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It is proved in this paper thatS(·) satisfies the strong law of large numbers that is uniform overA∈A, whereA is a family of subsets of [0, 1]d satisfying a mild condition.
      
On the transport equation with integral boundary conditions and its conservative law
      
Some spectral properties of the transport operator are discussed, the dominant eigenvalue is proved existing, and furthermore, the conservative law of migrating particle numbers is established.
      
The law of the iterated logarithm for wavelet series
      
We prove a law of iterated logarithm for wavelet series:
      
Using the Bayesian method, for certain choices of the prior distribution, several forms of estimators of the parameters in the normal stress Weibull distribution and the inverse power law model are derived.
      
The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ?--mixing random fields.
      
A nonclassical law of iterated logarithm for negatively associated random variables
      
A nonclassical law of iterated logarithm that holds for a stationary negatively associated sequence of random variables with finite variance is proved in this paper.
      
Precise rate in the law of iterated logarithm for ρ-mixing sequence
      
Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences
      
Furthermore, the precise asymptotics in the law of iterated logarithm of μ* is proved.
      
Precise rates in the law of the iterated logarithm for R/S statistics
      
By using only one state variable and its time derivatives, a control law is constructed to achieve the synchronization between the investigated chaotic systems and their observers, and the results are proved theoretically.
      
According to Swapping technique, we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed.
      
A new controller for SVC with closed-form analytic solution nonlinear optimal predictive control (NOPC) law was presented.
      
By using the exponential reaching law technology, a sliding mode controller was designed for Lorenz chaotic system subject to an unknown external disturbance.
      
On this basis, considering the unknown disturbance, an adaptive law was introduced to adaptively estimate the parameters of the disturbance bounds.
      
Using the density variation of standard plots of Cryptromeria fortunei plantation to verify the new model, it turns out that this model can well simulate the population density effect law of C.
      
kwangtungensis in Nanling was ranked Class A in terms of Raunkiaer's law of frequency.
      
 

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