查询词典 existence theorem of implicit function

Then, the system is linearized by variational approach, the local null controllability is proved by applying a generalized implicit function theorem and combining the good property of the solution mapping.

首先通过对系统线性化，构造泛函，利用对偶方程，给出控制函数具体形式的办法得到系统的逼近能控性；然后采用变分方法对系统线性化，再结合解映射好的性质，应用推广的隐函数定理，证明系统的局部零能控性；最后利用局部零能控性和逼近能控性结合给出系统零能控的结论。

Each of us has a superior function, which we prefer and which is best developed in us, a secondary function, which we are aware of and use in support of our superior function, a tertiary function, which is only slightly less developed but not terribly conscious, and an inferior function, which is poorly developed and so unconscious that we might deny its existence in ourselves.

每个人都有自己第一优先的方法，这是我们最喜欢或做的最好的方法；第二优先的方法，是我们知道或使用来辅助第一优先方法；第三顺位方法，是我们仅仅使用一点点但不太了解的方法；而最后考虑的方法，是做的不好而不了解，以致於我们自己可能会否定它的存在。

For a general parametric curve/surface, we usually cannot compute its exact implicit form. Even though its exact implicit form can be computed, the curve/surface implicitization involves relatively complicated computation and the degree is higher. Moreover, it may have unexpected components and self-intersections. All these unsatisfied properties limit the applications of the exact implicitization. So finding curve/surface approximate implicitization has become a practical problem. In this paper, we present an algorithm to solve the approximate implicitization of a given parametric curve by using a quadratic algebraic spline curve.

由于精确隐式化过程不一定可以实现，即使可以实现隐式曲线曲面的阶数高计算复杂，并且具有不希望的自交点和奇异分支，从而限制了隐式化的运用，所以寻求参数曲线曲面的近似隐式化问题成为很实际又重要的问题，提出利用二次代数样条曲线来实现一般平面参数曲线近似隐式化的一种算法。

In the light of the complex, high-level and non-linear feature of the mathematical model which describe the transport of the coalbed methane, this paper study the fully-implicit solving method of the mathematical model in detail. Based on the complexity of the algebraic equations which are formed eventually, according to the alternating direction implicit difference pattern, this paper use the iterative method and the fully main element Gauss-Jordan eliminating method to solve equations, which is to use the iterative method to determine coefficient matrix and use the fully main element Gauss-Jordan method to solve th linear algebraic equation group, at the same time of studying the solving method of the mathematical model, according to the devising requirement of FORTRAN77 program structure, this paper draw up computer program and form the corresponding computer model, and verify the validity and reliability of the model in theory by operating the model.

重点研究了模型内、外边界及有关参数的处理，针对描述煤层甲烷运移的数学模型是一个复杂、高阶非线性数学模型的特点，详细研究了模型的全隐式求解方法，根据最后形成的代数方程组的复杂性，按交替方向隐式差分格式，采用迭代与全选主元高斯约当消去法相结合的方法求解方程：即确定系数矩阵采用迭代法，求解线性方程组时采用全选主元高斯约当消去法，在研究模型解法的同时按FORTRAN结构化程序设计的要求，编制计算机程序，形成相应的CBMRS计算机模型，并通过模型的运行从理论上证明了模型的正确性与可靠性。

Since the visualization of implicit algebraic surface is still a difficult problem, it is doubtlessly meaningful to construct some convenient and effective parameterization method for some kind of concrete implicit surfaces.

由于隐式代数曲面的显示问题始终是困扰人们的一个关键性难题，从而针对具体形式的代数曲面，能给出方便有效的参数化方法无疑是有意义的。

By using very general implicit shape primitive—algebraic surface, our scheme can represent more general 3D surfaces than other implicit surface reconstruction techniques.

同其它隐曲面重建方法相比，我们的方法通过使用很具一般性的隐式形状单元—代数曲面—可以表示更一般的三维表面。

Based on wave propagation feature, this paper analyses 3D seismic migration algorithms such as alternating direction implicit method, LU decomposition method, and inverse operator approach method. The result shows that the alternating direction implicit method is fast but causes distortion in wave field extrapolation and affects image accuracy; however LU decomposition and inverse operator approach methods are fast while holding circular symmetry of wave field, and are promising in oilfield exploration and development.

在波的传播特征分析基础上，对交替方向隐式法、LU分解法、逆算子逼近法等三维地震偏移算法进行了分析研究，结果表明，交替方向隐式法虽然快捷但是在波场外推中明显产生畸变并影响成像的准确性，而LU分解和逆算子逼近法是保持波场圆对称特征前提下的快速算法，在油田勘探开发中具有较好的应用前景。

The Implicit Pension Debt is calculated by terminate hypothesis method: assumed that the "pay-as-you-go" pension system terminated immediately, computing all annuitant and employees pension rights, but not take account of the possible new obligation or income from pay or interest in the future, and then an actuarial model of Implicit Pension Debt is constructed.

本文采用了终止假定法计算养老金隐性债务：假定现收现付制度立即终止，计算所有养老金领取者和职工在原制度下积累起来的养老金权益数量，而不考虑可能的新债务或者来自未来的缴费或利息收入。

The design of the messaging services should not result in implicit tight coupling between the supposed to be loose coupling components, e.g. a straight forward use of imperative delegate/event have no chance of preventing implicit tight coupling and the formation of potential deadlock or infinite loop due to bad design or the lack of implementation details of other components.

该信息服务的设计不应导致隐含之间应该是松耦合组件，例如：紧耦合一个简单的使用必须委托/事件有没有防止隐紧耦合，以及潜在的死锁或无限循环，由于恶劣的设计或其他组件的实施细节没有形成机会。

We shall first apply the technique ofμ-bases and local cohomology to study the minimal generators for the moving surface ideals of rational cubic space curves and rational quartic space curves,and then study the implicit equations of rational space curves under different definitions of implicit equations.

在第五章中，我们将同调代数理论与μ基理论相结合，详细分析三次及四次空间有理曲线的动曲面理想生成元，为一般空间有理曲线的动曲面理想生成元的(来源：A21B12ceC论文网www.abclunwen.com)研究开辟可能的道路。

Finally, the Knight strung a line between two of the monoliths and tied the horses up there.

最后，骑士们在两颗巨石之间拉了一条绳子，将他们的座骑绑在上面。

T7zN/hyS0 The island lies south by east from here.

那个岛位于此地的正南偏东方向。