Rationalized Haar functions are developed to approximate the solution of the nonlinear Volterra–Fredholm–Hammerstein integral equations. The properties of rationalized Haar functions are first presented. These properties together with the Newton–Cotes nodes and Newton–Cotes integration method are then utilized to reduce the solution of Volterra–Fredholm–Hammerstein integral equations to the sol...

1. The number of zeroes of a polynomial over a finite field 1 2. Interpretation in terms of zeta functions 3 2.1. Eigenvalues in the smooth case 4 2.2. Some easy examples 5 3. The Newton polygon 7 3.1. Newton polygons in families 8 4. Abstract Hodge polygons and Newton polygons 9 5. Results of Deligne, Katz, Mazur and Ogus 10 6. Some special cases 11 6.1. Abelian varieties 11 6.2. Curves 12 Ref...

It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent nonsmooth Newton methods for nonsmooth equations have been well established via the concept of semismoothness. In this paper, we focus our discussions on a way of globalizing nonsmooth Newton methods based on a smoothing-nonsmooth reformulation of nonsm...