For a double array of independent random elements {Vmn,m ≥ 1,n ≥ 1} in a real separable Banach space,conditions are provided under which the weak and strong laws of large numbers for the double sums mi=1 nj=1Vij,m ...For a double array of independent random elements {Vmn,m ≥ 1,n ≥ 1} in a real separable Banach space,conditions are provided under which the weak and strong laws of large numbers for the double sums mi=1 nj=1Vij,m ≥ 1,n ≥ 1 are equivalent.Both the identically distributed and the nonidentically distributed cases are treated.In the main theorems,no assumptions are made concerning the geometry of the underlying Banach space.These theorems are applied to obtain Kolmogorov,Brunk–Chung,and Marcinkiewicz–Zygmund type strong laws of large numbers for double sums in Rademacher type p（1 ≤ p ≤ 2） Banach spaces.展开更多
A crosstalk-free integral imaging display consisting of a display panel and double piano-convex micro-lens array is proposed. The double piano-convex micro-lens array includes two micro-lens arrays, A and B. Micro-len...A crosstalk-free integral imaging display consisting of a display panel and double piano-convex micro-lens array is proposed. The double piano-convex micro-lens array includes two micro-lens arrays, A and B. Micro-lens array A is used to eliminate crosstalk by completely reflecting crosstalk lights. Micro-lens array B, located near microqens array A, is used to display three-dimensional images. Computer simulations based on ray-tracing are conducted. Crosstalk-free reconstruction images may be clearly observed from the simulation results.展开更多
Estimation and control problems with binary-valued observations exist widely in practical systems.However,most of the related works are devoted to finite impulse response(FIR for short)systems,and the theoretical prob...Estimation and control problems with binary-valued observations exist widely in practical systems.However,most of the related works are devoted to finite impulse response(FIR for short)systems,and the theoretical problem of infinite impulse response(IIR for short)systems has been less explored.To study the estimation problems of IIR systems with binary-valued observations,the authors introduce a projected recursive estimation algorithm and analyse its global convergence properties,by using the stochastic Lyapunov function methods and the limit theory on double array martingales.It is shown that the estimation algorithm has similar convergence results as those for FIR systems under a weakest possible non-persistent excitation condition.Moreover,the upper bound for the accumulated regret of adaptive prediction is also established without resorting to any excitation condition.展开更多
基金supported by the Vietnam Institute for Advanced Study in Mathematics(VIASM)the Vietnam National Foundation for Sciences and Technology Development NAFOSTED(Grant No.101.01.2012.13)supported by NAFOSTED(Grant No.101.03.2012.17)
文摘For a double array of independent random elements {Vmn,m ≥ 1,n ≥ 1} in a real separable Banach space,conditions are provided under which the weak and strong laws of large numbers for the double sums mi=1 nj=1Vij,m ≥ 1,n ≥ 1 are equivalent.Both the identically distributed and the nonidentically distributed cases are treated.In the main theorems,no assumptions are made concerning the geometry of the underlying Banach space.These theorems are applied to obtain Kolmogorov,Brunk–Chung,and Marcinkiewicz–Zygmund type strong laws of large numbers for double sums in Rademacher type p（1 ≤ p ≤ 2） Banach spaces.
基金supported by the National "973" Program of China (No. 2013CB328802)the National Natural Science Foundation of China (Nos. 61036008 and61225022)the National "863" Program of China(No. 2012AA011901)
文摘A crosstalk-free integral imaging display consisting of a display panel and double piano-convex micro-lens array is proposed. The double piano-convex micro-lens array includes two micro-lens arrays, A and B. Micro-lens array A is used to eliminate crosstalk by completely reflecting crosstalk lights. Micro-lens array B, located near microqens array A, is used to display three-dimensional images. Computer simulations based on ray-tracing are conducted. Crosstalk-free reconstruction images may be clearly observed from the simulation results.
基金supported by the National Natural Science Foundation of China(No.12288201)。
文摘Estimation and control problems with binary-valued observations exist widely in practical systems.However,most of the related works are devoted to finite impulse response(FIR for short)systems,and the theoretical problem of infinite impulse response(IIR for short)systems has been less explored.To study the estimation problems of IIR systems with binary-valued observations,the authors introduce a projected recursive estimation algorithm and analyse its global convergence properties,by using the stochastic Lyapunov function methods and the limit theory on double array martingales.It is shown that the estimation algorithm has similar convergence results as those for FIR systems under a weakest possible non-persistent excitation condition.Moreover,the upper bound for the accumulated regret of adaptive prediction is also established without resorting to any excitation condition.
