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A study on the stem form
樹幹形に関する研究
長嶋, 郁
18890
NAGASHIMA, Iku
18891
Stem form formula
Orthonormal expansion
Growth process
1991-12
This study is concerned with the expression of stem form in mathematical formulae which had been discussed in terms of theoretical background as the moment problem and the biological growth process (Chapter 1). Research on the stem form is essential in order to estimate of stem volume more accurately and to contribute for the morphology, and numerous efforts have been made in this regard to date. It remains both a traditional problem and forth coming one (Chapter 2). The present study presents two new opinions that will hopefully add to the knowledge provided by traditional stem form research. First, we may consider a stem form as a vector. When we take the set of diameters at each of 10 positions located equidistantly along the stem axis length, we can define the vector as a very stem form itself, or the stem taper. On the other hand, when we take the stem base as the origin, using the moment system created form the diameters at each of the aformementioned 10 positions, we note that the moment system and the set of diameters are equivalent based on their one-to-one correspondence (Chapter 3). The problem of stem form redounds to the selection of a stem form model to be applied for the actual stem taper and the method of calculation in employing the model in the approximation. In the present study, we propose that the stem curve be generally expanded in the the FOURIER series using some orthogonal systems. To this end, the CHARLIER orthogonal system was investigated originally, because it was derived from the POISSON distribution resembling the stem form configuration (Chapter 3). Next, the discrete orthonormal system and the LEGENDRE system were revised for stem form expression under the condition that the value is null at the stem canopy (Chapter 4,5). Using these functions for stem taper fitting, one can readily determine the coefficients of each term in the orthonormal expansion so as to minimize the square sum of deviations. Moreover, the value of square sum of the coefficients gives precisely the stem volume. Then, if the approximation does not suffice, the fitting will be improved to add a term of higher order. In this case, the coefficient will be independently determined with other coefficients, and this is a great advantage over the ordinal method of least squares (Chapter 4.5). Second, some new stem form formulae were derived theoretically based upon the biological growth process. Thus, supposing that the growth in height of stem follows the MITSCHERLICH growth process and the diameter at the canopy on the stem axis starts growing in the horizontal direction just as it does for hight, then one stem form formula may be theoretically constructed, then somewhat revised subsequently. This stem form model is well-suited to the actual stem if coniferous trees except for the butt-swell portion. Although many stem formulae have been reported to date, these new models are theoretically derived for the first time in terms of the biological process and very simply (Chapter 6).
農林水産研究情報センターで作成したPDFファイルを使用している。
departmental bulletin paper
名古屋大学農学部付属演習林
1991-12
名古屋大学農学部演習林報告
11
193
279
http://hdl.handle.net/2237/8692
0469-4708
jpn
http://rms1.agsearch.agropedia.affrc.go.jp/contents/JASI/pdf/academy/56-1666.pdf