四元的

The least norm solutions of symmetric and skew antisymmetric matrix equations (A~TXA, XA — YAD)=(D, 0)are also considered. 3. The least-squares solutions and the least norm solutions of the quaternion matrix equations AX = B and XD = E are studied by using

借助四元数的复表示方法，研究四元数矩阵方程组AX=B，XD=E的最小二乘问题和极小范数解的问题，并对主子阵约束下的方程组的解进行了讨论，得到了它们的显式表示。

The quaternary GalnAsSb can be used for the bolometer, IR radar, monitoring of the environment, trace gases and other interesting purpose for its special response wavelength. GalnAsSb infrared detectors are novel compound detectors with advantages of fast response, high sensitivity, high stability, low price, especially its character to work at room temperature.

当其晶格参数与InP衬底的晶格参数相匹配时，其覆盖波长基本不变(1.6～1.7μm)：但是匹配于InAs衬底时，覆盖波长从1.7μm变到3.4μm；而与GaSb衬底晶格匹配时AlGaAsSb、GaInAsSb四元系化合物材料可以覆盖从1.7μm至4.3μm的波段，所以GaInAsSb四元系化合物材料在红外成像、红外技术方面有重要的实用价值，同时在未来的超低损耗光纤通信中也具有潜在的应用。

The result of numeric computation demonstrates that the approximate directional algorithm is robust, the result of Monte Carlo simulation shows that the performance of the optimum four-element array structure is better than the common one or the regular tetrahedron one.

数值计算结果表明，提出的近似定向算法是可靠的；计算机蒙特卡罗仿真结果表明，导出的最佳四元阵列性能优于普通的四元阵和正四面体阵。

A on the stock market, gold stocks rose this news to stimulate the market, Shandong Gold (600,547, the closing price of 30.69 yuan), gold in gold (600,489, the closing price of 26.42 yuan) are reported to limit Admission, Zijin Mining (601899, the closing price of 4.07 yuan), your research Platinum (600,459, the closing price of 10.82 yuan) were up, or are more than 5%.

对股市，黄金库存增加这一消息刺激市场，山东黄金（600547，在30.69元收盘价），中金黄金（600489，在26.42元收盘价）的报告限制入学，紫金矿业（601899，在4.07元的收盘价），您的研究铂（六十〇万零四百五十九的达到10.82元的收盘价），增加了，或5％以上。

This paper first elaborated the principle of SINS, some interrelated information,and the affect of renewed arithmetic to the system"s precision. Then, we studied thequaternion in traditional renewed attitude arithmetic. The quaternion is simple, andwhen run it into computer, it"s time saving. So, this arithmetic is often adopted byengineering. However, the quaternion brought unexchangeable error inevitably. Whenthe carrying body moves in highly dynamic situation, the error would become larger.So we should take effective measure to get over it.

本文首先论述了捷联式惯性导航系统的工作原理及相关知识，捷联惯导系统姿态更新算法对系统精度的影响；其次研究了传统的姿态更新算法中四元数法，该算法简单，计算量小，因而在工程中经常被采用，但是在四元数法中不可避免的引入了不可交换性误差，特别是在载体处于高动态环境时，这种误差就会很大，必须采取有效措施加以克服。

We give different kinds of iterative methods of some quaternion matrix equations,and using structure-preserving property for complexification operator of the quaternion matrices,which analysis and character the convergence of various algorithms.

给出了若干类四元数矩阵方程的多种迭代算法，并利用四元数矩阵复表示运算的性质与保结构特性，分析和刻画了各种算法的收敛性。

By using it, we solve the Yamabe problem on quaternionic contact manifolds when the Yamabe invariant is smaller than that of the sphere.

我们还建立了四元切触流形的分析基础，应用建立的分析工具，在流形Yamabe不变量与球面的不同时，解决了四元切触流形上的Yamabe问题。

The metastable phase equilibrium of the quaternary system Na(superscript +)∥Cl(superscript -), CO3(superscript 2-), B4O7(superscript 2-)-H2O was studied at 273 K by isothermal evaporation method, the solubility and density of the equilibrium solution of this system were determined and the metastable equilibrium phase diagram was plotted in line with the experimental data. The phase diagram of the system consists of three univariant curves, three crystallization fields and one invariant point.

采用等温蒸发法研究简单四元体系Na∥Cl，CO3(上标 2-)，B4O7(上标 2-)-H2O273K时的介稳相平衡，并测定该体系273K平衡液相中各组分的溶解度及密度，该体系的介稳相图和密度组成图显示：该四元体系在273K时的相图由3条溶解度单变量线、3个结晶区及1个共饱和点组成。

Originally, the blessing bag is very over-valued, a thousand dollar inside of the blessing bags, usually the marked price 1000 dollars or so merchandise have 34;Sometimes 1 the inside of the blessing bag of 20,000 yens, the digital camera which has already been worth 3410000 yens also perhaps.

原来，福袋非常超值，一个千元的福袋里，往往标价千元左右的商品就有三四件；有时一个两万日元的福袋里，有价值三四万日元的数码相机也说不定。

The conjugation by a unit quaternion (a quaternion of absolute value 1) with real part cos is a rotation by an angle 2''t'', the axis of the rotation being the direction of the imaginary part.

单位四元数（绝对值为1的四元数）若实部为 cos，它的共轭作用是一个角度为2''t''的转动，转轴为虚部的方向。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。