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A general result on precise asymptotics for linear processes of positively associated sequences 被引量:10
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作者 TAN Xi-li YANG Xiao-yun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第2期190-196,共7页
Let {εt; t ∈ Z^+} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2+1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^+} is a sequence of real numbers s... Let {εt; t ∈ Z^+} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2+1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^+} is a sequence of real numbers satisfying ∑j=0^∞|aj|〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E|ε1|^2+δ′〈 for some δ′〉0 and μ(n)=O(n^-ρ) for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}. 展开更多
关键词 PA sequence linear process general law precise asymptotics.
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The SCUSUM Estimation of Variance Change Point in Linear Process 被引量:1
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作者 ZHAO Wen-zhi XIA Zhi-ming 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期170-173,共4页
This paper considers the estimation problem of a variance change-point in linear process.Consistency of a SCUSUM type change-point estimator is proved and its rate of convergence is established.The mean-unknown case i... This paper considers the estimation problem of a variance change-point in linear process.Consistency of a SCUSUM type change-point estimator is proved and its rate of convergence is established.The mean-unknown case is also considered. 展开更多
关键词 variance change point linear process rate of convergence
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Central limit theolrem for linear processes generated byⅡD random variables under the sub-linear expectation
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作者 LIU Wei ZHANG Yong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2021年第2期243-255,共13页
In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expec... In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive. 展开更多
关键词 central limit theorem invariance principle ⅡD random variables sub-linear expectation linear process
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THE MONITORING FOR PHYSICAL DEVELOPING PROCESS WITH A LINEAR CCD
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作者 Jing Kun XU Ping CHEN +1 位作者 Li ZHANG De Shui ZHENG(Institute of Photographic Chemistry, Academy of Sciences, Beijing. 100101) 《Chinese Chemical Letters》 SCIE CAS CSCD 1996年第4期361-364,共4页
In this work, we used a linear CCD to detect the whole physical developing process of silver diffusion transfer reversal process in photographic chemistry. The influence of the ingredient of the working solution was s... In this work, we used a linear CCD to detect the whole physical developing process of silver diffusion transfer reversal process in photographic chemistry. The influence of the ingredient of the working solution was studied. 展开更多
关键词 THE MONITORING FOR PHYSICAL DEVELOPING PROCESS WITH A linear CCD
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LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES 被引量:6
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作者 胡舒合 王学军 《Acta Mathematica Scientia》 SCIE CSCD 2008年第2期295-300,共6页
Let (Xi) be a martingale difference sequence and Sn=∑^ni=1Xi Suppose (Xi) i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny (Stochastic Process. Appl. 96 (2001) 143) obtained the estimation μ(Sn ... Let (Xi) be a martingale difference sequence and Sn=∑^ni=1Xi Suppose (Xi) i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny (Stochastic Process. Appl. 96 (2001) 143) obtained the estimation μ(Sn 〉 n) ≤ cn^-p/2, Yulin Li (Statist. Probab. Lett. 62 (2003) 317) generalized the result to the case when p ∈ (1,2] and obtained μ(Sn 〉 n) ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ(Sn 〉 n) as those for martingale difference sequence. 展开更多
关键词 Large deviation φ-mixing sequence NA sequence linear process
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STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS 被引量:2
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作者 林正炎 李德柜 《Acta Mathematica Scientia》 SCIE CSCD 2008年第1期217-224,共8页
Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependen... Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes. 展开更多
关键词 Strong approximation long memory process linear process fractional Brownian motion the law of the iterated logarithm
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A dynamic programming algorithm for scheduling problems on earliness award and tardiness penalty with time-dependent processing time 被引量:1
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作者 余英 孙世杰 何龙敏 《Journal of Shanghai University(English Edition)》 CAS 2008年第3期204-209,共6页
In this paper, a single-machine scheduling model with a given common due date is considered. Job processing time is a linear decreasing function of its starting time. The objective function is to minimize the total we... In this paper, a single-machine scheduling model with a given common due date is considered. Job processing time is a linear decreasing function of its starting time. The objective function is to minimize the total weighted earliness award and tardiness penalty. Our aim is to find an optimal schedule so as to minimize the objective function. As the problem is NP-hard, some properties and polynomial time solvable cases of this problem are given. A dynamic programming algorithm for the general case of the problem is provided. 展开更多
