Improved third‐order weighted essentially nonoscillatory scheme

A new third‐order WENO scheme is proposed to achieve the desired order of convergence at the critical points for scalar hyperbolic equations. A new reference smoothness indicator is introduced, which satisfies the sufficient condition on the weights for the third‐order convergence. Following the truncation error analysis, we have shown that the proposed scheme achieves the desired order accurate for smooth solutions with arbitrary number of vanishing derivatives if the parameter ε satisfies certain conditions. We have made a comparative study of the proposed scheme with the existing schemes such as WENO‐JS, WENO‐Z, and WENO‐N3 through different numerical examples. The result shows that the proposed scheme (WENO‐MN3) achieves better performance than these schemes.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Strong cliques in vertex-transitive graphs

A clique (resp, independent set) in a graph is strong if it intersects every maximal independent set (resp, every maximal clique). A graph is clique intersect stable set (CIS) if all of its maximal cliques are strong and localizable if it admits a partition of its vertex set into strong cliques. In this paper we prove that a clique $C$ in a vertex-transitive graph $\mathrm{\Gamma }$ is strong if and only if $\text{◂=▸}\text{◂⋅▸}\mid C\mid \mid I\mid =\mid V\left(\mathrm{\Gamma }\right)\mid$ for every maximal independent set $I$ of $\mathrm{\Gamma }$. On the basis of this result we prove that a vertex-transitive graph is CIS if and only if it admits a strong clique and a strong independent set. We classify all vertex-transitive graphs of valency at most 4 admitting a strong clique, and give a partial characterization of 5-valent vertex-transitive graphs admitting a strong clique. Our results imply that every vertex-transitive graph of valency at most 5 that admits a strong clique is localizable. We answer an open question by providing an example of a vertex-transitive CIS graph which is not localizable.     

强点火作用下C3HF7对甲烷-空气爆炸的抑制

为解决瓦斯输送过程中的爆炸安全问题,探索寻找绿色环保且阻火性能优越的新型抑爆剂,开展了当量比下甲烷-空气预混气体爆炸传播过程中的七氟丙烷抑爆效果研究。实验采用长径比L/D=108的水平管道爆炸特性测试系统,研究了在强点火作用下不同体积分数的七氟丙烷对9.5%甲烷-空气预混气体最大爆炸压力、最大压力上升速率和火焰传播速度的影响。实验结果显示:将2.5 m长的管段作为七氟丙烷抑爆区时,七氟丙烷阻断9.5%甲烷-空气预混气体爆炸火焰传播的最小体积分数为5%;当七氟丙烷的体积分数为1%~4%时,不仅无法阻断爆炸火焰的传播,而且与对照组相比,会使火焰传播速度加快;当七氟丙烷的体积分数为1%~6%时,爆炸源及管道末端处的爆炸压力峰值随着七氟丙烷体积分数的增加而逐渐减小;当七氟丙烷的体积分数为3%时,抑爆区处的爆炸压力峰值与对照组相比增幅为10.9%。     

Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappin...     

Fixed points of multivalued quasi-nonexpansive mappings using a faster iterative process

In this article, we prove some strong and weak convergence theorems for quasi-nonexpansive multivalued mappings in Banach spaces. The iterative process used is independent of Ishikawa iterative process and converges faster. Some examples are provided to validate our results. Our results extend and unify some results in the contemporary literature.     

On the Relative Gain Array (RGA) with singular and rectangular matrices

This paper identifies a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, it is shown that the conventional use of the Moore–Penrose pseudoinverse is inappropriate because it fails to preserve critical properties that can be assumed in the nonsingular case. It is then shown that such properties can be rigorously preserved using an alternative generalized matrix inverse.     

On weak–strong uniqueness for the compressible Navier–Stokes system with non-monotone pressure law

We show the weak–strong uniqueness property for the compressible Navier–Stokes system with general non-monotone pressure law. A weak solution coincides with the strong solution emanating from the same initial data as long as the latter solution exists.     

Strong solutions to 3D compressible magnetohydrodynamic equations with Navier‐slip condition

We consider the short time strong solutions to the compressible magnetohydrodynamic equations with initial vacuum, in which the velocity field satisfies the Navier‐slip condition. The Navier‐slip condition differs in many aspects from no‐slip conditions, and it has attracted considerable attention in nanoscale and microscale flows research. Inspired by Kato and Lax's idea, we use the Lax–Milgram theorem and contraction mapping argument to prove local existence. Moreover, under the Navier‐slip condition, we establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of L^∞ norm of the deformation tensor D(u). Copyright © 2015 John Wiley & Sons, Ltd.