A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

Congenital hypothyroidism in a kitten resulting in decreased IGF-I concentration and abnormal liver function tests

A 7-month-old male kitten was presented with chronic constipation and retarded growth. Clinical examination revealed disproportional dwarfism with mild skeletal abnormalities and a palpable thyroid gland. The presumptive diagnosis of congenital hypothyroidism was confirmed by low serum total thyroxine (tT(4)) concentration prior to and after the administration of thyroid stimulation hormone (TSH), increased endogenous TSH concentration and abnormal thyroid scintigraphic scan. The kitten had abnormal liver function tests and decreased insulin-like growth factor 1 (IGF-1) concentration, both of which returned to normal in correspondence with an improvement of the clinical signs after 6 weeks of thyroxine therapy. Congenital hypothyroidism is a rare disease that may present with considerable variation in clinical manifestation. In cases in which clinical signs are ambiguous, disorders such as portosystemic shunt and hyposomatotropism have to be taken into account as differential diagnosis. As hypothyroidism may be associated with abnormal liver function tests and low IGF-1 concentrations, test results have to be interpreted carefully

Mielograma de ratas com disfunção tireoidiana

The cells of the myelo id, lymphoid , and erythroid lineage s of the bone marrow were quantified in rats with hypo and hyperthyroidism. Fifteen Wistar rats were divided into three groups: hypothyroid (n=5), hyperthyroid (n=5) , and control (n=5). Three months after the onset of the treatment s, euthanasia was performed . Bone marrow was aspirated from femurs of each animal to perform smear s that were stained with Quick Panoptic. T he percentage s of rubroblast, prorubrocyte, metarubrocyte, myeloblast, promyelocytes, metamyelocytes, myel ocytes, segmented, eosinophils, basophils, lymphocytes, plasma cells and monocytes in were determined a total of 500 cells. The bone marrow of animals with hypothyroidism had hypoplasia. The myeloid:erythroid ratio was higher in animals with thyroid dysfun ction. In hypo and hyperthyroidism, there was a significant reduction of the percentage of rubrocyte, metarubrocyte , and lymphocytes and increase of myelocytes and segmented cells. In hypothyroidism, there was a significant increase in the percentage of me tamyelocytes. It is c oncluded that both hypo and hyperfunction of thyroid increase the myeloid:erythroid ratio by increasing the number of cells of the myeloid lineage and reducing the cells of the erythroid lineage