SUMMARYHuber, Smalian and Newton methods, to estimate tree stem and log volume by sections, were theoretically evaluated applying them to the geometries of paraboloid, cone and neiloid. The study follows approximation procedures from calculus for volume estimation of solids of revolution as function of the number of segments and error analysis methods from forest measurement research. The errors in using Huber and Smalian methods have been determined. Additionally, it was algebraically proved that the Huber's error is exactly one half of the Smalian's error and opposite in sign. The results predict that, for any tree stem modeled classically, Huber's and Smalian's average absolute percent errors should be: less than 13.5 % and 27 %, respectively, for five or more segments; less than 7 % and 14 %, for 10 or more segments; less than 3.6 % and 7.2 %, for 20 or more segments; less than 2.5 % and 5 %, for 30 or more segments. This work provides a quantization on the classical theory of tree stem and log volume estimation. It could help to unify that theory and make it a more compact reference for forest measurement teaching and research.Key words: sectional methods, tree stem volume. RESUMENLos métodos de Huber, Smalian y Newton para estimar el volumen de troncos y trozas de árbol por secciones, fueron evaluados teóricamente, aplicándolos a las geometrías de paraboloide, cono, y neiloide. El estudio sigue procedimientos de aproximación del cálculo para estimación de volumen de sólidos de revolución, como función del número de segmentos, y métodos de análisis de error de investigación en mediciones forestales. Se han determinado los errores en el uso de los métodos de Huber y Smalian. Adicionalmente, se probó algebraicamente que el error de Huber es exactamente la mitad del error de Smalian y de signo opuesto. Los resultados predicen que, para cualquier tronco modelado clásicamente, los errores porcentuales absolutos promedio de Huber y de Smalian deberían ser: menores que 13,5 % y 27 %, respectivamente, para cinco o más segmentos; menores que 7 % y 14 % para 10 o más segmentos; menores que 3,6 % y 7,2 %, para 20 o más segmentos; menores que 2,5 % y 5 %, para 30 o más segmentos. Este trabajo proporciona una cuantificación sobre la teoría clásica de estimación de volumen de troncos y trozas de árbol. Podría ser de utilidad para unificar dicha teoría y hacerla una referencia más compacta para enseñanza e investigación sobre mediciones forestales.Palabras clave: métodos seccionales, volumen de tronco de árbol.

Lateral diffusion measurements, most commonly accomplished through Fluorescence Photobleaching Recovery (FPR or FRAP), provide important information on cell membrane molecules' size, environment and participation in intermolecular interactions. However, serious difficulties arise when these techniques are applied to weakly expressed proteins of either of two types: fusions of membrane receptors with visible fluorescent proteins or membrane molecules on autofluorescent cells. To achieve adequate sensitivity in these cases, techniques such as interference fringe FPR are needed. However, in such measurements, cytoplasmic species contribute to the fluorescence recovery signal and thus yield diffusion parameters not properly representing the small number of surface molecules. A new method helps eliminate these difficulties. High Probe Intensity (HPI)-FPR measurements retain the intrinsic confocality of spot measurements to eliminate interference from fluorescent cytoplasmic species. However, HPI-FPR methods lift the previous requirement that FPR procedures be performed at probe beam intensities low enough to not induce bleaching in samples during measurements. The high probe intensities now employed provide much larger fluorescence signals and thus more information on molecular diffusion from each measurement. We report successful measurement of membrane dynamics by this technique.

A close analysis of traditional geometries and volume equations in forest measurements lead us to propose the use of conic geometry by segments as an alternative method to approach the whole form of any regular tree bole, log or bolt. The model is general and applies to any solid of revolution and is supported on the truncated cone volume equation. It is called The Segmental Conic Model. The model accuracy depends on the number of segments and is exact in the limit when that number goes to infinity.

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