Duplication coefficients via generating functions

In this paper, we solve the duplication problem P_n(ax) = sum_{m=0}^{n}C_m(n,a)P_m(x) where {P_n}_{n>=0} belongs to a wide class of polynomials, including the classical orthogonal polynomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) for the specific case a = −1. We give closed-form expressions as well as recurrence relations satisfied by the duplication coefficients.

On the system of rational difference equations x(n) = A+(1)over-bar y(n-p), y(n) = A+(gamma(n-1))over-bar x(n-r)y(n-5)

In this paper, we study the behavior of the positive solutions of the system of two difference equations [GRAPHICS] where p >= 1, r >= 1, s >= 1, A >= 0, and x(1-r), x(2-r),..., x(0), y(1-max) {p.s},..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.

Experimental evidence of the spin-glass transition in the diluted magnetic semiconductor Zn(1-x)Mn(x)In(2)Se(4)

This work reports on magnetic measurements of the quasi-two-dimensional (quasi-2D) system Zn(1-x)Mn(x)In(2)Se(4), with 0.01 <= x <= 1.00. For x > 0.67, the quasi-2D system seems to develop a spin-glass behaviour. Evidence of a true phase transition phenomenon is provided by the steep increase of the nonlinear susceptibility chi(nl) when approaching T(C) from above. The static scaling of chi(nl) data yields critical exponents delta = 4.0 +/- 0.2, phi = 4.37 +/- 0.17 and TC = 3.4 +/- 0.1 K for the sample with x = 1.00 and similar values for the sample with x = 0.87. These critical exponents are in good agreement with values reported for other spin-glass systems with short-range interactions.

Distances between critical points and midpoints of zeros of hyperbolic polynomials

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

Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Correlation between photoluminescence and structural defects in Ca 1+x Cu 3 - X Ti 4 O 12 systems

Ca1+xCu3-xTi4O12 powders were synthesized by a conventional solid-state reaction. X-ray diffraction (XRD) was performed to verify the formation of cubic CaCu3Ti4O 12 (CCTO) and orthorhombic CaTiO3 (CTO) phases at long range. Rietveld refinements indicate that excess Ca atoms added to the Ca 1-xCu3-xTi4O12 (x = 1.0) composition segregated in a CaTiO3 secondary phase suggesting that solubility limit of Ca atoms in the CaCu3Ti4O12 lattice was reached for this system. The FE-SEM images show that the Ca 1+xCu3-xTi4O12 (0 < x < 3) powders are composed of several agglomerated particles with irregular morphology. X-ray absorption near-edge structure spectroscopy (XANES) spectra indicated [TiO5Vo z]-[TiO6] complex clusters in the CaCu3Ti4O12 structure which can be associated with oxygen vacancies (Vo z = V o x, Vo •, and Vo ••) whereas in the CaTiO3 powder, this analysis indicated [TiO6]-[TiO6] complex clusters in the structure. Ultraviolet-visible (UV-vis) spectra and photoluminescence (PL) measurements for the analyzed systems revealed structural defects such as oxygen vacancies, distortions, and/or strains in CaCu3Ti4O12 and CaTiO3 lattices, respectively. © 2012 The American Ceramic Society.

Polinômios ortogonais e L-ortogonais associados a medidas relacionadas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Measurement of the p(p)over-bar -> W plus b plus X production cross section at root s=1.96 TeV D0 Collaboration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sn(1-x)LaxO2 thin films deposited on AISI 304 stainless steel substrates

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On some Jacobi Series

Георги С. Бойчев - Настоящата статия съдържа свойства на някои редове на Якоби.

Some Coefficient Estimates for Polynomials on the Unit Interval

2000 Mathematics Subject Classification: 26C05, 26C10, 30A12, 30D15, 42A05, 42C05.

Highly dispersed Ptδ+ on TixCe(1−x)O2 as an active phase in preferential oxidation of CO

Structure–activity relationships for 1 wt.% Pt catalysts were investigated for a series of TixCe(1−x)O2 (x = 1, 0.98, 0.9, 0.5, 0.2 and 0) supports prepared by the sol–gel method. The catalysts prepared by impregnation were characterized in detail by applying a wide range of techniques as N2-isotherms, XRF, XRD, Raman, XPS, H2-TPR, Drifts, UV–vis, etc. and tested in the preferential oxidation of CO in the presence of H2. Also several reaction conditions were deeply analyzed. A strong correlation between catalyst performance and the electronic properties let us to propose, based in all the experimental results, a plausible reaction mechanism where several redox cycles are involved.

Spin-wave fluctuations in ferrimagnetic Mg(x)Fe(3-x)O(4) nanoparticles

We have performed a systematic study of the magnetic properties of a series of ferrimagnetic nanoparticles of Mg(x)Fe(3-x)O(4) (0.8 <= x <= 1.5) prepared by the combustion reaction method. The magnetization data can be well fitted by Bloch's law with T(3/2). Bloch's constant B determined from the fitting procedure was found to increase with Mg content x from similar to 3.09 X 10(-5) K(-3/2) for x = 0.8 to 6.27 X 10(-5) K(-3/2) for x=1.5. The exchange integral J(AB) and the spin-wave stiffness constant D of Mg(x)Fe(3-x)O(4) nanoparticles were also determined as similar to 0.842 and 0.574 meV and 296 and 202 meV angstrom(2) for specimens with x=0.8 and 1.5, respectively. These results are discussed in terms of cation redistribution among A and B sites on these nanostructured spinel ferrites. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3359709]

Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.

Estudo sôbre as temperaturas médias em Campinas

This paper deals with the study by orthogonal polynomials of trends in the mean annual and mean monthly temperatures (in degrees Centigrade) in Campinas (State of São Paulo, Brasil), from 1890 up to 1956. Only 4 months were studied (January, April, July and October) taken as typical of their respective season. For the annual averages both linear and quadratic components were significant, the regression equation being y = 19.95 - 0.0219 x + 0.00057 x², where y is the temperature (in degrees Centigrade) and x is the number of years after 1889. Thus 1890 corresponds to x = 1, 1891, to x = 2, etc. The equation shows a minimum for the year 1908, with a calculated mean y = 19.74. The expected means by the regression equation are given below. Anual temperature means for Campinas (SP, Brasil) calculated by the regression equation Year Annual mean (Degrees Centigrade) 1890 19.93 1900 10.78 1908 19.74 (minimum) 1010 19.75 1920 19.82 1930 20.01 1940 20.32 1950 20.74 1956 21.05 The mean for 67 years was 20.08°C with standard error of the mean 0.08°G. For January the regression equation was y = 23.08 - 0.0661 x + 0.00122 x², with a minimum of 22.19°C for 1916. The average for 67 years was 22.70°C, with standard error 0.12°C. For April no component of regression was significant. The average was 20.42°C, with standard error 0.13°C. For July the regression equation was of first degree, y = 16.01 + 0.0140X. The average for 67 years was 16.49°C, with standard error of the mean 0.14°C. Finally, for October the regression equation was y = 20.55 - 0.0362x + 0.00078x², with a minimum of 20.13°C for 1912. The average was 20.52°C, with standard error of the mean equal to 0.14°C.