Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations

In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without certain time-step restrictions. The key is to estimate directly the solution bounds in the H²-norm for both the nonlinear wave equation and the corresponding fully discrete scheme, while the previous investigations rely on the temporal-spatial error splitting approach. Numerical examples are presented to confirm energy-conserving properties, unconditional convergence and optimal error estimates, respectively, of the proposed fully discrete schemes.

     

A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.     

基于模糊综合评判的大学数学考核方式改革

独立高校数学课程的开设旨在让学生掌握数学知识的基础上,提高数学应用能力.然而现行的考核方式存在重考试结果,轻学习过程等问题.从传统考核方式入手,指出其不足之处,基于模糊综合评判法建立新型评价体系和数学模型,通过试点运行验证了新的考核方式的可行性、客观性、合理性和科学性.     

Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays

Journal of Optimization Theory and Applications - This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to...     

Bejan flow visualization of free convection in a Jeffrey fluid from a semi-infinite vertical cylinder

Journal of Thermal Analysis and Calorimetry - This article studies the pattern of heat lines in free convection non-Newtonian flow from a semi-infinite vertical cylinder via Bejan’s heat...     

Global asymptotic stability for a periodic delay hematopoiesis model with impulses

In this paper, sufficient conditions for the global asymptotic stability of a broad family of periodic impulsive scalar delay differential equations are obtained. These conditions are applied to a periodic hematopoiesis model with multiple time-dependent delays and linear impulses, in order to establish criteria for the global asymptotic stability of a positive periodic solution. The present results are discussed within the context of recent literature. In conclusion, when compared with previous works, not only sharper stability criteria are obtained here, even for models without impulses, but also the usual constraints imposed on the linear impulses are relaxed.