The numerical radius and specttural matrices

In this paper we investigate spectral matrices, i.e., matrices with equal spectral and numerical radii. Various characterizations and properties of these matrices are given.     

An extremal problem concerning matrices of 0's and 1 's

We determine the smallest number f(n,k) such that every (0,1)-matrix of order n what zero main diagonal which has at least f(n,k) 1's contains an irreducible, principal submatrix of order K. We characterize those matrices with f(n,k)-1 l's having no irreducible, principal submatrix of order k     

Phase transition in the fine structure constant

Within the context of mass-varying neutrinos, we construct a cosmological model that has a phase transition in the electromagnetic fine structure constant at a redshift of 0.5. The model accommodates hints of a time variable in quasar spectra and the nonobservance of such an effect at very low redshifts. It is consistent with limits from the recombination and primordial nucleosynthesis eras and is free of instabilities.     

Scaling in soft hadroproduction by positive projectiles in the range of 32–147 GeV/c

The total hadron multiplicity and the multiplicity in the three-jet events ine ⁺ e ^?-annihilation are considered. The formula for the total multiplicity (with account for the heavy quark contribution) agrees well with experiment. The value of the multiplicity for three-jet events is predicted.     

Novel ring-cleaving reaction of 4-nitro-1,1,2,2,9,9,10,10-octafluoro[2.2]paracyclophane with nucleophiles

When 4-nitro-AF4 is treated with nucleophiles such as alkoxides and cyanide, a novel ring opening, cyclophane destroying reaction is observed whereby, via an S_NAr mechanism, the nucleophile attacks the bridgehead aryl carbon vicinal to the nitro group with subsequent aryl-CF₂ bond cleavage.