一种场站设置问题中的几个结论

本文研究如下一种场站设置问题:设S是欧空间E~m中由有限个点A_1,A_2,…,A_n组成的集合.d(A_i,A_j)表示点A_i和A_j之间的距离.令σ(S)=Σ_(1≤i相似文献   

A note on global stability of three-dimensional Ricker models

In the recent paper [E. C. Balreira, S. Elaydi, and R. Luís, J. Differ. Equ. Appl. 23 (2017), pp. 2037–2071], Balreira, Elaydi and Luís established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luís' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application.     

Small faces in stationary Poisson hyperplane tessellations

We consider the tessellation induced by a stationary Poisson hyperplane process in d‐dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the k‐faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical k‐face, under the condition of given size and this tending to zero. The limit distribution is concentrated on simplices. This extends a result of Gilles Bonnet.     

A dual strategy for solving the linear programming relaxation of a driver scheduling system

A Mathematical Programming model of a driver scheduling system is described. This consists of set covering and partitioning constraints, possibly user-supplied side constraints, and two pre-emptively ordered objectives. The previous solution strategy addressed the two objectives using separate Primal Simplex optimisations; a new strategy uses a single weighted objective function and a Dual Simplex algorithm initiated by a specially developed heuristic. Computational results are reported.     

与"求线性规划问题可行基的一种方法"的再商榷

再次说明文[1]提出的方法不能直接使用，仍须按文[2]的修正结果实行才是正确的。同时指出最近提出的某些算法的不实之处，以飨读者，避免误导。     

线性规划的约束条件“滚雪球”算法

为使线性规划的每个约束条件部分或全部地拥有原整个约束条件所包含的信息,将线性规划的约束条件“滚雪球”后得到与原约束条件等价的新约束条件,对新约束条件所构成的线性规划采用目标函数最速递减算法.有一定规模的随机数值算例显示了该算法只需进行m(约束条件数)次迭代即可求得最优解.     

单形构造定理的一种代数证法

给出n维欧氏空间En中n维单形构造定理的一种代数证法,这种代数证法十分简洁.     

Norm-Closed Intervals of Norm-Complete Ordered Abelian Groups

Let (G,u) be an Archimedean norm-complete dimension group with order-unit. Continuing a previous paper, we study intervals (i.e., nonempty upward directed lower subsets) of G which are closed with respect to the canonical norm of (G,u). In particular, we establish a canonical one-to-one correspondence between closed intervals of G and certain affine lower semicontinuous functions on the state space of (G,u), which allows us to solve several problems of K. R. Goodearl about inserting affine continuous functions between convex upper semicontinuous and concave lower semicontinuous functions. This yields in turn new results about analogues of multiplier groups for norm-closed intervals.     

Elementary formulas for a hyperbolic tetrahedron

We derive some elementary formulas expressing the relation between the dihedral angles and edge lengths of a tetrahedron in hyperbolic space.     

关于垂足单形的两个不等式及其应用

利用距离几何的理论与方法研究了n维欧氏空间En中n维单形的几何不等式问题,建立了垂足单形的两个新的几何不等式,作为其特例,得n维Euler不等式及其推广.