The inversion of a non-singular square matrix applying a Computer Algebra System (CAS) is straightforward. The CASs make the numeric computation efficient but mock the mathematical characteristics. The algorithms cond...The inversion of a non-singular square matrix applying a Computer Algebra System (CAS) is straightforward. The CASs make the numeric computation efficient but mock the mathematical characteristics. The algorithms conducive to the output are sealed and inaccessible. In practice, other than the CPU timing, the applied inversion method is irrelevant. This research-oriented article discusses one such process, the Cayley-Hamilton (C.H.) [1]. Pursuing the process symbolically reveals its unpublished hidden mathematical characteristics even in the original article [1]. This article expands the general vision of the original named method without altering its practical applications. We have used the famous CAS Mathematica [2]. We have briefed the theory behind the method and applied it to different-sized symbolic and numeric matrices. The results are compared to the named CAS’s sealed, packaged library commands. The codes are given, and the algorithms are unsealed.展开更多
黄海呈现独有的地形条件,且该海域的潮波运动独具特征。本文利用静止海洋水色成像仪(Geostationary Ocean Color Imager, GOCI)遥感反演和俄勒冈州立大学(Oregon State University,OSU)潮流模式分别获取了黄海海域的海表流场,基于该海...黄海呈现独有的地形条件,且该海域的潮波运动独具特征。本文利用静止海洋水色成像仪(Geostationary Ocean Color Imager, GOCI)遥感反演和俄勒冈州立大学(Oregon State University,OSU)潮流模式分别获取了黄海海域的海表流场,基于该海域独特的潮波系统提出并识别潮波干涉区,进而对GOCI反演的流场做潮流提取,并对两种潮流数据作分区可用性评价,通过实测的漂流浮标数据验证评估。结果表明:利用GOCI反演和OSU潮流模式获取的海表流场具有一定程度的可靠性,GOCI反演的海表流场的流速平均相对大小误差值为0.77,OSU潮流模式获取的海表流场流速平均相对大小误差值为0.49;在靠近潮波干涉区的黄海中部海域,GOCI潮流数据与实测数据在方向上的一致性要优于OSU潮流数据,两者平均角度误差值分别为48.45°和63.10°;在远离潮波干涉区的黄海近岸海域,OSU潮流数据与实测数据在速度大小和方向上的一致性要优于GOCI潮流数据。展开更多
By comprehension of earthquake focal mechanism solutions and the data of in-situ stress measurements, the tectonic stress field in Shanxi region has been summarized, which indicate that the stress state in this region...By comprehension of earthquake focal mechanism solutions and the data of in-situ stress measurements, the tectonic stress field in Shanxi region has been summarized, which indicate that the stress state in this region is different from that of its eastern surrounding regions. The next, by fitting the measured data, the boundary forces that influenced the distribution of the stress field in this region has been studied using inversion method. The inversion results showed the following messages: the effect of the boundary force between the blocks is the main determinative factor for the recent tectonic stress field in Shanxi and the regional material and its property is a secondary factor; the horizontal main stress of tectonic stress field in Shanxi region is consistent with the stretch of fault basins.展开更多
文摘The inversion of a non-singular square matrix applying a Computer Algebra System (CAS) is straightforward. The CASs make the numeric computation efficient but mock the mathematical characteristics. The algorithms conducive to the output are sealed and inaccessible. In practice, other than the CPU timing, the applied inversion method is irrelevant. This research-oriented article discusses one such process, the Cayley-Hamilton (C.H.) [1]. Pursuing the process symbolically reveals its unpublished hidden mathematical characteristics even in the original article [1]. This article expands the general vision of the original named method without altering its practical applications. We have used the famous CAS Mathematica [2]. We have briefed the theory behind the method and applied it to different-sized symbolic and numeric matrices. The results are compared to the named CAS’s sealed, packaged library commands. The codes are given, and the algorithms are unsealed.
文摘黄海呈现独有的地形条件,且该海域的潮波运动独具特征。本文利用静止海洋水色成像仪(Geostationary Ocean Color Imager, GOCI)遥感反演和俄勒冈州立大学(Oregon State University,OSU)潮流模式分别获取了黄海海域的海表流场,基于该海域独特的潮波系统提出并识别潮波干涉区,进而对GOCI反演的流场做潮流提取,并对两种潮流数据作分区可用性评价,通过实测的漂流浮标数据验证评估。结果表明:利用GOCI反演和OSU潮流模式获取的海表流场具有一定程度的可靠性,GOCI反演的海表流场的流速平均相对大小误差值为0.77,OSU潮流模式获取的海表流场流速平均相对大小误差值为0.49;在靠近潮波干涉区的黄海中部海域,GOCI潮流数据与实测数据在方向上的一致性要优于OSU潮流数据,两者平均角度误差值分别为48.45°和63.10°;在远离潮波干涉区的黄海近岸海域,OSU潮流数据与实测数据在速度大小和方向上的一致性要优于GOCI潮流数据。
文摘By comprehension of earthquake focal mechanism solutions and the data of in-situ stress measurements, the tectonic stress field in Shanxi region has been summarized, which indicate that the stress state in this region is different from that of its eastern surrounding regions. The next, by fitting the measured data, the boundary forces that influenced the distribution of the stress field in this region has been studied using inversion method. The inversion results showed the following messages: the effect of the boundary force between the blocks is the main determinative factor for the recent tectonic stress field in Shanxi and the regional material and its property is a secondary factor; the horizontal main stress of tectonic stress field in Shanxi region is consistent with the stretch of fault basins.
