查询词典 tensor calculus

We have studied a model of a non-Newtonian viscous compressible fluid in 3D bounded domains, in which the viscous part of the stress tensor satisfies the coerciveness condition and the values of the growth condition ., are positive constants. Here is the tensor of the velocity gradient, is the strain tensor and ,which depends on the tensor of the velocity gradient, is the hefts of .

对满足强制性条件，以及增长性条件的非牛顿粘性可压缩流体在三维有界区域中的流动进行了研究，其中和为正常数，为速度梯度张量，是偏应力张量，为的分量，它依赖于速度梯度张量。

Based on the definitions of metric tensor and curvature tensor, the full expressions of their changes are put forward with asymptotic analysis, where the metric tensor change expression coincides with Ciarlet's, and the curvature tensor change expression is described more accurately than Ciarlet's.

提出的度量张量的改变量与Ciarlet给出的一致，而曲率张量的改变量比Ciarlet给出的更精确。

The mathematical form of material energy-momentum tensor is the same as a sum of the energymomentum tensor in elastic material and the Maxwell stress tensor in electromagnetic field Moreover, under infinitesimal symmetrical transformations, the infinitesimal invariance condition gives a balance of the field variables and material energy-momentum tensor.

另外，在无穷小对称变换条件下，它指出—种场变量与物质能量-动量张量的平衡关系。

Two merging methods of Bézier curves are generalized to tensor product Bé zier surfaces, we propose two methods to approximate two pieces of adjacent tensor product Bézier surfaces by a piece of tensor product Bézier surface. We offer the explicit formulas of the merged tensor product Bézier surfaces with all kinds of merging conditions.

同样，Bézier曲线的两种合并方法也被成功的推广到张量积Bézier曲面上，得到把两片相邻张量积Bézier曲面合并成一片张量积Bézier曲面的两种合并方法，并给出在各种合并条件下的合并曲面控制顶点的显示表示式。

Two above methods are generalized to tensor product Bézier surfaces and triangular Bézier surfaces, we give two approaches of degree reduction for tensor product Bézier surfaces, each of which reduces a given degree n×m tensor product Bézier surface to a n〓×m〓 one, and two methods of degree reduction for triangular Bézier surfaces, which reduce a given degree n triangular Bézier surface to a degree m one. The explicit formulas of control points for reduced tensor product and triangular Bézier surfaces are obtained respectively.

张量积Bézier曲面的两种降阶方法均可把n×m阶张量积Bézier曲面一次降阶为n〓×m〓阶张量积Bézier曲面；三角Bézier曲面的两种降阶方法均可把n阶三角Bézier曲面一次降阶为m阶三角Bézier曲面，并给出降阶张量积Bézier曲面和降阶三角Bézier曲面控制顶点的显示表示式。

Using differential calculus knowledge to testify inequality, Calculus of higher mathematics is the core and calculus method of higher mathematics is typical of the whole mathematical method, the method is introduced for calculus ideas to solve the problem of finding an inequation, to make way for obtaining inequalities can be simple, the application of differential mid-value theorem and Taylor formula illustrate some of the inequality proof method.

运用微分学知识证明不等式；微积分是高等数学的核心，微积分思想方法是高等数学乃至整个数学的典型方法，微积分思想方法的引入为解决不等式证明的难题找到了突破，用来解不等式可使解题思路变得简单，文章应用微分中值定理及泰勒公式举例说明了部分不等式的证明方法。

The calcalus learns is a mathematic branch connected closely with scientific application.Infinitesimal is an important componant in the theoretical system and has an outstanding effect on the forming of the basis and conception of the theory. infinitesimal ; calculus ; the calculus learns ; differential calculus ; integral calculus

引 言微积分学是建立在实数、函数和极限理论基础上，研究函数微分、积分以及有关概念与应用的数学分支。17世纪精密科学的飞速发展，天文学、力学、光学、工业技术要求数学彻底革新，导致了无穷小概念的问世，促使费马增量理论开创微分学的先河，同时奠定了柯西的极限理论。

In SPVT (security protocol verifying tool), the specification language is the π-like calculus extended with three appendixes, the Dolev-Yao model is described with Horn logic rules, the π-like calculus model of security protocol is transformed into the logic program model by abstract rules, the security properties are verified based on the calculus of the logic program's fixpoint, and the counter-examples on security properties are constructed from the process of the fixpoint calculus and the process of the property verification.

在SPVT中，以扩展附加项的类演算作为安全协议描述语言，以扩展附加项的Horn逻辑规则描述协议攻击者的Dolev-Yao模型，通过一组抽象规则将安全协议的类(演算模型转换为逻辑程序模型，基于安全协议逻辑程序的不动点计算验证安全性质，从安全协议逻辑程序的不动点计算和安全性质的验证过程中构造不满足安全性质的安全协议反例。

Prolonged markedly the time of sleep in mice with the hypnotic effect induced by phenobarbital sodium, while SWNH (50 mg/kg), the natural calculus bovis (100 mg/kg), and the artificial calculus bovis (100 mg/kg) did not. SWNH (500, 1,000, 2,000 mg/kg), the natural calculus bovis (1,000 mg/kg), and the artificial calculus bovis (1,000 mg/kg) i.g.

生物牛黄中间体100mg/kg体重、150mg/kg体重腹腔注射给药，可使苯巴比妥钠引起的小鼠睡眠时间明显延长；生物牛黄中间体50mg/kg体重、天然牛黄100mg/kg体重和人工牛黄100mg/kg体重对睡眠时间的延长无明显影响。

During the study of incidence calculus theory, we firstly clarified original incidence calculus and the probabilistic reasoning mechanism on it. We then introduced the improvement of generalized incidence calculus theory proposed by Liu~[18], which establishes incidence calculus theory on Lukasiewiczs three valued logic.

本文首先阐述了原始的发生率计算理论及其上的概率推理机制，然后引入Liu对该理论的改进，以Lukasiewicz三值逻辑为基础，并提出了这个扩展的理论与证据理论之间的等价关系。

Dixie itself is a nickname for the American South.

Dixie 本身是美国南部的别称。

I think John Terry epitomises that and a big reaction is what we will be looking for.

而我认为特里就是这样一个典型，他正是我们期望看到的那个领秀。