Computational methods for integrals involving functions and Daubechies wavelets

Maleknejad, K.; Yousefi, Mehdi; Nouri, Kazem

doi:10.1016/j.amc.2006.12.064

Cited by 18 publications

(19 citation statements)

References 11 publications

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“…Assuming the signal f ( t )∈ L 2 ( R ), its discrete wavelet expansion can be expressed as (You et al , 2003, 2004) and the wavelet power spectrum is Among wavelet functions, Haar wavelet is the earliest compact support orthogonal wavelet (Haar, 1910); real Morlet wavelet function has strong nonlinearity and stability (Neupauer and Powell, 2005) and Daubechies wavelets, a family of orthogonal wavelets defining a discrete wavelet transform and characterized, are most commonly used and have many good properties (Maleknejad et al , 2007).…”

Section: Methodsmentioning

confidence: 99%

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Bolliger

Blacque

Frech

2008

Chemistry A European J

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The aminophosphine-based pincer complexes [C6H3-2,6-(XP(piperidinyl)2)2Pd(Cl)] (X=NH 1; X=O 2) are readily prepared from cheap starting materials by sequential addition of 1,1',1''-phosphinetriyltripiperidine and 1,3-diaminobenzene or resorcinol to solutions of [Pd(cod)(Cl)2] (cod=cyclooctadiene) in toluene under N2 in "one pot". Compounds 1 and 2 proved to be excellent Heck catalysts and allow the quantitative coupling of several electronically deactivated and sterically hindered aryl bromides with various olefins as coupling partners at 140 degrees C within very short reaction times and low catalyst loadings. Increased reaction temperatures also enable the efficient coupling of olefins with electronically deactivated and sterically hindered aryl chlorides in the presence of only 0.01 mol % of catalyst. The mechanistic studies performed rule out that homogeneous Pd 0 complexes are the catalytically active forms of 1 and 2. On the other hand, the involvement of palladium nanoparticles in the catalytic cycle received strong experimental support. Even though pincer-type Pd IV intermediates derived from 1 (and 2) are not involved in the catalytic cycle of the Heck reaction, their general existence as reactive intermediates (for example, in other reactions) cannot be excluded. On the contrary, they were shown to be thermally accessible. Compounds 1 and 2 show a smooth halide exchange with bromobenzene to yield their bromo derivatives in DMF at 100 degrees C. Experimental observations revealed that the halide exchange most probably proceeded via pincer-type Pd IV intermediates. DFT calculations support this hypothesis and indicated that aminophosphine-based pincer-type Pd IV intermediates are generally to be considered as reactive intermediates in reactions with aryl halides performed at elevated temperatures.

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Section: Methodsmentioning

confidence: 99%

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Bolliger

Blacque

Frech

2008

Chemistry A European J

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“…Among wavelet functions, Haar wavelet is the earliest compact support orthogonal wavelet (Haar, 1910); real Morlet wavelet function has strong nonlinearity and stability (Neupauer and Powell, 2005) and Daubechies wavelets, a family of orthogonal wavelets defining a discrete wavelet transform and characterized, are most commonly used and have many good properties (Maleknejad et al, 2007). Haar wavelet, Morlet wavelet and Daubechies wavelet were used.…”

Section: Wavelet Transformmentioning

confidence: 99%

Response analysis of rainfall–runoff processes using wavelet transform: a case study of the alpine meadow belt

Liu

Bao

Chen

et al. 2011

Hydrological Processes

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Abstract:Rainfall-runoff processes appear to be highly nonlinear in Bayinbluk watersheds of the northwestern China. In this study, the time-scale wavelet transform has been used for the analysis of this nonstationary system. The Haar and Morlet wavelet transform were used to analyse the rainfall-runoff conversion relationship. Wavelet power spectrum and change point methods are also employed to analyse rainfall rates and runoffs measured at daily to half-hourly sampling rate. The four experimental sites (Luoto, Haer, Kuce and Shengl) are located in the Tianshan Mountains (Xinjiang province, China). Correlation analysis and wavelet transform are first applied to runoff process in different underlying surfaces. Wavelet analyses of rainfall rates and runoffs also give meaningful information on the temporal variability of the rainfall-runoff relationship. Change point and wavelet power spectrum analysis provide simple interpretation of energy distribution between different scales. The results indicate that wavelet transform is a good method for analysing the nonlinear relationship of temporal-spatial responses between rainfall and runoff. This method allowed quantification of the processes affecting runoff and provided an insight into their implications in surface water management.

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“…Barinka et al employed this approach to derive quadrature rules for cardinal B-splines. Later on, Maleknejad et al [10] employed the same approach on the Daubechies' family of classical, extremal phase wavelets [4].…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we follow the methodology proposed by Barinka et al to derive weighted Gaussian quadratures to integrals involving CDV scaling functions. Since the CDV functions were developed from the Daubechies' leastasymmetric (i.e., symmlet) family [5], it is natural to consider [10] as a starting point. The algorithm proposed therein is improved by avoiding the evaluation of determinants with the aid of the Chebyshev algorithm [7] and by a more convenient selection of the support of the interior scaling functions.…”

Section: Introductionmentioning

confidence: 99%

Weighted Gaussian Quadratures for Orthogonal Wavelet Functions in the Interval

Azevedo¹,

Oliveira²,

Wisniewski³

2015

Int. J. of Appl. Math.

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We study the numerical evaluation of integrals involving scaling functions from the Cohen-Daubechies-Vial (CDV) family of compactly supported orthogonal wavelets on the interval. The computation of the wavelet coefficients is performed by a weighted Gaussian quadrature, in conjunction with the Chebyshev and modified Chebyshev algorithms. We validate the proposed quadratures with the numerical approximation of a Fredholm integral equation of second kind by the Galerkin method with CDV scaling functions as basis functions.

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Computational methods for integrals involving functions and Daubechies wavelets

Cited by 18 publications

References 11 publications

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Response analysis of rainfall–runoff processes using wavelet transform: a case study of the alpine meadow belt

Weighted Gaussian Quadratures for Orthogonal Wavelet Functions in the Interval

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Computational methods for integrals involving functions and Daubechies wavelets

Cited by 18 publications

References 11 publications

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: PdIV Intermediates and Palladium Nanoparticles

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: PdIV Intermediates and Palladium Nanoparticles

Response analysis of rainfall–runoff processes using wavelet transform: a case study of the alpine meadow belt

Weighted Gaussian Quadratures for Orthogonal Wavelet Functions in the Interval

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Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles

Rationally Designed Pincer‐Type Heck Catalysts Bearing Aminophosphine Substituents: Pd^IV Intermediates and Palladium Nanoparticles