Christoffel transformation for a matrix of Bi-variate measures.

We consider the sequences of matrix bi-orthogonal polynomials with respect to the bilinear forms ((R) over cap) and ((L) over cap) (L) over cap = (TxT)integral P(z(1))L(z(1))d mu(z(1), z(2))Q(z(2)), where mu(z1, z2) is a matrix of bi-variate measures supported on T x T, with T the unit circle, L pxp[ z] is the set of matrix Laurent polynomials of size p x p and L(z) is a special polynomial in L pxp[ z]. A connection formula between the sequences of matrix Laurent bi-orthogonal polynomials with respect to ((R) over cap) and resp ((L) over cap) and the sequence of matrix Laurent bi-orthogonal polynomials with respect to d mu(z(1), z(2)) is given

Coherent pairs of linear functionals on the unit circle

In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. [...]info:eu-repo/semantics/publishedVersio

Stratifying diffuse large B-cell lymphoma patients treated with chemoimmunotherapy: GCB/non-GCB by immunohistochemistry is still a robust and feasible marker

Diffuse large B cell lymphoma (DLBCL) is a heterogeneous group of aggressive lymphomas that can be classified into three molecular subtypes by gene expression profiling (GEP): GCB, ABC and unclassified. Immunohistochemistry-based cell of origin (COO) classification, as a surrogate for GEP, using three available immunohistochemical algorithms was evaluated in TMA-arranged tissue samples from 297 patients with de novo DLBCL treated by chemoimmunotherapy (R-CHOP and R-CHOP-like regimens). Additionally, the prognostic impacts of MYC, BCL2, IRF4 and BCL6 abnormalities detected by FISH, the relationship between the immunohistochemical COO classification and the immunohistochemical expression of MYC, BCL2 and pSTAT3 proteins and clinical data were evaluated. In our series, non-GCB DLBCL patients had significantly worse progression-free survival (PFS) and overall survival (OS), as calculated using the Choi, Visco-Young and Hans algorithms, indicating that any of these algorithms would be appropriate for identifying patients who require alternative therapies to R-CHOP. Whilst MYC abnormalities had no impact on clinical outcome in the non-GCB subtype, those patients with isolated MYC rearrangements and a GCB-DLBCL phenotype had worse PFS and therefore might benefit from novel treatment approaches

On Polynomials Orthogonal With Respect To Sobolev Inner Product On The Unit Circle

We study polynomials orthogonal with respect to an indefinite Sobolev inner product on the unit circle. We establish the existence of such polynomials of large degree. Algebraic properties and asymptotic behavior of such polynomials are obtained

Zeros of para-orthogonal polynomials and linear spectral transformations on the unit circle

We study the interlacing properties of zeros of para–orthogonal polynomials associated with a nontrivial probability measure supported on the unit circle dμ and para–orthogonal polynomials associated with a modification of dμ by the addition of a pure mass point, also called Uvarov transformation. Moreover, as a direct consequence of our approach, we present some results related with the Christoffel transformation.info:eu-repo/semantics/publishedVersio

Orthogonal Polynomials and their Applications

The Segovia meeting set out to stimulate an intensive exchange of ideas between experts in the area of orthogonal polynomials and its applications, to present recent research results and to reinforce the scientific and human relations among the increasingly international community working in orthogonal polynomials. This volume contains original research papers as well as survey papers about fundamental questions in the field (Nevai, Rakhmanov & López) and its relationship with other fields such as group theory (Koornwinder), Padé approximation (Brezinski), differential equations (Krall, Littlejohn) and numerical methods (Rivlin)