Teorema de Bayes y lenguaje matemático Maple. Estimación de la función de densidad posterior

El objetivo de este trabajo es explicar el uso del teorema de Bayes en la estimación de la función de densidad posterior (fdp) de parámetros de interés, usando el software matemático Maple. Se presenta el caso de la distribución de Pareto como una aproximación a la distribución de los ingresos de una población. Se estima la fdp del parámetro alfa de la distribución de Pareto para el caso de datos agrupados.

Maple Leaf Mills Records 1955, 1960-1964, 1975-1987, 1989, n.d.

Ontario Editorial Bureau (O.E.B.)

Impacto del uso de Maple en el proceso de enseñanza y aprendizaje del álgebra lineal.

Análisis del programa Maple como herramienta didáctica para la enseñanza de las Matemáticas. En el artículo se pretende cuantificar los efectos en la enseñanza del álgebra lineal atendiendo a dos variables; el grado de acierto y la resolución de los ejercicios.

Una experiencia innovadora con carácter interdisciplinar utilizando Maple y la plataforma e-learning en las Escuelas de Ingeniería.

Realizado en la Escuela Politécnica Superior, por 4 profesores del centro y dos colaboradores, para las Titulaciones de Ingeniería Técnica en Obras Públicas e Ingeniería de Caminos, Canales y Puertos. Los objetivos principales han sido, por un lado, introducir al alumnado en los conocimientos fundamentales de las matemáticas y, por otro lado, incorporar el Campus Electrónico, de reciente creación en la Universidad de Burgos, como una nueva estrategia en el proceso de enseñanza-aprendizaje. En cuanto a la metodología empleada: se realizaron guías, programas y hojas de problemas; se elaboraron prácticas de matemáticas a modo de evaluación continua; se presentaron en un Congreso Internacional; se programaron cuestionarios con Scientific Notebook; se utilizó el campus electrónico para programar distintos foros y tutorías. En el curso 2004/2005 se pone en práctica en las clases y los resultados se tendrán que comparar con los siguientes años académicos.

Un modelo de enseñanza-aprendizaje de los conceptos de límites de sucesiones, límites de funciones y derivadas a través de MAPLE (libro electrónico interactivo).

Construir un libro electrónico interactivo como modelo de enseñanza-aprendizaje de los conceptos de límites de sucesiones, límites de funciones y derivadas a través de MAPLE para que los alumnos de Bachillerato adquieran un conocimiento profundo de los mismos.

Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

The effects of a changing climate on root respiration of woody plants in sugar maple forests and northern peatlands

Global climate change might significantly impact future ecosystems. The purpose of this thesis was to investigate potential changes in woody plant fine root respiration in response to a changing climate. In a sugar maple dominated northern hardwood forest, the soil was experimentally warmed (+4 °C) to determine if the tree roots could metabolically acclimate to warmer soil conditions. After one and a half years of soil warming, there was an indication of slight acclimation in the fine roots of sugar maple, helping the ecosystem avoid excessive C loss to the atmosphere. In a poor fen northern peatland in northern Michigan, the impacts of water level changes on woody plant fine root respiration were investigated. In areas of increased and also decreased water levels, there were increases in the CO2 efflux from ecosystem fine root respiration. These studies show the importance of investigating further the impacts climate change may have on C balance in northern ecosystems.

Investigating within-canopy variation of functional traits and cellular structure of sugar maple (Acer saccharum) leaves

