多约束膜结构截面优化及在MSC/Nastran上的程序实现

将准则法和数学规划法相结合,借助满应力准则将应力约束转化为动态尺寸约束,利用单位虚载荷法将位移约束转化为设计变量的显式表达式建立优化模型,然后用数学规划法求解;采用无量纲设计变量实现设计变量连接,对膜结构的厚度进行优化设计;根据对偶理论,应用对偶规划精确映射原问题,再按泰勒展式建立对偶问题的二阶近似。为了提高优化效率,采用射线步调整结构性态,运用粗选有效约束技术筛选约束,并采用主、被动变量循环确保收敛稳定。以MSC／Nastran软件作为结构分析的求解器,以MSC／Patran软件作为开发平台,完成了膜结构截面优化程序。对膜结构的单变位、多变位的结构优化问题进行了优化计算,并与MSC／Nastran优化模块的计算结果进行比较。算例结果表明程序的可靠性、高效性和稳定性以及理论算法的优越性。     

Combining Cryo-EM Density Map and Residue Contact for Protein Secondary Structure Topologies

Although atomic structures have been determined directly from cryo-EM density maps with high resolutions, current structure determination methods for medium resolution (5 to 10 Å) cryo-EM maps are limited by the availability of structure templates. Secondary structure traces are lines detected from a cryo-EM density map for α-helices and β-strands of a protein. A topology of secondary structures defines the mapping between a set of sequence segments and a set of traces of secondary structures in three-dimensional space. In order to enhance accuracy in ranking secondary structure topologies, we explored a method that combines three sources of information: a set of sequence segments in 1D, a set of amino acid contact pairs in 2D, and a set of traces in 3D at the secondary structure level. A test of fourteen cases shows that the accuracy of predicted secondary structures is critical for deriving topologies. The use of significant long-range contact pairs is most effective at enriching the rank of the maximum-match topology for proteins with a large number of secondary structures, if the secondary structure prediction is fairly accurate. It was observed that the enrichment depends on the quality of initial topology candidates in this approach. We provide detailed analysis in various cases to show the potential and challenge when combining three sources of information.     

均衡约束数学规划问题的一种新的约束规格

本文研究了均衡约束数学规划(MPEC)问题.利用其弱稳定点,获得了一种新的约束规格–MPEC的伪正规约束规格.用一种简单的方式,证明了该约束规格是介于MPEC-MFCQ(即MPEC,Mangasarian-Fromowitz约束规格)与MPEC-ACQ(即MPEC,Abadie约束规格)之间的约束规格,因此该约束规格也可以导出MPEC问题的M-稳定点.最后通过两个例子,说明了该约束规格与MPEC-MFCQ以及与MPEC-ACQ之间是严格的强弱关系.     

重复性建设项目中确定关键路线的方法研究

本文提出了一种确定重复性建设项目关键路线的新方法。借助约束线,首先给出了工序间存在各种约束条件(时间和距离约束)下潜在关键点的确定方法;为处理大规模项目,进一步提出了与图示法相对应的数值算法。以此为基础,提出了确定关键工序和关键路线的具体步骤,并定义和分析了三种不同类型的关键工序。与现有的方法相比,本文提出的确定关键路线的方法更为准确,适用性更强,而且有利于调度优化目标的实现。     

求解带界约束的非线性方程组的混合方法

基于非单调技术和L-M算法, 提出了一种新的求解带界约束的非线性方程组的混合方法. 在一定条件下, 该算法具有全局收敛性. 数值试验表明该算法是有效的.     

Redshift drift constraints on f(T) gravity

We explore the impact of the Sandage−Loeb (SL) test on the precision of cosmological constraints for f(T) gravity theories. The SL test is an important supplement to current cosmological observations because it measures the redshift drift in the Lyman-α forest in the spectra of distant quasars, covering the “redshift desert” of 2≲z≲5. To avoid data inconsistency, we use the best-fit models based on current combined observational data as fiducial models to simulate 30 mock SL test data. We quantify the impact of these SL test data on parameter estimation for f(T) gravity theories. Two typical f(T) models are considered, the power-law model f(T)_PL and the exponential-form model f(T)_EXP. The results show that the SL test can effectively break the existing strong degeneracy between the present-day matter density Ω_m and the Hubble constant H₀ in other cosmological observations. For the considered f(T) models, a 30-year observation of the SL test can improve the constraint precision of Ω_m and H₀ enormously but cannot effectively improve the constraint precision of the model parameters.     

Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomie mechanic systems with unilateral constraints axe established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups axe also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.     

Optimal policy for a two-facility inventory problem with storage constraints and two freight modes

This paper considers a two-facility supply chain for a single product in which facility 1 orders the product from facility 2 and facility 2 orders the product from a supplier in each period. The orders placed by each facility are delivered in two possible nonnegative integer numbers of periods. The difference between them is one period. Random demands in each period arise only at facility 1. There are physical storage constraints at both facilities in each period. The objective of the supply chain is to find an ordering policy that minimizes the expected cost over a finite horizon and the discounted stationary expected cost over an infinite horizon. We characterize the structure of the minimum expected cost and the optimal ordering policy for both the finite and the discounted stationary infinite horizon problems.     

Competitive facility location on decentralized supply chains

This paper addresses a novel competitive facility location problem about a firm that intends to enter an existing decentralized supply chain comprised of three tiers of players with competition: manufacturers, retailers and consumers. It first proposes a variational inequality for the supply chain network equilibrium model with production capacity constraints, and then employs the logarithmic-quadratic proximal prediction–correction method as a solution algorithm. Based on this model, this paper develops a generic mathematical program with equilibrium constraints for the competitive facility location problem, which can simultaneously determine facility locations of the entering firm and the production levels of these facilities so as to optimize an objective. Subsequently, a hybrid genetic algorithm that incorporates with the logarithmic-quadratic proximal prediction–correction method is developed for solving the proposed mathematical program with an equilibrium constraint. Finally, this paper carries out some numerical examples to evaluate proposed models and solution algorithms.