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Some basic properties of σ- LFSR over F4 are studied, such as nonlinearity, cycle structure distribution of state graph, the largest period and counting problem related. The conclusions are as follows:The coefficient ring of σ-LFSR is isomorphic to the matrix ring over F,. The cycle structure of σ- LFSR is consistent with that of the determinant of the corresponding polynomial matrix if and only if the feedback polynomial of - LFSR does not contain nontrivial factor over F2,. The counting formula of the number of σ- LFSR with inconsistent cycle structure is also showed in that part. The period of σ-LFSR with degree n is maximum if and only if the determinant of the corresponding polynomial matrix is the primitive polynomial with order 2n over F2,.

本文研究了有限域F_4上的σ-LFSR的一些基本性质,如非奇异性、状态图的圈结构的分布、最大圈的充要条件及相关的计数问题等,得到以下结论:σ-LFSR的系数环同构于F_2上的矩阵环;σ-LFSR的状态图的圈结构与对应的多项式矩阵的行列式的圈结构一致的充要条件为σ-LFSR的反馈多项式不含有非平凡的F_2上的因式,给出了圈结构不一致的σ-LFSR的计数公式; n次σ-LFSR周期达到最大,当且仅当对应多项式矩阵的行列式为F_2上的2n次本原多项式。

The method includes steps: each point in sequence x with length L, i=0, 1, 2,apostrophe L-1 is served as a independent variable of k order polynomial; changing coefficient of polynomial to generate multiple sequence f with length L, where k is nonnegative integer; operation in polynomial is carried out in Galois Field GF, where Q=pm, p as a prime number, and m as nonnegative integer; assigning generated sequences to multiple sectors to set of create biased sequences for each sector; it is different in constant terms of polynomial, and identical to other coefficients of coefficients corresponding to sequence assigned to same sector; creating corresponding time - frequency pattern unit from biased sequences of the sector; repeating TFP unit with equal interval in frequency domain so as to obtain integrated TFP.

本发明涉及一种时频资源的分配方法,所述方法包括:把一个长度为L的序列{x,i=0,1,2,…L-1}中的每一点作为一个k次多项式的自变量,改变多项式的系数生成多个长度为L的序列{f},其中k是非负整数,多项式中的运算在伽罗华域GF中进行,其中Q=p m ,p是一个素数,m是非负整数;把生成的序列分配给多个小区,生成各小区的偏置序列集合,其中分配给同一个小区的序列所对应的生成多项式的常数项不同,其他项的系数都相同;由所述小区的偏置序列生成对应的时频图案单元,将时频图案单元经过频域等间隔重复,得到完整的时频图案。

Finally it mathematically calculates the CRC at bit and byte level and deducts a 16-bit CRC. The calculation and deduction consolidate the CRC theory. Chapter three also introduces the modulation by two, CRC polynomial, reflection polynomial applied in noise environment and the relationship between reflection polynomial and general polynomial.

第三章首先阐述了循环冗余码与循环码的关系——循环冗余码是一种短循环码、循环冗余码具有所有循环码的很多性质;然后,简单介绍循环冗余码的编码、译码原理和实现;最后,从普通数学的角度,分别用按比特、按字节求解CRC,详细推导了校验码宽度为16的CRC的理论过程,进一步为循环冗余码的研究提供有力的理论基础。

Romberg first use of the method is integral for integration, Then the results obtained by using the interpolation method were obtained Lagrange polynomial interpolation polynomial interpolation and Newton, re-use of least squares fitting of thinking obtained polynomial, the last of these different types of polynomial, identify their respective strengths and weaknesses.

首先运用Romberg积分方法对给出定积分进行积分,然后对得到的结果用插值方法,分别求出Lagrange插值多项式和Newton插值多项式,再运用最小二乘法的思想求出拟合多项式,最后对这些不同类型多项式进行比较,找出它们各自的优劣。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容,包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵,同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

The division with surplus, the comprehensive division and Eisenstein Test applications on polynomial that can not be divided are mainly discussed; the sufficient condition of that polynomial with coefficient being integer has no integer root, that cubic polynomial with coefficient being integer is irreducible in rational domain and that polynomial with coefficient being integer has not two completely same roots are summed up.

