The one to one correspondence between the existence of a unique equilibrium state and the differentiability of the free energy density with respect to the external field previously shown for Ising ferromagnets is extendend to higher valued spin systems as well as to continuum systems satisfying the Fortuin, Kasteleyn and Ginibre inequalities. In particular this is shown to hold for a mixture of...

In an important recent paper, [2], S. Franz and M. Leone prove rigorous lower bounds for the free energy of the diluted p-spin model and the K-sat model at any temperature. We show that the results for these two models are consequences of a single general principle. Our calculations are significantly simpler than those of [2], even in the replica-symmetric case.

in this paper we consider the european continuous installment call option. then  its linear complementarity formulation is given. writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. finally finite element method is applied to price the european continuous installment call option.

the risk free rate of return plays a main role in financial economic theory and financial markets. due to prohibition of interest in islamic countries there is no specific financial instrument with risk free rate of return as a criterion for measuring the risk free rate of market. we apply the kalman filter to estimate this variable for financial markets in iran. the technique is based on a sta...