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 Computation of Fourier Coefficients

In this paper we derive an identity for the Fourier coefficients of a differentiable function f(t) in terms of the Fourier coefficients of its derivative f'(t). This yields an algorithm to compute the Fourier coefficients of f(t) whenever the Fourier coefficients of f'(t) are known, and vice versa. Furthermore this generates an iterative scheme for N times differentiable functions complementing the direct computation of Fourier coefficients via the defining integrals which can be also treated automatically in certain cases.

On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials

In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger’s algorithm, q-Zeilberger’s algorithm, the Petkovšek-van-Hoeij algorithm, the q-Petkovšek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.

Blackboard 9 Drag and Drop

The fourth 3-minute video in a series introducing the new featurs of Blackboard 9.

Statistical inference for testing Gini coefficients: an application for Colombia

This paper uses Colombian household survey data collected over the period 1984-2005 to estimate Gini coe¢ cients along with their corresponding standard errors. We Önd a statistically signiÖcant increase in wage income inequality following the adoption of the liberalisation measures of the early 1990s, and mixed evidence during the recovery years that followed the economic recession of the late 1990s. We also Önd that in several cases the observed di§erences in the Gini coe¢ cients across cities have not been statistically signiÖcant.

Análisis de la cadena cinemática del drag-flick.

Resumen tomado de la publicación

Performatividad y roles de género en lo Drag en el escenario quiteño: el teatro Dionisios

Puesto que la representación de la diferencia es el resultado de un proceso de clasificación social relacionada con los imaginarios sociales, una construcción arbitraria basada en la necesidad del hombre de clasificar el mundo para darle sentido, la práctica del teatro Drag y del performance Drag puede, en general, entenderse como una camino hacia la deconstrucción y resignificación de los márgenes de las convenciones sobre género y sexualidad. Sin embargo, es importante analizar la respuesta del público a este performance, así como qué códigos maneja y cómo estos son decodificados para entender hasta qué punto estas representaciones son elementos deconstructores de las políticas de género o si en realidad dan lugar a interpretaciones ambiguas que pueden reforzar estereotipos tanto masculinos como femeninos. Así, el presente trabajo presenta el resultado de la investigación sobre cómo se representan los roles de género en los perfomances Drag Queen y Drag King en el marco del Teatro Diniosios en Quito.

Reactive uptake coefficients for heterogeneous reaction of N2O5 with submicron aerosols of NaCl and natural sea salt

The kinetics of uptake of gaseous N2O5 on submicron aerosols containing NaCl and natural sea salt have been investigated in a flow reactor as a function of relative humidity (RH) in the range 30-80% at 295±2K and a total pressure of 1bar. The measured uptake coefficients, γ, were larger on the aerosols containing sea salt compared to those of pure NaCl, and in both cases increased with increasing RH. These observations are explained in terms of the variation in the size of the salt droplets, which leads to a limitation in the uptake rate into small particles. After correction for this effect the uptake coefficients are independent of relative humidity, and agree with those measured previously on larger droplets. A value of γ=0.025 is recommended for the reactive uptake coefficient for N2O5 on deliquesced sea salt droplets at 298K and RH>40%.

Parameter estimation using a particle method: inferring mixing coefficients from sea level observations

This paper presents a first attempt to estimate mixing parameters from sea level observations using a particle method based on importance sampling. The method is applied to an ensemble of 128 members of model simulations with a global ocean general circulation model of high complexity. Idealized twin experiments demonstrate that the method is able to accurately reconstruct mixing parameters from an observed mean sea level field when mixing is assumed to be spatially homogeneous. An experiment with inhomogeneous eddy coefficients fails because of the limited ensemble size. This is overcome by the introduction of local weighting, which is able to capture spatial variations in mixing qualitatively. As the sensitivity of sea level for variations in mixing is higher for low values of mixing coefficients, the method works relatively well in regions of low eddy activity.

CISK or WISHE as the mechanism for tropical cyclone intensification

Examination of conditional instability of the second kind (CISK) and wind-induced surface heat exchange (WISHE), two proposed mechanisms for tropical cyclone and polar low intensification, suggests that the sensitivity of the intensification rate of these disturbances to surface properties, such as surface friction and moisture supply, will be different for the two mechanisms. These sensitivities were examined by perturbing the surface characteristics in a numerical model with explicit convection. The intensification rate was found to have a strong positive dependence on the heat and moisture transfer coefficients, while remaining largely insensitive to the frictional drag coefficient. CISK does not predict the observed dependence of vortex intensification rate on the heat and moisture transfer coefficients, nor the insensitivity to the frictional drag coefficient since it anticipates that intensification rate is controlled by frictional convergence in the boundary layer. Since neither conditional instability nor boundary moisture content showed any significant sensitivity to the transfer coefficients, this is true of CISK using both the convective closures of Ooyama and of Charney and Eliassen. In comparison, the WISHE intensification mechanism does predict the observed increase in intensification rate with heat and moisture transfer coefficients, while not anticipating a direct influence from surface friction.

Time-varying coefficients in the almost ideal demand system: An empirical appraisal

This paper provides a generalisation of the structural time series version of the Almost Ideal Demand System (AIDS) that allows for time-varying coefficients (TVC/AIDS) in the presence of cross-equation constraints. An empirical appraisal of the TVC/AIDS is made using a dynamic AIDS with trending intercept as the baseline model with a data set from the Italian Household Budget Survey (1986-2001). The assessment is based on four criteria: adherence to theoretical constraints, statistical diagnostics on residuals, forecasting performance and economic meaningfulness. No clear evidence is found for superior performance of the TVC/AIDS, apart from improved short-term forecasts.