Harmonic Analyses

2006 ◽  
pp. 157-186
Keyword(s):  
2020 ◽  
Vol 6 (1) ◽  
pp. 50-62
Author(s):  
Syed Mustafizur Rahman ◽  
Syed Mahbubur Rahman ◽  
Md. Shuzon Ali ◽  
Md. Abdullah Al Mamun ◽  
Md. Nezam Uddin

Abstract Seasons are the divisions of the year into months or days according to the changes in weather, ecology and the intensity of sunlight in a given region. The temperature cycle plays a major role in defining the meteorological seasons of the year. This study aims at investigating seasonal boundaries applying harmonic analysis in daily temperature for the duration of 30 years, recorded at six stations from 1988 to 2017, in northwest part of Bangladesh. Year by year harmonic analyses of daily temperature data in each station have been carried out to observe temporal and spatial variations in seasonal lengths. Periodic nature of daily temperature has been investigated employing spectral analysis, and it has been found that the estimated periodicities have higher power densities of the frequencies at 0.0027 and 0.0053 cycles/day. Some other minor periodic natures have also been observed in the analyses. Using the frequencies between 0.0027 to 0.0278 cycles/day, the observed periodicities in spectral analysis, harmonic analyses of minimum and maximum temperatures have found four seasonal boundaries every year in each of the stations. The estimated seasonal boundaries for the region fall between 19-25 February, 19-23 May, 18-20 August and 17-22 November. Since seasonal variability results in imbalance in water, moisture and heat, it has the potential to significantly affect agricultural production. Hence, the seasons and seasonal lengths presented in this research may help the concerned authorities take measures to reduce the risks for crop productivity to face the challenges arise from changing climate. Moreover, the results obtained are likely to contribute in introducing local climate calendar.


2016 ◽  
Vol 833 (2) ◽  
pp. 242 ◽  
Author(s):  
Adrian Liu ◽  
Yunfan Zhang ◽  
Aaron R. Parsons

The westward drift of the non-dipole part of the earth’s magnetic field and of its secular variation is investigated for the period 1907-45 and the uncertainty of the results discussed. It is found that a real drift exists having an angular velocity which is independent of latitude. For the non-dipole field the rate of drift is 0.18 ± 0-015°/year, that for the secular variation is 0.32 ±0-067°/year. The results are confirmed by a study of harmonic analyses made between 1829 and 1945. The drift is explained as a consequence of the dynamo theory of the origin of the earth’s field. This theory required the outer part of the core to rotate less rapidly than the inner part. As a result of electromagnetic forces the solid mantle of the earth is coupled to the core as a whole, and the outer part of the core therefore travels westward relative to the mantle, carrying the minor features of the field with it.


2019 ◽  
Vol 22 (4) ◽  
pp. 1039-1062 ◽  
Author(s):  
Victor Ginting ◽  
Yulong Li

Abstract We present an analysis of existence, uniqueness, and smoothness of the solution to a class of fractional ordinary differential equations posed on the whole real line that models a steady state behavior of a certain anomalous diffusion, advection, and reaction. The anomalous diffusion is modeled by the fractional Riemann-Liouville differential operators. The strong solution of the equation is sought in a Sobolev space defined by means of Fourier Transform. The key component of the analysis hinges on a characterization of this Sobolev space with the Riemann-Liouville derivatives that are understood in a weak sense. The existence, uniqueness, and smoothness of the solution is demonstrated with the assistance of several tools from functional and harmonic analyses.


Author(s):  
A. Rguiti ◽  
I. Naciri ◽  
L. Elmaimouni ◽  
Y. Bel Kassimi ◽  
J. E. Lefebvre ◽  
...  

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