Each linear program (LP) has an optimal basis. The space of linear programs can be partitioned according to these bases, so called the basis partition. Discovering the structures of this partition is our goal. We represent the space of linear programs as the space of projection matrices, i.e. the Grassmann manifold. A dynamical system on the Grassmann manifold, first presented in [5], is used t...

The statistical mechanics of systems whose evolution is governed by mixed quantum-classical dynamics is investigated. The algebraic properties of the quantum-classical time evolution of operators and of the density matrix are examined and compared to those of full quantum mechanics. The equilibrium density matrix that appears in this formulation is stationary under the dynamics and a method for...

The evolution of demographic characteristics is considered in terms of the density-dependent Lefkovitch matrix model, which describes a species' population dynamics with a stage-specific pattern of reproduction and mortality. We obtain the invadability condition of a mutant-type into the wild-type population at the equilibrium state. The condition depends on the left and right eigenvectors at t...

among various reported membrane-based gas separation processes, the best explanation is generally achieved by the solution-diffusion model. the main factors in this model are the solubility and diffusivity of permeationcomponents through the membrane. the prediction of permeability and diffusivity in multicomponent gas permeation as well as the separation evaluation equilibrium and kinetic inte...

The equilibrium problem with equilibrium constraints (EPEC) can be looked on as a generalization of Nash equilibrium problem (NEP) and the mathematical program with equilibrium constraints (MPEC) whose constraints contain a parametric variational inequality or complementarity system. In this paper, we particularly consider a special class of EPECs where a common parametric P-matrix linear compl...

A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players’ actions. The players communicate over a strongly connected digraph to send/receive the estimates of the other players’ actions to/from the other local players according to a gossip communication protocol. Due to asymmetric infor...

First-order (i.e., gradient-based) methods for solving two-person zero-sum sequential games of imperfect information have recently become important tools in the construction of game theory-based agents. The computation time per iteration is typically dominated by matrix-vector product operations involving the payoff matrix A. In this paper, we describe two techniques for scaling up this operati...