函数符号

This research method is independent of Green"s function and variational structure. So it can tackle with the BVP for non self-adjoint and self-adjoint difference equations and overcome the difficulties brought about by the establishment of Green"s function, a study of the sign and the estimate of below and above bounded for Greens function.

本章的研究方法既不依赖于Green函数又不依赖于变分结构，因而能解决非自共轭的差分方程边值问题，且克服了Green函数的建立、其符号的判断及其上下界的估计给研究带来的困难，该方法同样适用于研究自共轭的差分方程边值问题。

Besides, through the study of essentially bounded functions on the unit circle, we get the necessary and sufficient conditions for the essential commutativity of k~-order slant Toeplitz operators with special symbols.

在此基础上，通过对单位圆周T上本性有界函数性质的研究，给出了以特殊函数为符号的两个k阶斜Toeplitz算子本性可交换的充要条件。

Applying this transformation once, we can make the degree of the first r rows of the polyphase matrix decrease one order, and avoid decreasing the degree row by row as the traditional methods. This method is not restricted by the length of the filter, and needn't factorize the polyphase matrix into a special form.

本文对紧支撑小波构造方面的一些问题进行了探讨和研究，得到一系列有意义的结果，主要包括：在一元小波构造方面，给出由m-带紧支撑正交插值尺度函数显式构造相应正交小波符号函数的公式，这部分内容在第2章中给出。

A function or functor, as usual, may be attached to the symbol table.

通常，可以将一个函数或仿函数附加至符号表。

To overcome the false result with piecewise constant regions produced by the binary zero-crossing decision process, a hyperbolic tangent function is used to substitute the symbol function, governing softly the varieties of gray levels of pixels beside the zero-crossing of edges.

为了克服二值的零交叉决策过程导致的虚假的分片常数图像，利用双曲正切函数代替符号函数，柔和地控制边缘的零交叉点两侧像素的灰度值变化。

Three elements should be calculated in first-order circuit, which can synthesise analytical solution. Second-order series RLC and parallel RLC both can be calculated by the general function, which uses the Matlab to calculate differential equations. Generally, second-order and high-order circuits use Laplace transformation to formulate circuit equation, and get analytical solution by using Laplace inverse transform.

一阶电路先计算3要素，后合成解析结果；RLC串联和并联的二阶电路采用自编的通用函数计算，自编函数采用了Matlab求解微分方程的符号运算方法；一般的二阶电路和高阶电路采用拉氏变换列写电路方程，再用拉氏反变换得到解析结果。

Chapter 3 is devoted to equistability and equiboundedness of matrix differential equations by making use of the symbol property of the matrix Liapunov function and its Dini derivate on specific set.

第三章研究了矩阵微分方程的渐近行为，给出了直接运用矩阵Liapunov函数在某特定集合上的符号与其广义Dini导数符号的性质研究矩阵微分方程的稳定性和有界性。

In terms of average Symbol-Error Rate at the destination, the performances of multi-relay cooperative transmission with Maximal Ratio Combining detection and opportunistic relaying with multi-node listening were analyzed, one relay retransmitting in Amplify-and-Forward networks under independent Rayleigh slow fading channels. The closed-form expressions of SER for M-PSK and M-QAM modulations are also derived based on Moment Generating Function.

该文从接收端平均误符号率的角度，分析了独立的瑞利衰落信道下，采用放大转发的多中继协同最大比合并检测方案和多节点侦听，单中继转发的机会中继方案的性能；并基于矩生成函数推导出两种方案下M-PSK和M-QAM调制信号平均误符号率的闭合表达式。

A function f: V→{-1,1} defined on the vertices of a graph G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one.

函数f：V→{-1，1}称为图G的符号全控制函数，如果对每一个开邻域集上的点的函数值的和都大于等于1。

Finally the whole system is obtained using a proper nonlinear function based on signum functions.

首先选取合适的不稳定线性系统，利用一系列相互平行的分界面对相空间进行划分，然后通过对该线性系统进行平移变换，使新系统作用于相应的空间区域，最后利用基于符号函数的非线性函数来统一表示整个系统。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。