The Asymptotics of Wilkinson's Iteration: Loss of Cubic Convergence

One of the most widely used methods for eigenvalue computation is the $QR$ iteration with Wilkinson's shift: here the shift $s$ is the eigenvalue of the bottom $2\times 2$ principal minor closest to the corner entry. It has been a long-standing conjecture that the rate of convergence of the algorithm is cubic. In contrast, we show that there exist matrices for which the rate of convergence is strictly quadratic. More precisely, let $T_X$ be the $3 \times 3$ matrix having only two nonzero entries $(T_X)_{12} = (T_X)_{21} = 1$ and let $T_L$ be the set of real, symmetric tridiagonal matrices with the same spectrum as $T_X$. There exists a neighborhood $U \subset T_L$ of $T_X$ which is invariant under Wilkinson's shift strategy with the following properties. For $T_0 \in U$, the sequence of iterates $(T_k)$ exhibits either strictly quadratic or strictly cubic convergence to zero of the entry $(T_k)_{23}$. In fact, quadratic convergence occurs exactly when $\lim T_k = T_X$. Let $X$ be the union of such quadratically convergent sequences $(T_k)$: the set $X$ has Hausdorff dimension 1 and is a union of disjoint arcs $X^\sigma$ meeting at $T_X$, where $\sigma$ ranges over a Cantor set.Comment: 20 pages, 8 figures. Some passages rewritten for clarit

Callan-Symanzik-Lifshitz approach to generic competing systems

We present the Callan-Symanzik-Lifshitz method to approaching the critical behaviors of systems with arbitrary competing interactions. Every distinct competition subspace in the anisotropic cases define an independent set of renormalized vertex parts via normalization conditions with nonvanishing distinct masses at zero external momenta. Otherwise, only one mass scale is required in the isotropic behaviors. At the critical dimension, we prove: i) the existence of the Callan-Symanzik-Lifshitz equations and ii) the multiplicative renormalizability of the vertex functions using the inductive method. Away from the critical dimension, we utilize the orthogonal approximation to compute higher loop Feynman integrals, anisotropic as well as isotropic, necessary to get the exponents $\eta_{n}$ and $\nu_{n}$ at least up to two-loop level. Moreover, we calculate the latter exactly for isotropic behaviors at the same perturbative order. Similarly to the computation in the massless formalism, the orthogonal approximation is found to be exact at one-loop order. The outcome for all critical exponents matches exactly with those computed using the zero mass field-theoretic description renormalized at nonvanishing external momenta.Comment: 58 pages, RevTex4, no figure

The effect of bone marrow-derived stem cells associated with platelet-rich plasma on the osseointegration of immediately placed implants

Stem cells associated with growth factors have been shown to improve bone healing and the osseointegration of dental implants. A Brazilian miniature pig model was used to evaluate the effect of autologous bone marrow-derived mesenchymal stem cells (BM-MS

Quantificação do carbono das substâncias húmicas em diferentes sistemas de uso do solo e épocas de avaliação.

A quantificação do carbono nas diferentes frações da matéria orgânica do solo (MOS) torna-se necessária devido ao interesse de se conhecer o potencial de captura e armazenamento do carbono nos diferentes sistemas de uso do solo. O objetivo deste trabalho foi quantificar o carbono das substâncias húmicas em diferentes sistemas de uso do solo e épocas de avaliação e correlacioná-lo com algumas propriedades químicas e físicas do solo. Os sistemas selecionados foram: preparo convencional (PC-milho/feijão), plantio direto (PD-berinjela/milho), consórcio maracujá/Desmodium sp, cultivo com figo e sistema agroflorestal. As amostras de solo foram coletadas em duas profundidades (0-5 e 5-10 cm) e épocas (17/11/2005–verão e 23/6/2006-inverno). Foi determinado o carbono orgânico total (COT) e realizado o fracionamento químico da MOS, quantificando-se o carbono da fração humina (C-HUM), fração ácido húmico (C-FAH) e fração ácido fúlvico (C-FAF). O C-HUM constituiu a maior parte do COT, havendo correlação significativa com o COT em todos os sistemas avaliados e estações. Analisando o C-FAH foi possível identificar alterações no solo relacionadas aos sistemas de uso, na profundidade de 0-5 cm e no verão, destacando-se o PD com os maiores teores. Com o C-FAF ocorreu este mesmo comportamento, mas na profundidade de 5-10 cm e no inverno, destacando-se o PC com maiores valores. Foram verificadas correlações significativas entre Valor S, Valor T e DMP em todos os sistemas, com exceção da área de PC. O PD aumenta os teores de C-FAH, nas duas profundidades e nas duas estações, quando comparado ao PC do solo

