with real global optimization problems.</p>

<p>Energy consumption accounting and prediction in the medium and thick plate rolling process are crucial for controlling costs, improving production efficiency, optimizing equipment management, and enhancing the market competitiveness of enterprises. Starting from the perspective of integrating process mechanism and industrial big data, we overcame the difficulties brought by complex and highly nonlinear coupling of process variables, proposed a rolling power consumption accounting algorithm based on time slicing method, and gave a calculation method for the additional power consumption of the main motor for rough rolling and finishing rolling (auxiliary system power consumption, power loss, main motor power consumption deviation); with the help of SIMS model, forward recursion, and reverse recursion pass rolling force estimation strategies are proposed, and the rated power consumption of the main motor was predicted. Furthermore, a random forest regression model of additional power consumption based on data was established, and then a prediction algorithm for the comprehensive power consumption of billet rolling was given. Experiments showed the effectiveness of the proposed method.</p>

<p>We study here the special decay properties of real solutions to the initial value problem associated with the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation. More precisely, we prove the properties of exponential decay of order $ 3/2 $ above the plane $ x+y+z = 0 $ as time evolves. This property is related with the persistence properties of the solution flow in weighted Sobolev spaces and sharp unique continuation properties of solutions to this problem.</p>

<p>We have presented a maximum principle preserving the unconditionally stable scheme for the Allen–Cahn (AC) equation with a high-order polynomial potential. The proposed method ensures the preservation of the maximum principle, a critical characteristic for accurately modeling phase transitions and maintaining physical consistency in simulations. The proposed method uses an operator splitting technique, a numerical approach that decomposes a complex problem into simpler subproblems, solved sequentially, to improve computational efficiency and stability. The operator splitting method applied to the AC equation yields one nonlinear equation and several linear equations. To solve the nonlinear equation, we applied the frozen coefficient method, which approximates variable coefficients in differential equations by treating them as constants within small regions, simplifies the problem, and enables more efficient numerical solutions. For several linear equations, which are diffusion equations, we applied a fully implicit finite difference scheme to obtain unconditional stability. By using these methods, we achieved unconditional stability for the AC equation. To validate the superior performance of the developed algorithm, we performed computational tests. Computational experiments demonstrated its unconditional stability, particularly in handling high-order polynomial potentials. Furthermore, we highlighted a distinctive feature of the AC equation in modeling phase separation under noisy data conditions.</p>

<p>An improved metaheuristic algorithm called the Crossover strategy integrated Secretary Bird Optimization Algorithm (CSBOA) is proposed in this work for solving real optimization problems. This improved algorithm integrated logistic-tent chaotic mapping initialization, an improved differential mutation operator, and crossover strategies with the Secretary Bird Optimization Algorithm (SBOA) for a better quality solution and faster convergence. To evaluate the performance of CSBOA, two sets of a standard benchmark set, CEC2017 and CEC2022, were applied first. The Wilcoxon rank sum test and Friedman test were also used to statistically compare the proposed CSBOA algorithm with seven common metaheuristics. The comparisons demonstrated that CSBOA is more competitive than other metaheuristic algorithms on most benchmark functions. Additionally, the performance of CSBOA was validated for two challenging engineering design case studies. Comparative results showed that CSBOA provides more accurate solutions than the SBOA and the other seven algorithms, suggesting viability in dealing with real global optimization problems.</p>

<p>Let $ \left(u_n\right)_{n\geq0} $ be the special Lucas $ u $-sequence defined by</p><p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{n+2} = Au_{n+1}-Bu_n,\quad u_0 = 0,\, u_1 = 1, $\end{document} </tex-math></disp-formula></p><p>where $ n\geq0 $, $ B = \pm1 $, and $ A $ is an integer such that $ A^2-4B > 0 $. Let</p><p><disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ a_k = \frac{1}{u_{mk}^s},\,\frac{1}{u_{mk}+u_{mk+l}},\,\frac{1}{\sum\nolimits_{i = 0}^l u_{mk+i}},\,\frac{1}{u_{mk}u_{mk+2l}},\,\frac{1}{u_{mk}u_{mk+2l-1}},\,\frac{1}{u_{mk}+C}, $\end{document} </tex-math></disp-formula></p><p>where $ m, \, l $ are positive integers, $ s = 1, 2, 3, 4 $, and $ C $ is any constant. The aim of this paper is to find a form $ g_n $ such that</p><p><disp-formula> <label/> <tex-math id="FE3"> \begin{document}$ \underset{n\to\infty}{\lim}\left(\left(\sum\limits_{k = n}^\infty a_k\right)^{-1}-g_n\right) = 0. $\end{document} </tex-math></disp-formula></p><p>For example, we show that</p><p><disp-formula> <label/> <tex-math id="FE4"> \begin{document}$ \underset{n\to\infty}{\lim}\left(\left( \sum\limits_{k = n}^\infty \frac{1}{u_{mk}}\right)^{-1}-\left(u_{mn}-u_{m(n-1)}\right)\right) = 0. $\end{document} </tex-math></disp-formula></p>

