The convexity and logarithmic convexity of the arithmetic sequence are studied. And then by using methods on the theory of majorization, some arithmetic sequence inequalities are proved.

As we all know，arithmetic -geometric mean inequalities are the most basic and important inequalities． To seek different method to prove them has been one of the study focuses and they have been proven by more than a hundred ways． By using methods based on the theory of majorization and combined with the analysis techniques，the weighted arithmetic-geometric means inequality is proved in a new way．

In this paper, by operating the shifting and addition in parallel, an error-compensated adder-tree (ECAT) is proposed to deal with the truncation errors and to achieve low-error and high-throughput discrete cosine transform (DCT) design. Instead of the 12 bits used in previous works, 9-bit distributed arithmetic-precision is chosen for this work so as to meet peak-signal-to-noise-ratio (PSNR) requirements. Thus, an area-efficient DCT core is implemented to achieve 1 Gpels/s throughput rate with gate counts of 22.2 K for the PSNR requirements outlined in the previous works.

为有效地获取滚珠丝杠副精度寿命特征,利用滚珠丝杠副磨损特征建立加速退化模型,并且根据设计的试验装置和试验过程的摩擦力矩值变化情况,采用参数估计方法进行退化数据的统计分析,获得不同应力水平下的滚珠丝杠副加速退化参数模型.同时,根据不同应力条件下实测的滚珠丝杠副摩擦力矩退化数据,计算出滚珠丝杠副定位反向变动量,为滚珠丝杠副的定位精度退化提供一种新的评价方法.建立的滚珠丝杠副加速退化模型针对其磨损进程极为缓慢的特性,利用该退化方法能较准确地推算出滚珠丝杠副精度寿命,能节约滚珠丝杠副试验费用、试验时间和指导滚珠丝杠副的设计.