This note considers Tobin’s average Q in a framework where firms finance investment by equities and debt. The determination of its long-run equilibrium value Qo is based on positing equality of the loan rate and, adjusted for a risk premium, the return on equities. Qo can thus be characterized as a ratio of two rates representing the somewhat modified interest costs and profits of the firms. Th...

The analysis of equilibrium in double auctions is complicated, with almost no closed-form examples and with formal results limited to bounds on bidding behavior. We consider the buyer’s bid double auction in a correlated, private values model. Sellers have the incentive to submit their costs as their asks while buyers strategically underbid. We determine (i) the asymptotic distribution of the e...

The relationship between equilibrium convergence to a uniform quality distribution and price is investigated in the Qmodel, a self-organizing, evolutionary computational matching model of a fixed-price post-secondary higher education system created by Ortmann and Slobodyan (2006). The Q-model is replicated with price equaling its Ortmann and Slobodyan (2006) value P*. Varying the fixed price be...

The system of shallow water waves is one of the classical examples for nonlinear, twodimensional conservation laws. The paper investigates a simple kinetic equation depending on a parameter " which leads for " ! 0 to the system of shallow water waves. The corresponding 'equilibrium' distribution function has a compact support which depends on the eigenvalues of the hyperbolic system. It is show...

Time correlation function expressions for quantum reaction-rate coefficients are computed in a quantum-classical limit. This form for the correlation function retains the full quantum equilibrium structure of the system in the spectral density function but approximates the time evolution of the operator by quantum-classical Liouville dynamics. Approximate analytical expressions for the spectral...

Spatial interaction modeling can be embedded in the framework of statistical thermodynamics. This has been shown in part by Wilson and by Erlander, in particular. However, to complete the embedding, it is necessary to ask the dynamic question of how a migratory population evolves over time from one (observed) distribution at time t0 to another (observed) distribution at time tx, rather than jus...

this paper investigates the stability analysis of fuzzy relational dynamic systems. a new approach is introduced and a set of sufficient conditions is derived which sustains the unique globally asymptotically stable equilibrium point in a first-order fuzzy relational dynamic system with sumproduct fuzzy composition. this approach is also investigated for other types of fuzzy relational composit...

Thermodynamic analysis of the cracking of hexane has been conducted by the Gibbs free energy minimization method and second law analysis of overall reactions. By-products have been divided into three groups of methane, alkynes and aromatics and their possible production paths have been discussed. Effect of operating conditions such as temperature and steam-to-hexane ratio on the cracking perfor...