One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal two-point methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in...

In this paper, we deal with the étale cohomology of a proper regular arithmetic scheme X Z p ( r ) and Q -coefficients, where coefficients are complexes sheaves that author introduced in [SH] . We will prove -coefficients agrees Selmer group Bloch-Kato for any ≧ dim Using fundamental result, further discuss an approach to study zeta values (or residue) at s = , via relating Tamagawa number conj...

This paper unifies the representations of different kinds of computer arithmetic. It is motivated by ideas developed in the book The End of Error by John Gustafson [5]. Here interval arithmetic just deals with connected sets of real numbers. These can be closed, open, half-open, bounded or unbounded. The first chapter gives a brief informal review of computer arithmetic from early floating-poin...

the total version of geometric–arithmetic index of graphs is introduced based on the endvertexdegrees of edges of their total graphs. in this paper, beside of computing the total gaindex for some graphs, its some properties especially lower and upper bounds are obtained.

residue number system (rns) is a non-weighted number system for integer number arithmetic, which is based on the residues of a number to a certain set of numbers called module set. the main characteristics and advantage of residue number system is reducing carry propagation in calculations. the elimination of carry propagation leads to the possibility of maximizing parallel processing and reduc...

‎The concept of self-similarity on subsets of algebraic varieties‎ ‎is defined by considering algebraic endomorphisms of the variety‎ ‎as `similarity' maps‎. ‎Self-similar fractals are subsets of algebraic varieties‎ ‎which can be written as a finite and disjoint union of‎ ‎`similar' copies‎. ‎Fractals provide a framework in which‎, ‎one can‎ ‎unite some results and conjectures in Diophantine g...