that g* has the same derived algebra as g itself and that every ideal in g is also an ideal in t*. Let g be any algebraic Lie algebra. Denote by b the radical of g (i.e., the largest solvable ideal in g) and by n the largest ideal of g composed only of nilpotent matrices. By Levi's theorem, g is the direct sum of t and of a semi-simple subalgebra J. It can be proved that f is the direct sum of ...

In this study, the existence and uniqueness of the solution of a class of nonlinear finite-part singular integral equations with Carleman shift preserving orientation has been investigated in the generalized Holder space () Γ ϕ H. 1. Introduction Many important problems of engineering mechanics like elasticity, plasticity, and fracture mechanics and aerodynamics can be reduced to the solution o...

in this work, we present a numerical method for solving nonlinear fredholmand volterra integral equations of the second kind which is based on the useof block pulse functions(bpfs) and collocation method. numerical examplesshow eciency of the method.

Solitary wave solutions to the Broer-Kaup equations and approximate long water wave equations are considered challenging by using the rst integral method.The exact solutions obtained during the present investigation are new. This method can be applied to nonintegrable equations as well as to integrable ones.

In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.