Boolean and logical hypercubes are discussed as providers of tags to object sets, transforming them into tagged a generalization fuzzy sets. The equivalence sets permits consider natural an equivalent basis hypercube concatenation easily allows studying how information is transmitted. From there Gödel-like behavior thus can be unveiled. Later, it the iterative building numbers, considering Mers...

The study of the function β(n) originated in the paper of Nelson, Penney, and Pomerance [7], where the question was raised as to whether the set of Ruth-Aaron numbers (i.e., natural numbers n for which β(n) = β(n+ 1)) has zero density in the set of all positive integers. This question was answered in the affirmative by Erdős and Pomerance [5], and the main result of [5] was later improved by Po...

In this appendix, we examine the 64-bit integer output sequences of the SFMT19937 generator (or the double-precision floating-point numbers in [0, 1) converted from them). In fact, the SFMT generators are optimized under the assumption that one will mainly be using 32-bit output sequences, so that the dimensions of equidistribution with v-bit accuracy for 64-bit output sequences are worse than ...

This work presents an ultra-lightweight, cryptographic, mutual authentication protocol for radio-frequency identification (RFID) tags. The proposed scheme is more secure than its predecessors. The vulnerabilities of previous schemes based on triangular functions and rotation have been demonstrated in traditional and rotational cryptanalysis. In this paper, we summarize the successful attacks on...

A finite transitive permutation group is said to be elusive if it has no fixed point free elements of prime order. In this paper we show that all elusive groups G = N oG1 with N an elementary abelian minimal normal subgroup and G1 cyclic, can be constructed from transitive subgroups of AGL(1, p2), for p a Mersenne prime, acting on the set of p(p + 1) lines of the affine plane AG(2, p).