关于具有二次相关性收获率的捕食与被捕食系统极限环的存在性分析

讨论了一类两种群具有二次相关性收获率的捕食与被捕食系统,利用常微分定性方法和分支理论,得到了系统平衡点处的性态和极限环的存在性条件,并用Matlab软件对其进行数值模拟,推广了相关文献中两种群捕食模型定性分析的相应结论.     

叶丝在增温增湿与滚筒烘丝工序中香味组分变化分析

该文研究了制丝线增温增湿和滚筒烘丝工序加工对叶丝香味组分的影响,采用溶剂超声萃取前处理结合GC-MS法测定叶丝的香味组分,并对SIROX增温增湿工序和滚筒烘丝工序前后叶丝香味组分的相对含量进行了分析,比较了工序前后、工序间香味组分的变化趋势。结果显示:①经SIROX增温增湿工序加工后,乙酸、苯甲醇等18种组分相对含量减少,糠醇、2,4-二羟基-2,5-二甲基-3(2H)-呋喃-3-酮等6种组分相对含量增加;②经滚筒烘丝工序加工后,乙酸、麦芽酚等14种组分相对含量减少,糠醇、糠醛等6种组分相对含量增加;③经增温增湿及滚筒烘丝两工序后,乙酸、2,3-丁二醇等23种组分相对含量减少,糠醇、2,4-二羟基-2,5-二甲基-3(2H)-呋喃-3-酮等4种组分相对含量增加;④两工序间的温度、湿度剧烈变化,使叶丝内部组分发生了美拉德反应、降解反应、挥发等,香味组分经两个工序后发生了一系列显著变化。该研究对提升卷烟产品质量、优化工艺参数、开发高质量产品具有重要意义。     

On the cut‐off phenomenon for the transitivity of randomly generated subgroups

Consider K ≥ 2 independent copies of the random walk on the symmetric group S_N starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time $n\in \mathbb{N}$, let G_n be the subgroup of S_N generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut‐off phenomenon at time N ln(N)/(2K) for the non‐existence of fixed point of G_n and for the transitivity of G_n, thus showing that these properties occur before the chains have reached equilibrium. In the uniform neighbor transposition model, a transition for the non‐existence of a fixed point of G_n appears at time of order $N^{1+\frac{2}{K}}$ (at least for K ≥ 3), but there is no cut‐off phenomenon. In the latter model, we recover a cut‐off phenomenon for the non‐existence of a fixed point at a time proportional to N by allowing the number K to be proportional to ln(N). The main tools of the proofs are spectral analysis and coupling techniques. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Safe bounds in linear and mixed-integer linear programming

Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic, cheap pre- and postprocessing of the linear programs arising in a branch-and-cut framework can guarantee that no solution is lost, at least for mixed-integer programs in which all variables can be bounded rigorously by bounds of reasonable size. Mathematics Subject Classification (2000):primary 90C11, secondary 65G20     

Maximum directed cuts in digraphs with degree restriction

For integers m, k≥1, we investigate the maximum size of a directed cut in directed graphs in which there are m edges and each vertex has either indegree at most k or outdegree at most k. © 2009 Wiley Periodicals, Inc. J Graph Theory     

Computing finest mincut partitions of a graph and application to routing problems

Let G=(V,E,w) be an n-vertex graph with edge weights w>0. We propose an algorithm computing all partitions of V into mincuts of G such that the mincuts in the partitions cannot be partitioned further into mincuts. There are O(n) such finest mincut partitions. A mincut is a non-empty proper subset of V such that the total weight of edges with exactly one end in the subset is minimal. The proposed algorithm exploits the cactus representation of mincuts and has the same time complexity as cactus construction. An application to the exact solution of the general routing problem is described.     

Dynamic evolution of economically preferred facilities

In a sustained development scenario, it is often the case that an investment is to be made over time in facilities that generate benefits. The benefits result from joint synergies between the facilities expressed as positive utilities specific to some subsets of facilities. As incremental budgets to finance fixed facility costs become available over time, additional facilities can be opened. The question is which facilities should be opened in order to guarantee that the overall benefit return over time is on the highest possible trajectory. This problem is common in situations such as ramping up a communication or transportation network where the facilities are hubs or service stations, or when introducing new technologies such as alternative fuels for cars and the facilities are fueling stations, or when expanding the production capacity with new machines, or when facilities are functions in a developing organization that is forced to make choices of where to invest limited funding.     

Finding multiple solutions to general integer linear programs

Integer linear programming (ILP) problems occur frequently in many applications. In practice, alternative optima are useful since they allow the decision maker to choose from multiple solutions without experiencing any deterioration in the objective function. This study proposes a general integer cut to exclude the previous solution and presents an algorithm to identify all alternative optimal solutions of an ILP problem. Numerical examples in real applications are presented to demonstrate the usefulness of the proposed method.     

正多边形的最优分割问题

记平面边长为1的正m边形为S_m,将S_m剖分成n块:S_(m1),S_(m2),…,S_(mn),这样的剖分称S_m的n剖分,并以T(m,n)表示.以d_(mi)表示区域S_(mi)(i=1,2,…,n)的直径(即区域S_(mi)任意两点之间距离的最大者).记D(m,n)=max{d_(m1),d_(m2),…,d_(mn)}及Ψ(m,n)=■{D(m,n)}.本文将估计Ψ(m,n)的上下界.证明Ψ(6,3)=3/2,Ψ(6,4)=3-3~(1/2),Ψ(6.6)=1,Ψ(6,7)=3/2,估计Ψ(6,n)的渐进性.提出几个猜想.     

Lamb wave sensors array for nonviscous liquid sensing

The interdigital transducer (IDT) can excite Lamb wave in a piezoelectric plate loading with a liquid layer, and the phase velocity of Lamb wave is associated with the properties of the liquid layer. In this paper, the concept of effective permittivity is introduced to study the Lamb wave’s potential application in liquid sensing. Considering the measuring of ideal nonviscous liquid, the sensors array is designed to sense the density and the dielectric constant of the liquid layer simultaneously. Using LiNbO₃ as piezoelectric material, in order to improve the sensors array sensitivity and the electro-mechanical coupling coefficient, the optimized results including plate thicknesses and cut orientations are presented by numerical simulation. These studies show that the Lamb wave sensors array can be potential in liquid sensing.