欧氏空间中的标准格

给出了欧氏空间中标准格的定义,证明了在1维,2维欧氏空间中所有格都是标准格,并构造了当维数大于4时非标准格的例子.还给出了标准格的若干性质.     

Remark on the Successive Projection Algorithm for the Multiple-Sets Split Feasibility Problem

Recently, assuming that the metric projection onto a closed convex set is easily calculated, Liu et al. (Numer. Func. Anal. Opt. 35:1459–1466, 2014) presented a successive projection algorithm for solving the multiple-sets split feasibility problem (MSFP). However, in some cases it is impossible or needs too much work to exactly compute the metric projection. The aim of this remark is to give a modification to the successive projection algorithm. That is, we propose a relaxed successive projection algorithm, in which the metric projections onto closed convex sets are replaced by the metric projections onto halfspaces. Clearly, the metric projection onto a halfspace may be directly calculated. So, the relaxed successive projection algorithm is easy to implement. Its theoretical convergence results are also given.     

On the constrained error bound condition and the projected Levenberg–Marquardt method

In this paper, we first derive a characterization of the solution set of a continuously differentiable system of equations subject to a closed feasible set. Assuming that a constrained local error bound condition is satisfied, we prove that the solution set can locally be written as the intersection of a differentiable manifold with the feasible set. Based on the derivation of this result, we then show that the projected Levenberg–Marquardt method converges locally R-linearly to a possibly nonisolated solution under significantly weaker conditions than previously done.     

On the outage performance of multi-user NOMA system with adaptive SIC

The performance of non-orthogonal multiple-access (NOMA) is significantly determined by the successive interference cancellation (SIC) technique. However, the interference redundancy can happen during the NOMA receiver performing SIC. To tackle this issue, this paper proposes a novel adaptive successive interference cancellation (ASIC) method. Specifically, the decoding error is considered as interference during the SIC process, and an adaptive filter with various weights is introduced for detection error mitigation. For the multi-user downlink NOMA system, the outage probability is analyzed under conventional and the proposed SIC methods. Simulation results verify our analysis, which also demonstrate the superiority of the proposed ASIC method.     

The fractal statistics of liquid slug lengths

A rescaled range (R/S) analysis is presented of gas-liquid and gas-liquid-liquid slug length data from two extremely different pipeline systems with i.d. = 32 and 189 mm and length-to-diameter ratios of about 800 and 2000, respectively. The results indicate that slug lengths in horizontal pipe flow obey fractal statistics. The R/S analysis of 30–250 slugs for each experiment shows that the length spectrum satisfies Hurst's law with a Hurst exponent in the range 0.53–0.76, linearly dependent on the total superficial velocity. Conversely, if the Hurst exponent and average slug length with standard deviation are given, slug length spectra may be obtained in good agreement with experimental data.     

Random responses of a two-degree-of-freedom structure with strongly nonlinear coupling and parametric interaction

This paper investigates the random responses of a TDOF structure with strongly nonlinear coupling and parametric vibration. With the nonlinear coupling of inertia in the equations of motion of the system being removed by successive elimination, the non-Gaussian moment equation method (NGM) is applied and 69 moment equations are integrated with central cumulative truncation technique. The stochastic central difference-cum-statistical linearization method(SCD-SL) and the digital simulation method(DSM) are also used. A comparison of results by different methods are given and the SCD-SL method is the most efficient method. The project supported by National Natural Science Foundation of China     

非压缩性流体的湍流理论

 本文是作者50年的湍流研究工作的一个总结. 整个研究工作分成 4个阶段. 第一阶段是在上一世纪的40年代，提出研究湍流必须研究脉动 速度场，给出了湍流模式理论的基础. 第二阶段是上一世纪的50年代到 60年代，提出了先求解后平均的旋涡结构的湍流统计理论. 第三阶段是 上一世纪的70年代，他和黄永念提出了准相似性假设，完成了均匀各向 同性湍流统计理论的工作. 第四阶段是上一世纪的80年代到90年代初， 提出了广义准相似性假设，给出了处理一般具有剪应力的湍流流动的奇 阶截断法和逐级逼近法.     

Stochastic equilibrium assignment with variable demand: Theoretical and implementation issues

Recently, it has been pointed out that transport models should reflect all significant traveler choice behavior. In particular, trip generation, trip distribution, modal split as well as route choice should be modeled in a consistent process based on the equilibrium between transport supply and travel demand. In this paper a general fixed-point approach that allows dealing with multi-user stochastic equilibrium assignment with variable demand is presented. The main focus was on investigating the effectiveness of internal and external approaches and of different algorithmic specifications based on the method of successive averages within the internal approach. The vector demand function was assumed non-separable, non-symmetric cost functions were adopted and implementation issues, such updating step and convergence criterion, were investigated. In particular the aim was threefold: (i) compare the internal and the external approaches; (ii) investigate the effectiveness of different algorithmic specifications to solve the variable demand equilibrium assignment problem through the internal approach; (iii) investigate the incidence of the number of the links with non-separable and/or asymmetrical cost functions. The proposed analyses were carried out with respect to two real-scale urban networks regarding medium-size urban contexts in Italy.     

Entanglement spectrum and block eigenvalue spacing distribution of correlated electron states

Entanglement spectrum of finite-size correlated electron systems are investigated using the Gutzwiller projection technique. The product of largest eigenvalue and rank of the block reduced density matrix, which is a measure of distance of the state from the maximally entangled state of the corresponding rank, is seen to characterise the insulator to metal crossover in the state. The fraction of distinct eigenvalues exhibits a ‘chaotic’ behaviour in the crossover region, and it shows a ‘integrable’ behaviour at both insulating and metallic ends. The integrated entanglement spectrum obeys conformal field theory (CFT) prediction at the metal and insulator ends, but shows a noticeable deviation from CFT prediction in the crossover regime, thus it can also track a metal–insulator crossover. A modification of the CFT result for the entanglement spectrum for finite size is proposed which holds in the crossover regime also. The adjacent level spacing distribution of unfolded non-zero eigenvalues for intermediate values of Gutzwiller projection parameter g$g$ is the same as that of an ensemble of random matrices obtained by replacing each block of reduced density matrix by a random real symmetric Toeplitz matrix. It is strongly peaked at zero, with an exponential tail proportional to e^−(n/R)s$e^{-(n/R)s}$, where s$s$ is the adjacent level spacing, n$n$ is number of distinct eigenvalues and R$R$ is the rank of the reduced density matrix.     

A robust algorithm for quadratic optimization under quadratic constraints

Most existing methods of quadratically constrained quadratic optimization actually solve a refined linear or convex relaxation of the original problem. It turned out, however, that such an approach may sometimes provide an infeasible solution which cannot be accepted as an approximate optimal solution in any reasonable sense. To overcome these limitations a new approach is proposed that guarantees a more appropriate approximate optimal solution which is also stable under small perturbations of the constraints.