轴流式转轮三元粘性流动数值计算

为进一步提高轴流式转轮的设计精度与性能,采用时均Navier-Stokes控制方程,标准k-ε湍流模型及SIMPLEC算法,对一轴流定浆式水轮机转轮内三元粘性流动进行了数值模拟。提出了水力损失计算方法,获得了转轮的预测效率。分析了转轮内部流场分布规律,建立了叶片表面压力在包角范围内的变化曲线,有助于认识转轮内真实流动现象,为改善设计提供可视化数据支持。     

FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

Computer Algebra Derivation of the Bias of Linear Estimators of Autoregressive Models

Abstract. A symbolic method which can be used to obtain the asymptotic bias and variance coefficients to order O(1/n) for estimators in stationary time series is discussed. Using this method, the large‐sample bias of the Burg estimator in the AR(p) for p = 1, 2, 3 is shown to be equal to that of the least squares estimators in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for the Burg estimator's bias because this problem is too intractable without using computer algebra. The asymptotic bias coefficient to O(1/n) of Yule–Walker as well as least squares estimates is also derived in AR(3) models. Our asymptotic results show that for the AR(3), just as in the AR(2), the Yule–Walker estimates have a large bias when the parameters are near the nonstationary boundary. The least squares and Burg estimates are much better in this situation. Simulation results confirm our findings.     

基于Msp430无线安防传感网的设计研究

文中给出了一种面向无线传感网络协议的改进方法,设计并实现了一种面向于中小型场所的远程智能安防系统。该改进方法采用只在中心节点形成与维护路由表的策略,形成多路径单跳网络。通信节点采用具有超低功耗特性的Msp430单片机和CC1101射频模块构架,中心节点采用PC机外接CC1101RS-232串口模块方案,将汇聚节点和基站服务器合二为一,实现通信协议的转换,同时为远端移动终端节点提供通信接口。通信过程增加接收确认信号环节以确保信号的有效发送。实验结果表明,文中的设计方法能够高效地完成在有效通信范围内的信息传感。     

Holographic algorithms on bases of rank 2

An essential problem in the design of holographic algorithms is to decide whether the required signatures can be realized under a suitable basis transformation (SRP). For holographic algorithms with matchgates on domain size 2, , ,  and  have built a systematical theory. In this paper, we reduce SRP on domain size k≥3$k\ge 3$ to SRP on domain size 2 for holographic algorithms with matchgates on bases of rank 2. Furthermore, we generalize the collapse theorem of [3] to domain size k≥3$k\ge 3$.     

基于GPU-CUDA的共轭斜量法实现及性能对比

偏微分方程数值解法(包括有限差分法、有限元法)以及大量的数学物理方程数值解法最终都会演变成求解大型线性方程组。因此,探讨快速、稳定、精确的大型线性方程组解法一直是数值计算领域不断深入研究的课题且具有特别重要的意义。在迭代法中,共轭斜量法(又称共轭梯度法)被公认为最好的方法之一。但是,该方法最大缺点是仅适用于线性方程组系数矩阵为对称正定矩阵的情况,而且常规的CPU算法实现非常耗时。为此,通过将线性方程组系数矩阵作转换成对称矩阵后实施基于GPU-CUDA的快速共轭斜量法来解决一般性大型线性方程组的求解问题。试验结果表明:在求解效率方面,基于GPU-CUDA的共轭斜量法运行效率高,当线性方程组阶数超过3000时,其加速比将超过14;在解的精确性与求解过程的稳定性方面,与高斯列主元消去法相当。基于GPU-CUDA的快速共轭斜量法是求解一般性大型线性方程组快速而非常有效的方法。     

基于宇宙计算的图形处理器算法实现

下一代观测望远镜将会产生数以亿计的星系测量数据值,这将导致使用中央处理器处理数据时效率低下、成本较高。为了解决这一问题,提出了基于宇宙计算的图形处理器算法。研究了两点式角相关函数以及孔径质量统计这两种宇宙学的计算方法,构建算法代码,并使用统一计算设备架构在图形处理器上实现了这两种算法;比较了算法在中央处理器和图形处理器上使用的运行速度。实验结果表明,与中央处理器相比,使用图形处理器的计算速度得到了显著提高。     

基于博弈论的百万富翁协议

在经典的百万富翁协议中,一方在得到最后的财富比较结果后,没有动机将结果告诉另一方,或者告诉另一方一个错误的结果。结合博弈论和密码算法,提出一种百万富翁协议。在此协议中,参与者背离协议的收益小于遵守协议的收益,遵守协议是参与者的最优策略,任何百万富翁的欺骗行为都能被鉴别和发现,因此理性的参与者有动机发送正确的数据。最后每个参与者都能公平地得到最后的财富比较结果。     

基于矩阵初等变换的量子可逆逻辑电路双向综合算法

基于矩阵初等变换,提出了量子可逆逻辑电路双向综合算法。该算法依据两数字间的汉明距离,通过交换矩阵行号或矩阵元素对量子可逆逻辑电路的矩阵进行初等行变换。在变换的过程中,利用邻接矩阵的电路转化规则,生成任意给定置换的量子可逆逻辑电路。与其它同类算法相比,由于不需要穷尽搜索,该算法的时空复杂度有大幅降低;又由于采用任意n量子扩展通用Toffoli门,该算法可综合任一置换(奇或偶置换)的量子可逆逻辑电路,并且电路中门的数量有所减少。     

A Normalization Method of Moment Invariants for 3D Objects on Different Manifolds

3D objects can be stored in computer of different describing ways, such as point set, polyline, polygonal surface and Euclidean distance map. Moment invariants of different orders may have the different magnitude. A method for normalizing moments of 3D objects is proposed, which can set the values of moments of different orders roughly in the same range and be applied to different 3D data formats universally. Then accurate computation of moments for several objects is presented and experiments show that this kind of normalization is very useful for moment invariants in 3D objects analysis and recognition.