On the behaviour of zeros of Jacobi polynomials

Denote by x(n,k)(alpha, beta) and x(n,k) (lambda) = x(n,k) (lambda - 1/2, lambda - 1/2) the zeros, in decreasing order, of the Jacobi polynomial P-n((alpha, beta))(x) and of the ultraspherical (Gegenbauer) polynomial C-n(lambda)(x), respectively. The monotonicity of x(n,k)(alpha, beta) as functions of a and beta, alpha, beta > - 1, is investigated. Necessary conditions such that the zeros of P-n((a, b)) (x) are smaller (greater) than the zeros of P-n((alpha, beta))(x) are provided. A. Markov proved that x(n,k) (a, b) < x(n,k)(α, β) (x(n,k)(a, b) > x(n,k)(alpha, beta)) for every n is an element of N and each k, 1 less than or equal to k less than or equal to n if a > alpha and b < β (a < alpha and b > beta). We prove the converse statement of Markov's theorem. The question of how large the function could be such that the products f(n)(lambda) x(n,k)(lambda), k = 1,..., [n/2] are increasing functions of lambda, for lambda > - 1/2, is also discussed. Elbert and Siafarikas proved that f(n)(lambda) = (lambda + (2n(2) + 1)/ (4n + 2))(1/2) obeys this property. We establish the sharpness of their result. (C) 2002 Elsevier B.V. (USA).

SZEGO POLYNOMIALS FROM HYPERGEOMETRIC FUNCTIONS

Szego polynomials with respect to the weight function w(theta) = e(eta theta)[sin(theta/2)](2 lambda), where eta, lambda is an element of R and lambda > -1/2 are considered. Many of the basic relations associated with these polynomials are given explicitly. Two sequences of para-orthogonal polynomials with explicit relations are also given.

Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Existence and asymptotic behaviour for the parabolic-parabolic Keller-Segel system with singular data

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bi-Lipschitz A-triviality of map germs and Newton filtrations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Implicit differential equations with impasse singularities and singular perturbation problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Simultaneous Determination of Phenanthrene and Benzo(a)pyrene in Water Samples by Synchronous Fluorescence Spectroscopy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Surface characterization of feldspathic ceramic using ATR FT-IR and ellipsometry after various silanization protocols

Objectives. This study characterized the feldspathic ceramic surfaces after various silanization protocols.Methods. Ceramic bars (2 mm x 4 mm x 10 mm) (N = 18) of feldpathic ceramic (VM7, VITA Zahnfabrik) were manufactured and finished. Before silane application, the specimens were ultrasonically cleaned in distilled water for 10 min. The ceramic specimens were randomly divided into nine groups (N = 2 per group) and were treated with different silane protocols. MPS silane (ESPE-Sil, 3M ESPE) was applied to all specimens and left to react at 20 degrees C for 2 min (G20). After drying, the specimens were subjected to heat treatment in an oven at 38 degrees C (G38), 79 degrees C (G79) or 100 degrees C (G100) for 1 min. Half of the specimens of each group were rinsed with water at 80 degrees C for 15 s (G20B, G38B, G79B, G100B). The control group (GC) received no silane. Attenuated total reflection infrared Fourier transform analysis (ATR FT-IR) was performed using a spectrometer. Thickness of silane layer was measured using a spectroscopic ellip-someter working in the lambda = 632.8 nm (He-Ne laser) at 70 degrees incidence angle. Surface roughness was evaluated using an optical profilometer. Specimens were further analyzed under the Scanning Electron Microscopy (SEM) to observe the topographic patterns.Results. ATR FT-IR analysis showed changes in Si-O peaks with enlarged bands around 940 cm(-1). Ellipsometry measurements showed that all post-heat treatment actions reduced the silane film thickness (30.8-33.5 nm) compared to G20 (40 nm). The groups submitted to rinsing in hot water (B groups) showed thinner silane films (9.8-14.4 nm) than those of their corresponding groups (without washing) (30.8-40 nm). Profilometer analysis showed that heat treatments (Ra approximate to 0.10-0.19 mu m; Rq approximate to 0.15-0.26 mu m) provided a smoother surface than the control group (Ra approximate to 0.48 mu m; Rq approximate to 0.65 mu m). Similar patterns were also observed in SEM images.Significance. Heat treatment after MPS silane application improved the silane layer network. Rinsing with boiling water eliminated the outmost unreacted regions of the silane yielding to thinner film thicknesses. (C) 2011 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Measurement of the p(p)over-bar -> WZ+X cross section at root s=1.96 TeV and limits on WWZ trilinear gauge couplings

