the object of this paper is to establish a summability factor theorem for summabilitya, , k  1 k  where a is the lower triangular matrix with non-negative entries satisfying certain conditions.

we obtain sufficient conditions for the series σanλn to be absolutely summable of order k by atriangular matrix.

it is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive de niteness and stability of interval matricescan be presented. these conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.furthermore we introduce a new necessary and sucient condition for checkingstability of interv...

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...

begin{abstract} the relations between the spectrum of the matrix $q+r$ and the spectra of the matrices $(gamma + delta)q+(alpha + beta)r-qr-rq$, $qr-rq$, $alpha beta r-qrq$, $alpha rqr-(qr)^{2}$, and $beta r-qr$ have been given on condition that the matrix $q+r$ is diagonalizable, where $q$, $r$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $...

in this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation xa=b to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. as applications, we derive sufficient and necess...

results migration of cells started on the fifth day. as a result of this migration, most cells were located on the surface of the scaffold and formed epiderm-like structure and some penetrated into the scaffold. by day 25, cells which had penetrated into the scaffold had various destinies such as becoming elongated spindle-shaped cells and creating blood vessel-like structures. conclusions adm ...

Human behavior depends crucially on the ability to interact with others and empathy has a critical role in enabling this to occur effectively. This can be an unconscious process and based on natural instinct and inner imitation (Montag et al., 2008) responding to observed and executed actions (Newman-Norlund et al., 2007). Motor empathy relating to painful stimuli is argued to occur via the mir...