We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and several examples are calculated. As a consequence, we show that for the prime p = 641491 the class number of the maximal real subfield of the pth cyclotomic field is divisible by the prime 1566401. In an a...

In this paper, we investigate the reduced form of circulant matrices and we show that the problem of computing the q-th roots of a nonsingular circulant matrix A can be reduced to that of computing the q-th roots of two half size matrices B - C and B + C.

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

A new Schulz-type method to compute the Moore-Penrose inverse of a matrix is proposed. Every iteration of the method involves four matrix multiplications. It is proved that this method converge with fourth-order. A wide set of numerical comparisons shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods.

the linear system of equations ax = b where a = [aij ] in cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. in this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as drazin inverse andpseudo-inverse are investigated.

Systemic hormonal control exerts its effect through the regulation of local target tissues, which in turn regulate upstream signals in a feedback loop. The parathyroid hormone (PTH) axis is a well defined hormonal signaling system that regulates calcium levels and bone metabolism. To understand the interplay between systemic and local signaling in bone, we examined the effects of deficiency of ...

During vertebrate limb development, growth plate chondrocytes undergo temporally and spatially coordinated differentiation that is necessary for proper morphogenesis. Parathyroid hormone-related peptide (PTHrP), its receptor, the PTH/PTHrP receptor, and Indian hedgehog are implicated in the regulation of chondrocyte differentiation, but the specific cellular targets of these molecules and speci...