Blocking and anti-blocking pairs of polyhedra

Some of the main notions and theorems about blocking pairs of polyhedra and antiblocking pairs of polyhedra are described. The two geometric duality theories conform in many respects, but there are certain important differences. Applications to various combinatorial extremum problems are discussed, and some classes of blocking and anti-blocking pairs that have been explicitly determined are mentioned.This paper was presented at the 7th Mathematical Programming Symposium 1970, The Hague, The Netherlands.     

Equations arising from Jordan *-derivation pairs

Summary. We study certain functional equations derived from the definition of a Jordan *-derivation pair. More precisely, if A is a complex *-algebra and M is a bimodule over A, having the structure of a complex vector space compatible with the structure of A, such that implies m = 0 and implies m = 0 and if are unknown additive mappings satisfying then E and F can be represented by double centralizers. The obtained result implies that one of the equations in the definition of a Jordan *-derivation pair is redundant. Furthermore, a remark on the extension of this result to unknown additive mappings such that is given in a special case.     

Superprocesses arising from interactive stochastic flows

In this paper, we give a unified construction for superprocesses with dependent spatial motion constructed by Dawson, Li, Wang and superprocesses of stochastic flows constructed by Ma and Xiang. Furthermore, we also give some examples and rescaled limits of the new class of superprocesses.     

Recollements arising from cotorsion pairs on extriangulated categories

This paper is devoted to constructing some recollements of additive categories associated to concentric twin cotorsion pairs on an extriangulated category. As an application, this result generalizes the work by W. J. Chen, Z. K. Liu, and X. Y. Yang in a triangulated case [J. Algebra Appl., 2018, 17(5): 1–15]. Moreover, it highlights new phenomena when it applied to an exact category. Finally, we give some applications of our main results. In particular, we obtain Krause's recollement whose proofs are both elementary and very general.     

Ergodicity of cylinder flows arising from irregularities of distribution

LetT be the mod 1 circle group, α∈T be irrational and 0<β<1. LetE be the closed subgroup ofR generated by β and 1. DefineX=T×E andT:X→X byT(x, t)=(x+α,t+1 _[0,β] (x)−β). Then we have the theorem:T is ergodic if and only if β is rational or 1, α and β are linearly independent over the rationals. This paper was prepared while I was very graciously hosted by the Centro de Investigacion y Estudios Avanzados, Mexico City.     

Impact of a varying capacity on the all pairs 2-route network flows

Given an undirected edge-weighted network in which one edge capacity is allowed to vary, we propose in this paper a polynomial algorithm that needs only two 2-cut-trees computations to provide the all pairs maximum 2-route flow values.     

Hierarchical Preconditioning for PT AP-Systems arising from particulate flows

Particulate flows, i.e. flow of an incompressible, Newtonian carrier fluid loaded with (many) rigid bodies, play an important role in diverse technical applications. In [1] a finite element method was introduced to simulate such flows. The method relies on a splitting method and a subspace projection method to incorporate the rigid body motion of the particles in a so called one domain approach [2]. The resulting systems arising after discretization are ill conditioned in general. Thus preconditioning is mandatory for instance when using an iterative Krylov subspace methods. In this paper we present a Schur complement based preconditioner well suited for this type of application. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical analysis of a simplified Hookean dumbbells model arising from viscoelastic flows

A stochastic model corresponding to a simplified Hookean dumbbells viscoelastic fluid is considered, the convective terms being disregarded. Existence on a fixed time interval is proved provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem.     

Blocking,antiblocking, and pairs of matroids and polymatroids

I extend two theorems of Edmonds concerning common independent vectors in two polymatroids. These results give a proof of conjecture of Fulkerson on the blocker associated with the collection of k-sets independent in two matroids.     

Maximum-throughput dynamic network flows

This paper presents and solves the maximum throughput dynamic network flow problem, an infinite horizon integer programming problem which involves network flows evolving over time. The model is a finite network in which the flow on each arc not only has an associated upper and lower bound but also an associated transit time. Flow is to be sent through the network in each period so as to satisfy the upper and lower bounds and conservation of flow at each node from some fixed period on. The objective is to maximize the throughput, the net flow circulating in the network in a given period, and this throughput is shown to be the same in each period. We demonstrate that among those flows with maximum throughput there is a flow which repeats every period. Moreover, a duality result shows the maximum throughput equals the minimum capacity of an appropriately defined cut. A special case of the maximum dynamic network flow problem is the problem of minimizing the number of vehicles to meet a fixed periodic schedule. Moreover, the elegantsolution derived by Ford and Fulkerson for the finite horizon maximum dynamic flow problem may be viewed as a special case of the infinite horizon maximum dynamic flow problem and the optimality of solutions which repeat every period.     

Nonlinear damped wave equation arising in viscoelastic fluid flows

We consider the nonlinear damped wave equation arising in unsteady Poiseuille flow of shear thinning Maxwell fluid. We show the global existence of the smooth solution to the corresponding nonlinear system. We also give some numerical examples.     

Efficient enumeration of the vertices of polyhedra associated with network LP's

Algorithms are given to list the vertices of polyhedra associated with network linear programs and their duals. Each algorithm has running time which is quadratic in the number of vertices of the polyhedron, and does not require that the polyhedron be either bounded or simple. The algorithms use characterizations of adjacent vertices in network and dual network LP's to perform an efficient traversal of the edge graph of the polyhedron. This contrasts with algorithms for enumerating the vertices of a general polyhedron, all of which have worst-case complexity which is exponential in the number of vertices of the polyhedron.