Supersymmetry breaking via gaugino condensation is studied in vacua of heterotic M–theory with five–branes. We show that supersymmetry is still broken by a global mechanism and that the non–perturbative superpotential takes the standard form. When expressed in terms of low energy fields, a modification arises due to a threshold correction in the gauge kinetic function that depends on five–brane...

We present a characterization of the approximation errors of the PostWidder and the Gamma operators in Lp(0,∞), 1 ≤ p ≤ ∞, with a weight x for any real γ. Two types of characteristics are used – weighted Kfunctionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it. AMS classification: 41A25, 41A27, 41A35, 41A36.

In this paper we answer a question raised in [25], Sec. 4, by showing that the genus zero moduli operad {M0,n+1} can be endowed with natural descent data that allow it to be considered as the lift to SpecZ of an operad over F1. The relevant descent data are based on a notion of constructible sets and constructible functions over F1, which describes suitable differences of torifications with a p...

We establish quantitative results for the approximation properties of the q-analogue of the Bernstein operator defined by Lupaş in 1987 and for the approximation properties of the limit Lupaş operator introduced by Ostrovska in 2006, via Ditzian-Totik modulus of smoothness. Our results are local and global approximation theorems. 2000 Mathematics Subject Classification. 41A25, 41A36.

We investigate a rearrangement inequality for pairs of n × n matrices: Let ‖A‖p denote (Tr(A∗A)p/2)1/p, the C trace norm of an n×n matrix A. Consider the quantity ‖A+B‖p+‖A−B‖p. Under certain positivity conditions, we show that this is nonincreasing for a natural “rearrangement” of the matrices A and B when 1 ≤ p ≤ 2. We conjecture that this is true in general, without any restrictions on A and...

Size matters. Human perception most naturally relates relative extent, area or volume to importance, nearness and weight. Reversely, conveying importance of something by depicting it at a different size is a classic artistic principle, in particular when importance varies across a domain. One striking example is the neuronal homunculus; a human figure where the size of each body part is proport...