We present measurements of the process p (P) over bar -> WZ + X -> l 'nu(l ')l (l) over bar at root s = 1:96 TeV,where l and l ' are electrons or muons. Using 1 fb(-1) of data from the D0 experiment, we observe 13 candidates with an expected background of 4.5 +/- 0.6 events and measure a cross section sigma(WZ) = 2.7(-1.3)(+1.7) pb. From the number of observed events and the Z boson transverse momentum distribution, we limit the trilinear WWZ gauge couplings to -0: 17 <= lambda(Z) <= 0.21 (Delta k(Z) <= 0.29(lambda(Z) = 0) at the 95% C.L. for a form factor scale Lambda = 2 TeV. Further, assuming that Delta g(1)(Z) = Delta k(Z), we find -0.12 <= Delta k(Z) <= 0.29(lambda(Z) = 0) at the 95% C. L. These are the most restrictive limits on the WWZ couplings available to date.

Indirect constraints on the triple gauge boson couplings from Z -> b(b)over-bar partial width: An update

We update the indirect bounds on anomalous triple gauge couplings coming from the non-universal one-loop contributions to the Z --> width. These bounds, which are independent of the Higgs boson mass, are in agreement with the standard model predictions for the gauge boson self-couplings since the present value of R-b agrees fairly well with the theoretical estimates. Moreover, these indirect constraints on Delta g(1)(Z) and g(5)(Z) are most stringent than the present direct bounds on these quantities, while the indirect limit on lambda(Z) is weaker than the available experimental data.

Search for resonant second generation slepton production at the Fermilab Tevatron

We present a search for supersymmetry in the R-parity violating resonant production and decay of smuons and muon sneutrinos in the channels mu ->chi(0)(1)mu, mu ->chi(0)(2,3,4)mu, and nu(mu)->chi(+/-)(1,2)mu. We analyzed 0.38 fb(-1) of integrated luminosity collected between April 2002 and August 2004 with the D0 detector at the Fermilab Tevatron Collider. The observed number of events is in agreement with the standard model expectation, and we calculate 95% C.L. limits on the slepton production cross section times branching fraction to gaugino plus muon, as a function of slepton and gaugino masses. In the framework of minimal supergravity, we set limits on the coupling parameter lambda(')(211), extending significantly previous results obtained in Run I of the Tevatron and at the CERN LEP collider.

Search for production of single top quarks via tcg and tug flavor-changing-neutral-current couplings

We search for the production of single top quarks via flavor-changing-neutral-current couplings of a gluon to the top quark and a charm (c) or up (u) quark. We analyze 230 pb(-1) of lepton+jets data from p (p) over tilde collisions at a center of mass energy of 1.96 TeV collected by the D0 detector at the Fermilab Tevatron Collider. We observe no significant deviation from standard model predictions, and hence set upper limits on the anomalous coupling parameters kappa(c)(g)/Lambda and kappa(u)(g)/Lambda, where kappa(g) define the strength of tcg and tug couplings, and Lambda defines the scale of new physics. The limits at 95% C.L. are kappa(c)(g)/Lambda < 0.15 TeV-1 and kappa(u)(g)/Lambda < 0.037 TeV-1.

Kinematics of a spacetime with an infinite cosmological constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant L is discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. When Lambda --> infinity, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c --> infinity. is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.

Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring

It has recently been shown that the ten-dimensional superstring can be quantized using the BRST operator Q = philambda(alpha)d(alpha), where lambda(alpha) is a pure spinor satisfying; lambdagamma(m)lambda = 0 and dalpha is the fermionic supersymmetric derivative. In this paper, the pure spinor version of superstring theory is formulated in a curved supergravity background and it is shown that nilpotency and holomorphicity of the pure spinor BRST operator imply the on-shell superspace constraints of the supergravity background. This is shown to lowest order in alpha' for the heterotic and Type II superstrings, thus providing a compact pure spinor version of the ten-dimensional superspace constraints for N = 1 Type IIA and Type IIB supergravities. Since quantization is straightforward using the pure spinor version of the superstring, it is expected that these methods can also be used to compute higher-order alpha' corrections to the ten-dimensional superspace constraints. (C) 2002 Elsevier B.V. B.V. All rights reserved.