convergence

摘要： Dear editor,Primal-dual dynamics(PDD)and its variants are prominent first-order continuous-time algorithms to determine the primal and dual solutions of a constrained optimization problem(COP).Due to the simple structure,they have received widespread attention in various fields,such as distributed optimization[1],power systems[2],and wireless communication[3].In view of their wide applications,there are numerous theoretic studies on the convergence properties of PDD and its variants,including the exponential stability analysis[4]-[9].

摘要： In Hashim and Harfash(Appl.Math.Comput.2021),using a finite element method,the attraction-repulsion chemotaxis model(P)in space is discretised;finite differences were used to do the same in time.Furthermore,the existence of a global weak solution to the system(PΔt M)was demonstrated by means of analysis of the convergence of the fully discrete approximate problem(P h,Δt M,).Moreover,the functions{U,Z,V}were proved to represent a global weak solution to the system(PΔt M)by means of a passage to the limit,h→0 of the approximate system.This paper’s purpose is to demonstrate that the solutions can be bounded,independent of M.The analysis contained in this paper illustrates the idea of the existence of weak solutions to the model(P),that requires passing to the limits,Δt→0+and M→∞.The time stepΔt is subsequently linked to the cutoff parameter M>1 by positing a demand thatΔt=o(M−1),as M→∞,with the result that the cutoff parameter becomes the only parameter in the problem(PΔt M).The solutions can be bounded,independ-ent of M,with the use of special energy estimates,as demonstrated herein.Then,these M-independent bounds on the relative entropy are employed with the purpose of deriving M-independent bounds on the time-derivatives.Additionally,compactness arguments were utilised to explore the convergence of the finite element approximate problem.The conclu-sion was that a weak solution for(P)existed.Finally,we introduced the error estimate and the implicit scheme was used to perform simulations in one and two space dimensions.

摘要： In this paper,a finite element scheme for the attraction-repulsion chemotaxis model is analyzed.We introduce a regularized problem of the truncated system.Then we obtain some a priori estimates of the regularized functions,independent of the regularization parameter,via deriving a well-defined entropy inequality of the regularized problem.Also,we propose a practical fully discrete finite element approximation of the regularized problem.Next,we use a fixed point theorem to show the existence of the approximate solutions.Moreover,a discrete entropy inequality and some stability bounds on the solutions of regularized problem are derived.In addition,the uniqueness of the fully discrete approximations is preformed.Finally,we discuss the convergence to the fully discrete problem.

摘要： This research proposes a synergistic meta-heuristic algorithm for solving the extreme operational complications of combined heat and power economic dispatch problem towards the advantageous economic outcomes on the cost of generation. The combined heat and power (CHP) is a system that provides electricity and thermal energy concurrently. For its extraordinary efficiency and significant emission reduction, it is considered a promising energy prospect. The broad application of combined heat and power units requires the joint dispatch of power and heating systems, in which the modelling of combined heat and power units plays a vital role. The present research employs the genetic optimization algorithm to evaluate the cost function, heat and power dispatch values encountered in a system with simple cycle cogeneration unit and quadratic cost function. The system was first modeled to determine the various parameters of combined heat and power units towards solving its economic dispatch problem directly. In order for modelling to be done, a general structure of combined heat and power must be defined. The test system considered consists of four units: two conventional power units, one combined heat and power unit and one heat-only unit. The algorithm was applied to test system while taking into account the power and heat units, bounds of the units and feasible operation region of cogeneration unit. Output decision variables of 4-unit test systems plus cost function from Genetic Algorithm (GA), was determined using appropriate codes. The proposed algorithm produced a well spread and diverse optimal solution and also converged reasonably to the actual optimal solution in 51 iterations. The result obtained compared favourably with that obtained with the direct solution algorithm discussed in a previous paper. We conclude that the genetic algorithm is quite efficient in dealing with non-convex and constrained combined heat and power economic dispatch problem.

摘要： In this manuscript,we analyze the solution for class of linear and nonlinear Caputo fractional Volterra Fredholm integro-differential equations with nonlinear time varying delay.Also,we demonstrate the stability analysis for these equations.Our paper provides a convergence of semi-analytical approximate method for these equations.It would be desirable to point out approximate results.

摘要： In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by combining this method with it, we obtain a new method. It can be said that this method, due to not using the function derivative, would be a good method for solving the nonlinear equation compared to Newton’s method. Finally, we will see that Newton’s method and Steffensen’s hybrid method both have a two-order convergence.

摘要： Low-complexity detectors play an essential role in massive multiple-input multiple-output (MIMO) transmissions. In this work, we discuss the perspectives of utilizing approximate message passing (AMP) algorithm to the detection of massive MIMO transmission. To this end, we need to efficiently reduce the divergence occurrence in AMP iterations and bridge the performance gap that AMP has from the optimum detector while making use of its advantage of low computational load. Our solution is to build a neural network to learn and optimize AMP detection with four groups of specifically designed learnable coefficients such that divergence rate and detection mean squared error (MSE) can be significantly reduced. Moreover, the proposed deep learning-based AMP has a much faster converging rate, and thus a much lower computational complexity than conventional AMP, providing an alternative solution for the massive MIMO detection. Extensive simulation experiments are provided to validate the advantages of the proposed deep learning-based AMP.

