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When scaled factor circulant matrices are nonsingular, we can find the single solution of the scaled factor circulant matrix equation; When scaled factor circulant matrices are singular, we can find the special as well as the general solution of the scaled factor circulant matrix equation; There is only an error of approximation when the fast algorithm is implemented on computers, and only the elements in the first row of the scaled factor circulant matrix and the constants in the diagonal matrix are needed by the fast algorithm.

当鳞状因子循环矩阵非奇异时，该快速算法求出线性方程组的唯一解；当鳞状因子循环矩阵奇异时，该快速算法求出线性方程组的特解与通解。该快速算法仅用到鳞状因子循环矩阵的第一行元素及对角矩阵中的对角上的常数进行计算。在计算机上实现时只有舍入误差。

In addition, the voltage-current characteristic of linear resistive components is the general solution of Clairaut equation, and the voltage-current characteristic of non- linear components is the singular solution of Clairaut equation.

论文摘要：本文讨论了任意伏安特性电阻元件满足的基本微分方程以及非线性电路的功率匹配问题的几个定理，指出任意伏安特性电阻元件均满足非线性一阶的clairaut方程，并且，线性电阻元件的伏安特性是clairaut 方程通解，而非线性电阻元件的伏安特性是clairaut 方程的奇解。

But the solution of these two problem or not and the degree of the solution, have close relations with the geography humanities environment, with the civilizing of the clansmen and the education of the schools, with the whole characters of the leaders.

而这两个问题的解决与否及解决的程度，是与宗族的地理人文环境、宗族教化和文化教育、领导班子的整体素质等等三方面有着密切的关系。

Solve et coagula, the one is mutually dependent on the other, without solution there is no bonding, without bonding no solution, without hate there is no love, and without darkness there is no light.

Solve et Coagula】，相辅相成相生相克，--没有解决就没有难题，没有难题就没有解决，没有恨就没有爱，没有黑暗就没有光明。

The second was to compare the effects of the different floating liquids on the destruction of rabbit coccidia oocysts. The results indicated that magnesium sulfate solution showed the lowest rate of coccidia oocyst destruction at 20 min; saturated salt water had the greatest rate of destruction. The destruction increased with time; in the saturated salt water and urea solution damage or deformation of a few coccidia oocysts at were observed 60 min.

其二，不同漂浮液对兔球虫卵囊破坏作用比较；结果表明20min时硫酸镁溶液对卵囊破坏率最低，破坏率最大的是饱和食盐水，随着时间延长各种破坏作用增大，60min时饱和食盐水和尿素溶液中有极少卵囊破损和卵囊变形现象。

Aiming at above problem, this paper put forward the strategy of separation as follows. Firstly, in view of great amount of coloring matter in solution, the quality of product is declined. So we decolor the solution by acticarbon, which makes 80% coloring matter be removed, but the loss of nucleotides is only about 2%. Secondly, on the basis of physical and chemical properties of four nucleotides, we first synthesized a kind of cation exchange resin by ourselves which is used to separate four matters preliminarily.

针对以上问题，本文提出了如下的分离策略：首先，由于酶解液中色素含量较多，使经树脂分离所得UMP和GMP中色素残留较多，最终导致成品质量的下降，所以我们用活性炭对酶解液进行脱色处理，使溶液中80％以上的色素被吸附除去，而核苷酸的吸附损失仅为2％左右。

Fast algorithm of minimal norm least square solution for Cauchy linear system;2. For the m×n Cauchy-type matrix with full column rank,the fast algorithm of the minimal norm least square solution to the linear system Cx=b was obtained by construction of a special block matrix and study of the triangular decomposition.

对于秩为n的m×n阶Cauchy型矩阵C，通过构造特殊分块矩阵并研究其三角分解，进而得到了线性方程组C x=b的极小范数最小二乘解的快速算法，所需运算量为O+O(n2)，而通常构造法方程组的方法所需运算量为O(m n2)+O(n3)，用正交化法虽然避免了构造法方程组，但所需的运算量更大些。

Then the matrix Having these solution vectors as its column vectors is called a fundamental matrix for the system in Fundamental Matrix Solution Because the column vector .

则以这些解向量为列的矩阵被称为这个系统的基本矩阵。

The fry of black seabreamand giant sea perch with 4.0cm-8.5cm using the methods of dyeing, i.e., the fish immersed in the water solution containing comestible pigment, immersion in tetracycline, i.e., the fish immersed in the water solution containing tetracycline, and marking by spraying, i.e., the fish sprayed with fluorescent pigment spraying on the skin of fish, and double marking, i.e., the fish sprayed with fluorescent pigment spraying on the skin of fish after feed with tetracycline, and control group. The survival rates, mark retention rates and hydrology data were separately measured every three days for black sea bream and every two days for giant sea perch. The results were as follows.

本研究针对体长4.0cm-8.5cm的黑鲷及金目鲈的鱼苗采用染色法(将鱼只浸泡在含有食用色素的水溶液中)、四环霉素浸泡法(将鱼只浸泡在含有四环霉素的水溶液中)、喷枪法(利用高压喷枪将萤光色素打在鱼的表皮)以及双重标识法（四环霉素投餵法加上喷枪法）与一组空白组进行试验，黑鲷每三天一次、金目鲈每两天一次，调查标识后鱼只的时间别残存率、时间别标识残留率以及水质资料，结果如下。

Beginning with some cases, the article gives basic definitions of inverse problems and ill-posed problems. Then it discusses the Moore-Penrose generalized solution and the Moore-Penrose generalized inverse, and makes a conclusion that linear compact operator equations are ill-posed, that is, the Moore-Penrose generalized solution is unstable.

本文从一些实例出发，介绍了反问题和不适定问题的基本概念，并讨论了方程的Moore-Penrose广义解和Moore-Penrose广义逆，得出了线性紧算子方程的不适定性，即Moore-Penrose广义解的不稳定性的结论。

Don not attempt to do something which you can not to do.

不要企图做那些办不到的事情。

The expression of CTGF and TNF-αweredetected by immunochemistry and the number of Clara Cells was calculated.

光镜下观察肺组织的病理变化，采用免疫组化染色观察肺组织中结缔组织生长因子和肿瘤坏死因子-α的表达和Clara细胞的数量。