VIBRATION CONTROL AND EXPERIMENT OF THREE-RING REDUCER

The three ring reducer is studied both in theory and experiment. In order to improve the dynamic characteristics and reduce the vibration and noise, based on the sensitivity analysis of design parameters of dynamic characteristics, the system geometry parameters are optimized, and the structure of reducer is developed according to the optimum result, then the specimens of reducer are designed and manufactured. The effect of the structure development has been verified by comparing the original and developed reducer through the vibration tests.

MATRICES OVER A REDUCED RING AS SUMS OF THREE TRIPOTENTS

In this paper,we study reduced rings in which every element is a sum of three tripotents that commute,and determine the integral domains over which every n£n matrix is a sum of three tripotents.It is proved that for an integral domain R,every matrix in M_(n)(R)is a sum of three tripotents if and only if R■Zp with p=2,3,5 or 7.

面向深度学习图像分类的GPU并行方法研究

针对深度学习图像分类场景中多GPU并行后传输效率低的问题,提出一种低时间复杂度的Ring All Reduce改进算法。通过分节点间隔配对原则优化数据传输流程,缓解传统参数服务器并行结构的带宽损耗。基于数据并行难以支撑大规模网络参数及加速延缓的问题,根据深度学习主干网络所包含的权重参数低于全连接层权重参数、同步开销小、全连接层权重大与梯度传输开销过高等特点,提出GPU混合并行优化算法,将主干网络进行数据并行,全连接层进行模型并行,并通过改进的Ring All Reduce算法实现各节点之间的并行后数据通信,用于基于深度学习模型的图像分类。在Cifar10和mini ImageNet两个公共数据集上的实验结果表明,该算法在保持分类精度不变的情况下可以获得更好的加速效果,相比数据并行方法,可达到近45%的提升效果。

Reduced thermal sensitivity of hybrid air-core photonic band-gap fiber ring resonator

A novel hybrid air-core photonic band-gap fiber(PBF) ring resonator with twin 90° polarization-axis rotated splices is proposed and demonstrated. Frist, we measure the temperature dependent birefringence coefficient of air-core PBF and Panda fiber. Experimental results show that the relative temperature dependent birefringence coefficient of air-core PBF is 1.42×10^(-8)/℃, which is typically ~16 times less than that of Panda fiber. Then, we extract the geometry profile of air-core PBF from scanning electron microscope(SEM) images. Numerical modal is built to distinguish the fast axis and slow axis in the fiber. By precisely setting the length difference in air-core PBF and Panda fiber between two 90° polarization-axis rotated splicing points, the hybrid air-core PBF ring resonator is constructed, and the finesse of the resonator is 8.4. Environmental birefringence variation induced by temperature change can be well compensated, and experimental results show an 18-fold reduction in thermal sensitivity, compared with resonator with twin 0° polarization-axis rotated splices.

Semicommutative Subrings of Matrix Rings

A ring R is called semicommutative if for every α∈ R, rR （α） is an ideal of R. It is well-known that the n by n upper triangular matrix ring is not semicommutative for any ring R with identity when n ≥ 2. We show that a special subring of upper triangular matrix ring over a reduced ring is semicommutative.

On Almost Armendariz Ring

In this paper,we introduce the notion of an almost Armendariz ring,which is a generalization of an Armendariz ring,and discuss some of its properties.It has been found that every almost Armendariz ring is weak Armendariz but the converse is not true.We prove that a ring R is almost Armendariz if and only if R[x]is almost Armendariz.It is also shown th at if R/I is an almost Armendariz ring and I is a semicommutative ideal,then H is an almost Armendariz ring.Moreover,the class of minimal non-commutative almost Armendariz rings is completely determined,up to isomorphism(minimal means having smallest cardinality).

Remarks on Centers of Rings

It is proved that for matrices A,B in the n by n upper triangular matrix ring T_(n)(R)over a domain R,if AB is nonzero and central in T_(n)(R)then AB=BA.The n by n full matrix rings over right Noetherian domains are also shown to have this property.In this article we treat a ring property that is a generalization of this result,and a ring with such a property is said to be weakly reversible-over-center.The class of weakly reversible-over-center rings contains both full matrix rings over right Noetherian domains and upper triangular matrix rings over domains.The structure of various sorts of weakly reversible-over-center rings is studied in relation to the questions raised in the process naturally.We also consider the connection between the property of being weakly reversible-over-center and the related ring properties.

On Skew Armendariz Matrix Rings

Let R be a ring.We show in the paper that the subring Un（R） of the upper triangular matrix ring Tn（R） is α-skew Armendariz if and only if R is α-rigid,also it is maximal in some non α-skew Armendariz rings,where α is a ring endomorphism of R with α（1） = 1.

Maximal Armendariz Subrings Relative to a Monoid of Matrix Rings

Let M be a monoid. Maximal M-Armendariz subrings of upper triangular matrix rings are identified when R is M-Armendariz and reduced. Consequently, new families of M- Armendariz rings are presented.

A Class of Maximal General Armendariz Subrings of Matrix Rings

An associative ring with identity R is called Armendariz if, whenever （∑^m i=0^aix^i）（∑^n j=0^bjx^j）=0 in R[x],aibj=0 for all i and j. An associative ring with identity is called reduced if it has no non-zero nilpotent elements. In this paper, we define a general reduced ring （with or without identity） and a general Armendariz ring （with or without identity）, and identify a class of maximal general Armendariz subrings of matrix rings over general reduced rings.