A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

Shorts in self-checking circuits

It has been noted by several authors that the classical stuck-at logical fault model might not be an appropriate representation of certain real failures occurring in integrated circuits. Shorts are an important class of such faults. This article gives a detailed analysis of the effects of shorts in self-checking circuits and proposes techniques for dealing with them. More precisely, we show that, unlike other faults such as stuck-at, stuck-on, and stuck-open—which produce only single errors in the place they occur—shorts can produce double errors on the two shorted lines. In particular, feedback shorts can produce double errors on the two shorted lines. The double error is unidirectional for some feedback shorts and non-unidirectional for some others. Furthermore, in some technologies (e.g., CMOS), non-feedback shorts can also produce double non-unidirectional errors. We also show that unlike stuck-at, stuck-on, and stuck-open faults, redundant shorts can destroy the SFS property. Then we propose several techniques for coping with these problems and we illustrate the results by circuit implementation examples.The present study is given for NMOS and CMOS circuits but we show that it is valid for any other technology.     

再论变化电磁场中带电超微粒子的精确量子论

利用创新的SU(1 ,1 )Lie代数理论及SO(3)Lie代数理论 ,得到变化电磁场中带电超微粒子的精确量子论 ,由此进一步明确微观领域中的时空概念     

gain bounds for systems with sector bounded and slope‐restricted nonlinearities

This paper proposes a new method for calculating a bound on the gain of a system comprising a linear time invariant part and a static nonlinear part, which is odd, bounded, zero at zero and has a restriction on its slope. The nonlinear part is also assumed to be sector bounded, with the sector bound being (possibly) different from that implied by the slope restriction. The computation of the gain bound is found by solving a set of linear matrix inequalities, which arise from an integral quadratic constraint formulation of a multiplier problem involving both Zames‐Falb and Popov multipliers. Examples illustrate the effectiveness of the results, and comparisons are made against the state‐of‐the‐art. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

ESTIMATION FOR NONNEGATIVE AUTOREGRESSIVE PROCESSES WITH AN UNKNOWN LOCATION PARAMETER

Abstract. Consider an AR(1) process given by X ^t=γ+ø X _t+ Z _t≥ 1. where 0 ≤γ, 0 ≤ø 1 are unknown parameters and the innovations Z _t, ≥ 1, are independently and identically distributed positive random variables. We propose estimates of (γø) which are obtained as the solution to a linear programming problem and establish their strong consistency. When the Z _ts have the exponential distribution. our estimate becomes the conditional maximum likelihood estimate given X ₀. Under the assumption of regular variation of the innovation distribution at its left and right endpoints (assumed to be 0 and ∝ respectively), we establish asymptotic limit laws for the estimates. Consistent estimators for a class of moving-average processes with heavy-tailed innovation distribution are also presented.     

一种合成聚焦的便携式B型超声成像方法

传统合成聚焦超声成像方法在图像重建过程中处理数据量较大,致使其在便携式B型超声设备中应用受限。针对该问题,提出一种基于压缩感知理论和合成聚焦波束形成算法的便携式B型超声成像方法(SFCS)。该方法通过对接收到的射频回波信号进行随机采样得到欠采样的测量信号,将测量信号经过合成聚焦波束形成处理获得欠采样的射频信号线,基于压缩感知的信号重构算法,由欠采样的射频信号线高质量地恢复信号后供后续成像处理使用。仿真实验结果表明,SFCS可有效地解决合成聚焦超声成像过程中数据量大的问题,从而在保证较高成像质量的前提下满足便携式B型超声设备小型化、低成本的技术要求,具有工程应用价值。     

受限波兹曼机联合稀疏近似的脑功能检测模型

人脑功能连通性检测是神经科学研究的重要技术．使用受限制波兹曼机（RestrictedBoltzmannMachine,RBM）对大量多被试功能磁共振（functionalMagneticResonanceImaging,fMRI）数据进行建模可以检测人脑功能连接,但是不能有效检测单被试数据的功能连接．本文研究一种新颖的融合了稀疏近似与RBM技术的脑功能连通性检测模型,该模型充分利用fMRI数据的稀疏性,采用稀疏近似理论对fMRI数据进行空间域稀疏近似压缩,然后使用RBM建立模型,以检测脑功能连通性．实验结果表明,该融合模型可以有效地提取单被试数据的脑功能时间域混合模型及其相应的脑功能图谱,解决了RBM在单被试数据分析上的瓶颈．     

3D Object Recognition Based on Linear Lie Algebra Model

A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed.Then an algorithm of 3D object recognition using the linear Lie algebra models is presented.It is a convenient recognition method for the objects which are symmetric about some axis.By using the presented algorithm,the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained.At last some recognition results of practicalities are given.     

缺失数据下m相依样本的大样本性质

讨论了缺失数据在随机补充方式下均值的估计,证明了估计的相合性和渐进正态性,并给出了经验似然比统计量的渐进分布．