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This article presented a new fast algorithm of Moore-Penrose inverse for an m×n symmetric Loewner-type matrix with full column rank by forming a special block matrix and studied its inverse. Its computation complexity was O+O(n^2), but it was O(mn^2)+O(n^3) by using L(superscript +)=L(superscript TL^(-1)L.

论文通过构造特殊分块矩阵并研究其逆矩阵，给出了秩为n的m×n对称Loewner矩阵Moore-Penrose逆的快速算法，该算法的计算复杂度为O+O(n^2)，而通过L=L(上标 TL^(-1)L计算的复杂度为O(mn^2)+O(n^3)。

In this paper, for m× n Loewner-type matrix or symmetric Loewner-type matrix with full column rank, we form special block matrix firstly and research their triangular factorization or of its inverse, and then get the fast algorithm of the minimal norm least squaresolution .

本文对于秩为n的m×n阶Loewner型或对称Loewner型矩阵L，通过构造特殊分块矩阵并研究其逆的三角分解或自身三角分解，进而得到了线性方程组Lx=b的极小范数最小二乘解快速算法，计算复杂度为O+O(n~2)，而一般方法的计算复杂度为O(mn~2)+O(n~3)。

Based on the two normal forms, the decidability theorem in L is then proved and a deduction-based decision algorithm P is designed. The time complexity O(n3) of P is much less than the complexity O(2n) of the true value table method and the complexity O(n5) of HAL based on the tactic scheme.

首先定义了消解复杂性的两种范式：最简范式和文字范式，在此基础上采用演绎方法证明了L中的可判定性定理，并设计了命题公式的演绎判定算法P。P的时间复杂度为O(n^3)，远远小于基于真值表法的O(2^n)和基于策略方案HAL的O(n^5)。

Justify the correctness of the recursive division algorithm given in page 15, and show that it takes time O(n^2) on n-bit inputs.

证明15页递归除法算法的正确性，然后证明对于n位输入，他需要O(n^2)的时间。

Adjacency search, double linked element list, random direction search, adjacency rotation, and heredity of geometrical quantities are applied to increase the efficiency of mesh generation. The relationship between the computing time and the number of generated elements is nearly linear and the time complexity is O(N^1.05), where N is the number of elements.

采用了邻接单元搜索、双向链表存储、随机方向搜索、邻接旋转、几何量继承等技术，使算法的计算时间与生成单元数近似呈线性关系，时间复杂度达到O(N^1.05)，N为生成单元数。

Anchor points based Isometric Embedding under least square error criterion has a time complexity of O n log( n , and after obtained geodesic distances it has linear time complexity for embedded points and can be fully realized in parallel.

基于锚点集的最小平方误差等距嵌入算法AIE具有O n log( n 的时间复杂性，而且在获得测地线距离后的计算时间复杂度达到对嵌入点数的线性关系，且可以完全并行实现。

The effects of velocity and time of high-energy ball milling on the structure and the micrograph of Y-Al-Mg-Si-O-N powder were investigated.

通过X线衍射和扫描电子显微镜观察，研究球磨转速和球磨时间对Y-Al-Mg-Si-O-N氧氮玻璃原料粉末结构和形貌的影响。

According to the above study results, especially the steady operation of two-sludge system（2A/O+N 2SBR）, it can be proved that denitrification and excess phosphorus uptake are relatively independent and intersectant biological processes. The overlap is that denitrifying phosphorus removing bacteriawhich possesses the two bacterial metabolisms, could utilize nitrate as an electron acceptor for phosphorus uptake. The two-sludge system can not only combined biological phosphorus removal and denitrification processes to form a process in practical wastwater treatment , but also solved the main difficulties of current single-sludge systems:①the sludge age competition between phosphorus removing bacteria and nitrifier;② the substrate competition between denitrification and dephosphatation.

以上的研究结果，尤其是时间序列的双泥生物反硝化除磷脱氮系统工艺（2A/O+N 2SBR法）的稳定运行，不仅证明了生物脱氮与生物除磷是两个既相对独立又相互交叉的生理过程，其交叉点是同时拥有硝酸盐还原性和超量吸磷这两种生化特性的细菌进行的反硝化吸磷脱氮生化反应，而且双泥系统工艺克服了常规单泥生物脱氮除磷工艺的两大问题（①聚磷菌和硝化菌的SRT相互干扰；②反硝化与生物除磷竞争VFA），同时保证了脱氮和除磷效果，排水指标达到污水综合排水标准（GB8978-1996）的一级标准，具有实际工程使用价值。

The results suggest that the electronic π-π* transitions in AlQ_3 are localized on the quinolate ligands; the transition from a phenoxide donor to a pyridyl acceptor includes C→C and O→N transferences. There hardly is any relation to the metal aluminum.

结果表明，电子从基态跃迁到低激发态时主要为π-π*跃迁；电荷从含氧的苯酚环转移至含氮的吡啶环上，包括两环之间 C→ C转移和 O→ N转移，与金属离子关系不大。

We give an O(n^2) time and O(n^2) space solution for this problem.

我们提供一O(n^2)时间以及O(n^2)空间复杂度之解法。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。