Exercices de calcul intégral sur divers ordres de transcendantes et sur les quadratures: Exercices de calcul intégral sur divers ordres de transcendantes et sur les quadratures

Legendre, Adrien Marie

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Multivolume work

Persistent identifier:: 1019336226

Author:: Legendre, Adrien Marie

Title:: Exercices de calcul intégral sur divers ordres de transcendantes et sur les quadratures

Year of publication:: 1811

Place of publication:: Paris

Publisher of the original:: Courcier, Imprimeur-Libraire pour les Mathématiques

Identifier (digital):: 1019336226

Language:: French

Document type:: Multivolume work

Volume

Persistent identifier:: 1019336730

Author:: Legendre, Adrien Marie

Title:: Exercices de calcul intégral sur divers ordres de transcendantes et sur les quadratures

Scope:: 1 Online-Ressource (2 ungezählte Blätter, 386 Seiten, 1 ungezähltes Blatt, 1 ungezähltes gefaltetes Blatt mit Bildtafeln)

Year of publication:: 1811

Place of publication:: Paris

Publisher of the original:: Courcier, Imprimeur-Libraire pour les Mathématiques

Identifier (digital):: 1019336730

Language:: French

Usage licence:: Public Domain Mark 1.0

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2018

Document type:: Volume

Collection:: Mathematics

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Document type:: Multivolume work

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will be ents on efficient quency istribu- ig wind we can ulation 388.{c.Z. lled by nential v speed ion can ugh the slightly poorly s lower ation is implies imulat- aytime, pected, 1 circle), 1dustrial T. Shoji | Computers & Geosciences 32 (2006) 1025-1039 1037 therefore, that efficiency of wind power generation is high in daytime. NEDO (New Energy and Industrial Technology Development Organization) operated test plants of wind power generation at several sites in Japan from 1999 to 2000. Fig. 20 shows temporal experimental variograms of gener- ated electric power. Among them, Gunma and Miura are located in northern and southern Kanto, respectively. One of the most remarkable characters seen in temporal experimental variograms of wind velocities including wind directions and wind speeds (Figs. 7-10) is the daily period. On the other hand, the daily period is also seen, but not so clear in most of temporal experimental variograms of electric powers generated by wind (Fig. 20). The daily period is not also clear in temporal experimental variograms of wind speeds measured in power plants (most of temporal experimental variograms of wind directions show the daily period). The reason of the difference seen between temporal variograms based on AMeDAS data and NEDO's data is not clear at present. We should have to clarify the reason at the next step for assessing wind power generation based on AMeDAS data. Most of spatial experimental variograms (Figs. 18 and 19) do not show clear ranges, but are flat or linearly increasing. These patterns are considered to be a result reduced from either of the reasons that the density of stations is low, or that wind data are momentary. Anyway, the fact that most spatial variograms are not typical means that kriging will not be able to give a good estimate for wind data. It is concluded, therefore, that more observatories are necessary, when geostatistics is applied to assessing wind power generation. 6. Conclusions Statistical and geostatistical analyses of wind data in the mountainous Chubu and plain Kanto districts in central Japan have given the following conclusions: (1) wind speeds show exponential distributions or Weibull distributions independently of the districts; (2) wind is stronger in Kanto than in Chubu, though this seems not to indicate the difference in wind characteristics between the district, but to be caused on the locations of observatories (few stations at peaks or ridges in the mountainous district); (3) all temporal vario- grams of speeds, directions and velocities suggest a daily period, and wind is stronger by day than by night; (4) spatial variograms are classified into three types: the traditional type defined by a clear range (50-130 km) and sill, the flat type having only a sill, and a linear type where variogram values increase with increasing lag; (5) averaging cannot change untypical type variograms to typical type ones; and (6) more observation stations are necessary for the assessment of wind power generation. Acknowledgments I would like to thank Emeritus Prof. Ryuji Kimura of The University of Tokyo and Dr. Chang-Jo F. Chung of Geological Survey of Canada for their critical reading of the manuscript and valuable suggestions. Appendix The variograms of wind directions shown in Fig. 9 show two remarkable points: (1) the sills are almost constant independently of locations, and (2) the values are near but slightly smaller than 2. Let us consider here the reasons. The reason why sill is almost 2 is proven by a uniform and continuous distribution model. When a pair of unit vectors are shown by iij and ij, and their NS and WE components are denoted by subscripts NS and WE, respectively, the square part of Eq. (7) is written as follows (Fig. A1): — —> 12 2 2 {th — 9} = (UINS — Uans)” + (U1wE — WWE) =} = (2 sin y. (A.1) 1z2sin (x/2) Fig. Al. A diagram showing relation between a central angle and a chordal length on a circle.

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