in this paper, we try and valuate preemption rights by modifying the black-scholes model, which is widely used to valuate options and other derivatives. here we first present the basics of the black-scholes model and then we discus modification of the model to be fit for preemption right valuation. at the end, we valuate four of the preemptive rights using the proposed model

In the polluted bootstrap percolation model, vertices of the cubic lattice Z are independently declared initially occupied with probability p or closed with probability q. Under the standard (respectively, modified) bootstrap rule, a vertex becomes occupied at a subsequent step if it is not closed and it has at least 3 occupied neighbors (respectively, an occupied neighbor in each coordinate). ...

The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the inverse cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatilities in the MF model do not show sound long memory. We propose a modified version of the MF model by including...

The orbital stability of the peaked solitary-wave solutions for a generalization of the modified Camassa-Holm equation with both cubic and quadratic nonlinearities is investigated. The equation is a model of asymptotic shallow-water wave approximations to the incompressible Euler equations. It is also formally integrable in the sense of the existence of a Lax formulation and bi-Hamiltonian stru...

Since Amaranth (AM) is one of the dye compounds which is harmful to human’s life its removal from industrial waste water would reduce their environmental impact and health effect. Copper nanoparticle (CuNP) is a simple and eco-friendly material which can be used to remove this pollutant. In this paper, copper nanoparticles were synthesized, for removal of AM dye. The experiments were designed b...

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal tha...