Patterns of increasing leaf mass per area (LMA), area-based leaf nitrogen (Narea), and carbon isotope composition (δ13C) with increasing height in the canopy have been attributed to light gradients or hydraulic limitation in tall trees. Theoretical optimal distributions of LMA and Narea that scale with light maximize canopy photosynthesis; however, sub-optimal distributions are often observed due to hydraulic constraints on leaf development. Using observational, experimental, and modeling approaches, we investigated the response of leaf functional traits (LMA, density, thickness, and leaf nitrogen), leaf carbon isotope composition (δ13C), and cellular structure to light availability, height, and leaf water potential (Ψl) in an Acer saccharum forest to tease apart the influence of light and hydraulic limitations. LMA, leaf and palisade layer thickness, and leaf density were greater at greater light availability but similar heights, highlighting the strong control of light on leaf morphology and cellular structure. Experimental shading decreased both LMA and area-based leaf nitrogen (Narea) and revealed that LMA and Narea were more strongly correlated with height earlier in the growing season and with light later in the growing season. The supply of CO2 to leaves at higher heights appeared to be constrained by stomatal sensitivity to vapor pressure deficit (VPD) or midday leaf water potential, as indicated by increasing δ13C and VPD and decreasing midday Ψl with height. Model simulations showed that daily canopy photosynthesis was biased during the early growing season when seasonality was not accounted for, and was biased throughout the growing season when vertical gradients in LMA and Narea were not accounted for. Overall, our results suggest that leaves acclimate to light soon after leaf expansion, through an accumulation of leaf carbon, thickening of palisade layers and increased LMA, and reduction in stomatal sensitivity to Ψl or VPD. This period of light acclimation in leaves appears to optimize leaf function over time, despite height-related constraints early in the growing season. Our results imply that vertical gradients in leaf functional traits and leaf acclimation to light should be incorporated in canopy function models in order to refine estimates of canopy photosynthesis.

Evaluation of sugar maple dieback in the Upper Great Lakes region and development of a forest health youth education program

Acer saccharum Marsh., is one of the most valuable trees in the northern hardwood forests. Severe dieback was recently reported by area foresters in the western Upper Great Lakes Region. Sugar Maple has had a history of dieback over the last 100 years throughout its range and different variables have been identified as being the predisposing and inciting factors in different regions at different times. Some of the most common factors attributed to previous maple dieback episodes were insect defoliation outbreaks, inadequate precipitation, poor soils, atmospheric deposition, fungal pathogens, poor management, or a combination of these. The current sugar maple dieback was evaluated to determine the etiology, severity, and change in dieback on both industry and public lands. A network of 120 sugar maple health evaluation plots was established in the Upper Peninsula, Michigan, northern Wisconsin, and eastern Minnesota and evaluated annually from 2009-2012. Mean sugar maple crown dieback between 2009-2012 was 12.4% (ranging from 0.8-75.5%) across the region. Overall, during the sampling period, mean dieback decreased by 5% but individual plots and trees continued to decline. Relationships were examined between sugar maple dieback and growth, habitat conditions, ownership, climate, soil, foliage nutrients, and the maple pathogen sapstreak. The only statistically significant factor was found to be a high level of forest floor impacts due to exotic earthworm activity. Sugar maple on soils with lower pH had less earthworm impacts, less dieback, and higher growth rates than those on soils more favorable to earthworms. Nutritional status of foliage and soil was correlated with dieback and growth suggesting perturbation of nutrient cycling may be predisposing or contributing to dieback. The previous winter's snowfall totals, length of stay on the ground, and number of days with freezing temperatures had a significant positive relationship to sugar maple growth rates. Sapstreak disease, Ceratocystis virescens, may be contributing to dieback in some stands but was not related to the amount of dieback in the region. The ultimate goal of this research is to help forest managers in the Great Lakes Region prevent, anticipate, reduce, and/or salvage stands with dieback and loss in the future. An improved understanding of the complex etiology associated with sugar maple dieback in the Upper Great Lakes Region is necessary to make appropriate silvicultural decisions. Forest Health education helps increase awareness and proactive forest management in the face of changing forest ecosystems. Lessons are included to assist educators in incorporating forest health into standard biological disciplines at the secondary school curricula.

Molecular Machanics of Water Monomer-Maple Code

This is the Maple code to support the molecular dynamics of a water monomer molecule, allowing investigation of the classical vibrations of this molecule.

Guessing Harmonic Oscillator Wavefunctions Using Maple

The guessing of eigenfunctions is not trivial at higher quantum numbers, no matter what the system being considered. Instead of guessing, one can employ a symbolic calculus progam (Maple in this case) to aid in the reasoning process.

Butadiene via the Huckel Scheme (using Maple)

The Huckel Molecular Orbtial method is used to treat the MO's of butadiene. The method employs analytical tools and Maple.

Using the Morse Potential to Understand Reaction Coördinates using Maple

The interactions employed in the “linear” reaction A(g)+BC(g) -> AB(g) + C(g) in a “one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum path on the surface created.“one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum path on the surface created.