We derive an expansion for the fundamental solution of Laplace’s equation in flat-ring cyclide coordinates three-dimensional Euclidean space. This is a double series products functions that are harmonic interior and exterior coordinate surfaces which peanut shaped orthogonal to flat-rings. These internal external expressed terms Lamé—Wangerin functions. Using solution, we addition theorem azimu...

Several years of sea surface temperature data (1997–2003) for the coast of Antofagasta Bay—a semi-enclosed bay in northern Chile—were analyzed in order to further exploring the nature of a warm-water retention pattern inside the bay. Based on time series techniques, we were able to confirm the persistence of warm water in the bay. This warm feature was found immediately downwind of the upwellin...

This paper presents an optimum combination of two robust statistical techniques that can be used to improve the skill of long-range weather forecasts in subCarpathian zone in comparison with plane zone. The first method uses decomposition and analysis based on EEOF (Extended Empirical Orthogonal Functions), with a 3-month data window, for temperature and precipitation fields in Romania. The pro...

A three-step wavelet Galerkin method based on Taylor series expansion in time is proposed. The scheme is third-order accurate in time and O(2−jp) accurate in space. Unlike Taylor–Galerkin methods, the present scheme does not contain any new higher-order derivatives which makes it suitable for solving non-linear problems. The compactly supported orthogonal wavelet bases D6 developed by Daubechie...

Detecting changes to the transparency of the water column is critical for understanding the responses of marine organisms, such as corals, to light availability. Long-term patterns in water transparency determine geographical and depth distributions, while acute reductions cause short-term stress, potentially mortality and may increase the organisms’ vulnerability to other environmental stresso...

We introduce dynamic orthogonal components (DOC) for multivariate time series and propose a procedure for estimating and testing the existence of DOCs for a given time series. We estimate the dynamic orthogonal components via a generalized decorrelation method that minimizes the linear and quadratic dependence across components and across time. We then use Ljung–Box type statistics to test the ...

Let (X; Y) be a pair of random variables with supp(X) 0; 1] and EY 2 < 1. Let m be the corresponding regression function. Estimation of m from i.i.d. data is considered. The L 2 error with integration with respect to the design measure (i.e., the distribution of X) is used as an error criterion. Estimates are constructed by estimating the coeecients of an orthonormal expansion of the regression...

In this paper we obtain some sufficient conditions on |N, pn, qn|k summability of an orthogonal series. These conditions are expressed in terms of the coefficients of the orthogonal series. Also, several known and new results are deduced as corollaries of the main results. c ©2014 All rights reserved.

Inference for statistics of a stationary time series often involve nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some of these issues. For a broad class of statistics, an orthogonal sample is constructed through a slight modification of the original statistic, such that it s...

In this paper, we prove two theorems on ∣A∣k, 1 ≤ k ≤ 2, summability of orthogonal series. The first one gives a sufficient condition under which an orthogonal series is absolutely summable almost everywhere, and the second one, is a general theorem, which also gives a sufficient condition so that an orthogonal series is absolutely summable almost everywhere, but it involves a positive numerica...