一类最优跳频序列族的代数构造

在通信系统中,直接序列扩频和跳频扩频是两种最主要的扩散编码技术.而在FHCDMA系统中,跳频序列被广泛使用.利用分圆法和离散对数函数,首先构造了一类具有新参数的跳频序列族,并给出了各类汉明相关值的计算公式.其次,证明了所构造的跳频序列(族)所具有的最优性.     

全部 n 级 M 序列构造方法的计算机实现

<正> 最长 n 级非线性移位寄存器序列简称为 n 级 M 序列,记为(a_0,a_1,…,a_2~n-1),a_i=0或1,它是以2~n 为周期的序列.在序列中连续 n 个元(a_ia_(i+1)…a_(i+n-1))称为状态,n级 M 序列中,全部2~n 个状态两两不同.M 序列具有较好的伪随机性与相关特性,而且数目多,容易保密,因此在通信等工程领域得到了重要应用.例如,M 序列可以在多址通信     

关于 M 序列的相关函数

关于正交码,双正交码和等距码作为信号集应用于各种通信系统的性能已经有了广泛的研究.近年来由于扩展频谱多址通信网络的发展,应用 M 序列作信号集受到注意.由于一般信号集应用于通信系统的性能依赖于信号的相关系数矩阵,对于循环序列则依赖于序列的周期相关函数,本文对 M 序列的相关函数的性质与计算进行研究,得到一些初步结果,也许能对某些应用或对这方面的进一步研究提供一些帮助.     

利用有限域上交错矩阵构造Cartesian认证码

设Fq是q元有限域,q是素数的幂.令信源集S为Fq上所有的n×n交错矩阵的合同标准形,编码规则集E为Fq上所有的n×n非奇异矩阵,信息集M为Fq上所有的n×n交错矩阵,构造映射f:S×E→M,(K'(v,n),g)→gK'(v,n)gT.证明了该四元组(S,E,M;f)是一个Cartesian认证码,并计算了它的参数.进而,假定编码规则按照均匀的概率分布所选取,计算出了该码的成功模仿攻击概率PI和替换攻击概率Ps.     

考虑检验错误的集团抽样检验接收概率函数

本文给出存在集团检验误差时的集团抽样检验接受概率计算公式,该公式可用于设计抽样方案、分析集团检验错误对抽样方案的影响.采用计算机模拟抽样检验的方法对给出的公式加以验证,证明了该所给公式的正确性.同时通过对集团检验错误存在与否的抽样检验特征(OC)曲线的比较,指出:以往的集团抽样检验方案设计,都是在假设无检验误差前提下设计的,在抽样检验中,若存在检验错误,会严重影响抽样检验的接收概率,使抽样检验结果不能客观地反映检验批的质量.     

M序列一个周期的复杂度

在流密码中,M序列及M序列一个周期复杂度是一个重要课题。Chan等人在文献[2]中对M序列的界和分布进行了讨论。本文将对M序列一个周期复杂度进行一些研究,并且主要讨论M序列一个周期复杂度的上下界,遍历性和分布情况。 注 本文在GF(2)上和n≥3情况下讨论。     

产生 M 序列的一个递推算法

§1.引言M 序列又称 de Bruijn 序列,是一类具有最长周期的非线性移位寄存器序列。本文研究产生 M 序列的算法。早在70年代万哲先等对构造 M 序列的方法已有系统的研究。此后有一系列的文章研究 M 序列的构造问题。最近 Fredricksen 对这方面的工作给出了一个很好的综述。产生 M 序列的一个常用方法是先由一个较简单的移位寄存器产生许多短圈,再用并圈法将这些短圈合并起来构成 M 序列。如在[1,6]中就已给出过一些将 n 级纯轮换移位寄存器(简记为 PCK_n)和 n 级补轮换移位寄存器(简记为 CCR_n)产生的圈合并为 M 序列的方法。与[1—7]不同,Fredricksen 给出一个将 PCR_n 产生的圈合并为 M 序列的递推算法。最近 Etzion 和 Lempe 在 Fredricksen 算法的基础     

2002年高考新课程卷中概率解题剖析与思考

20 0 2年新课程卷概率题目 :某单位 6个员工借互联网开展工作 ,每个员工上网的概率都是 0 .5 (相互独立 ) .(Ⅰ )求至少 3人同时上网的概率 ;(Ⅱ )至少几人同时上网的概率小于 0 .3 .(注 :本小题考查相互独立事件同时发生或互斥事件有一个发生的概率的计算方法 ,考查运用概率知识解决实际问题的能力 ) .2 0 0 2年 7月笔者参加了全国高考新课程卷(江西省考区 )数学概率题目的评卷工作 .在评卷过程中遇到许多错误解法 ,下面例举其中一些典型错误并进行剖析 ,并对中学概率与统计教与学进行相应探讨 .1　概率解题中典型错误剖析错误一 :考生不能…     

有限队列M/G/1排队系统的解析模型

本文应用广义马尔柯夫更新过程研究了M|C|1|N混合制排队系统的随机特性,提出了一种求解系统稳态概率的算法,从而给出了系统稳态运行指标的计算公式。     

伪随机序列

在数字通信、测距及跟踪系统中常用伪随机序列来调制信号(即将信号波形用此种序列编码),以达到提高可靠性和有效性或保密等目的.其重要的应用是在测距方面.据报导,早期曾用长度为2~(13)-1=8191的 m-序列于金星测距,在极低的信噪比情况下提取信号,达到极高的测量精度;但这是用长的积累时间换取到的.后来,为了能快速检测,有的深空测距系统用几个短 m-序列的 Boole 组合序列调制连续载波,从而大大缩减了积累时间.伪随机序列亦曾用于可由单人背负的便携式连续波 Doppler 雷达,供前沿侦察之用;在功率相当低的情况下,提供了清晰的距离与速度信息.本文将国外资料中有关伪随机序列的主要结果作一侧重于数学方法的介绍,主要参考资料列在后面.     

