Efficient Asymmetrical Extended Designs Under Wrap-Around L_2-Discrepancy

The purpose of the present article is to introduce a class of mixed two-and three-level extended designs obtained by adding some new runs to an existing mixed two-and three-level design.A formulation of wrap-around L_2-discrepancy for the extended designs is developed. As a benchmark of obtaining(nearly) uniform asymmetrical extended designs, a lower bound to the wrap-around L_2-discrepancy for our proposed designs is established. Thorough numerical results are displayed, which provide further corroboration to the derived theoretical results.     

Efficient Asymmetrical Extended Designs Under Wrap-Around <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>-Discrepancy

The purpose of the present article is to introduce a class of mixed two- and three-level extended designs obtained by adding some new runs to an existing mixed two-and three-level design. A formulation of wrap-around L₂-discrepancy for the extended designs is developed. As a benchmark of obtaining (nearly) uniform asymmetrical extended designs, a lower bound to the wrap-around L₂-discrepancy for our proposed designs is established. Thorough numerical results are displayed, which provide further corroboration to the derived theoretical results.     

On Construction of Optimal Two-Level Designs with Multi Block Variables

When running an experiment, inhomogeneity of the experimental units may result in poor estimations of treatment effects. Thus, it is desirable to select a good blocked design before running the experiment. Mostly, a single block variable was used in the literature to treat the inhomogeneity for simplicity. However, in practice, the inhomogeneity often comes from multi block variables. Recently, a new criterion called B²-GMC was proposed for two-level regular designs with multi block variables. This paper proposes a systematic theory on constructing some B²-GMC designs for the first time. Experimenters can easily obtain the B²-GMC designs according to the construction method. Pros of B²-GMC designs are highlighted in Section 4, and the designs with small run sizes are tabulated in Appendix B for practical use.     

Nonhomogeneous boundary value problems for the Korteweg-de Vries equation on a bounded domain

<正> This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vriesequation posed on a finite interval with general nonhomogeneous boundary conditions.Using thestrong Kato smoothing property of the associated linear problem,the IBVP is shown to be locallywell-posed in the space H~s(0,1) for any s≥0 via the contraction mapping principle.     

Stabilization of Euler-Bernoulli beam with a nonlinear locally distributed feedback control

This paper studies the stabilization problem of uniform Euler-Bernoulli beam with a nonlinear locally distributed feedback control. By virtue of nonlinear semigroup theory, energy-perturbed approach and polynomial multiplier skill, the authors show that, corresponding to the different values of the parameters involved in the nonlinear locally distributed feedback control, the energy of the beam under the proposed feedback decays exponentially or in negative power of time t as t → ∞.     

THE HAMMING DISTANCES OF NEGACYCLIC CODES OF LENGTH 2^s OVER GR （2^α, m）

The Hamming distances of all negacyclic codes of length 28 over the Gaiois ring GR （2^α, m） are given. In particular, the Lee distances of all negacyclic codes over Z4 of length 2^s are obtained. The Gray images of such negacyclic codes over Z4 are also determined under the Gray map.     

Semi On-Line Scheduling Problem for Maximizing the Minimum Machine Completion Time on Two Uniform Machines

Ia this paper, we consider a semi on-line version on two uniform machines Mi, i = 1, 2, where the processing time of the largest job is known in advance. A speed si（s1 = 1, 1 ≤s2 = s） is associated with machine Mi. Our goal is to maximize the Cmin. We give a Cmin 2 algorithm and prove its competitive ratio is at most 2s＋1/s＋1 We also claim the Cmin 2 algorithm is tight and the gap between the competitive ratio of Cmin2 algorithm and the optimal value is not greater than 0.555. It is obvious that our result coincides with that given by He for s =1.     

