The Deficiency One Theorem tells us about certain chemical reaction systems that they cannot admit multiple interior equilibria. The theorem was proven by Feinberg. In this paper we provide a relatively short proof of that theorem for the special case of one linkage class. We also extend that result by giving an equivalent condition to the fact that the set of interior equilibria is nonempty fo...

We propose a unified framework for the update of the barrier parameter in interior-point methods for nonlinear programming. The original primal-dual system is augmented to incorporate explicitly an updating function. We analyze local convergence properties and recover known updating strategies as special cases. We report numerical experiments on nonlinear problems and compare our results to a s...

In this talk, we consider the well-posedness, ill-posedness and the regularity of stationary solutions to the hydrodynamic model of semiconductors represented by Euler-Poisson equations with sonic boundary, and make a classification on these solutions. When the doping profile is subsonic, we prove that, the corresponding steady-state equations with sonic boundary possess a unique interior subso...

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...

where e e IR", b e IR" and A is an m x n matrix. In the last four years there has been a vast amount of work on "interior point" algorithms, motivated by Karmarkar's algorithm [16]. Unlike the traditional simplex method which moves from vertex to vertex around the feasible region {x;>4x > b}, interior point methods proceed through the interior {x;Ax > b] of the feasible region. Karmarkar's algo...

The Asian interior arid zone is the largest desert landform system in the Northern Hemisphere, and has high biodiversity. Little is currently known about the evolutionary history of its biota. In this study, we used Zygophyllum, an important and characteristic component of the Asian interior arid zone, to provide new insights into the evolution of this biota. By greatly enlarged taxon sampling,...