Two iterative methods of order four and five, respectively, are presented for solving nonlinear systems of equations. Numerical comparisons are made with other existing second- and fourth-order schemes to solve the nonlinear system of equations of theGlobal Positioning Systemand some academic nonlinear systems.

The purpose of this paper was to investigate the structure of semi-Heyting chains and the variety CSH generated by them. We determine the number of non-isomorphic n-element semi-Heyting chains. As a contribution to the study of the lattice of subvarieties of CSH; we investigate the inclusion relation between semi-Heyting chains. Finally, we provide equational bases for CSH and for the subvarieties of CSH introduced in [5].

In this paper we construct, given a Wajsberg hoop A, an MV-algebra MV(A) such that the underlying set A of A is a maximal filter of MV(A) and the quotient MV(A)/A is the two element chain. As an application we provide a topological duality for locally finite Wajsberg hoops based on a previously known duality for locally finite MV-algebras. We also give another duality for k-valued Wajsberg hoops based on a different representation of k-valued MV-algebras and show the relation to the first duality. We also apply this construction to give a topological representation for free k-valued Wajsberg hoops.

In this paper we investigate those subvarieties of the variety SH of semi-Heyting algebras which are term-equivalent to the variety L H of Gödel algebras (linear Heyting algebras). We prove that the only other subvarieties with this property are the variety L Com of commutative semi-Heyting algebras and the variety L ∨ generated by the chains in which a < b implies a → b = b . We also study the variety C generated within SH by L H , L ∨ and L Com . In particular we prove that C is locally finite and we obtain a construction of the finitely generated free algebra in C.

In this paper we give a description of an implication algebra A as a union of a unique family of filters of a suitable Boolean algebra Bo(A), called the Boolean closure of A. From this representation we obtain a notion of topological implication space and we give a dual equivalence based in the Stone representation for Boolean algebras. As an application we provide the implication space of all free implication algebras.