the sharp upper bounds and the sharp lower bounds of the largest eigenvalues $lambda_1$, the least eigenvalue $lambda_n$, the second largest eigenvalue $lambda_2$, the spread and the separator among all firefly graphs on $n$ vertices are determined.

We provide generalisations of two Schwarz-type lemmas — the first a result of Globevnik and the other due to Ransford and White — for holomorphic mappings into the spectral unit ball. The first concerns mappings of the unit disc in C into the spectral unit ball, while the second concerns self-mappings. The aforementioned results apply to holomorphic mappings that map the origin to the origin. W...

We show that an essential part of the new (Jones-type) polynomial link invariants can be computed in subexponential time. This is in a sharp contrast to the result of Jaeger, Vertigan and Welsh that computing the whole polynomial and most of its evaluations is #P-hard.

A supersymmetric model with two copies of the Standard Model gauge groups is constructed in the gauge mediated supersymmetry breaking scenario. The supersymmetry breaking messengers are in a simple form. The Standard Model is obtained after first step gauge symmetry breaking. In the case of one copy of the gauge interactions being strong, a scenario of electroweak symmetry breaking is discussed...

We show that it is #P-complete to count the number of bases of matroids representable over a fixed infinite field or fields of fixed characteristic.

Let M be an n × n square matrix and let p(λ) be a monic polynomial of degree n. Let Z be a set of n × n matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix Z ∈ Z such that the product matrix MZ has characteristic polynomial p(λ). In this paper we provide new necessary and sufficient conditions when Z is an affine variety over an algebraically closed field.

Hadronic final states with a hard isolated photon are studied using data taken at centre-of-mass energies around MZ with the OPAL detector at LEP. The strong coupling αS is extracted by fitting event shape variables for the reduced centre-of-mass energies ranging from 20 GeV to 80 GeV, and the energy dependence of αS is studied. Combining all the values using different event shape variables and...