查询词典 piecewise linear function

A new simplified three-dimensional piecewise continuous autonomous system (a modified model of unified chaotic system) was introduced by replacing a quadratic nonlinear term in a unified chaotic system with a piecewise linear signum function.

通过用分段线性符号函数替换统一混沌系统中部分二次项，得到一个新分段连续的自治系统(称为统一混沌系统修改模型)。

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。

Theinitializations both use the cost function with nominal head. Their difference is thatcontinuous function is adopted in successive linear programming while piecewiseapproximation employs the two piecewise linear segment function.

大量计算的结果表明，初始迭代点的计算采用电厂设计水头下的出力 I特性能加快整个模型的收敛性，在逐次线性规划中采用这种方式计算的初始迭代点尤其接近问题的最优点。

At the same time, we prove that the best linear unbiased prediction of a linear predictable variable Qy and the best linear unbiased prediction βn=(X"sV-1Xs)-1 X"sVs-1ys of regression coefficients of the finite populations βn=(X"V-1X)-1X"V-1y are admissible under matrix loss function and in the class of the linear predictions and the class that contains all predictions, and under quadratic loss function in the class of the linear predictions.

在线性预测类和一切预测类中是可容许预测，而在二次损失函数下其在线性预测类中是可容许预测。

In this paper,we give the error expressions of piecewise linear Lagrange polynomial interpolation and piecewise cubic polynomial interpolation using the Taylor expansions.

中文摘要：本文利用Taylor展开得到三角形上线性Lagrange插值和三次Lagrange插值的导数余项公式，对这些余项公式进行分析，给出了两类能以四阶精度逼近被插函数在对称点的导数值的格式，一种是在均匀剖分时其分片线性插值的相邻单元的导数值的后处理格式，一种是在六片强正规剖分时的三次插值在对称点上的导数值的后处理格式，使得在已知原函数在各节点的值后，通过一个简单的线性计算就可得到原函数在对称点的导数的一个超逼近值，将以往提出的平均导数的二阶精度提高到四阶。

Finite element methods are analyzed, where the stress is approximated by the discontinuous Raviart-Thomas element of lowestorder,and the velocity by the piecewise constant element,and the Lagranian multiplier by the trace space of the piecewise continuous linear element.

然后发展其有限元方法：对应四变量分别用间断型Raviart-Thomas最低阶元，分片常数元，连续线性元和连续线性元的迹空间，我们获得了稳定性和最优误差界，通过后处理办法，我们得到一个适合于计算的速度-压力格式，该格式可视为"mini"元方法的一个变形（本文格式中引用了局部投影算子）。

Theoretical analysis and experimental results demonstrate that some well known piecewise linear representation methods are special situations of proposed method. 2 A systemic method of indexing and similarity based querying in time series databases based on Piecewise Polynomial representation is proposed.

这项研究还从理论上证明了分段多项式表示是一种理想的时间序列高级数据表示形式，而著名的分段直线表示法和分段合计表示法只是PPR的特例。

Linear Algebra is mainly a subject which studies the linear structure of finite dimensional linear space and its linear transformation while linear concept is in itself from the old Euclid Geometry. The concept of "Linear Space" is a kind of algebraic abstract. In many fields of modern engineering project and technology, because of the influence of computer and graph showing, the algebraic disposal of geometric questions, the visual disposal of algebraic questions, algebra and geometry are tightly combined.

线性代数主要是研究有限维线性空间及其线性变换这一代数结构的学科，而线性概念究其根源则是来自古老的Euclid几何，线性空间概念是几何空间的一种代数抽象，在现代工程技术的许多领域里，由于计算机及图形显示的强大威力，几何问题的代数化处理，代数问题的可视化处理，把代数与几何更加紧密地结合在一起。

The representation of sequences is very helpful for the research of their linear complexity,so this paper we first research trace representation of periodic sequences,and the trace representation of a New Generalized Cyclotomic Sequence of order two of length pq is given,then for 2~mp~n period binary sequences,where p is an odd prime and 2 is a primitive root modulo p~2,we present a relation-ship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity and have the upper bound and lower bound of the value k, finally we discuss the k-error linear complexity of legendre sequences,also have the upper bound and lower bound of the value k,and discusses the situation where the linear complexity drop again for some Legendre sequences.

序列的表达形式对于其线性复杂度的研究是十分有帮助的，本文我们首先研究的是周期序列的迹表示，给出了2阶pq长度的扩展分圆序列的迹表示，然后讨论了周期为2~mp~n(m≥2)序列的线性复杂度与使得线性复杂度变小的最小的k值的关系，给出了k值的上界和下界，这里p为奇素数，2是模p~2的本原根，并通过例子讨论了其线性复杂度的稳定性，最后对Legendre序列k-错线性复杂度进行了分析，也给出了k值的上界和下界，并对某些Legendre序列讨论了线性复杂度再次下降的情况。

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骏彩现有产品十大系列、三十多种机型，包括玻璃双直边磨边机，高档家具系列（26磨头）、通用系列（22磨头）、建筑系列（16磨头）、夹层中空玻璃系列（12磨头）、自动切割机组系列，直线双边机系列，直线双圆边机系列，斜边机系列，直线单边机系列，直线单圆边机系列，自动、手动异形机系列，自动立式、卧式钻孔机系列，喷砂机系列，清洗机系列。

Chinese traditional virtue is humility and wariness,the compliment and praise to the others should be declination

中国人的传统美德是谦虚谨慎，对别人的恭维和夸奖应是推辞。如

We bought this house on the never-never.

我们以分期付款的方式买下这座房子。