查询词典 variational derivative

The first rank derivative is a reflection of curve change and its rate, at certain range, if the sign of the first rank derivative has changed, the logging value of the correspondence depth point means maximum in this range; the second rank derivative is the knaggy property reflection of curve, at certain range, if the sign of the second rank derivative has changed, the correspondence depth point represent the inflexion of geophysical logging curve, it＇s also a turning point of the reflection of knaggy change property of the curve, it is the interface of stratum.

测井曲线的值是深度的函数，测井曲线的一阶导数表示了曲线变化的趋势和变化的快慢，在某一范围内，当一阶导数呈现符号转换时，相对应的深度点的测井值即为该范围内极大值；测井曲线的二阶导数则表示曲线的凹凸性，在某一范围内，当二阶导数呈现符号转换时，相对应的深度点代表了测井曲线的拐点，即反映曲线凹凸性变化的转折点，亦即地层的分界面。

At the same time, the variational stability of bounded variation solutions at the effect of perturbation and non-perturbation for the impulsive differential system are discussed, the Ljapunov type theorems for variational stability and asymptotically variational stability for impulsive differential systems are established.

同时，讨论了在无扰动和有扰动的情况下，这类固定时刻脉冲微分方程有界变差解的变筹稳定性，建立了此类微分系统有界变差解变差稳定性和渐近变界稳定性的两个Ljapunov型定理。

The numercial simulation has been carried out, and the experimental results show that this method has been improved significantly comparing with the traditional one in nonlinear optics. Secondly, a second order system of semilinear elliptic equations, which comes from a mathematics model of the electric potential distribution of a media surrounded with the protein, is transformed into a variational problem, the existence of solution of it is proved by using variational principle and Trudinger—Moser inequality, and the relation between the solutions of variational problem and the solutions of its dual problem is obtained.

首先，讨论了非线性光学中的二次谐波产生的耦合方程组，利用变分法证明了耦合方程组非平凡解的存在性，然后进行了数值模拟，实验结果表明文中方法比经典的非线性光学中的方法有较大的改进，这对优化光倍频器件的设计将有所帮助；其次，将一类二阶半线性椭圆型方程组转化为一个变分问题，然后利用变分法和

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

Firstly, the generalization of Fan-Ha section theorem and a general vector variational inequality without convexity assumption and minimax theorem of vector-valued function are obtained. Then, the quasi-montone vector variational inequality problem is concerned. Cx-quasi-monotone operator is defined in topological vector space, inner point of a closed convex set K is introduced, the relation between inner point and relative algebraic interior point is given, an existence result for quasi-monotone vector variational inequality is obtained.

第三章主要研究了向量变分不等式和极小极大定理(来源：3282AB83C论文网www.abclunwen.com)，建立了广义的Fan-Ha截口定理、新的向量变分不等式与极小极大定理，并在拓扑向量空间中定义了C_x-拟单调算子，引入了闭凸集K的inner点，给出了inner点与相对代数内点的关系，利用innK_c代替K的拓扑内部，建立了新的拟单调向量变分不等式。

Theory of variational inequality is an important part of nonlinear functional analysis, and variational inclusions are generalizations of variational inequalities.

在非线性分析中，变分不等式理论是一个重要组成部分。而变包含问题是变分不等式的一种重要推广形式。

Variational identity play a important role to prove nonexistence and get prior estimate of solution, In this thesis, we study following parts on the relationship of symmetry group of partial differential equations with variational structure and the variational identity.

变分恒等式在证明具有变分结构偏微分方程解的不存在性以及得到方程解的先验估计时有着非常重要的作用，本文研究了一些具有变分结构偏微分方程的对称群与其变分恒等式的关系。

The average relativeerror was 3.63%, less much than mostly used group-contribution methods for alkyne, chlorine derivative, iodine derivative, especially for alkane, bromine derivative, aromatic hydrocarbon, alicyclic hydrocarbon and sulfur-containing organic compounds.

对4068种有机物的正常沸点进行了估算，其平均相对误差为3.63%，总体估算精度明显优于相比较的基团贡献法，对炔烃、氯衍生物、碘衍生物，尤其是对烷烃类、溴衍生物、芳烃、脂环烃和含硫化合物的估算误差明显减小。

We investigate mainly solving the hyperbolic and parabolic equations by using the MQ quasi-interpolation. The underlying idea of our means is that: employing the derivative of the MQ quasi-interpolation to approximate the spatial derivative of the PDE, while the approach of the temporal derivative of the PDE is used a finite difference.

我们主要就MQ拟插值在双曲型方程和抛物型方程中的应用进行了研究，其基本思路是：利用MQ拟插值的导数逼近微分方程的空间导数，而微分方程的时间导数则采用有限差分逼近。

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

So it was last week in Selma , alabama.

上星期在亚拉巴马州塞尔马市发生的事件也是这样一个转折点。

The group also spearheads various social programs in China.

该组织还带头参与中国的各种社会活动。