This paper, a contribution to “micro set theory”, is the study promised by the first author in [M4], but improved and extended by work of the second. We use the rudimentarily recursive (set theoretic) functions and the slightly larger collection of gentle functions to develop the theory of provident sets, which are transitive models of PROVI, a very weak subsystem of KP which nevertheless suppo...

The theory of fuzzy sets is used in various Mathematical fields. Zadeh [1] 1965 developed the concept of fuzzy sets which is the basis of fuzzy Mathematics. Since then various researchers worked on the development of fuzzy set theory. Atanassov [2,3,4,5,6,7] has given idea about intuitionistic fuzzy sets. Im and Lee [8] studied about the determinant of square intuitionistic fuzzy matrices (IFMs...

Let G = (V,E) be a multigraph (it has multiple edges, but no loops). We call G maximally edge-connected if λ(G) = δ(G), and G super edge-connected if every minimum edge-cut is a set of edges incident with some vertex. The restricted edgeconnectivity λ′(G) of G is the minimum number of edges whose removal disconnects G into non-trivial components. If λ′(G) achieves the upper bound of restricted ...

We present two new transitive closure algorithms that are based on strong component detection. The algorithms scan the input graph only once without generating partial successor sets for each node. The new algorithms eliminate the redundancy caused by strong components more e ciently than previous transitive closure algorithms. We present statistically sound simulation experiments showing that ...

The automorphism groups of the symmetric 2-(64, 28, 12) designs with the symmetric difference property (SDP), as well as the groups of their derived and residual designs, are computed. The symmetric SDP designs all have transitive automorphism groups. In addition, they all admit transitive regular subgroups, or equivalently, (64, 28, 12) difference sets. These results are used for the enumerati...

Non-affine groups acting doubly transitively on a Hadamard matrix have been classified by Ito. Implicit in this work is a list of Hadamard matrices with non-affine doubly transitive automorphism group. We give this list explicitly, in the process settling an old research problem of Ito and Leon. We then use our classification to show that the only cocyclic Hadamard matrices developed form a dif...