We describe maximal nilpotent subsemigroups of a given nilpotency class in the semigroup Ωn of all n × n real matrices with nonnegative coefficients and the semigroup Dn of all doubly stochastic real matrices.

the degree kirchhoff index of a connected graph $g$ is defined as‎ ‎the sum of the terms $d_i,d_j,r_{ij}$ over all pairs of vertices‎, ‎where $d_i$ is the‎ ‎degree of the $i$-th vertex‎, ‎and $r_{ij}$ the resistance distance between the $i$-th and‎ ‎$j$-th vertex of $g$‎. ‎bounds for the degree kirchhoff index of the line and para-line‎ ‎graphs are determined‎. ‎the special case of regular grap...

We introduce the notion of N-topo nilpotent fuzzy set in a fuzzy neighborhood ring and develop some fundamental results. Here we show that a fuzzy neighborhood ring is locally inversely bounded if and only if for all 0 < α < 1, the α-level topological rings are locally inversely bounded. This leads us to prove a characterization theorem which says that if a fuzzy neighborhood ring on a division...

We obtain an explicit bound for the nilpotency class of n-Engel Lie algebras of characteristic zero. 1991 Mathematics Subject Classification (Amer. Math. Soc.): 17B30.

We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at most two. 6-divisible Moufang loops with commuting inner mappings have nilpotency class at most two. There is a Moufang loop of order 2 with commuting inner mappings and of nilpotency class three.

Consider the problem: given a real number x and an error bound ε, find an interval such that it contains n √ x and its width is less than ε. One way to solve the problem is to start with an initial interval and to repeatedly update it by applying an interval refinement map on it until it becomes narrow enough. In this paper, we prove that the well known Secant-Newton map is optimal among a cert...

For binary polynomial optimization problems (POPs) of degree d with n variables, we prove that the ⌈(n+ d− 1)/2⌉th semidefinite (SDP) relaxation in Lasserre’s hierarchy of the SDP relaxations provides the exact optimal value. If binary POPs involve only even-degree monomials, we show that it can be further reduced to ⌈(n + d − 2)/2⌉. This bound on the relaxation order coincides with the conject...

We show nilpotency and completeness results for the homotopy automorphisms of a marked n-stage an unstable coalgebra. These objects figure in moduli problem coalgebras. Our theorems extend classical work Dror, Zabrodsky, Maruyama Møller.