We calculate the exact fragmentation functions for c and b quark fragmentation taking into account the spin orientation of the initial heavy quark in the form of analytical and rather simple expressions. Our calculations show that spin orientation may have an important effect on the fragmentation spectrum. This effect is more striking in the cases of c ?D, D*; c? ? , ? , and ?B , B *.

The main purpose of this paper is to determine the fine spectrum of the generalized upper triangular double-band matrices uv over the sequence spaces c0 and c. These results are more general than the spectrum of upper triangular double-band matrices of Karakaya and Altun[V. Karakaya, M. Altun, Fine spectra of upper triangular doubleband matrices, Journal of Computational and Applied Mathematics...

there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.