In their seminal work which initiated random graph theory Erd os and R enyi discovered that many graph properties have sharp thresholds as the number of vertices tends to in nity We prove a conjecture of Linial that every monotone graph property has a sharp threshold This follows from the following theorem Let Vn p f g denote the Hamming space endowed with the probability measure p de ned by p ...

A Boolean k-monotone function defined over a finite poset domain D alternates between the values 0 and 1 at most k times on any ascending chain in D. Therefore, k-monotone functions are natural generalizations of the classical monotone functions, which are the 1-monotone functions. Motivated by the recent interest in k-monotone functions in the context of circuit complexity and learning theory,...

In this article, we investigate sufficient conditions for existence of maximal and minimal solutions to a coupled system of highly nonlinear differential equations of fractional order with mixed type boundary conditions. To achieve this goal, we apply monotone iterative technique together with the method of upper and lower solutions. Also an error estimation is given to check the accuracy of th...

In this paper, we introduce and study a new class of generalized nonlinear mixed quasi-variational inequalities involving maximal η-monotone mapping. Using the resolvent operator technique for maximal η-monotone mapping, we prove the existence of solution for this kind of generalized nonlinear multi-valued mixed quasi-variational inequalities without compactness and the convergence of iterative...

the equilibrium constant of adduct formation between some triorganotin chloride of the type r3sncl (r=c6h5, p-ch3c6h4, n-ch3)ch2)3, c6h5-ch2 and lewis bases cl¯, br¯, and i¯, were measured in 50% v/v ethanol-water solvent spectrophotometrically. the average equilibrium constant values for the systems studied shows the following acceptor trend of tin(iv) in the triorganotin chlorides: p-tolyl > ...

We provide the operations of matrix addition, multiplication, transposition, and matrix comparisons as executable functions over ordered semirings. Moreover, it is proven that strongly normalizing (monotone) orders can be lifted to strongly normalizing (monotone) orders over matrices. We further show that the standard semirings over the naturals, integers, and rationals, as well as the arctic s...