主要论述了带余除法、综合除法及不可约多项式艾森斯坦判别法的应用;总结出了整系数多项式的无整数根的充分性,三次整系数多项式在有理数域上不可约的充分性,整系数多项式无重根的充分性。

As an example to cubic trigonometric polynomial Bézier,the characters of trigonometric polynomial Bézier curve is analyzed,and deduced that cubic trigonometric polynomial Bézier curve is more smooth than cubic polynomial Bézier curve.

Bézier曲线是计算机辅助几何设计中的一类重要曲线,文献[1]介绍了三次Bézier曲线插值,文献[2]介绍了三次Bézier曲线的保凸插值,但难以解决一端曲率为0,另一端曲率比较大的插值问题。

Polynomial smooth techniques are applied to SVM model and replace x+ by a very accurate smooth approximation that is Hermite Interpolation polynomial,thus the undifferential model is converted into a differential model.The deduction procedure of Hermite Interpolation polynomial smoothing x+ is extended.

三次Hermite插值多项式光滑的支持向量机模型采用的是一种多项式光滑技术,用三次Hermite插值多项式代替单变量函数x+,将原来不可微的模型变为可微的模型,并且给出了三次Hermite插值多项式光滑化单变量函数x+的推导过程。

The polynomials, such as the Zernike polynomial, the orthogonal Zernike polynomial in square zone and the Legendre polynomial, are used to describe the phase of the wavefront in the algorithm of the Hartmann Sensor's model reconstruction in square zone.

方形区域上的哈特曼波前传感器的波前模式重构算法中可用Zernike多项式、方域上正交的Zernike多项式以及Legendre多项式来重构波前相位。

On the design of algorithms, a novel exact hierarchical delay analysis method for general circuits is proposed; based on the sensitization theorem for sequential circuits, an exact minimizing clocking method is proposed; based on Boolean process, a waveform simulation method considering interconnecting delay for logic circuit and a parallel waveform simulation method are proposed; a new method that transforms bit-level waveform polynomial to word-level polynomial model is proposed; a multiple valued synthesis algorithm based on multiple valued Boolean process and a wire-centered delay synthesis policy are proposed, in which timing planning, floorplanning, wire planning and optimal clock skew in early design are considered; a two-layers channel routing method for minimizing crosstalk under grid mode is proposed; based on the transition numbers theorems for waveform polynomial, a new method for generation of test with noise effects is proposed.

算法设计方面,提出了一种精确的通用电路层次化延时分析方法;基于时序电路的敏化定理提出时序电路最小时钟周期精确确定方法;提出基于Boolean过程论的考虑互连延迟的逻辑电路波形模拟方法,在分析了波形模拟适合并行化基础上,进一步提出一种并行波形模拟算法;提出一种将位级电路波形多项式描述转化成字级多项式描述的新方法;提出一种基于多值Boolean过程的多值电路综合算法以及一种将前期设计定时规划、前期设计的布局规划和线网结构化方法及低偏移的时钟分配等技术相结合的面向互连延时的综合策略;提出一种串绕最小化的网格模式下的双层通道布线方法;从波形多项式描述跳变数的定理出发提出了一种考虑噪声效应的测试生成新方法。

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Foods high in this vitamin include oily fish such as salmon, tuna and, and fish liver oils.

维生素D含量高的食物包括诸如大麻哈鱼、金枪鱼和鲭鱼之类的油鱼以及鱼肝油。

We need you to cosign our public letter demanding that press intimidation cease immediately, and that all charges be dropped.

我们需要您cosign我们的公共信,要求记者立即停止恐吓,并要求所有收费下降。

Finally, some conclusions are generalized at the end of this thesis.

最后,对全文工作进行总结,归纳本文的主要结论。