A graph is n-e.c. (n-existentially closed) if for every pair of subsets A,B of vertex set V of the graph such that A∩B = ∅ and |A|+ |B| = n, there is a vertex z not in A∪B joined to each vertex of A and no vertex of B. Few explicit families of n-e.c. are known for n > 2. In this short note, we give a new construction of 3-e.c. graphs using the notion of quadrance in the finite Euclidean space Zdp.

Possible worlds, governed by known or unknown cosmic rules, if ever they existed, do ontologically exist in the realm of imaginary and relate to human potential imagine beyond what we recognize as reality. This cognitive potential, tinged with postmodernist narrative techniques, can create alternative histories through which contemplate possible scenarios reality that could have happened depend...

Answering a question of P. Bankston, we show that the pseudoarc is a co-existentially closed continuum. We also show that C(X), for X a nondegenerate continuum, can never have quantifier elimination, answering a question of the the first and third named authors and Farah and Kirchberg.

Assuming a certain form of resolution singularities, we prove general existential Ax-Kochen/Ershov principle for tamely ramified fields in all characteristics. This specializes to well-known results residue characteristic 0 and unramified mixed characteristic. It also encompasses the conditional decidability known F p ( t ) its finite extensions, due Denef-Schoutens. On other hand, it applies s...

We study existentially closed CSA-groups. We prove that existentially closed CSA-groups without involutions are simple and divisible, and that their maximal abelian subgroups are conjugate. We also prove that every countable CSA-group without involutions embeds into a finitely generated one having the same maximal abelian subgroups, except maybe the infinite cyclic ones. We deduce from this tha...

Linear feedback sequence register (LFSR) is a useful cryptographic primitive which is widely implemented in many cryptosystems to represent finite field elements with the counterparts of minimal polynomials. In this paper, an efficient transitive signature scheme from LFSR (LFSR-TS) is considered. First, two derived LFSR sequence operations are designed for LFSR-TS, which are not proposed prior...

A signature scheme is existentially unforgeable if, given any polynomial (in the security parameter) number of pairs where S(m) denotes the signature on the message m, it is computationally infeasible to generate a pair (m k+1 ; S(m k+1)) for any message m k+1 = 2 fm 1 ; : : :m k g. We present an existentially unforgeable signature scheme that requires at most 6 times the amount of time needed ...