Borel-Leroy summability of a nonpolynomial potential

We investigate the perturbation series for the spectrum of a class of Schrodinger operators with potential V = 1/2 x(2) + g(m-1)x(2m)/(1 + alpha gx(2)) which generalize particular cases investigated in the literature in connection with models in laser theory and quantum field theory of particles and fields. It is proved that the series obey a modified strong asymptotic condition of order (m - 1) and have an order (m - 1) strong asymptotic series in g which are shown to be summable in the sense of Borel-Leroy method.

The univalent polynomial of Suffridge as a summability kernel

A positive summability trigonometric kernel {K(n)(theta)}(infinity)(n=1) is generated through a sequence of univalent polynomials constructed by Suffridge. We prove that the convolution {K(n) * f} approximates every continuous 2 pi-periodic function f with the rate omega(f, 1/n), where omega(f, delta) denotes the modulus of continuity, and this provides a new proof of the classical Jackson`s theorem. Despite that it turns out that K(n)(theta) coincide with positive cosine polynomials generated by Fejer, our proof differs from others known in the literature.

BCR-ABL-mediated upregulation of PRAME is responsible for knocking down TRAIL in CML patients

Tumor necrosis factor-related apoptosis-inducing ligand-TNFSF10 (TRAIL), a member of the TNF-alpha family and a death receptor ligand, was shown to selectively kill tumor cells. Not surprisingly, TRAIL is downregulated in a variety of tumor cells, including BCR-ABL-positive leukemia. Although we know much about the molecular basis of TRAIL-mediated cell killing, the mechanism responsible for TRAIL inhibition in tumors remains elusive because (a) TRAIL can be regulated by retinoic acid (RA); (b) the tumor antigen preferentially expressed antigen of melanoma (PRAME) was shown to inhibit transcription of RA receptor target genes through the polycomb protein, enhancer of zeste homolog 2 (EZH2); and (c) we have found that TRAIL is inversely correlated with BCR-ABL in chronic myeloid leukemia (CML) patients. Thus, we decided to investigate the association of PRAME, EZH2 and TRAIL in BCR-ABL-positive leukemia. Here, we demonstrate that PRAME, but not EZH2, is upregulated in BCR-ABL cells and is associated with the progression of disease in CML patients. There is a positive correlation between PRAME and BCR-ABL and an inverse correlation between PRAME and TRAIL in these patients. Importantly, knocking down PRAME or EZH2 by RNA interference in a BCR-ABL-positive cell line restores TRAIL expression. Moreover, there is an enrichment of EZH2 binding on the promoter region of TRAIL in a CML cell line. This binding is lost after PRAME knockdown. Finally, knocking down PRAME or EZH2, and consequently induction of TRAIL expression, enhances Imatinib sensibility. Taken together, our data reveal a novel regulatory mechanism responsible for lowering TRAIL expression and provide the basis of alternative targets for combined therapeutic strategies for CML. Oncogene (2011) 30, 223-233; doi:10.1038/onc.2010.409; published online 13 September 2010

Differential expression of apoptosis-related genes from death receptor pathway in chronic myeloproliferative diseases

