The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of t...The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.展开更多
This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating mo...This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability generating functions of the steady state probabilities of several states of the system including the steady state queue size distribution. Further, we discuss some particular cases of the proposed queueing model. We present numerical examples in order to demonstrate the effects of server vacation and reneging on the various states of the system. The study revealed that an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, the probability of server vacation, the probability of system is under repair and the probabilities that the server provides service in three fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates.展开更多
半导电屏蔽层对绝缘层空间电荷的分布起着重要作用,绝缘层中空间电荷积累是制约高压直流(high voltage direct current,HVDC)电缆发展的关键因素之一。采用熔融接枝将氯乙酸丙烯酯(CAAE)接枝到乙烯-丙烯酸丁酯共聚物(ethylene-butyl acr...半导电屏蔽层对绝缘层空间电荷的分布起着重要作用,绝缘层中空间电荷积累是制约高压直流(high voltage direct current,HVDC)电缆发展的关键因素之一。采用熔融接枝将氯乙酸丙烯酯(CAAE)接枝到乙烯-丙烯酸丁酯共聚物(ethylene-butyl acrylate copolymer,EBA)大分子链上,制备了CAAE接枝EBA/炭黑(carbon black,CB)半导电屏蔽料,对其进行了形貌及结构表征,测试了其体积电阻率和其作电极时交联聚乙烯(crosslinked polyethylene,XLPE)绝缘层的空间电荷分布特性及击穿场强,系统研究了CAAE的含量对半导电屏蔽料电性能及XLPE绝缘层空间电荷分布特性和击穿场强的影响。结果表明,CAAE接枝EBA基半导电屏蔽料的体积电阻率随着CAAE含量的增加呈先增加后降低的趋势,CAAE接枝改性半导电屏蔽可以降低XLPE绝缘层中的电场畸变,其中CAAE含量为1.0phr时,接枝改性半导电屏蔽料的体积电阻率最低,相较于EBA/CB作电极时,XLPE中的最大电场畸变率在30、40和80℃时分别降低了43.2%、69.0%和72.4%,不同温度下XLPE的击穿场强得到了明显提高。展开更多
光学电流互感器具有测量精度高、结构简单、安全性高等特点,其关键组件光纤复合绝缘子承担着通信和电气绝缘的双重作用。然而,现有不同光纤植入型式的光纤复合绝缘子芯体存在相应材料、结构或工艺等缺陷,光纤与绝缘材料之间易产生界面隐...光学电流互感器具有测量精度高、结构简单、安全性高等特点,其关键组件光纤复合绝缘子承担着通信和电气绝缘的双重作用。然而,现有不同光纤植入型式的光纤复合绝缘子芯体存在相应材料、结构或工艺等缺陷,光纤与绝缘材料之间易产生界面隐患,威胁电气设备安全运行。该文提出采用低密度环氧基复合泡沫作为光纤芯体基体,植入聚乙烯型低烟无卤(low smoke zero halogen polyethylene,LSZHPE)、聚乙烯-四氟乙烯(ethylene-tetrafluoroethylene copolymer,ETFE)及裸纤3种光纤,对比分析不同类型光纤芯体物理、界面、电气等关键性能。结果表明:LSZHPE光纤体系芯体具有较优的综合性能,150 h水扩散泄漏电流低于100μA,界面击穿强度达到13.34 k V/mm,同时光纤植入后光导通损耗满足实际应用要求;ETFE光纤及裸纤体系芯体电气性能良好,但受限于材料自身特性,界面剪切强度较低,界面可靠性相对较差。该研究为光纤复合绝缘子材料选型、界面评估及结构优化提供了新思路。展开更多
文摘The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.
文摘This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability generating functions of the steady state probabilities of several states of the system including the steady state queue size distribution. Further, we discuss some particular cases of the proposed queueing model. We present numerical examples in order to demonstrate the effects of server vacation and reneging on the various states of the system. The study revealed that an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, the probability of server vacation, the probability of system is under repair and the probabilities that the server provides service in three fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates.
文摘半导电屏蔽层对绝缘层空间电荷的分布起着重要作用,绝缘层中空间电荷积累是制约高压直流(high voltage direct current,HVDC)电缆发展的关键因素之一。采用熔融接枝将氯乙酸丙烯酯(CAAE)接枝到乙烯-丙烯酸丁酯共聚物(ethylene-butyl acrylate copolymer,EBA)大分子链上,制备了CAAE接枝EBA/炭黑(carbon black,CB)半导电屏蔽料,对其进行了形貌及结构表征,测试了其体积电阻率和其作电极时交联聚乙烯(crosslinked polyethylene,XLPE)绝缘层的空间电荷分布特性及击穿场强,系统研究了CAAE的含量对半导电屏蔽料电性能及XLPE绝缘层空间电荷分布特性和击穿场强的影响。结果表明,CAAE接枝EBA基半导电屏蔽料的体积电阻率随着CAAE含量的增加呈先增加后降低的趋势,CAAE接枝改性半导电屏蔽可以降低XLPE绝缘层中的电场畸变,其中CAAE含量为1.0phr时,接枝改性半导电屏蔽料的体积电阻率最低,相较于EBA/CB作电极时,XLPE中的最大电场畸变率在30、40和80℃时分别降低了43.2%、69.0%和72.4%,不同温度下XLPE的击穿场强得到了明显提高。
文摘光学电流互感器具有测量精度高、结构简单、安全性高等特点,其关键组件光纤复合绝缘子承担着通信和电气绝缘的双重作用。然而,现有不同光纤植入型式的光纤复合绝缘子芯体存在相应材料、结构或工艺等缺陷,光纤与绝缘材料之间易产生界面隐患,威胁电气设备安全运行。该文提出采用低密度环氧基复合泡沫作为光纤芯体基体,植入聚乙烯型低烟无卤(low smoke zero halogen polyethylene,LSZHPE)、聚乙烯-四氟乙烯(ethylene-tetrafluoroethylene copolymer,ETFE)及裸纤3种光纤,对比分析不同类型光纤芯体物理、界面、电气等关键性能。结果表明:LSZHPE光纤体系芯体具有较优的综合性能,150 h水扩散泄漏电流低于100μA,界面击穿强度达到13.34 k V/mm,同时光纤植入后光导通损耗满足实际应用要求;ETFE光纤及裸纤体系芯体电气性能良好,但受限于材料自身特性,界面剪切强度较低,界面可靠性相对较差。该研究为光纤复合绝缘子材料选型、界面评估及结构优化提供了新思路。
