针对无网格并行计算的基于模糊均值聚类的分区方法*

针对国际上普遍采用的基于回归几何二分的分区方法的缺陷,提出了基于模糊均值聚类的均匀模糊均值聚类分区算法。采用该方法对不同类型的无网格几何模型进行了分区,并根据分区信息对三维实体模型进行了并行计算。通过与基于回归几何二分法的比较,充分验证该算法的有效性和可行性。     

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.     

化学反应蚁群优化算法

针对化学反应优化对反馈信息利用不足导致后期求解效率低的问题,提出化学反应蚁群优化算法.该算法利用化学反应优化生成较优解,通过信息素转换策略将较优解转换为蚁群算法的初始信息素,最后由蚁群算法累积更新信息素得到最优解.以TSP为例进行仿真,结果表明,与化学反应优化、蚁群算法、模拟退火算法相比,所提算法具有更高的寻优能力、收敛效率和计算效率.     

基于GPGPU的实体表面实时提取

为实时提取三维实体表面,提出一种基于GPGPU并行计算的实体表面实时提取方法。在分析深度剥离算法原理和GPU图形绘制管线的基础上,给出在GPU上利用深度剥离算法实现实时提取三维实体表面的算法;通过OpenGL的高级着色语言GLSL控制GPU的图形绘制管线实现了该算法,给出其伪代码。以龙、叶轮和刀具扫描体的模型为应用实例验证了该算法效果良好,特别是对于刀具扫描体表面的提取,可满足实时性要求。     

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.     

二维参数化图形技术研究进展

近几年来，参数化图形技术得到了不断的发展。目前已有多种参数化图形方法及系统。这些参数化图形方法可分为３种，即变分几何法、几何推理法和过程法。主要介绍这３种方法的研究进展。     

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$k\ge 3$.     

Undecidability of accordance for open systems with unbounded message queues

We study asynchronously communicating open systems modeled as Petri nets with an interface. An accordance preorder describes when one open system can be safely replaced by another open system without affecting some behavioral property of the overall system. Although accordance is decidable for several behavioral properties if we assume a previously known bound on the maximal number of pending messages, we show that it is not decidable without this assumption.