谱函数

In order to represent accurately and concisely the changing characteristics of one-dimensional spectrum density function in the chatter development. This thesis, for the first time, proposes the Edgeworth asymptotic expansion formulas of spectral density. A detailed proof is given. Some new statistic including spectral skewness, spectral kurtosis and spectral cumulants are proposed.

为了准确、简洁地表达一维谱密度函数在切削颤振建立过程中的变化特征，论文首次建立了一维谱密度函数的Edgeworth渐近谱展开式，给出了详细的证明；并由此提出了"谱偏态系数"、"谱峰态系数"和"谱累积量函数"等新的谱统计量。

There are many noise sources in measuring the seismometer transfer function, the main noise sources are investigated. The method of cross-special analysis is presented, flow process diagram of computing is given, the algorithms are discussed in detail, such as low-pass digital filter, computing of seismometer transfer function initial values, time domain convolution, bilinear transformation, estimation of power spectrum and cross-spectrum, window functions and preprocessing of measuring data etc.

在地震计传递函数测试过程中的存在多中噪声，本文分析了主要的噪声来源；介绍了用互谱分析方法测试地震计频率特性的基本原理和方法；给出采用该方法确定地震计传递函数的算法流程图；并对计算过程中采用的低通滤波器、地震计传递函数的初值确定方法、卷积运算方法、自谱和互谱估计、采用的窗函数和测试数据的预处理进行了详细讨论。

In the fourth chapter, firstly it introduces the Boolean functions algebraic expressions of the 2-value clock-controlled stop-and-go generator and Gunther generator. It reveals the balanced property of the two kinds of Boolean functions, and studies the Walsh cycle spectrum and the autocorrelation function. It also obtains the coincidence rate of their output sequences with affine sum of some bits of input sequences, and analyzes their ability of resisting the best affine approximation cryptanalysis and differential cryptanalysis. Secondly, we properly present a new definition of the Best Affine Approximation, namely BAA on the Boolean vector functions, followed by the spectral characteristic of such defined BAA attacks through using the decomposition formula of the union distribution for random variables. A lower bound of such BAA attacks is proposed. Finally, we also study the spectral characteristic of the second kind of nonlinearity of Boolean vector functions, followed by a higher bound of such nonlinearity. Furthermore, the limited relationship between the second kind of nonlinearity of Boolean vector functions and the linear structure of the linear combination of every component is analyzed.

在第四章中，首先给出了2值密钥流"停走生成器"和"衮特生成器"中实际存在的布尔函数的代数表示，揭示了这两类布尔函数的平衡性，随后研究了它们的Walsh循环谱和自相关函数等，得到了它们的输出序列与输入序列中的某些bit的仿射项的符合率，分析了它们抵抗最佳仿射逼近攻击和差分攻击的能力；其次，我们合理地给出了布尔向量函数最佳仿射逼近的新定义，利用布尔随机变量联合分布的分解式考察了相应的谱特征，并给出了布尔向量函数与其最佳仿射逼近的符合率的一个下界；最后，我们还考察了布尔向量函数第二类非线性度的谱特征，给出了布尔向量函数第二类非线性度的一个上界，并揭示了布尔向量函数第二类非线性度与其各个分量的线性和的线性结构之间存在的制约关系。

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

The preliminary chromatogram data were resolved with Mallat algorithm of wavelet analysis theory. This method that resetting the high frequency signals, reconstructing low frequency and then correcting the background signals in the original signal was to avoid the data skewness with negative digital points after background correction and achieve the baseline correction; according to the study and analysis of simulated data including curve background and real data of the needle-plate and free metal partials insulation defects, the method is effective; the best wavelet function of the background correction is Db5 and the best resolution times of the background correction is 8 for chromatogram data of SF_6 decomposition products, based on the calculation with different wavelet functions and resolution times.

在初步获取的气相色谱数据基础上，运用小波分析技术中的Mallat算法对色谱数据进行小波分解，采取将高频信号置零，重构低频背景信号，再用原始信号扣除背景信号的方法，并对背景信号进行纵向平移以避免扣除后出现负数据点造成色谱峰失真的题目及达到色谱图基线校正的目的；通过对含曲线背景信号的模拟色谱数据和针-板、自由金属微粒缺陷下的真实数据的计算研究表明，该方法的应用是有效的；并通过对不用小波函数和不同分解次数的背景扣除计算，确定了SF_6气体放电分解组分色谱背景扣除所选用的最佳小波函数为Db5小波和最佳分解次数为8次。

Dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesnt calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.

通过结构地震反应在小波基下的动力可靠性分析说明：无论是单自由度还是多自由度从理论上推导在这四种小波下的结构动力可靠性是可行的，而且考虑的结构地震反应都是非平稳的高斯过程，方法实现也比较容易；在Littlewood—Paley小波基下求得的结构的动力可靠度比较大，由改造的meyer小波和谐波小波求得的动力可靠度略有差异；单边指数小波下的结构动力可靠性分析非常简单，不用求功率谱函数来积分，只需求得结构地震反应的位移方差，速度方差，利用最大值分布公式就可得到结构的动力可靠时程；另外也考虑了超越界限对结构动力可靠度的影响，超越界限越小，结构的动力可靠度越小，即破坏概率越大。

According to static stability and avoiding the singularity induced bifurcation, saddle-node bifurcation, and Hopf bifurcation in power systems, this paper presents mathematical models for stability equilibrium solutions based on the semismooth property of spectral functions in mathematics.

针对电力系统中静态稳定和避免奇异诱导分岔、Saddle-Node分岔、Hopf分岔几类典型的系统稳定问题，基于数学上谱函数的半光滑特性，建立了系统稳定平衡解的数学模型。

Spherical Rossby wave ; spectrum function ; wave envelopes ; structure ; evolvement

球面Rossby波；谱函数；波包；结构；演变

We have made use of the spectral of effective gluons in static limit, calculated the effective thermodynamic potential in QGP with a soft exchange gluon at two-loop level, and studied the influence from the transverse gluon width to the potential.

我们先采用静极限下有效胶子的谱函数，通过计算含单个软交换胶子的QGP系统的热力学势直到两圈，研究了横胶子的有限宽度对系统热力学势的影响。

The effects of hot/dense hadronic environment on the spectral function of p meson is analyzed. It is found that hot/dense environment plays an important role to the spectral function: when the temperature or the density is not too high.

本文基于虚时形式的有限温度场论，分析了热密强作用物质环境对ρ介子性质的影响，计算得到了ρ介子的谱函数。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。