we consider the problem of Computing threshold functions wing directed and undirected monotone contact networks. Our main results are the following. First, we show that there exist directed monotone contact networks that compute T,“, 2 5 k 5 n 1, of size O(k(n k + 2)log(n k + 2)). This bound is almost optimal for small thresholds, since there exists an R(knlog(n/(k 1))) lower bound. OUT network...

A new high-resolution indecomposable quasi-characteristics scheme with monotone properties based on pyramidal stencil is considered. This scheme is based on consideration of two high-resolution numerical schemes approximated governing equations on the pyramidal stencil with different kinds of dispersion terms approximation. Two numerical solutions obtained by these schemes are analyzed, and the...

In the investigation of boundary value problems the construction of a twosided inclusion of the solution can be as important as a numerical approximation of the solution itself. In the present paper we analyze a monotone discretization technique of higher order based upon piecewise interpolation and shifting such that bounding upper and lower solutions are obtained. The monotone discretization ...

The method of monotone iterative technique together with coupled lower and upper solutions is employed to prove the existence of coupled extremal solutions when the forcing function is the sum of an increasing and decreasing functions. This is referred to as generalized monotone method. This will include the usual monotone method results as special cases. Further using uniqueness condition uniq...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...