ON GENERALIZED FRACTIONAL PROCESSES

Abstract. A class of stationary long-memory processes is proposed which is an extension of the fractional autoregressive moving-average (FARMA) model. The FARMA model is limited by the fact that it does not allow data with persistent cyclic (or seasonal) behavior to be considered. Our extension, which includes the FARMA model as a special case, makes use of the properties of the generating function of the Gegenbauer polynomials, and we refer to these models as Gegenbauer autoregressive moving-average (GARMA) models. While the FARMA model has a peak in the spectrum at f = 0, the GARMA process can model long-term periodic behavior for any frequency 0 f 0.5. Properties of the GARMA process are examined and techniques for generation of realizations, model identification and parameter estimation are proposed. The use of the GARMA model is illustrated through simulated examples as well as with classical sunspot data.     

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.     

Algorithms for Quantum Branching Programs Based on Fingerprinting

In the paper, we develop a method for constructing quantum algorithms for computing Boolean functions by quantum ordered read-once branching programs (quantum OBDDs). Our method is based on ˉngerprinting technique and representation of Boolean functions by their characteristic polynomials. We use circuit notation for branching programs for desired algorithms presentation. For several known functions our approach provides optimal QOBDDs. Namely we consider such functions as MODm, EQn, Palindromen, and PERMn (testing whether given Boolean matrix is the Permutation Matrix). We also propose a generalization of our method and apply it to the Boolean variant of the Hidden Subgroup Problem.     

Leslie素矩阵的一个充要条件

Leslie矩阵模型在带年龄结构的种群动力学中具有重要地位,研究成果表明当Leslie矩阵为素矩阵时,目标种群将趋向一稳定的年龄分布。该文给出了一个无需通过烦琐的矩阵幂运算来判定Leslie矩阵是素矩阵的充分必要条件,它为Leslie模型的实际应用提供了很大方便。     

围长为2的奇数阶本原极小强连通有向图的1-指数集

研究了围长为2的n阶本原极小强连通有向图的1-指数集,证明了当n(≥5)为奇数时,En(1)={4,5,6,7,…,2n-5},无缺数段。     

一类特殊本原不可幂定号有向图的广义基

考虑了一类含有三个n—2圈和一个n圈本原不可幂定号有向图的广义基,通过分析图中是否存在寻求的途径及SSSD途径对,运用本原不可幂定号有向图的一些定义和性质,给出了此类图的广义本原指数及广义基.     

一种多基元类的布局迁移自适应算法及在闸机设计中的应用

布局问题研究物体的布局先后或布局定位以满足设计要求,布局迁移设计是在已有布局基础上高效设计新布局的方法。在轨道交通自动控制系统中,闸机表面传感器的布局对人与物的识别有重要的影响。为了实现闸机在不同地域环境中的快速设计,首先以闸机布局中的传感器作为研究对象,进行基元划分,提出了多种基元类型;并分析了基于拓扑结构的基元迁移变换方法,研究了人群特征因素、机械结构约束的数学表达;然后提出基于包围圆搜索的基元运动与干涉分析算法,其参数能够根据求解精度进行自适应调整;并利用多目标归一化函数对各基元的解进行择优,以获取最终布局。最后以18对传感器的闸机布局设计为例进行实例分析,应用此方法并借助于Visual Basic可视化编译平台,实现了闸机在不同地域环境中的传感器布局快速设计。     

Anticipating Degradation in State Estimation Accuracy via Online Nonlinear Observability Analysis

A methodology is proposed to enable real-time evaluation of the observability of local motions, and generate a local observability cost map to enable informed local motion planning in order to avoid potential degradation or degeneracy in state estimator performance. The proposed approach leverages efficient numerical techniques in nonlinear observability analysis and motion primitive-based planning technique to realize the local observability prediction with real-time performance. The degradation of the state estimation performance can be readily predicted with the local observability evaluation result. The proposed approach is specialized to a representative optimization-based monocular visual-inertial state estimation formulation and evaluated through simulation and experiments. The experimental results demonstrated the ability of the proposed methodology to correctly anticipate the potential state estimation degradation.     

基于Legendre多项式展开的双基SAR二维频域成像算法

针对任意构型双基SAR基于传统Taylor级数展开斜距方法的边缘点散焦问题,提出了一种基于Legendre正交多项式逼近的双基SAR二维频域成像算法。该算法基于对斜距函数的Legendre多项式展开推导了点目标二维频谱,解除了回波信号距离—方位的耦合,使成像处理更高效。在二维频域对场景区域的点目标采用二维频域成像算法进行成像。该算法改善了场景边缘点的聚焦效果,增加了场景边缘点的聚焦深度。理论推导和仿真结果验证了该算法的有效性和可行性。     

二元生成自由群的幂单性质(英文)

为了研究二元生成自由群的幂单性质,依据组合群理论,讨论了本原元素的若干组合方式,证明了可用于处理幂零的几组新方程.证明了可以嵌入一般线性群的二元生成自由群是幂单群的充要条件是它的每个本原元素均是幂单的.