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This paper presents a processed phytoplankton dataset from Lake Zerendi and other Kokshetau Upland lakes, Kazakhstan. The study aimed to develop an automated method for controlling the distribution of phytoplankton in fresh open water using a gradient descent approach with the search for a starting point for research. The paper also presents the reconstructed biomass indicators for changes in water temperature, with model calibration based on results from 5 years of surface sampling. A special feature of the proposed computer data processing is the cubic spline interpolation, which allows a higher calculation accuracy. This method reduces the sample size required, providing a comprehensive picture of the condition of the infrastructure and allowing for a more efficient response to emerging ecosystem issues. [ABSTRACT FROM AUTHOR]

[Objective] With the implementation of the “dual carbon” strategic goals, China is experiencing a rapid increase in natural gas demand. However, the occurrence of leakage accidents in pipelines carrying this flammable and explosive gas poses potential threats, including casualties, environmental pollution, and economic losses. As a result, the research on detecting leaks in natural gas pipelines becomes particularly significant. [Methods] Utilizing the Gaussian plume model and Unmanned Aerial Vehicles (UAVs) equipped with methane concentration sensors, this study employed the Markov Chain Monte Carlo (MCMC) method based on Bayesian inference to determine the positions and rates of leakage sources along natural gas pipelines. The inverse computation method of gas source intensity, relying on probability statistics, was employed to calculate leakage parameter intervals with the highest probability. To verify the effectiveness of the MCMC algorithm in identifying leakage sources in natural gas pipelines, gas leakage simulations were conducted in a scenario featuring continuous leakage accidents of overhead natural gas pipelines. [Results] The MCMC algorithm demonstrated its effectiveness in calculating the positions and rates of leakage in natural gas pipelines. However, its success rate declined due to increasing overall errors. Nonetheless, data cleaning greatly enhanced the algorithm’s ability to adapt to errors, with a success rate exceeding 90% when supported by data cleaning. In contrast, the success rates gradually declined without any data processing. By applying inverse computation of hazardous gas source intensity to leakage detection, more accurate results were obtained regarding the positions and rates of pipeline leakage. It was observed that when the initial points were distant from the actual leakage source, the algorithm’s performance diminished. Hence,a rational selection of the initial point proved beneficial for the overall operation of the algorithm. [Conclusion] The combined approach involving the MCMC algorithm and UAVs equipped with methane concentration sensors effectively enables the simultaneous identification of leakage positions and rates in natural gas pipelines. The findings of this study hold significant importance for facilitating emergency response measures to leakage accidents.

Newton's method is a popular numeric approach due to its simplicity and quadratic convergence to solve nonlinear equations that cannot be solved with exact solutions. However, the initial point chosen to activate the iteration of Newton's method may cause difficulties in slower convergence, stagnation, and divergence of the iterative process. The common advice to deal with these special cases was to choose another inner point to repeat the process again or use a graph of the nonlinear equation (function) to choose a new initial point. Based on the recent experiences in teaching preservice secondary-school mathematics teachers, this classroom note presents a simple and practical strategy to avoid many of the difficulties encountered in using Newton's method during solving nonlinear equations. Instead of plotting the graph of an equation to help choose the initial point, the practical strategy is to use the middle point of the range as the initial point to start the iterative process of Newton's method. By solving ten different nonlinear equations using Newton's method initiated from the endpoints and the middle point respectively, the results show that choosing the middle point of a defined range to initiate the iterative process for Newton's method seems a general and practical strategy to avoid the difficulties encountered in using the method to solve nonlinear equations with faster convergence in most cases.

In this study, a convex proximal point algorithm (CPPA) is considered for solving constrained non-convex problems, and new theoretical results are proposed. It is proved that every cluster point of CPPA is a stationary point, and the initial point of CPPA is key to global optimization. Several sufficient conditions for the initial point selection are provided for CPPA to find the global minimum. Motivated by these results, numerical experiments were conducted on non-convex quadratic programming problems with convex quadratic constraints. The performance of CPPAs was compared, with the initial point randomly selected or obtained through the Lagrangian dual problem. The numerical results demonstrate that the quality of the CPPA with the computed Lagrangian dual initial point is much better than that with the random initial point, in terms of the objective function value. [ABSTRACT FROM AUTHOR]

