In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [−1, 1] to arbitrary complex poles outside [−1, 1]. The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrat...

In this paper we characterize rational Szegő quadrature formulas associated with Chebyshev weight functions, by giving explicit expressions for the corresponding para-orthogonal rational functions and weights in the quadratures. As an application, we give characterizations for Szegő quadrature formulas associated with rational modifications of Chebyshev weight functions. Some numerical experime...

We present several new quadrature formulas in the triangle for exact integrationof polynomials. The points were computed numerically with a cardinal function algorithm whichimposes that the number of quadrature points N be equal to the dimension of a lower dimensionalpolynomial space. Quadrature forumulas are presented for up to degree d = 25, all which havepositive weights and ...

Aims. We report the discovery of a peculiar object observed serendipitously with XMM-Newton. We present its timing and spectral properties and investigate its optical counterpart. Methods. The light curve of the X-ray source, its spectrum, and the spectrum of the best optical counterpart are presented and analyzed. Results. The X-ray flux decreases by a factor of 6.5 within 1 h and stays in a l...

We report a dramatic variability event in the X–ray history of the Narrow–Line quasar PHL 1092 (z = 0.396). Our latest 2008 XMM–Newton observation reveals a flux drop of ∼ 200 with respect to the previous observation performed about 4.5 years earlier, and a drop of ∼ 135 with respect to its historical flux. Despite the huge X–ray variation, the UV flux remains constant producing a very signific...

This describes the map χ in the exact sequence. The map L in the sequence gives us a matrix such that ImL = kerχ. This matrix will generate a integer lattice Λ ⊆ Zm−n. Such an exact sequence gives rise to many different interpretations. The most familiar interpretation is that of a polytope in R which introduces geometry to the system. We can also view the exact sequence as defining a system of...

The Newton-Wu conditions for the cancellation of quadratic divergences in a class of two-Higgs-doublet models are analyzed as to how they may be satisfied with a typical extension of the Standard Model of particle interactions. In the Standard Model (SM) of particle interactions, there is one physical scalar Higgs boson H . Its mass may be constrained by the requirement that the one quadratic d...

Let Xj be smooth varieties over a field k of characteristic zero, for 1 ≤ j ≤ p. Consider a family f of p functions fj : Xj → A 1 k. We shall denote also by fj the function on the product X = ∏ j Xj obtained by composition with the projection. We denote by X0(f) the set of common zeroes in X of the functions fj. Let P ∈ k[y1, . . . , yp] be a polynomial, which we assume to be non-degenerate wit...

The X-ray properties of a sample of 11 high-redshift (0.6 < z < 1.0) clusters observed with Chandra and/or XMM-Newton are used to investigate the evolution of the cluster scaling relations. The observed evolution in the normalisation of the L− T, M− T, Mg − T, and M− L relations are consistent with simple self-similar predictions, in which the properties of clusters reflect the properties of th...

This paper investigates inexact Uzawa methods for nonlinear saddle point problems. We prove that the inexact Uzawa method converges globally and superlinearly even if the derivative of the nonlinear mapping does not exist. We show that the Newton-type decomposition method for saddle point problems is a special case of a Newton-Uzawa method. We discuss applications of inexact Uzawa methods to se...