关键词 scheduling SINGLE-MACHINE linear decreasing processing time EARLINESS TARDINESS
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The Meaning of Accelerated Motion 被引量:1
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作者 Qing Li 《Applied Mathematics》 2021年第7期535-545,共11页
In classic mechanics, the force is the interaction of matter, and it is also the basic reason for accelerated motion of objects. In general relativity, the force is no longer the interaction of objects, but the result... In classic mechanics, the force is the interaction of matter, and it is also the basic reason for accelerated motion of objects. In general relativity, the force is no longer the interaction of objects, but the result of curvature of space and time. In this paper, the significance of acceleration is elaborated according to Axioms 1 and 3. Being different from Axiom 2 in which the acceleration force of the continuum is given by the ratio of variables, the accelerated motion in Axiom 1 is carried out in units superimposed because there is only one space or time independently where space-time bending is meaningless. The accelerated motion in Axiom 3 can be considered to be described by using the equation of the linear and curvilinear process of the continuum extending to infinitely distance. Further, this linear and curvilinear process of the continuum is only a quantitative continuum in essence and thus an accelerated motion transmitting from finite to infinite quantities must be jumping by an infinitely great accelerating force. 展开更多
关键词 The linear and Curvilinear Process of the Continuum One Quantitative Continuum The Infinitely Great Accelerating Force
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A heuristic MBLS algorithm for the two semi-online parallel machine scheduling problems with deterioration jobs
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作者 程明宝 孙世杰 《Journal of Shanghai University(English Edition)》 CAS 2007年第5期451-456,共6页
The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processi... The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processing time are considered. In the first problem, it is assumed that the deterioration rates of jobs are known in an interval, that is, bj ∈[0, α], where 0 〈α≤ 1 and bj denotes the linear deterioration rate. In the second problem, it is assumed that the largest deterioration rate of jobs is known in advance, that is, b = max1≤j≤n {bj }. For each of the two problems, a heuristic MBLS algorithm is worked out and its worst-case ratio is analyzed. At the same time, the worst-case ratio of the list (LS) algorithm is investigated and it is proved that all the ratios are tight. 展开更多
关键词 SCHEDULING SEMI-ONLINE linear deteriorating processing tirne worst-case ratio.
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The Invariance Principle for Linear Processes Generated by a Negatively Associated Sequence and Its Applications 被引量:2
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作者 Chuan-rong LuZhejiang University of Finance and Economics, Hongzhou 310012. China 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2003年第4期641-646,共6页
In this paper, we obtain the invariance principle for linear processes generated by a negatively associated sequence.
关键词 linear process Negatively associated sequence Weak convergence
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Linear all-optical signal processing using silicon micro-ring resonators 被引量:3
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作者 Yunhong DING Haiyan OU +11 位作者 Jing XU Meng XIONG Yi AN Hao HU Michael GALILI Abel Lorences RIESGO Jorge SEOANE Kresten YVIND Leif Katsuo OXENLOWE Xinliang ZHANG Dexiu HUANG Christophe PEUCHERET 《Frontiers of Optoelectronics》 EI CSCD 2016年第3期362-376,共15页
Silicon micro-ring resonators (MRRs) are compact and versatile devices whose periodic frequency response can be exploited for a wide range of applications. In this paper, we review our recent work on linear all-opti... Silicon micro-ring resonators (MRRs) are compact and versatile devices whose periodic frequency response can be exploited for a wide range of applications. In this paper, we review our recent work on linear all-optical signal processing applications using silicon MRRs as passive filters. We focus on applications such as modulation format conversion, differential phase-shift keying (DPSK) demodulation, modulation speed enhancement of directly modulated lasers (DMLs), and monocycle pulse generation. The possibility to implement polarization diversity circuits, which reduce the polarization dependence of standard silicon MRRs, is illustrated on the particular example of DPSK demodulation. 展开更多
关键词 linear all-optical signal processing micro-ring resonator (MRR) polarization diversity silicon-on-insulator (SOI)
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Robust Fault-tolerant Iterative Learning Control for Discrete Systems via Linear Repetitive Processes Theory 被引量:2
