Find the dual of each of these compound propositions: (a) p or Not q, (b) p and q or r and T), (c) p and Not q or q and F Determine which of the following simple graphs is feasible. If the graph is...
Third, we introduce some of the more technical, but important, notions used in the proofs in Sect.2, and in particular-flat nearlyk-distance sets, defined in Sect.1.3.1. It is via the notion of-flat nearlyk-distance sets that we actually establish the link between the “nearlyk-distance...
Some foundational propositions of hesitant fuzzy information systems are proposed with respect to parameter reductions and an example and an algorithm are given to illustrate the processes of parameter reduction. Finally, a multi-strength intelligent classifier is proposed to make health state diagnoses ...
. in the following two propositions we list the properties of the cross-ambiguity function and the cross-wigner distribution that we will be using throughout the exposition. for the proofs we refer the reader to [ 11 ]. proposition 2.2 for \(f,g\in {l^2}(\mathbb {r}^d)\) the ...
If 0∈M, then GM⊆M and the subset M∕GM⊆G∕GM is aperiodic. Before stating the following two propositions, following [14] , we introduce some special sets of integers: N0={pk:p prime, k≥0}; N1={pkq:p,q distinct primes, k≥1}; N2={p2q2:p,q distinct primes }; N3={...
The following propositions are true. Proof Propositions (1) and (2) are straightforward. The proof is left to Acknowledgments The author would like to thank two anonymous referees for their comments on the paper.References (25) BrightwellG. Balanced pairs in Partial orders Discrete Math. (...
P Frankl,Z Füredi - 《Discrete Mathematics》 被引量: 46发表: 1984年 The High-Order-Multiplicity of Unusually Wide M-dwarf Binaries: Eleven New Triple and Quadruple Systems M-dwarfs in extremely wide binary systems are very rare, and may thus have different formation processes from those found...
It starts from a symbolic model that consists of predicates or propositions in rough logic. Such a model is referred to as a theory in formal logic. By experts’ suggestion, called fuzzificaton, t he symbolic model can be transformed into a fuzzy model that usually consists of rules of ...
The following two propositions can be obtained from our results obtained in Sect.3immediately. Proposition 4.1 Letp\in \mathbb{R}\setminus \{0\}.Then Theorem3.5leads to \begin{aligned}& \biggl\vert \biggl(\frac{1}{6} \biggr)^{\dot{\alpha }} \biggl[{P}_{ \dot{\alpha }}( \...
Furthermore, the two following propositions show that in the defining condition C(A g(n)) ≥ n of i.o. autocomplexity and i.o. complexity the lower bound n can equivalently be replaced by a wide range of lower bounds in case g may depend on this bound. Proposition 15. The following...