格蕴涵代数中的扩张滤子

在格蕴涵代数中提出了扩张滤子的概念,讨论了扩张滤子与滤子,扩张滤子与素滤子,扩张滤子与滤子的根,扩张滤子与准素滤子,扩张滤子与最大滤子之间的关系.得到了扩张滤子的一些性质.最后,证明了在格H蕴涵代数中,扩张滤子与扩张滤子的根相等.     

Optimal boundedness criteria for extended-real-valued functions

The notion of genuinely bounded below function is introduced and characterized by means of the concept of co-equilibrated function. As an application, we state two boundedness criteria for extended-real-valued functions, both optimal in a clearly defined sense. The first one says that an extended-real-valued function minorized by an affine map and coinciding from some value up with a co-equilibrated function is bounded below. The second criterion states that an extended-real-valued function minorized by an affine map is bounded below provided that one of its sub-level sets is co-equilibrated.     

On the Structure of Order Domains

The notion of an order domain is generalized. The behaviour of an order domain by taking a subalgebra, the extension of scalars, and the tensor product is studied. The relation of an order domain with valuation theory, Gröbner algebras, and graded structures is given. The theory of Gröbner bases for order domains is developed and used to show that the factor ring theorem and its converse, the presentation theorem, hold. The dimension of an order domain is related to the rank of its value semigroup.     

A stochastic representation for the Poisson–Vlasov equation

A stochastic representation for the solutions of the Poisson–Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence proof and an intuitive characterization of the solutions, may also be used to obtain an intrinsic definition of the fluctuations.     

On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

The self-induced rotational and oscillatory motions of an aerodynamic pendulum

The behaviour of an oscillatory mechanical system with alternating dissipation is considered taking an aerodynamic pendulum as an example. The phase portraits are investigated, their rearrangements are studied and the critical values of a parameter are determined. The equilibrium positions of the pendulum and the self induced rotational and oscillatory states of the motion are determined and their stability is investigated.     

On a periodic motion of a rigid body carrying a material point in the presence of impacts with a horizontal plane

A material system consisting of an outer rigid body (a shell) and an inner body (a material point) is considered. The system moves in a uniform field of gravity over a fixed absolutely smooth horizontal plane. The central ellipsoid of inertia of the shell is an ellipsoid of rotation. The material point moves according to the harmonic law along a straight-line segment rigidly attached to the shell and lying on its axis of dynamical symmetry. During its motion, the shell may collide with the plane. The coefficient of restitution for an impact is supposed to be arbitrary. The periodic motion of the shell is found when its symmetry axis is situated along a fixed vertical, and the shell rotates around this vertical with an arbitrary constant angular velocity. The conditions for existence of this periodic motion are obtained, and its linear stability is studied.     

The Stress Boundary Value Problem for an Ideal Fibre-reinforced Rectangular Plate with a Hole

The title problem is examined for plane deformations of an idealfibre-reinforced rectangular plate with a hole. The solutionis found to depend on simultaneous ordinary differential equationswhich may be integrated without difficulty. This is in markedcontrast with the corresponding problems for an anisotropicelastic body and enables approximate solutions for stronglyanisotropic bodies to be derived without difficulty. The particularcases of a line crack in the plate at an angle to the fibresand an arbitrary symmetrical hole are examined in detail.     

偏心裂纹板在裂纹面受两对反平面点力的弹塑性解析解

采用线场分析方法对理想弹塑性材料偏心裂纹板在裂纹面受两对反平面点力的情形进行弹塑性分析,分析不受小范围屈服条件的限制,求得了裂纹线附近应力场和位移场的弹塑性解析解、裂纹线上的塑性区长度随外荷载的变化规律及有限宽板具有偏心裂纹的承载力.     

Truck routing and scheduling

The problem is part of a complex software solution for truck itinerary construction for one of the largest public road transportation companies in the EU. In practice a minor improvement on the operational cost per tour can decide whether a freight services company is profitable or not. Thus the optimization of routes has key importance in the operation of such companies. Given an initial location and an asset state one must be able to calculate a cost optimal itinerary containing all Point of Interests. Such an itinerary is an executable plan which exactly specifies the location and activity of an asset during the whole timespan of the itinerary. If parking places and gas stations are included in the planning then it is NP hard to find an optimal solution. This means that for long range tours an approximately optimal solution for refueling has to be given within an acceptable running time. Also the corridoring of the trucks is an important problem so that we try to optimize the performance, hence tours cannot be recalculated at each data arrival. The vehicle assignment part of this work is already finished and applied with very good results. The remaining part is subject of an ongoing research which started at January 2014. The company started to apply and test our product in the beginning of 2015 under increased human supervision. As a consequence of the project a large cost saving is anticipated by the company.