<p>In this paper, I define and classify the algebraic Schouten solitons associated with the Bott connection on three-dimensional Lorentzian Lie groups with three different distributions.</p>

<p>Accurate interval prediction of wind speed plays a vital role in ensuring the efficiency and stability of wind power generation. Due to insufficient traditional wind speed interval prediction methods for mining nonlinear features, in this paper, a novel interval prediction method was proposed by combining improved wavelet threshold and deep learning (BiTCN-BiGRU) with the nutcracker optimization algorithm (NOA). First, NOA was used to optimize the wavelet transform (WT) and BiTCN-BiGRU. Second, we applied NOA-WT to smooth the wind speed data. Then, to capture nonlinear features of time series, phase space reconstruction (PSR) was utilized to identify chaotic characteristics of the processed data. Finally, the NOA-BiTCN-BiGRU model was built to perform wind speed interval prediction. Under the same hyperparameters and network structure settings, a comparison with other deep learning methods showed that the prediction interval coverage probability (PICP) and prediction interval mean width (PIMW) of NOA-WT-BiTCN-BiGRU model achieves the best balance, with good prediction accuracy and generalization performance. This research can provide reference and guidance for nonlinear time-series interval prediction in the real world.</p>

<p>In this work, an energy-preserving scheme is proposed for the nonlinear Dirac equation by combining the exponential time differencing method with the scalar auxiliary variable (SAV) approach. First, the original equations can be transformed into the equivalent systems by utilizing the SAV technique. Then the exponential time integrator method is applied for discretizing the temporal derivative, and the standard central difference scheme is used for approximating the spatial derivative for the equivalent one. Finally, the reformulated systems, the semi-discrete spatial scheme, and the fully-discrete, linearly implicit exponential scheme are proven to be energy conserving. The numerical experiments confirm the theoretical results.</p>

<p>In this paper, we focused on the Caputo-Hadamard fractional reaction sub-diffusion equations. By using the nonuniform L1 scheme and nonuniform Alikhanov scheme in the temporal domain, we formulated two efficient numerical schemes, where the second order difference method was used in the spatial dimension. Furthermore, we derived the stability and convergence of these proposed schemes. Remarkably, both derived numerical methods exhibited $ \alpha $-robustness, that is, it remained valid when $ \alpha\rightarrow 1^- $. Numerical experiments were given to demonstrate the theoretical statements.</p>

<p>Energy consumption accounting and prediction in the medium and thick plate rolling process are crucial for controlling costs, improving production efficiency, optimizing equipment management, and enhancing the market competitiveness of enterprises. Starting from the perspective of integrating process mechanism and industrial big data, we overcame the difficulties brought by complex and highly nonlinear coupling of process variables, proposed a rolling power consumption accounting algorithm based on time slicing method, and gave a calculation method for the additional power consumption of the main motor for rough rolling and finishing rolling (auxiliary system power consumption, power loss, main motor power consumption deviation); with the help of SIMS model, forward recursion, and reverse recursion pass rolling force estimation strategies are proposed, and the rated power consumption of the main motor was predicted. Furthermore, a random forest regression model of additional power consumption based on data was established, and then a prediction algorithm for the comprehensive power consumption of billet rolling was given. Experiments showed the effectiveness of the proposed method.</p>

<p>Using an optimal control framework, the optimization of production and maintenance processes is investigated in this paper. We focused on analyzing system behavior, managing costs, and controlling quality. Differential equations are utilized to model the relationship between inventory level, production, and maintenance strategies. A cost function is built combining different cost elements, and the optimal production and maintenance rates were obtained. A sensitivity analysis is performed to assess the impact of different parameters on the total cost and on the optimal solution. The key findings demonstrated that higher initial inventory levels significantly decreased long-term costs and improved production efficiency. The optimal preventive maintenance strategy emphasized the importance of early investments in quality and maintenance, leading to sustained operational stability.</p>

<p>Using the complex method, Guoqiang Dang and Qiyou Liu [Guoqiang Dang, Qiyou Liu, Electron. Res. Arch., 31 (2023), 1303–1322] have found some exact solutions of the conformable Huxley equation. In this comment, we first demonstrate that the elliptic function solutions and rational function solutions do not satisfy the complex conformable Huxley equation. Finally, all exact solutions of the conformable Huxley equation are given by us.</p>