Dynamic price model based on transmission delay — Petroleum price fluctuation in China

Petroleum is a kind of fundamental energy resource. Its price fluctuation transmits from upper-stream industry to the lower-stream industry as the production factors price changes. And this leads to the price changes of final consumption. Meantime, due to the cycle of industrial chain, the price changes of lower-stream industry also affect the upper-stream industry in return. This price transmission path is quite complicated. Firstly, it includes both direct and indirect paths; secondly, the transmission process is accompanied with time delay. The traditional input-output price model based on cost-push theory can efficiently solve the first problem when estimating the impact of price fluctuation on the whole price system. However, it neither reflects the dynamic characteristics of price transmission with time nor solves the second problem. To solve this problem, this paper uses the directed weighted network to describe the price transmission among industrial sectors by taking the time-dimension into account, and dynamic price transmission network model is constructed. This model not only describes transmission time delay more accurately, but also calculates the price fluctuation dynamically. On this basis, by utilizing the 2007 Chinese input-output table, this paper conducts empirical analysis on the impact of petroleum price fluctuation on other sectors. The empirical results indicate that the price fluctuation transmission mainly depends on two factors, the orice reaction period Tk and the consumption relationship with petroleum aik. 1） If t 〈 Tk, then the price change of sector k at period t △pkt = 0, the petroleum price fluctuation has not transmitted to the sector k, so the price of sector k remains unchanged. 2） If t 〉 Tk, then Apt 〉 0, and the greater aik, the higher price change rate. 3） If t →∞, it is the same with that in traditional input-output price model. So it can be clearly seen that dynamic price transmission network model is more general than the traditional model, and the traditional model is just an asymptotical special case when time approaches to infinity. Keywords Directed weighted network, input-output price model, petroleum price, transmission time delay.     

自适应试验遗传算法研究与应用

均匀设计与遗传算法相结合已有许多成功例子,但在应用中均匀设计表一般囿以固定形式而使二者的结合缺乏灵活性和普适性.为此提出应用亚遗传算法获得若干个任意水平数的均匀设计,并将其以3种方式嵌入标准遗传算法中:1)初始种群的均匀性分布;2)进化过程中对变量空间均匀性投点搜索;3)应用均匀设计进行调优试验,同时还增加了正态随机和摄动调优等试验操作技术,以上形成了基于试验设计、具有自适应能力的试验遗传算法.算例表明,通过以上方法改进的遗传算法可较好地保持种群多样性,寻优效率有较大提高,并能自动适应算法对搜索精度的要求.     

The limit theorem for dependent random variables with applications to autoregression models

This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {X _t } be a linear process defined by X _t = Σ _k=0^∞ψ _k ɛ _t−k , where {ψ _k , k ≥ 0} is a sequence of real numbers and {ɛ _k , k = 0, ±1, ±2, …} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {ɛ _k , k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent (ALNQD) random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d. innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter α when {ɛ _k , k ≥ 1} is a sequence of negatively associated (NA) random variables, and ψ ₀ = 1, ψ _k = 0, k ≥ 1.     

NNMDS codes

C is an[n,k,d]_q linear code over F₉.And s（C）=n+1-k-d is the Singleton defect of C.An MDS code C with s（C）=0 has been studied extensively.Recently,a near-MDS code C with s（C）=s（C^⊥）=1 is studied by many scholars,where C^⊥denotes the dual code of C.This paper concentrates on the linear code C with s（C）=s（C^⊥）=2,and the author calls it an NNMDS code.A series of iff conditions of NNMDS codes are presented.And the author gives an upper bound on length of NNMDS codes.In the last,some examples of NNMDS are given.     

Invariant density,Lapunov exponent,and almost sure stability of Markovian-regime-switching linear systems

This paper is concerned with stability of a class of randomly switched systems of ordinary differential equations. The system under consideration can be viewed as a two-component process (X(t), α(t)), where the system is linear in X(t) and α(t) is a continuous-time Markov chain with a finite state space. Conditions for almost surely exponential stability and instability are obtained. The conditions are based on the Lyapunov exponent, which in turn, depends on the associate invariant density. Concentrating on the case that the continuous component is two dimensional, using transformation techniques, differential equations satisfied by the invariant density associated with the Lyapunov exponent are derived. Conditions for existence and uniqueness of solutions are derived. Then numerical solutions are developed to solve the associated differential equations.     

面向多极值质量特性的全局式序贯性实验设计方法

针对多极值质量特性的全局性建模和参数优化问题, 为降低实验设计样本量, 提高模型预测性能, 提出一种全局式序贯性设计方法. 首先在一定的初始实验设计方式下, 建立过程粗略的SVR模型; 而后根据模型中支持向量的分布, 在支持向量样本各维度的45度角或轴向方向同步地增加实验点, 再拟合过程新的SVR模型; 如此迭代进行, 当模型精度达到要求或样本量达到上限时终止序贯性设计. 仿真与实证研究表明, 该方法能够在可行域全局的范围内将实验点合理地分配在质量特性的多个极值附近, 避免了传统的单路径式序贯性设计只能发现单个极值的不足, 充分提高了实验效率; 与均匀空间网格设计、 拉丁超立方设计和均匀设计相比, 在样本量接近的情况下, 基于全局式序贯性设计的SVR 模型的预测均方误差至少降低了30%; 而在预测误差较为接近的情况下, 全局式序贯性设计的样本量至少降低了12%.     

