In this paper we propose an explicit solution to the polynomial least squares approximation problem on Chebyshev extrema nodes. We also show that the inverse of the normal matrix on this set of nodes can be represented as the sum of two symmetric matrices: a full rank matrix which admits a Cholesky factorization and a 2-rank matrix. Finally we discuss the numerical properties of the proposed fo...

We say that a square complex matrix is condensable if it can be reduced to a bandform through a nite sequence of elementary uni-tary similarities. The two main results of this paper are the following assertions: (1) Any matrix with a low rank skew-Hermitian part is condens-able. (2) If A is a normal condensable matrix, then any rank one perturbation of A (generally nonnormal) is condensable as ...

We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points. MSC: 14D15, 14H45, 83E30 PACS: 02....

It was hypothesized that schizophrenics exceed normal Ss in beliefs enhanced by the response biases of halo and logical error. 16 schizophrenics and 16 normal Ss, matched on reliability, rank ordered 1 sets of 9 items on 3 dimensions. 2 of the dimensions were evaluative dimensions that could be seen as "logically" related to one another. The 3rd was a neutral dimension that was included to meas...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

It is well known that when data are non-normally distributed, a test of the significance of Pearson's r may inflate Type I error rates and reduce power. Statistics textbooks and the simulation literature provide several alternatives to Pearson’s correlation. However, the relative performance of these alternatives has been unclear. Two simulation studies were conducted to compare 12 methods, inc...

normal 0 false false false en-us x-none ar-sa microsoftinternetexplorer4 aim : the present study aimed to investigate the influence of histological factors on survival of patients with esophageal cancer. background : esophageal cancer is almost the common form of malignancy in the eastern world. patients and methods : through a retrospective cohort study a consecutive series of 134 patients wit...

For perfect fields k satisfying [k ¯:k]>2, we construct new normal subgroups of the plane Cremona group and provide an elementary proof its non-simplicity, following melody recent by Blanc, Lamy Zimmermann that rank n over (subfields of) complex numbers is not simple for n≥3.

The randomized Kaczmarz algorithm has received considerable attention recently because of its simplicity, speed, and the ability to approximately solve large-scale linear systems equations. In this paper we propose double triple algorithms extended normal equations form $$\mathbf{A}^\top \mathbf{Ax}=\mathbf{A}^\top \mathbf{b}-\mathbf{c}$$ . proposed avoid forming \mathbf{A}$$ explicitly work fo...