In the canonical approach to Lorentzian Quantum General Relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through the introduction of a Hilbert space structure which was later proved to be a faithful representation of the canonical commutation and adjointness relations of the quantum field algebra of diffeomor...

in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

depending on the moisture contents, the soil behavior is revealed as solid, semisolid, plastic and liquid states. liquid limit is an important property of fine-grained soils and casagrande and cone penetrometer are two different methods employed for the determination of liquid limit of the soil. in forest environment, the casagrande method is the classic method for liquid limit determination, b...