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In this note, we show that for any two matrices A and B over a generalized quaternion algebra defined on an arbitrary field F of characteristic not equal to two, if A and B are similar and the main diagonal elements of A and B are in F, then their traces are equal.

本文对于特征不是2的任意域F上定义的广义四元数代数上的两个矩阵A和B,给出如果A和B相似并且它们的主对角线上的元素在F中,那么它们的迹相等。

In this note, we show that for any two matrices $A$ and $B$ over a generalized quaternion algebra defined on an arbitrary field ${\bf F}$ of characteristic not equal to two, if $A$ and $B$ are similar and the main diagonal elements of $A$ and $B$ are in $\bf F$, then their traces are equal.

本文对于特征不是2的任意域${\bf F}$上定义的广义四元数代数上的两个矩阵$A$和$B$,给出如果$A$和$B$相似并且它们的主对角线上的元素在${\bf F}$中,那么它们的迹相等。

At length the ship groaned and creaked; the thick planks gave way under the lashing of the sea as it broke over the deck; the mainmast snapped asunder like a reed; the ship lay over on her side; and the water rushed in.

她的惟一安慰是坐在她的小花园里,双手抱着与王子相似的那尊美丽的大理石像。可是她再也不照料她的花儿了。这些花儿好像生在旷野才知道他们遭到了危险。

While in the BMP/HA group, although the fibrous callus was appeared in the 4th and 8th weeks, the HA was not absorbed. In the 12th and 16th weeks the change was similar to that in the 8th week and no recanalization of bone marrow cavity.

而BMP/HA复合组,虽然在第4、8周也有纤维性骨痂形成,但HA不被吸收;第12、16周与第8周相似,无髓腔再通现象。

It shows that the formation of structural hierarchy is caused by the initial stage of formation of rock massif and the successive tectonic motion processes.

任岩石形成时,由于不平衡状态的存在及与周围环境进行能量及物质交换,出现了自组织过程及耗散结构,从而形成了相互嵌入的自相似分形结构。

There were different contamination conditions for different PAHs components in soils. Soils in urban area were severer contaminated by the height-weight-molecule PAHs than soils in agriculture area. However, there were the similar contamination level among different usages soils for the light-weight-molecule PAHs, such as naphthalene and methylnaphthalene.

不同种类的PAHs对不同利用类型土壤的污染情况也不相同,分子量较大的多环芳烃与总PAHs污染情况相似,表现为城市用地的污染程度要明显高于其它类型土壤;但分子量较小的组分,如萘和甲基萘,在不同利用类型土壤中污染程度相近。

During this transition period, we could see an outcome that echoes 1999, when the Fed told markets it would provide liquidity to protect financial systems against a possible slowdown induced by the 『millennium bug』(Y2K).

在这个过渡期内,我们可能看到与1999年相似的情况。当时,美联储对市场表示,它将提供流动资金,以保护金融体系不受"千年虫"(Y2K)可能引发的经济衰退的影响。

Can be seen from the above, many of the color of jade and precious stones have the same or similar places, when the color distinction is not open, the necessary knowledge and equipment by means of mineralogical identification.

可以从以上,许多玉器和宝石有相同或相似的地方,当颜色区别不开的颜色,必要的知识和设备的矿物学鉴定手段。

Of all materials available, calcium phosphate cement is an important biomaterial for hard tissue repair because of its chemical and crystallographic similarity to the carbonated apatite in bones and has received considerable attention. CPC consists of a mixture of fine particles of calcium phosphate salts, the CPC powder can be mixed with water to form a thick paste that can conform to osseous defects to form degradable hydroxyapatite, therefore, CPC's moldability, together with its excellent biocompatibility and osteoconductivity, make it a highly desirable material for orthopaedic repair.

磷酸钙骨水泥是一种非陶瓷型羟基磷灰石类材料,生物学特性与骨的化学组成相似,其良好的生物相容性和骨传导性引起人们的广泛重视,同时具有可吸收性,良好的蛋白亲和性,可复合骨形成蛋白而具有骨诱导性,制备简便、固化迅速、易塑形、在结晶过程中不产热等许多明显的优势使其广泛用于骨缺损修复、骨强化和骨替代。

Gunckel, who on the evening card ginkgo auxin from the stem end is not at Health Organization, or young leaves, and some Monocotyledon similar, from a rib-like sub-section of the Health Organization.

Gunckel等人的研究证晚银杏生长素不是来自茎端分生组织或幼叶,而与某些单子叶植物相似,来自具肋状分生组织的节间。

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I didn't watch TV last night, because it .

昨晚我没有看电视,因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来,在北京的很多小区里,电梯液晶电视被撤了下来。

I'm running my simile to an extreme.

我比喻得过头了。