基于果蝇算法的约束区域均匀实验设计方法

针对已有的基于差分演化算法的两阶段均匀实验设计方法仍存在种群在约束区域分布多样性不佳和局部搜索能力不强的问题,提出了一种基于果蝇算法的两阶段均匀实验设计方法(two phase fruit fly optimization algorithm, ToPFOA)。ToPFOA第1阶段运用融合差分算子的果蝇搜索策略、基于K-means聚类及外部文档更新类中心等方法,以动态改进种群在约束区域分布的多样性;在此基础上,第2阶段进一步使用自定义果蝇算子提高约束区域内局部搜索能力。实验结果表明ToPFOA在解质量和稳定性上均优于ToPDE和ToPDEEDA。     

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

Effective lower bounds of wrap-around <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>-discrepancy on three-level combined designs

How to obtain an effective design is a major concern of scientific research. This topic always involves high-dimensional inputs with limited resources. The foldover is a quick and useful technique in construction of fractional designs, which typically releases aliased factors or interactions. This paper takes the wrap-around L₂-discrepancy as the optimality measure to assess the optimal three-level combined designs. New and efficient analytical expressions and lower bounds of the wraparound L₂-discrepancy for three-level combined designs are obtained. The new lower bound is useful and sharper than the existing lower bound. Using the new analytical expression and lower bound as the benchmarks, the authors may implement an effective algorithm for constructing optimal three-level combined designs.     

Superconvergence of mixed covolume method on quadrilateral grids for elliptic problems

This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals.Superconvergence results are established in this paper on quadrilateral grids satisfying the h~2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method.The authors prove O(h~2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L~2 norm.Numerical experiments illustrating the theoretical results are provided.     

A class of constacyclic codes over ring <Emphasis Type="Italic">R</Emphasis> + <Emphasis Type="Italic">vR</Emphasis>

By constructing a Gray map, a class of constacyclic codes over ring R = R+vR is studied. Using cyclic codes and negacyclic codes of length p ^s over ring R, the structure of (1?2v)-constacyclic codes and dual codes of length p ^s over ring R are given, the Gray images of (1 ? 2v)-constacyclic codes in a particular case are also studied. It is shown that linear codes of length p ^s over ring R are (1?2v)-constacyclic codes if and only if their Gray images are distance-invariant cyclic codes of length 2p ^s over ring R.     

Minimum Hausdorff distance under rigid motions and comparison of protein structures

Hausdorff distance between two compact sets, defined as the maximum distance from a point of one set to another set, has many application in computer science. It is a good measure for the similarity of two sets. This paper proves that the shape distance between two compact sets in R ⁿ defined by minimum Hausdorff distance under rigid motions is a distance. The authors introduce similarity comparison problems in protein science, and propose that this measure may have good application to comparison of protein structure as well. For calculation of this distance, the authors give one dimensional formulas for problems (2, n), (3, 3), and (3, 4). These formulas can reduce time needed for solving these problems. The authors did some numerical experiments for (2, n). On these sets of data, this formula can reduce time needed to one fifteenth of the best algorithms known on average. As n increases, it would save more time.     

On-Line Scheduling on Parallel Machines to Minimize the Makespan

This paper considers two parallel machine scheduling problems,where the objectives of both problems are to minimize the makespan,and the jobs arrive over time,on two uniform machines with speeds 1 and s(s≥1),and on m identical machines,respectively.For the first problem,the authors show that the on-line LPT algorithm has a competitive ratio of(1 +5~(1/2))/2≈1.6180 and the bound is tight.Furthermore,the authors prove that the on-line LPT algorithm has the best possible competitive ratio if s≥1.8020.For the second problem,the authors present a lower bound of(15-(17)~(1/2))/8≈1.3596 on the competitive ratio of any deterministic on-line algorithm.This improves a previous result of 1.3473.