Saha Equation Normalized to Total Atomic Number

The Saha equation describes the relative number density of consecutive ionization levels of a given atomic species under conditions of thermodynamic equilibrium in an ionized gas. Because the number density in the denominator may be very small, special steps must be taken to ensure numerical stability. In this paper we recast the equation into a form in which each ionization fraction is normalized by the total number density of the atomic species, analogous to the Boltzmann equation describing the distribution of excitation states for a given ion

Accuracy and Precision of Insect Density and Impact Estimates

In estimating insect density and impact, entomologists are understandably interested in accuracy of estimation, but they almost always are dealing with precision because of bias due to an invalid estimator, probability sampling, or nonsampling errors. Definitions related to statistical estimation are reviewed and the concepts of accuracy and precision examined. Interval estimation and optimum sample size determination related to accuracy and precision, using the concept of allowable error, are examined. Criteria for selecting the best estimator in tenns of accuracy and precision are presented, and the distortion of probability statements due to bias is discussed. Accuracy and precision are compared and contrasted using two examples: (I) estimating insect density and (2) estimating insect impact. Adjusted and more accurate estimators can be obtained if the bias of an estimator can be estimated from a preliminary sample

Development of Empirical Models to Rate Spruce-Fir Stands in Michigan\u27s Upper Peninsula for Hazard From the Spruce Budworm (Lepidoptera: Tortricidae): A Case History

The procedure used to develop empirical models which estimate potential spruce budworm impact to spruce-fir stands in Michigan\u27s Upper Peninsula is reviewed. Criteria used to select independent variables, to select the best of alternative multiple linear regression models. and to validate final models are discussed. Preliminary, intermediate, and final results demonstrate a cyclic pattern to the development procedure. Validation is emphasized as an important step in the procedure. Implications of using the hazard-rating system as a pest management tool in the stand management process are discussed

Greenhouse gas emissions, inventories and validation

The emission of greenhouse gases has become a very high priority research and environmental policy issue due to their effects on global climate. The knowledge of changes in global atmospheric concentrations of greenhouse gases since the industrial revolution is well documented, and the global budgets are reasonably well known. However, even at this scale there are important uncertainties in the budgets, for example, in the case of methane while the main sources and sinks have been identified, temporal changes in the global average concentrations since the early 1990s are not understood. In the absence of a quantitative explanation with appropriate experimental support, it is clear that current knowledge of the causes of changes in the global methane budget is inadequate to predict the effect of changes in specific emission sectors. In developing control strategies to reduce emissions it is necessary to validate national emissions and their spatial disaggregation. The methodology to underpin such a process is at an early stage of development and is not fully implemented in any country, even though target emission reductions have already been announced. Furthermore, the scale of the emission reductions is large (eg of 60% reductions by 2050 relative to 1990 baseline). There is therefore an urgent requirement for measurement based verification processes to support such challenging emission reductions. In this paper we provide the background in greenhouse gas emissions globally and in the UK followed by examples of approaches to validate emissions at the UK scale and within the regions

Monte Carlo Approx. Methods for Stochastic Optimization

This thesis provides an overview of stochastic optimization (SP) problems and looks at how the Sample Average Approximation (SAA) method is used to solve them. We review several applications of this problem-solving technique that have been published in papers over the last few years. The number and variety of the examples should give an indication of the usefulness of this technique. The examples also provide opportunities to discuss important aspects of SPs and the SAA method including model assumptions, optimality gaps, the use of deterministic methods for finite sample sizes, and the accelerated Benders decomposition algorithm. We also give a brief overview of the Sample Approximation (SA) method, and compare it to the SAA method