An exactly solvable self-convolutive recurrence

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function $U(a,b,z)$. By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the $n$th coefficient is expressed as the $(n-1)$th moment of a measure, and also as the trace of the $(n-1)$th iterate of a linear operator. Applications of these sequences, and hence of the explicit solution provided, are found in quantum field theory as the number of Feynman diagrams of a certain type and order, in Brownian motion theory, and in combinatorics

2D-spectral estimation based on DCT and modified magnitude group delay

This paper proposes two new 2D-spectral estimation methods. The 2D-modified magnitude group delay (MMGD) is applied to 2D-discrete Fourier transform (2DDFT) for the first and to the analytic 2D-discrete Cosine transform for the second. The analytic 2D-DCT preserves the desirable properties of the DCT (like, improved frequency resolution, leakage and detectability) and is realized by a 2D-discrete cosine transform (2D-DCT) and its Hilbert transform. The 2D-MMGD is an extension from 1D to 2D, and it reduces the variance preserving the original frequency resolution of 2D-DFT or 2D-analytic DCT, depending upon to which is applied. The first and the second methods are referred to as DFT-MMGD and DCT-MMGD, respectively. The proposed methods are applied to 2D sinusoids and 2D AR process, associated with Gaussian white noise. The performance of the DCT-MMGD is found to be superior to that of DFT-MMGD in terms of variance, frequency resolution and detectability. The performance of DFT-MMGD and DCT-MMGD is better than that of 2D-LP method even when the signal to noise ratio is low

Distúrbios ondulatórios de leste (DOLs) na região do centro de lançamento de Alcântara-MA Easterly waves disturbance (DOLs) at the region of Alcântara Launching Center-MA

Neste artigo foi realizada uma climatologia dos Distúrbios Ondulatórios de Leste (DOLs) que passaram pela região de Alcântara-MA, no período de 1988 a 1997, utilizando-se de um método baseado na mudança do sinal da componente meridional do vento (V). Este método foi aplicado para 3 camadas distintas (entre 850 a 700 hPa, entre 700 e 500 hPa e entre 850 a 500 hPa), objetivando identificar a camada que melhor indicasse a ocorrência dos DOLs. Após a identificação dos eventos de DOLs, estes foram confirmados por um conjunto de dados independentes de cobertura de nuvens (dados ISCCP e imagens infravermelho de satélites GOES-E) e pelos espectros de potência da componente meridional do vento usando as re-análises do ECMWF. Ocorreram eventos de DOLs durante todo o ano com duração de tempo variando de 3 a 6 dias. Esse método mostrou-se adequado para caracterizar os eventos de DOLs e que, durante a época chuvosa, as 3 camadas identificam a passagem do sistema atmosférico. No caso do período seco (jul-dez), as camadas com espessura maior (camadas entre 700 e 500 hPa e entre 850-500 hPa) conseguiram identificar os eventos, mas não a camada mais baixa (entre 850-500 hPa).<br>A climatology of the easterly waves disturbances (DOLs) over Alcântara - MA was investigated using a method that compute the signal of the observational meridional wind (rawinsoundings from 1988 up to 1997). This technique has been applied to three different layers (850-700, 700-500 and 850-500 hPa) in order to identify the best layer to indicate the DOLs occurrence. The DOLs events have been confirmed by independent data-sets available: cloud cover (ISPCC data set), infra-red satellite images (from GOES-E) and power spectrum of the meridional component (ECMWF re-analysis). The method detected the presence of the DOLs during the whole year with time-scale of 3-6 days. During the wet period (jan-jun) all three layers identified these atmospheric systems. For the dry season (jul-dec), only the deeper layers (layers between 700 - 500 hPa and/or 850-500 hPa) were able to identify the events