Given the prime CNF representation φ of a monotone Boolean function f : {0, 1} 7→ {0, 1}, the dualization problem calls for finding the corresponding prime DNF representation ψ of f . A very simple method (called Berge multiplication [3, Page 52–53]) works by multiplying out the clauses of φ from left to right in some order, simplifying whenever possible using the absorption law. We show that f...

A renewal model in risk theory is considered, where H(u, y) is the tail of the distribution of the deficit at ruin with initial surplus u and F(y) is the tail of the ladder height distribution. Conditions are derived under which the ratio H(u, y)/F(u + y) is nondecreasing in u for any y ≥ 0. In particular, it is proven that if the ladder height distribution is stable and DFR or phase type, then...

It is shown that the inverse limit of an inverse system of smooth continua is a smooth continuum provided that there exists a thread composed of initial points and that the bonding mappings are monotone relative to these points. It also is proved that the property of being an arboroid, a dendroid, a generalized tree, a fan or a smooth fan is an invariant under the inverse limit operation if the...

We adapt the quasi-monotone method, an algorithm characterized by uniquely having convergence quality guarantees for last iterate, composite convex minimization in stochastic setting. For proposed numerical scheme we derive optimal rate of $$\text{ O }\left( \frac{1}{\sqrt{k+1}}\right)$$ terms rather than on average as it is standard subgradient methods. The theoretical guarantee individual reg...

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...

Any monotone Boolean function on a lattice can be described by the set of its minimal 1 values. If a lattice is given as a concept lattice, this set can be represented by the set of minimal hypotheses of a classification context. Enumeration of minimal hypotheses in output polynomial time is shown to be impossible unless P = NP, which shows that dualization of monotone functions on lattices wit...

In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on noncompact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pseudo-monotone type III operators, we shall use Ch...