Newton's method is a popular numeric approach due to its simplicity and quadratic convergence to solve nonlinear equations that cannot be solved with exact solutions. However, the initial point chosen to activate the iteration of Newton's method may cause difficulties in slower convergence, stagnation, and divergence of the iterative process. The common advice to deal with these special cases was to choose another inner point to repeat the process again or use a graph of the nonlinear equation (function) to choose a new initial point. Based on the recent experiences in teaching preservice secondary-school mathematics teachers, this classroom note presents a simple and practical strategy to avoid many of the difficulties encountered in using Newton's method during solving nonlinear equations. Instead of plotting the graph of an equation to help choose the initial point, the practical strategy is to use the middle point of the range as the initial point to start the iterative process of Newton's method. By solving ten different nonlinear equations using Newton's method initiated from the endpoints and the middle point respectively, the results show that choosing the middle point of a defined range to initiate the iterative process for Newton's method seems a general and practical strategy to avoid the difficulties encountered in using the method to solve nonlinear equations with faster convergence in most cases. [ABSTRACT FROM AUTHOR]

In the robotic polishing system for the wheel hubs, initial point alignment is a very important procedure before the robot starts to polish. Since the surface shapes of the wheel hubs are complex, traditional contact sensors are not suitable for the initial point alignment. Therefore, this paper presents a vision-based initial point alignment control method due to the merits of non-contact and high precision of the vision sensor. The main procedures of the new proposed initial point alignment methods are as follows. Firstly, the center point of the wheel hub is computed based on the growth of sampled points (GSP) method. Secondly, the center lines of the spokes of the wheel hub are extracted based on the edges of the spokes. Based on the center point and the center lines of the spokes, the needed rotation angle of the wheel hub denoting the current and target initial points can be computed. Thirdly, an alignment controller is designed to align the current initial point with the target one. Finally, experiments are well conducted to demonstrate the effectiveness of the proposed initial point alignment control method for the wheel hubs. [ABSTRACT FROM AUTHOR]

In this paper we have introduced a new class of problems of optimal control theory with differential inclusions described by polynomial linear differential operators. Consequently, there arises a rather complicated problem with simultaneous determination of the polynomial linear differential operators with variable coefficients and a Mayer functional depending on high order derivatives. The sufficient conditions, containing both the Euler-Lagrange and Hamiltonian type inclusions and transversality conditions are derived. Formulation of the transversality conditions at the endpoints of the considered time interval plays a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions. The main idea of the proof of optimality conditions of Mayer problem for differential inclusions with polynomial linear differential operators is the use of locally-adjoint mappings. The method is demonstrated in detail as an example for the semilinear optimal control problem and the Weierstrass-Pontryagin maximum principle is obtained. Then the optimality conditions are derived for second order convex differential inclusions with convex endpoint constraints. [ABSTRACT FROM AUTHOR]

In this paper, a global peak searching algorithm is proposed for multimodal optimization problem. The proposed algorithm is built through combining gradient-based stochastic extremum seeking method with iterative approach. By increasing the initial search point, the gradient-based stochastic extremum seeking algorithm with different initial condition is iteratively operated to seek a list of the local extreme values near different initial points. Then, the global peak can be found by comparing the list of the local extreme values. The stability anlysis and working process of the global peak searching algorithm is proven. Simulation results are given to show the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

Regarding the problems that the process of optimization is sensitive to the initial point and easily trapped into local optimum, we propose an improved collaborative optimization algorithm. The proposed algorithm takes into account of the distance between the disciplinary level design point and and the system level internal design point, as well as the disciplinary level's optimal design point. Besides, it can weaken the dependence of optimization results on the relaxing factor and the initial point, and find the optimal design point using the least times of optimization iteration. Two classical examples verify the effectiveness and stability of our proposal. [ABSTRACT FROM AUTHOR]

Parameter extraction of the five-parameter single-diode model of solar cells and modules from experimental data is a challenging problem. These parameters are evaluated from a set of nonlinear equations that cannot be solved analytically. On the other hand, a numerical solution of such equations needs a suitable initial guess to converge to a solution. This paper presents a new set of approximate analytical solutions for the parameters of a five-parameter single-diode model of photovoltaic (PV) cells and modules. The proposed solutions provide a good initial point which guarantees numerical analysis convergence. The proposed technique needs only a few data from the PV current-voltage characteristics, i.e. open circuit voltageVoc, short circuit currentIscand maximum power point current and voltageIm;Vmmaking it a fast and low cost parameter determination technique. The accuracy of the presented theoretical I–V curves is verified by experimental data. [ABSTRACT FROM AUTHOR]