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Secondly, the equivalence proposition of right pm-injective ring is obtained, and if R is right pm-injective ring, then the Jacobson radical of R coincide with the right singular ideal.

其次，得到右pm-内射环的一个等价命题，并证明若R是右pm-内射环，则R的Jacobson根与R的右奇异理想相等。

The following statement are the main results:Theorem 2.2.14 Let R be a reduced left morphic ring, then every left ideal of R is generated by a central idempotent. Hence every left ideal of R is also an ideal.

主要结果：定理2.2.14：设R是约化的左morphic环，则R的每一个左理想L都由中心幂等元生成，因而L也是理想。

Are some unknown measurable function from R to R.

U任R，Z一+〔，(21，·，吞)T〔卿是协变量；1，…，p都是从R到R的未知可测函数。

Let ω denote the common measure of the left monad and right monad of r, proves in standard mathematics that ω is a positive infinitesimal outside of R.;Ⅳ.

令ω代表r的左单子和r的右单子的共同测度，在标准数学中证明了ω是R之外的正无穷小；Ⅳ。

This is based on the definition of tensor product over R〓= R〓 R〓, where R is a noncommutative ring.

这是建立在〓上的张量积，其中R是非交换环。

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

Isolates CNR-1 and CNR-2 were from Brassica napus; CNA-1and CRW-1 from Rhododendron simsii and Oxalis corymbosa respectively. All isolates grew well in R-2 liquid medium and exhibited contractive movements. The colonies of all isolates were circinal and grain-like in solid medium. Through electron microscopy, all isolates exhibited helicity during their growth phase. All isolates could pass through a 0.22 μm filtrate membrane and resist to penicillin (2000 U/mL). They must grow in medium with serum.

这4株螺原体在R-2液体培养基中生长良好，都能通过孔径为0.22 mm的微孔滤膜；在R-2固体培养基上呈圆形或颗粒状菌落，菌落直径约50~600 mm；在生长的某个阶段可呈典型的螺旋状，菌体直径为37.04~370.40 nm，长度约0.89~11.88 mm；它们都能利用葡萄糖作为碳源，不能利用尿素；在不含胎牛血清的R-2培养基中，它们都不能生长；菌株CNR-1、CNA-1能强烈代谢精氨酸，而CNR-2和CRW-1不能代谢精氨酸；在氨苄青霉素钠浓度高达2000 U/mL的R-2培养基中，分离菌株生长良好。

In order to make problems simple relative map germs which map proper subspace R~s of R~m to proper subspace R~t of R~n are considered in the paper.

本文将相对映射芽的基本理论与经典奇点理论相结合，把A等价的判断条件应用到相对映射芽环中，推广了原有结论，得出了在两个C~r相对映射芽κ等价条件下判断其A等价的方法。

Ureg such that =; E (the ideal extension of a ring R by its ideal I) is an exchange ring if and only if R and I are both exchange.

一个一般环I是exchange的当且仅当对它的任意理想L以及=2∈I/L，存在w∈r.ureg使得=；E(环R通过它的理想I生成的理想扩张)是一个exchange环当且仅当R和I都是exchange环。

Shuffles elements of r using r as a shuffler. r must be a random-access range with length.

对Range r 洗牌，r 必须为一已知长度的随机访问区间。

He knows that he's one of the mostdominant players in the NBA right now.

我知道他现在是联盟里最有统治力的球员之一了。

Using analysis method of BCG , the dissertation analyzed the management of voluntary service organizations .

利用BCG分析方法对我国的志愿服务组织管理进行了分析。