A minimal perfect hash function maps a set S of n keys into the set { 0, 1, . . . , n− 1 } bijectively. Classical results state that minimal perfect hashing is possible in constant time using a structure occupying space close to the lower bound of log e bits per element. Here we consider the problem of monotone minimal perfect hashing, in which the bijection is required to preserve the lexicogr...

let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

We investigate the phenomenon of coherent perfect absorption in a high-order system with three passive resonators coupled to super-surface form this three-state absorber. The effective parity time (PT) symmetry has received much attention, and open PT symmetric system, incident wave is used as gain instead balancing material loss. analyze variation coupling coefficient by simulation.

We characterise the pairs of graphs $\{ X, Y \}$ such that all \}$-free (distinct from $C_5$) are perfect. Similarly, we $\omega$-colourable (that is, their chromatic number is equal to clique number). More generally, show characterizations for perfectness and $\omega$-colourability connected which independence at least~$3$, distinct an odd cycle, order least $n_0$, similar characterisations su...

Intrusion detection systems are designed to provide security in computer networks, so that if the attacker crosses other security devices, they can detect and prevent the attack process. One of the most essential challenges in designing these systems is the so called curse of dimensionality. Therefore, in order to obtain satisfactory performance in these systems we have to take advantage of app...

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

Let G be an infinite abelian group with |2G| = |G|. We show that if G is not the direct sum of a group of exponent 3 and the group of order 2, then G possesses a perfect additive basis; that is, there is a subset S ⊆ G such that every element of G is uniquely representable as a sum of two elements of S. Moreover, if G is the direct sum of a group of exponent 3 and the group of order 2, then it ...