In this paper, we construct a kind of bivariate real-valued orthogonal periodic wavelets. The corre-sponding decomposition and reconstruction algorithms involve only 8 terms respectively which are very simple in pract...In this paper, we construct a kind of bivariate real-valued orthogonal periodic wavelets. The corre-sponding decomposition and reconstruction algorithms involve only 8 terms respectively which are very simple in practical computation. Moreover, the relation between periodic wavelets and Fourier series is also discussed.展开更多
In this paper, we construct a kind of bivariate real-valued orthogonal periodic box-spline wavelets. There are only 4 terms in the two-scale dilation equations. This implies that the corresponding decomposition and re...In this paper, we construct a kind of bivariate real-valued orthogonal periodic box-spline wavelets. There are only 4 terms in the two-scale dilation equations. This implies that the corresponding decomposition and reconstruction algorithms involve only 4 terms respectively which are simple in practical computation. The relation between the periodic wavelets and Fourier series is also discussed.展开更多
In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the for...In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than that in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real valued. The relation between the periodic wavelets and the Fourier series is also discussed.展开更多
An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We exten...An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.展开更多
Large igneous provinces （LIPs） are considered a relevant cause for mass extinctions of marine life throughout Earth＇s history. Their flood basalts and associated intrusions can cause significant release of SO4 and ...Large igneous provinces （LIPs） are considered a relevant cause for mass extinctions of marine life throughout Earth＇s history. Their flood basalts and associated intrusions can cause significant release of SO4 and CO2 and consequently, cause major environmental disruptions. Here, we reconstruct the long-term periodic pattern of LIP emplacement and its impact on ocean chemistry and biodiversity from δ34Ssulfate of the last 520 Ma under particular consideration of the preservation limits of LIP records. A combination of cross-wavelet and other time-series analysis methods has been applied to quantify a potential chain of linkage between LIP emplacement periodicity, geochemical changes and the Phanerozoic marine genera record. We suggest a mantle plume cyclicity represented by LIP volumes （V） of V= （350-770） × 103km3sin（27πt/ 170 Ma）＋ （300-650）× 103 km3 sin（2πt/64.5 Ma ＋ 2.3） for t= time in Ma. A shift from the 64.5 Ma to a weaker -28-35 Ma LIP cyclicity during the Jurassic contributes together with probably independent changes in the marine sulfur cycle to less ocean anoxia, and a general stabilization of ocean chemistry and increasing marine biodiversity throughout the last -135 Ma. The LIP cycle pattern is coherent with marine biodiversity fluctuations corresponding to a reduction of marine biodiversity of -120 genera/Ma at 600 x 103 km3 LIP eruption volume. The 62-65 Ma LIP cycle pattern as well as excursion in -34Ssulfate and marine genera reduction suggest a not-vet identified found LIP event at - 440-450 Ma.展开更多
The periodic multiresolution analysis （PMRA） and the periodic frame multiresolution analysis （PFMRA） provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. Th...The periodic multiresolution analysis （PMRA） and the periodic frame multiresolution analysis （PFMRA） provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. This paper addresses PFMRAs by the introduction of the notion of spectrum sequence. In terms of spectrum sequences, the scaling function sequences generating a normalized PFMRA are characterized; a characterization of the spectrum sequences of PFMRAs is obtained, which provides a method to construct PFMRAs since its proof is constructive; a necessary and sufficient condition for a PFMRA to admit a single wavelet frame sequence is obtained; a necessary and sufficient condition for a PFMRA to be contained in a given PMRA is also obtained. What is more, it is proved that an arbitrary PFMRA must be contained in some PMRA. In the meanwhile, some examples are provided to illustrate the general theory.展开更多
文摘In this paper, we construct a kind of bivariate real-valued orthogonal periodic wavelets. The corre-sponding decomposition and reconstruction algorithms involve only 8 terms respectively which are very simple in practical computation. Moreover, the relation between periodic wavelets and Fourier series is also discussed.
文摘In this paper, we construct a kind of bivariate real-valued orthogonal periodic box-spline wavelets. There are only 4 terms in the two-scale dilation equations. This implies that the corresponding decomposition and reconstruction algorithms involve only 4 terms respectively which are simple in practical computation. The relation between the periodic wavelets and Fourier series is also discussed.
文摘In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than that in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real valued. The relation between the periodic wavelets and the Fourier series is also discussed.
基金Acknowledgements The authors express their gratitude to the anonymous referees for their kind suggestions and useful comments on the original manuscript, which resulted in this final version. This work was supported by the National Natural Science Foundation of China （No. 61071189）, the Natural Science Foundation for the Education Department of Henan Province of China （No. 13A110072）, and the Natural Science Foundation of Henan University （No. 2011YBZR001）.
文摘An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.
文摘Large igneous provinces （LIPs） are considered a relevant cause for mass extinctions of marine life throughout Earth＇s history. Their flood basalts and associated intrusions can cause significant release of SO4 and CO2 and consequently, cause major environmental disruptions. Here, we reconstruct the long-term periodic pattern of LIP emplacement and its impact on ocean chemistry and biodiversity from δ34Ssulfate of the last 520 Ma under particular consideration of the preservation limits of LIP records. A combination of cross-wavelet and other time-series analysis methods has been applied to quantify a potential chain of linkage between LIP emplacement periodicity, geochemical changes and the Phanerozoic marine genera record. We suggest a mantle plume cyclicity represented by LIP volumes （V） of V= （350-770） × 103km3sin（27πt/ 170 Ma）＋ （300-650）× 103 km3 sin（2πt/64.5 Ma ＋ 2.3） for t= time in Ma. A shift from the 64.5 Ma to a weaker -28-35 Ma LIP cyclicity during the Jurassic contributes together with probably independent changes in the marine sulfur cycle to less ocean anoxia, and a general stabilization of ocean chemistry and increasing marine biodiversity throughout the last -135 Ma. The LIP cycle pattern is coherent with marine biodiversity fluctuations corresponding to a reduction of marine biodiversity of -120 genera/Ma at 600 x 103 km3 LIP eruption volume. The 62-65 Ma LIP cycle pattern as well as excursion in -34Ssulfate and marine genera reduction suggest a not-vet identified found LIP event at - 440-450 Ma.
基金Supported by the National Natural Science Foundation of China (Grant No. 10671008)supported by the Excellent Talents Foundation of Beijing, China (20051D0501022)PHR(IHLB)+1 种基金the Project-sponsored by SRF for ROCS, SEM of Chinathe Scientific Research Foundation for the Excellent Returned Overseas Chinese Scholars, Beijing
文摘The periodic multiresolution analysis （PMRA） and the periodic frame multiresolution analysis （PFMRA） provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. This paper addresses PFMRAs by the introduction of the notion of spectrum sequence. In terms of spectrum sequences, the scaling function sequences generating a normalized PFMRA are characterized; a characterization of the spectrum sequences of PFMRAs is obtained, which provides a method to construct PFMRAs since its proof is constructive; a necessary and sufficient condition for a PFMRA to admit a single wavelet frame sequence is obtained; a necessary and sufficient condition for a PFMRA to be contained in a given PMRA is also obtained. What is more, it is proved that an arbitrary PFMRA must be contained in some PMRA. In the meanwhile, some examples are provided to illustrate the general theory.