Background Chronic myeloproliferative disorders (MPDs) are clonal haematopoietic stem cell malignancies characterised by an accumulation of mature myeloid cells in bone marrow and peripheral blood. Deregulation of the apoptotic machinery may be associated with MPD physiopathology. Aims To evaluate expression of death receptors` family members, mononuclear cell apoptosis resistance, and JAK2 allele burden. Subjects and Methods Bone marrow haematopoietic progenitor CD34 cells were separated using the Ficoll-hypaque protocol followed by the Miltenyi CD34 isolation kit, and peripheral blood leukocytes were separated by the Haes-Steril method. Total RNA was extracted by the Trizol method, the High Capacity Kit was used to synthesise cDNA, and real-time PCR was performed using SybrGreen in ABIPrism 7500 equipment. The results of gene expression quantification are given as 2(-Delta Delta Ct). The JAK2 V617F mutation was detected by real-time allelic discrimination PCR assay. Peripheral blood mononuclear cells (PBMCs) were isolated by the Ficoll-hypaque protocol and cultured in the presence of apoptosis inducers. Results In CD34 cells, there was mRNA overexpression for fas, faim and c-flip in polycythaemia vera (PV), essential thrombocythaemia (ET) and primary myelofibrosis (PMF), as well as fasl in PMF, and dr4 levels were increased in ET. In leukocytes, fas, c-flip and trail levels were increased in PV, and dr5 expression was decreased in ET. There was an association between dr5 and fasl expression and JAK2V617F mutation. PBMCs from patients with PV, ET or PMF showed resistance to apoptosis inducers. Conclusions The results indicate deregulation of apoptosis gene expression, which may be associated with MPD pathogenesis leading to accumulation of myeloid cells in MPDs.

The meson Z(+) (4430) as a tetraquark state

We test the validity of the QCD sum rules applied to the meson Z(+)(4430). by considering a diquark-antidiquark type of current with J(P) = 0(-) and with J(P) = 1(-). We find that, with the studied currents, it is possible to find an acceptable Borel window. In such a Borel window we have simultaneously a good OPE convergence and a pole contribution which is bigger than the continuum contribution. We get m(z) = (4.52 +/- 0.09) GeV and m(Z) = (4.84 +/- 0.14) GeV for the currents with J(P) = 0(-) and J(P) = 1(-), respectively. We conclude that the QCD sum rules results favors J(P) = 0(-) quantum numbers for the Z(+) (4430) meson. (C) 2008 Elsevier B.V. All rights reserved.

Photoproduction of J/psi and of high mass e(+)e(-) in ultra-peripheral Au plus Au collisions at root s(NN)=200 GeV

We present the first measurement of photoproduction of J/psi and of two-photon production of high-mass e(+)e(-) pairs in electromagnetic (or ultra-peripheral) nucleus-nucleus interactions, using Au + Au data at root s(NN) = 200 GeV. The events are tagged with forward neutrons emitted following Coulomb excitation of one or both Au* nuclei. The event sample consists of 28 events with m(e+e-) > 2 GeV/c(2) with zero like-sign background. The measured cross sections at midrapidity of d sigma/dy (J/psi + Xn, y = 0) = 76 +/- 33 (stat) +/- 11 (syst) pb and d(2)sigma /dm dy (e(+) e(-) + Xn, y = 0) = 86 +/- 23(stat) +/- 16(syst) mu b/ (GeV/c(2)) for m(e+e-) epsilon vertical bar 2.0, 2.8 vertical bar GeV/c(2) have been compared and found to be consistent with models for photoproduction of J/psi and QED based calculations of two-photon production of e(+)e(-) pairs. (C) 2009 Elsevier B.V. All rights reserved.

Dilepton mass spectra in p plus p collisions at root s=200 GeV

PHENIX has measured the electron-positron pair mass spectrum from 0 to 8 GeV/c(2) in p + p collisions at root s = 200 GeV. The contributions from light meson decays to e(+)e(-) pairs have been determined based on measurements of hadron production cross sections by PHENIX. Within the systematic uncertainty of similar to 20% they account for all e(+)e(-) pairs in the mass region below similar to 1 GeV/c(2). The e(+)e(-) pair yield remaining after subtracting these contributions is dominated by semileptonic decays of charmed hadrons correlated through flavor conservation. Using the spectral shape predicted by PYTHIA, we estimate the charm production cross section to be 544 +/- 39(stat) +/- 142(syst) +/- 200(model) pb. which is consistent with QCD calculations and measurements of single leptons by PHENIX. (C) 2008 Elsevier BV. All rights reserved.

SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

On maximizing measures of homeomorphisms on compact manifolds

We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g : X -> R, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral integral(X) g d mu, considered as a function on the space of all T-invariant Borel probability measures mu, attains its maximum on a measure supported on a periodic orbit.