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作者 Jian Ding Blazej Cichy +2 位作者 Krzysztof Galkowski Eric Rogers Hui-Zhong Yang 《International Journal of Automation and computing》 EI CSCD 2015年第3期254-265,共12页
This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput discrete linear systems with actuator faults. The stability theory for linear repetit... This paper addresses the problem of robust iterative learning control design for a class of uncertain multiple-input multipleoutput discrete linear systems with actuator faults. The stability theory for linear repetitive processes is used to develop formulas for gain matrices design, together with convergent conditions in terms of linear matrix inequalities. An extension to deal with model uncertainty of the polytopic or norm bounded form is also developed and an illustrative example is given. 展开更多
关键词 Iterative learning control linear repetitive processes linear matrix inequality(LMI) discrete linear systems fault-tolerant cont
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Linear optical signal processing with optical filters: a tutorial
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作者 Xinliang ZHANG Zhao WU 《Frontiers of Optoelectronics》 EI CSCD 2016年第3期377-389,共13页
An effective theoretical analysis method is presented to analyze different linear optical signal processing functions with optical fikers reported in literatures. For different applications, the optical filters are su... An effective theoretical analysis method is presented to analyze different linear optical signal processing functions with optical fikers reported in literatures. For different applications, the optical filters are supposed to operate on the analog or digital part of the signal separately, namely analog spectrum conversion and digital spectrum conversion. For instance, the return-to-zero (RZ) to non-return-to-zero (NRZ) format conversion for intensity or phase modulated signals are based on the analog spectrum conversion process, while the (N)RZ to (N)RZ phase-shift-keying (PSK) format conversion, logic NOT gate and clock recovery for RZ signals are based on the digital spectrum conversion process. Theoretical analyses with the help of numerical simulation are used to verify the reported experimental results, and all the experimental results can be effectively analyzed with this analytical model. The effect of the transmission spectrum of the filter on the performance of the converted signal is investigated. The most important factor is that the theoretical analysis provides an effective way to optimize the optical filter for different optical signal processing functions. 展开更多
关键词 linear optical signal processing format conversion optical filter clock recovery logic gate
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ε-arithmetics for real vectors and linear processing of real vector-valued signals
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作者 Xiang-Gen Xia 《Journal of Information and Intelligence》 2023年第1期2-10,共9页
In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values o... In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values of the same dimension withinεrange.For rational vectors of a fixed dimension m,they can form a field that is an mth order extension Q(α)of the rational field Q whereαhas its minimal polynomial of degree m over Q.Then,the arithmetics,such as addition,subtraction,multiplication,and division,of real vectors can be defined by using that of their approximated rational vectors withinεrange.We also define complex conjugate of a real vector and then inner product and convolutions of two real vectors and two real vector sequences(signals)of finite length.With these newly defined concepts for real vectors,linear processing,such as linear filtering,ARMA modeling,and least squares fitting,can be implemented to real vectorvalued signals with real vector-valued coefficients,which will broaden the existing linear processing to scalar-valued signals. 展开更多
关键词 Arithmetics Rational vectors Real vectors Rational field Algebraic number field Field extension Algebraic number Inner product linear processing of real vector-valued signals
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Hajek-Rényi-type Inequality and Strong Law of Large Numbers for Some Dependent Sequences 被引量:3
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作者 Wen-zhi YANG Yan SHEN +1 位作者 Shu-he HU Xue-jun WANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2012年第3期495-504,共10页
Abstract In this paper, we get the H^jek-R^nyi-type inequalities for a pairwise NQD sequence, an L^T (r 〉 1) mixingale and a linear process, which have the concrete coefficients. In addition, we obtain the strong l... Abstract In this paper, we get the H^jek-R^nyi-type inequalities for a pairwise NQD sequence, an L^T (r 〉 1) mixingale and a linear process, which have the concrete coefficients. In addition, we obtain the strong law of large numbers, strong growth rate and the integrability of supremum for the above sequences, which generalize and improve Corollary 2 for L^T(r 〉 1) mixingale of Hansen. 展开更多
关键词 Hajek-Renyi-type inequality pairwise NQD sequence L^r(r 1) mixingale linear process
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