摘要： Dear editor,This letter identifies two weaknesses of state-of-the-art k-winnerstake-all(k-WTA)models based on recurrent neural networks(RNNs)when considering time-dependent inputs,i.e.,the lagging error and the infeasibility in finite-time convergence based on the Lipschitz continuity.

摘要： Combining with the present situation of chemistry-related academic journals,the author of this paper has summarized and analyzed the current characteristics and development trends of academic periodicals in daily chemical field.Moreover,the author has proposed the coping strategies regarding the development of future chemical academic journals,focusing mainly on the system and concept innovation concerning media convergence,fusion path optimization,refinement of user needs experience as well as the improvement of editorial staff.

摘要： The theory of evolution was advanced by Darwin in 1859, prior to Mendel’s experiments demonstrating the particulate nature of inheritance. The modern synthesis was formulated in the early 1940s, well before the concept of coded information was understood. This paper outlines four mathematical challenges to the modern synthesis, which are based on current understanding of the proposed mechanisms of evolutionary change within the constraints of experimental molecular biology.

摘要： Considering the whole impact of mechanical and rnelectrical system nonlinearities, the direct feedback rnlinearization (DFL) rncontrol strategy was used in the AC all-electrical rntank gun control system to achieve a completely rndynamic decoupling model. On the rnbasis of DEF, in order to reduce the effect of rnchanges in the system parameters and load torque, an rnadaptive wavelet neural network rncompensator to compensate for DEF error is proposed, rnwhich can reduce DEF control law reliance on the tank rngun system model,rnand further enhance the speed tracking performance, rnrobustness and adaptive capacity of AC tank gun rncontrol system. Computer rnsimulations show that the tracking accuracy is much rnbetter and the control system has strong adaptability rnand robustness.

摘要： Considering the whole impact of mechanical and rnelectrical system nonlinearities, the direct feedback rnlinearization (DFL) rncontrol strategy was used in the AC all-electrical rntank gun control system to achieve a completely rndynamic decoupling model. On the rnbasis of DEF, in order to reduce the effect of rnchanges in the system parameters and load torque, an rnadaptive wavelet neural network rncompensator to compensate for DEF error is proposed, rnwhich can reduce DEF control law reliance on the tank rngun system model,rnand further enhance the speed tracking performance, rnrobustness and adaptive capacity of AC tank gun rncontrol system. Computer rnsimulations show that the tracking accuracy is much rnbetter and the control system has strong adaptability rnand robustness.

摘要： Considering the whole impact of mechanical and rnelectrical system nonlinearities, the direct feedback rnlinearization (DFL) rncontrol strategy was used in the AC all-electrical rntank gun control system to achieve a completely rndynamic decoupling model. On the rnbasis of DEF, in order to reduce the effect of rnchanges in the system parameters and load torque, an rnadaptive wavelet neural network rncompensator to compensate for DEF error is proposed, rnwhich can reduce DEF control law reliance on the tank rngun system model,rnand further enhance the speed tracking performance, rnrobustness and adaptive capacity of AC tank gun rncontrol system. Computer rnsimulations show that the tracking accuracy is much rnbetter and the control system has strong adaptability rnand robustness.

摘要： Considering the whole impact of mechanical and rnelectrical system nonlinearities, the direct feedback rnlinearization (DFL) rncontrol strategy was used in the AC all-electrical rntank gun control system to achieve a completely rndynamic decoupling model. On the rnbasis of DEF, in order to reduce the effect of rnchanges in the system parameters and load torque, an rnadaptive wavelet neural network rncompensator to compensate for DEF error is proposed, rnwhich can reduce DEF control law reliance on the tank rngun system model,rnand further enhance the speed tracking performance, rnrobustness and adaptive capacity of AC tank gun rncontrol system. Computer rnsimulations show that the tracking accuracy is much rnbetter and the control system has strong adaptability rnand robustness.

摘要： Considering the whole impact of mechanical and rnelectrical system nonlinearities, the direct feedback rnlinearization (DFL) rncontrol strategy was used in the AC all-electrical rntank gun control system to achieve a completely rndynamic decoupling model. On the rnbasis of DEF, in order to reduce the effect of rnchanges in the system parameters and load torque, an rnadaptive wavelet neural network rncompensator to compensate for DEF error is proposed, rnwhich can reduce DEF control law reliance on the tank rngun system model,rnand further enhance the speed tracking performance, rnrobustness and adaptive capacity of AC tank gun rncontrol system. Computer rnsimulations show that the tracking accuracy is much rnbetter and the control system has strong adaptability rnand robustness.

摘要： Considering the whole impact of mechanical and rnelectrical system nonlinearities, the direct feedback rnlinearization (DFL) rncontrol strategy was used in the AC all-electrical rntank gun control system to achieve a completely rndynamic decoupling model. On the rnbasis of DEF, in order to reduce the effect of rnchanges in the system parameters and load torque, an rnadaptive wavelet neural network rncompensator to compensate for DEF error is proposed, rnwhich can reduce DEF control law reliance on the tank rngun system model,rnand further enhance the speed tracking performance, rnrobustness and adaptive capacity of AC tank gun rncontrol system. Computer rnsimulations show that the tracking accuracy is much rnbetter and the control system has strong adaptability rnand robustness.