This paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp M-matrix. Thefuzzy linear system (FLS) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. However, solving this crisp system isdifficult for large n because of dimensionality problems . It is shown that thisdifficulty may be avoide...

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

Limited information is available on the role of MAPK phosphatase 1 (MKP1) signaling in osteoblasts. We have recently reported distinct roles for MKP1 during osteoblast proliferation, differentiation, and skeletal responsiveness to parathyroid hormone (PTH). As MKP1 regulates the phosphorylation status of MAPKs, we investigated the involvement of P-ERK and P-p38 MAPKs in MKP1 knockout (KO) early...

T =  1 1 1 1 2 1 1 3 3 1 .. . . .  = exp  0 1 0 0 2 0 0 3 0 . . .  with coefficients ti,j = (i j ) . This shows that det(P (n)) = 1 and that P (n) is positive definite for all n ∈ N. It implies furthermore that the characteristic polynomial det(tI(n)−P (n)) = ∑ k=0 αkt k (where I(n) denotes the identity matrix of order n) of P (n) has only positive real roots. The in...