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With the aid of the spectral decomposition and finite expression formula of matrix we can compute matrix function.

利用矩阵函数的谱分解与有限表示形式计算矩阵函数。

In order to compute the voltages at the inaccessible nodes of decomposition, a formula that is suitable to linear networks is derived and the several kinds of method that are suitable to nonlinear networks are discussed.

本文讨论了不可及撕裂节点电压的计算，给出了适合线性子网络的计算公式；对含有非线性子网络的情况，提出了几种有效的计算不可及撕裂节点电压的方法。

The purpose of this paper is to present some ways of transformation based on decomposition of trigonometric reasoned formula of integral calculus, and furthermore, it can promote student s ability of integral calculation and use of recursion serial.

结合积分的计算，分析积分递推式的化归问题，三角有理式在积分中的拆分法的化归问题，有利于促进学生对于积分的计算以及递推序列的巧妙应用等数学能力的培养。

Then we discuss the sufficient and necessary condition which can guarantee that the original signal can be completely recostructed when using our decomposition and reconstruction formula of wavelet.

其次，给出了信号用分解公式进行小波分解与重构公式进行小波重构后完全恢复原信号的充要条件，并对完全重构充要条件的实现作了处理。

In Chapter 2, we mainly study the exact inversion and approximate inversion of the exponential Radon transform, and obtain the Sobolev analytic results; for convenience of practical calculation, we establish the another form of reconstruction formula through harmonic decomposition.

第二章我们主要讨论平面上的指数型Radon变换的精确反演和近似反演，得到了它们的有关Sobolev分析结果；为了实际计算的方便，我们用调和分解法作了进一步讨论，得到了重构公式的另一种表达形式。

Inspired by it, we give a condition that allows the iterated function system having the overlapping property, and obtain the multifractal decomposition formula of M-W fractal through the code space.

正是在这样的背景下，我们研究了一类允许弱重叠条件下的图有向自相似集的重分形分解，并通过码空间的局部维数的方法，得到了它的的重分形分解公式。

From the point of algebra, ablock decomposition formula for coefficient matrix of discrete Hartley transform isgiven, from which a new fast DHT recursive algorithm is derived.

本文首先从代数角度出发，给出离散Hartley变换系数阵的一种块分解式，由此导出DHT的一种新的快速递归算法。

Lastly, we present some theories of wavelet-based analysis of fractal image compression in chapter five. The more details of wavelet transform、wavelet frame、 wavelet basis、scaling function、reconstruction algorithm、decomposition algorithm and inverse formula are also discussed.

最后，我们在第五章介绍了基于小波分析的分形图象压缩的一些理论，还详细地讨论了小波变换、小波标架、小波基、尺度函数、重构算法、分解算法和反演公式。

A necessary and sufficient condition for a fx + t(y + g to be a bent function is disscussed,on which basis a necessary and sufficient condition for a function F = fix + tq + g to be a bent function is given when q is not a balanced-function by use of cyclic walsh spectrum and decomposition formula of walsh spectrum.

讨论了形如fx+τ(y+g的布尔函数是Bent函数的充分必要条件，在此基础上利用Bent函数的循环Walsh谱及谱分解式，进一步给出了当q不是平衡函数时，形如F=fx+τ(yq+g布尔函数是Bent函数的充分必要条件。

In which the problem of the construction was merged into that of the decomposition of the cubic group.

我们在第四章讨论了这一问题，对于任意链长的算符分解给出了实际可操作的一般算法，并且给出了部分8-链的结果。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。