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Outline
To address the limitations of the algebraic expansion of the meridian arc length, this study is based on the principles of equivalent transformation and order-increment invariance. Using the first eccentricity or the third flattening, this study reconstructs polynomial function models for the meridian arc length and the meridian radius of curvature, respectively. Additionally, a constrained least squares method is derived for the direct estimation of the model constant coefficients. The results indicate that, regardless of whether the first eccentricity or the third flattening is used, the polynomial function models facilitate the high-order expansion and correctness verification of the algebraic expansion of the meridian arc length. Furthermore, their estimation accuracy can meet the requirements of practical applications such as high-precision geodesy and map projection.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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