global Liapunov function. The absolute stability of systems Mth infinite but totally disconnected sets of equilibrium points can then be studied using the LaSalle invariance principle, the theory of several complex variables, and sam's theorem. The symmetry of matrix C is important since competitive systems of the form (1) exist wherein C is arbitrarily close to a symmetric matrix but almost al...

Dynamics of the relaxation of a perturbed thermodynamic system to equilibrium is determined by the generalized eigenvalue equation (K̃ + λS)yβ = 0. Here S αβ is a matrix of linear response coefficients and K̃ is a matrix of kinetic coefficients. We describe LeChatelier’s Principle and both its static and dynamical symmetries, and treat cases in which there are multiple relaxation channels. The tr...

We investigate the angular normal modes for small oscillations about an equilibrium of a single-component Coulomb cluster confined by a radially symmetric external potential to a circle. The dynamical matrix for this system is a Laplacian symmetrically circulant matrix and this result leads to an analytic solution for the eigenfrequencies of the angular normal modes. We also show the limiting d...

In this document we will look at useful facts and definitions about Nash and correlated equilibria for two person games. More specifically we’ll give a brief definition of both equilibria, and then we’ll point out the relation between them. We will next introduce a numerical approach aimed at calculating Nash Equilibria of a symmetric game we wish to explore in CME 334. A motivation for this ap...

The solution of nonlinear dynamic equilibrium equations using mode superposition and substructuring is studied. The objective is to design schemes that in some analyses can significantly decrease the computational effort involved when compared to a complete direct integration solution. Specific schemes for mode superposition analysis and substructuring are proposed. These techniques have been i...

in the present paper, we introduce the sequence space [{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},] where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. we investigate its topological properties and inclusion relations. moreover, we consider the problem of fin...

We consider the problem of robust state-feedback stabilization for a multi-channel system in a game-theoretic framework. Specifically, we provide a sufficient condition for the existence of a robust feedback Nash equilibrium when every agent aims to optimize a different type of objective function while each function being associated with certain dissipativity properties of the system. We furthe...

Many problems in multiagent learning involve repeated play. As such, naive application of Nash equilibrium concepts are often inappropriate. A recent algorithm in the literature (Stimpson & Goodrich 2003) uses a Nash bargaining perspective instead of a Nash equilibrium perspective, and learns to cooperate in self play in a social dilemma without exposing itself to being exploited by selfish age...

In this paper, the asymptotic stability of neural networks with time varying delay is studied by using the nonsmooth analysis, Lyapunov functional method and linear matrix inequality (LMI) technique. It is noted that the proposed results do not require smoothness of the behaved function and activation function as well as boundedness of the activation function. Several sufficient conditions are ...

Solid Phase Microextraction (SPME) uses a small volume of sorbent dispersed typically on the surface of small fibres, to isolate and concentrate analytes from sample matrix. After contact with sample, analytes are absorbed or adsorbed by the fibre phase (depending on the nature of the coating) until an equilibrium is reached in the system. The amount of an analyte extracted by the coating at eq...