A general result on precise asymptotics for linear processes of positively associated sequences

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}.

Explicit solution of diffusion master equation under the action of linear resonance force via the thermal entangled state representation

Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.

Central limit theolrem for linear processes generated byⅡD random variables under the sub-linear expectation

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.

THE MONITORING FOR PHYSICAL DEVELOPING PROCESS WITH A LINEAR CCD

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.

LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES

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.

STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

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.

A dynamic programming algorithm for scheduling problems on earliness award and tardiness penalty with time-dependent processing time

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.

The Meaning of Accelerated Motion

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.

A heuristic MBLS algorithm for the two semi-online parallel machine scheduling problems with deterioration jobs

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.

ε-arithmetics for real vectors and linear processing of real vector-valued signals

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.

Response Process of Oceanto AtmosphericForcing and Optimal Response Frequency in the CZ Ocean Model

Ocean response to atmospheric forcing in the CZ ocean model is analyzed.The results show that Nino 3 indexfrom the CZ ocean model driven by linear composite of biennial,ENSO and even annual time scale wind stressanomalies is consistent well with composite of responding two or three components of observed Nino 3 index duringthe EI Nino period while the La Nina phenomena cannot be reproduced by the linear composite.It implies that linearresponse process for ocean response to atmospheric forcing is dominated during the EI Nino period while nonlinearresponse might be main process during the La Nina period.Simulated results also suggest that optimal response frequency of the CZ ocean model is the frequency lowerthan annual variability and ocean response to the atmospheric forcing with annual time scale can give rise to incorrectsignal-errors in the simulated SSTA field.

The Invariance Principle for Linear Processes Generated by a Negatively Associated Sequence and Its Applications

Abstract In this paper, we obtain the invariance principle for linear processes generated by a negativelyassociated sequence.

Robust Fault-tolerant Iterative Learning Control for Discrete Systems via Linear Repetitive Processes Theory

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.

Linear optical signal processing with optical filters： a tutorial

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.

Hajek-Rényi-type Inequality and Strong Law of Large Numbers for Some Dependent Sequences

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.