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For a formula F in conjunctive normal form (CNF), let sat(F) be the maximum number of clauses of F that can be satisfied by a truth assignment, and let m be the number of clauses in F. It is well-known that for every CNF formula F, sat(F) ≥ m/2 and the bound is tight when F consists of conflicting unit clauses (x) and $(\bar{x})$ . Since each truth assignment satisfies exactly one clause in each...
In the problem Max Lin, we are given a system Az = b of m linear equations with n variables over in which each equation is assigned a positive weight and we wish to find an assignment of values to the variables that maximizes the excess, which is the total weight of satisfied equations minus the total weight of falsified equations. Using an algebraic approach, we obtain a lower bound...
Let F be a CNF formula with n variables and m clauses. F is t-satisfiable if for any t clauses in F, there is a truth assignment which satisfies all of them. Lieberherr and Specker (1982) and, later, Yannakakis (1994) proved that in each 3-satisfiable CNF formula at least of its clauses can be satisfied by a truth assignment. Yannakakis’s proof utilizes the fact that ...
Pneumatic conveying has become a well established method of transporting materials in the resource and process industries. Erosion is a phenomenon that occurs in pneumatic conveying pipeline due to the inherent nature of conveying process. In pneumatic conveying, particulate material is transported by the motive of compressed gas with velocities usually less than 60 m/s. In the present investigation,...
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