The eigenpairs of a Sylvester-Kac type matrix associated with a simple model for one-dimensional deposition and evaporation

A straightforward model for deposition and evaporation on discrete cells of a finite array of any dimension leads to a matrix equation involving a Sylvester-Kac type matrix. The eigenvalues and eigenvectors of the general matrix are determined for an arbitrary number of cells. A variety of models to which this solution may be applied are discussed.Comment: 7 pages, no figure

Giant FAZ10 is required for flagellum attachment zone stabilization and furrow positioning in Trypanosoma brucei

The flagellum and flagellum attachment zone (FAZ) are important cytoskeletal structures in trypanosomatids, being required for motility, cell division and cell morphogenesis. Trypanosomatid cytoskeletons contain abundant high molecular mass proteins (HMMPs), but many of their biological functions are still unclear. Here, we report the characterization of the giant FAZ protein, FAZ10, in Trypanosoma brucei, which, using immunoelectron microscopy, we show localizes to the intermembrane staples in the FAZ intracellular domain. Our data show that FAZ10 is a giant cytoskeletal protein essential for normal growth and morphology in both procyclic and bloodstream parasite life cycle stages, with its depletion leading to defects in cell morphogenesis, flagellum attachment, and kinetoplast and nucleus positioning. We show that the flagellum attachment defects are probably brought about by reduced tethering of the proximal domain of the paraflagellar rod to the FAZ filament. Further, FAZ10 depletion also reduces abundance of FAZ flagellum domain protein, ClpGM6. Moreover, ablation of FAZ10 impaired the timing and placement of the cleavage furrow during cytokinesis, resulting in premature or asymmetrical cell division

Explicit inverses of some tridiagonal matrices

We give explicit inverses of tridiagonal 2-Toeplitz and 3-Toeplitz matrices which generalize some well-known results concerning the inverse of a tridiagonal Toeplitz matrix.http://www.sciencedirect.com/science/article/B6V0R-42KDHCJ-2/1/d6207c3bf9c66184210a9296f72fe1e

Explicit inverses of some tridiagonal matrices

We give explicit inverses of tridiagonal 2-Toeplitz and 3-Toeplitz matrices which generalize some well-known results concerning the inverse of a tridiagonal Toeplitz matrix.http://www.sciencedirect.com/science/article/B6V0R-42KDHCJ-2/1/d6207c3bf9c66184210a9296f72fe1e