In this note we generalize and unify two results on connectivity of graphs: one by Balinsky and Barnette, one by Athanasiadis. This is done through a simple proof using commutative algebra tools. In particular we use bounds for the Castelnuovo–Mumford regularity of their Stanley–Reisner rings. As a result, if ∆ is a simplicial d-pseudomanifold and s is the largest integer such that ∆ has a miss...

If N = qkn2 is an odd perfect number, where q is the Euler prime, then we show that σ(n) ≤ qk is necessary and sufficient for Sorli’s conjecture that k = νq(N) = 1 to hold. It follows that, if k = 1 then the Euler prime q is the largest prime factor of N and that q > 10500. We also prove that qk < 23n 2.

We give a review of the mathematical and physical properties of the celebrated family of Calogero-like models and related spin chains.

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...