Approximate solution for a variable-coefficient semilinear heat equation with nonlocal boundary conditions

This paper develops an iterative algorithm for the solution to a variable-coefficient semilinear heat equation with nonlocal boundary conditions in the reproducing space. It is proved that the approximate sequence u _n (x, t) converges to the exact solution u(x, t). Moreover, the partial derivatives of u _n (x, t) are also convergent to the partial derivatives of u(x, t). And the approximate sequence u _n (x, t) is the best approximation under a complete normal orthogonal system.     

A globally convergent trust region multidimensional filter SQP algorithm for nonlinear programming

We propose a trust region multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 15 (2005), pp. 17–38] is extended to solve constrained optimization problems. The constraints are partitioned into p parts. The entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but also the individual behaviour of each part of the constraints is considered. The filter's entries and the acceptance criteria are different from other filter-related algorithms in the literature. It should be noted that the undesirable link between the objective function and the constraint violation function in the filter acceptance criteria disappears. Our algorithm is also combined with the non-monotone technique for accepting a trial step, which leads to a more flexible acceptance criteria. Under mild conditions, global convergence is proved. Numerical results show the robustness and efficiency of our algorithm.     

带强迫项的KdV方程的非线性自伴随性和守恒律

应用非线性自伴随性的概念和伊布拉基莫夫的一般守恒律定理，研究了带强迫的KdV方程的非线性自伴随性和守恒律。首先讨论了自伴随性，结果表明这个方程具有非线性自伴随性，同时得到了这个方程的形式拉格朗日量。在对这个方程进行李对称分析之后，根据李对称的不同得到了这个方程的一些非平凡守恒律。     

Nonlinear optical responses of erbium-doped YAG ceramics

By performing the Z-scan measurements with ultrafast femtosecond laser centered at 800 nm wavelength, we can unambiguously distinguish the real and imaginary part of the third-order optical nonlinearity of the erbium-doped YAG ceramics. The reverse saturable absorption of the erbium-doped YAG ceramics has been observed experimentally, and the nonlinear refractive index of the ceramics is estimated to be about 10⁻²¹ m²/W. The experimental results may provide design guidelines for the high power laser design and its applications.     

A note on the Chen correlation of saturated flow boiling heat transfer

The Chen (Ind. Eng. Chem. Process Des. Dev., 1966, 5(3): 322–329) correlation of saturated flow boiling heat transfer is one of the most influential flow boiling heat transfer correlations. It adopted the additive concept and incorporated the Reynolds number factor F and the suppression factor S. Chen presented F and S as the best-fit curves without any parametric equation. However, the parametric equations of F and S were widely used in citing the Chen work, among which some were not accurate, and some had typos in the original sources and then used by others. The objective of this paper is to point out the incorrect and inaccurate equations in the literature. For this purpose, the existing expressions of F and S in the available literature are presented and compared with the Chen best-fit curves. The work provides a reference for the correct use of the Chen correlation.     

Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

In this paper, an adaptive dynamic surface control approach is developed for a class of multi‐input multi‐output nonlinear systems with unknown nonlinearities, bounded time‐varying state delays, and in the presence of time‐varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time‐varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed‐loop signals is guaranteed, and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

B-spline method for solving Bratu's problem

In this paper, we propose a B-spline method for solving the one-dimensional Bratu's problem. The numerical approximations to the exact solution are computed and then compared with other existing methods. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where two solutions occur.     

Partial constraint satisfaction approaches for optimal operation of a hydropower system

Optimal operation models for a hydropower system using partial constraint satisfaction (PCS) approaches are proposed and developed in this study. The models use mixed integer nonlinear programming (MINLP) formulations with binary variables. The models also integrate a turbine unit commitment formulation along with water quality constraints used for evaluation of reservoir downstream water quality impairment. New PCS-based models for hydropower optimization formulations are developed using binary and continuous evaluator functions to maximize the constraint satisfaction. The models are applied to a real-life hydropower reservoir system in Brazil. Genetic Algorithms (GAs) are used to solve the optimization formulations. Decision maker's preferences towards power production targets and water quality improvements are incorporated using partial satisfaction constraints to obtain compromise operating rules for a multi-objective reservoir operation problem dominated by conflicting goals of energy production, water quality and consumptive water uses.     

Modeling of Nonlinear Magnetizing Characteristics of Pole Transformer for Analyzing Islanding Prevention of Photovoltaic System

With increasing penetration of distributed generators such as photovoltaic (PV) systems in distribution systems, it is very important to quickly detect islanding caused by power system faults in order to assure electrical safety. We have developed a nonlinear magnetizing characteristics model of pole transformers for use in analyzing islanding prevention in PV systems. Basic experiments on the islanding detection were performed for verification of the proposed model. Analytical results obtained by the proposed model agreed well with experimental results.     

Necessary and sufficient conditions for the existence of a positive definite solution of a nonlinear matrix equation

Some necessary and sufficient conditions for the existence of a positive definite solution of the nonlinear matrix equation X+A*X ^?α A=Q (0<α≤1) are given. By the way an iterative method is presented. Furthermore, the convergence and error estimation of the iterative algorithm are derived. The illustrative numerical examples due to Peng are worked out.