The aim of this paper is to provide alternate proofs of all the results of our previous paper [2] in the particular case when the given two matrices A1 and A2 in the linear combination A = c1A1 + c2A2 commute.

it is well known that the matrix exponential function has practical applications in engineering and applied sciences. in this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $x$-form. for instance, $e^{mathbf{a}t}$, $t^{mathbf{a}}$ and $a^{mathbf{a}t}$ will be evaluated by the new formulas in this par...

the purpose of this review article is to characterize all of the parameters regarding the types, polymers used, and release kinetics of matrix tablets. matrix system was the earliest oral extended release platform for medicinal use. matrix tablets are most commonly used methods to modulate the release profile of drugs. they are much desirable and preferred for such therapy because they offer be...

for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

for vectors x, y ∈ rn, it is said that x is left matrix majorizedby y if for some row stochastic matrix r; x = ry. the relationx ∼` y, is defined as follows: x ∼` y if and only if x is leftmatrix majorized by y and y is left matrix majorized by x. alinear operator t : rp → rn is said to be a linear preserver ofa given relation ≺ if x ≺ y on rp implies that t x ≺ ty onrn. the linear preservers o...

in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

Bone marrow stromal cells can give rise to several mesenchymal lineages. The existence of a common stem/progenitor cell, the mesenchymal stem cell, has been proposed, but which developmental stages follow this mesenchymal multipotent progenitor is not known. Based on experimental evidence, a model of mesenchymal stem cell differentiation has been proposed in which individual lineages branch dir...

Mouse and human central nervous system progenitor cells can be propagated extensively ex vivo as stem cell lines. For the rat, however, in vitro expansion has proven to be problematic owing to proliferation arrest and differentiation. Here, we analyse the establishment, in adherent culture, of undifferentiated tripotent neural stem (NS) cell lines derived from rat foetal brain and spinal cord. ...

BACKGROUND A recent study has shown that pure neural stem cells can be derived from embryonic stem (ES) cells and primary brain tissue. In the presence of fibroblast growth factor 2 (FGF2) and epidermal growth factor (EGF), this population can be continuously expanded in adherent conditions. In analogy to continuously self-renewing ES cells, these cells were termed 'NS' cells (Conti et al., PLo...