Hypotensive effect and endothelium-dependent vascular action of leaves of Alpinia purpurata (Vieill) K. Schum

The aims of this study were to evaluate the chemical profile, vascular reactivity, and acute hypotensive effect (AHE) of the ethanolic extract of leaves of Alpinia purpurata (Vieill) K. Schum (EEAP). Its chemical profile was evaluated using HPLC-UV, ICP-OES, and colorimetric quantification of total flavonoids and polyphenols. The vascular reactivity of the extract was determined using the mesenteric bed isolated from WKY. AHE dose-response curves were obtained for both EEAP and inorganic material isolated from AP (IAP) in WKY and SHR animals. Cytotoxic and mutagenic safety levels were determined by the micronucleus test. Rutin-like flavonoids were quantified in the EEAP (1.8 ± 0.03%), and the total flavonoid and polyphenol ratios were 4.1 ± 1.8% and 5.1 ± 0.3%, respectively. We observed that the vasodilation action of EEAP was partially mediated by nitric oxide (·NO). The IAP showed the presence of calcium (137.76 ± 4.08 μg mg-1). The EEAP and IAP showed an AHE in WKY and SHR animals. EEAP did not have cytotoxic effects or cause chromosomic alterations. The AHE shown by EEAP could result from its endothelium-dependent vascular action. Rutin-like flavonoids, among other polyphenols, could contribute to these biological activities, and the calcium present in EEAP could act in a synergistic way

Dilepton mass spectra in p+p collisions at sqrt(s)= 200 GeV and the contribution from open charm

The PHENIX experiement has measured the electron-positron pair mass spectrum from 0 to 8 GeV/c^2 in p+p collisions at sqrt(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. They account for nearly all e^+e^- pairs in the mass region below 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) \mu b, which is consistent with QCD calculations and measurements of single leptons by PHENIX.Comment: 375 authors from 57 institutions, 18 pages, 4 figures, 2 tables. Submitted to Physics Letters B. v2 fixes technical errors in matching authors to institutions. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Inclusive cross section and double helicity asymmetry for \pi^0 production in p+p collisions at sqrt(s)=200 GeV: Implications for the polarized gluon distribution in the proton

The PHENIX experiment presents results from the RHIC 2005 run with polarized proton collisions at sqrt(s)=200 GeV, for inclusive \pi^0 production at mid-rapidity. Unpolarized cross section results are given for transverse momenta p_T=0.5 to 20 GeV/c, extending the range of published data to both lower and higher p_T. The cross section is described well for p_T < 1 GeV/c by an exponential in p_T, and, for p_T > 2 GeV/c, by perturbative QCD. Double helicity asymmetries A_LL are presented based on a factor of five improvement in uncertainties as compared to previously published results, due to both an improved beam polarization of 50%, and to higher integrated luminosity. These measurements are sensitive to the gluon polarization in the proton, and exclude maximal values for the gluon polarization.Comment: 375 authors, 7 pages, 3 figures. Submitted to Phys. Rev. D, Rapid Communications. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

System Size and Energy Dependence of Jet-Induced Hadron Pair Correlation Shapes in Cu+Cu and Au+Au Collisions at sqrt(s_NN) = 200 and 62.4 GeV

We present azimuthal angle correlations of intermediate transverse momentum (1-4 GeV/c) hadrons from {dijets} in Cu+Cu and Au+Au collisions at sqrt(s_NN) = 62.4 and 200 GeV. The away-side dijet induced azimuthal correlation is broadened, non-Gaussian, and peaked away from \Delta\phi=\pi in central and semi-central collisions in all the systems. The broadening and peak location are found to depend upon the number of participants in the collision, but not on the collision energy or beam nuclei. These results are consistent with sound or shock wave models, but pose challenges to Cherenkov gluon radiation models.Comment: 464 authors from 60 institutions, 6 pages, 3 figures, 2 tables. Submitted to Physical Review Letters. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm