Corrigendum:Stochastic resonance in a parallel array of linear elements

In this paper, we point out the errors occurring in the paper （Dong X J 2009 Chin. Phys. B 18 70） and present a correct conclusion.

An accurate and stable method of array element tiling for high-power laser facilities

Due to laser-induced damage, the aperture of optics is one of the main factors limiting the output capability of highpower laser facilities. Because of the general difficulty in achieving large-aperture optics, an alternative solution is to tile some small-aperture ones together. We propose an accurate, stable, and automatic method of array element tiling and verify it on a double-pass 1 × 2 tiled-grating compressor in the XG-III laser facility. The test results show the accuracy and stability of the method. This research provides an efficient way to obtain large-aperture optics for high-power laser facilities.

Intelligent Optimization Methods for the Design of an Overhead Travelling Crane

In design optimization of crane metal structures, present approaches are based on simple models and mixed variables, which are difficult to use in practice and usually lead to failure of optimized results for rounding variables. Crane metal structure optimal design（CMSOD） belongs to a constrained nonlinear optimization problem with discrete variables. A novel algorithm combining ant colony algorithm with a mutation-based local search（ACAM） is developed and used for a real CMSOD for the first time. In the algorithm model, the encoded mode of continuous array elements is introduced. This not only avoids the need to round optimization design variables during mixed variable optimization, but also facilitates the construction of heuristic information, and the storage and update of the ant colony pheromone. Together with the proposed ACAM, a genetic algorithm（GA） and particle swarm optimization（PSO） are used to optimize the metal structure of a crane. The optimization results show that the convergence speed of ACAM is approximately 20% of that of the GA and around 11% of that of the PSO. The objective function value given by ACAM is 22.23% less than the practical design value, a reduction of 16.42% over the GA and 3.27% over the PSO. The developed ACAM is an effective intelligent method for CMSOD and superior to other methods.

Characterization of Type p Banach Spaces by the Weak Law of Large Numbers

For weighted sums of the form ?j = 1kn anj Xnj\sum {_{j = 1}^{k_n } } a_{nj} X_{nj} where {a nj , 1 ?j?k n ↑∞,n?1} is a real constant array and {X aj , 1≤j≤k n, n≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.

On the Laws of Large Numbers for Double Arrays of Independent Random Elements in Banach Spaces

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.

Independent dual beams generated by array element division in integrated optical phased arrays

Optical phased arrays(OPAs)have broad application prospects due to their advanced capability in beamforming and steering.In this work,we achieve independent dual beams in the far field by dividing the array elements of the OPA,with the maximum scanning range reaching 100°.Based on the working principle of OPAs,theoretical considerations of such multibeam generation are presented.A phase data allocation approach for OPAs in the presence of fabrication-induced random phase variation is developed.Simulations of large ensembles of OPAs with various levels of random residual phase errors have been conducted to help analyze the results.This approach can help OPAs realize multi-beams for light detection and ranging(LiDAR).