内积

The notion of the adjoint operator of amodule homomorph ism defined on a densely submodule of a comp lete random inner p roduct module is introduced and discussed, in particular the closedness of adjoint operators is p roved.

摘 要 对定义在完备随机内积模的稠子模上的模同态引入了共轭算子的概念并讨论其基本性质，尤其证明了共轭算子的闭性。

In this paper,a systematic direct perturbation method of dark solitons is found.Having analyzed the mistakes in earlier works on perturbation method for dark solitonsand essence of the direct perturbation method for bright solitons,we notice that to in-troduce the adjoint solutions of the squared Jost solutions and to prove the completenessare crucial to the problem.Giving up the unnecessary scheme of introducing the adjointoperator in the bright soliton case,we directly find the adjoint solutions by meetingthe demand for the orthogonality that inner product of the squared Jost solutions andits adjoint should be proportional to a δ function in the case of continuous spectra.The corresponding adjoint operator is thus found.Taking into account the reductiontransformation,we find a correct description for the completeness of the squared Jostsolutions and directly verify its validity with explicit expressions of the squared Jostsolutions.

本论文建立了系统的暗孤子直接微扰方法，在对前人关于暗孤子微扰方法的错误以及亮孤子直接微扰方法的本质作了充分的分析后，认识到引入平方Jost解的伴随解和证明完备性是问题的关键，撇开过去亮孤子情况首先引入伴随算子的非必要作法，直接从平方Jost解与其伴随解的内积在连续谱时正比于δ函数这一正交性要求出发，找出了伴随解，同时得出了应有的伴随算子，在考虑到约化变换性后，得到了暗孤子情况的平方Jost解的完备性的正确表述，并在单个暗孤子的情况利用平方Jost解的显式直接验证了它的正确性。

Linear algebra (2) studies the structure, including the inner product, angle, and projection, of the Euclidean space .

线性代数介绍欧几里德空间的结构，包括内积、角度、投影等。

Methods 37 hypertension brain hemorrhage patients,by the hematocele quantity,the shape and patient's condition were treated with soft channel technology-micro wound in the ventricles of the brain and haematoma liquefication drainage,to eliminate the hematocele,rescue the life,improve prognosis.

对37例高血压脑室出血患者，依据脑室内积血的量、形态及患者的病情，行软通道技术-微创脑室内血肿液化引流术，清除血肿，抢救生命，改善预后。

Abstract］ Objective To discuss the clinical analysis on 37 cases of hypertension intraventricular hemorrhage with soft channel technology-liquefied drainage of hematoma.Methods 37 hypertension brain hemorrhage patients,by the hematocele quantity,the shape and patient's condition were treated with soft channel technology-micro wound in the ventricles of the brain and haematoma liquefication drainage,to eliminate the hematocele,rescue the life,improve prognosis.

目的 探讨应用软通道技术-微创脑室内血肿液化引流术治疗高血压脑室出血的疗效方法对37例高血压脑室出血患者，依据脑室内积血的量、形态及患者的病情，行软通道技术-微创脑室内血肿液化引流术，清除血肿，抢救生命，改善预后。

Results: Ultrasonographic manifestations of cholecystoduodenal fistula were gas inside the bile duct and gallladder; indistinction of the wall of gallbudder, gallstone disappeared and small intestinal obstruction.

结果：7例胆囊、二指肠瘘的超声检查表现：胆管和胆囊内积气；胆囊结构消失和原有胆囊内结石消失；小肠梗阻。

Firstly, this paper introduces a function space defined by Bouziani and takes the inner product in space L2 of the linear equation and an integrodifferential operator.

首先引入一个Bouziani定义的空间，利用该空间的一些特点，将原线性方程的两端在L~2空间内与一个积分微分算子作内积。

In addition, when calculating the products of various terms of equations, this paper uses the principle that the integrated function of highest order term meets algebraic precision as the one of determining the number of integral points.

另外，在计算方程各项的内积时，本文以具有最高次项的被积函数满足代数精度为积分点数目的选取原则。

Results Soft tissue swelling: 19 cases showed on CT (degree Ⅰ 6 cases; degree Ⅱ: 5 cases; degree Ⅲ: 8 cases), and 12 cases showed on MRI (degree Ⅰ 4 cases; degree Ⅱ 3 cases; degree Ⅲ 5 cases); Arthroedema seven on CT, and Ⅱ on MRI; Synovium granulation hyperblastosis 13 on CT, and 10 on MRI; Changes of joint space 13 on CT, and 17 on MRI. Destruction of bone (6 cases), osteosclerosis (15), osteoporosis (4), bone pneumatosis (6) and abscess-like cyst (1) were seen on CT.

结果 CT显示软组织肿胀19例（Ⅰ度6例，Ⅱ度5例，Ⅲ度8例），MRI显示12例（Ⅰ度4例，Ⅱ度3例，Ⅲ度5例）；CT显示关节腔积液7例，MRI显示Ⅱ例；CT显示滑膜肉芽组织增生13例，MRI显示10例；CT显示关节间隙改变13例，MRI显示7例；CT显示髋关节骨质破坏6例，骨质硬化15例，骨质疏松4例，骨内积气6例，脓肿样囊腔1例。

For this reason the inner product is called also the scalar product .

为此，内积也叫做纯量积。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。