Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Validation of back-calculation equations for juvenile bluefish (Pomatomus saltatrix) with the use of tetracycline-marked otoliths

In recent years, a decrease in the abundance of bluefish (Pomatomus saltatrix) has been observed (Fahay et al., 1999; Munch and Conover, 2000) that has led to increased interest in a better understanding the life history of the species. Estimates of several young-of-the-year (YOY) life history characteristics, including the importance and use of estuaries as nursery habitat (Kendall and Walford, 1979) and size-dependant mortality (Hare and Cowen, 1997), are reliant upon the accuracy of growth determination. By using otoliths, it is possible to use back-calculation formulae (BCFs) to estimate the length at certain ages and stages of development for many species of fishes. Use of otoliths to estimate growth in this way can provide the same information as long-term laboratory experiments and tagging studies without the time and expense of rearing or recapturing fish. The difficulty in using otoliths in this way lies in validating that 1) there is constancy in the periodicity of the increment formation, and 2) there is no uncoupling of the relationship between somatic and otolith growth. To date there are no validation studies demonstrating the relationship between otolith growth and somatic growth for bluefish. Daily increment formation in otoliths has been documented for larval (Hare and Cowen, 1994) and juvenile bluefish (Nyman and Conover, 1988). Hare and Cowen (1995) found ageindependent variability in the ratio of otolith size to body length in early age bluefish, although these differences varied between ontogenetic stages. Furthermore, there have been no studies where an evaluation of back-calculation methods has been combined with a validation of otolithderived lengths for juvenile bluefish.

Bessel functions and equations of mathematical physics

The aim of this dissertation is to introduce Bessel functions to the reader, as well as studying some of their properties. Moreover, the final goal of this document is to present the most well- known applications of Bessel functions in physics.

A reassessment of equations for predicting natural mortality in Mediterranean teleosts

This brief article presents new empirical models for prediction of natural mortality (M) from growth parameters (L and K, W and K) in Mediterranean teleosts, based on 56 data sets presented in an earlier paper in the January 1993 issue of Naga, the ICLARM Quarterly in which models were presented that included temperature as a predictor variable, although its effect was nonsignificant and its partial slope had the "wrong" sign.

Empirical equations for the estimation of natural mortality in Mediterranean teleosts

Empirical relationships were established linking estimates of the instantaneous rate of natural mortality (M), the von Bertalanffy growth parameters, L sub( infinity ) (or W sub( infinity )) and K, and annual mean water temperature in 56 stocks of Mediterranean teleosts fish. It is suggested that these relationships generate for these fish more reliable estimates of M than the widely-used model of Pauly (1980, J. Cons. CIEM 33(3):175-192), which was based on 175 fish stocks, but included only five stocks from the Mediterranean.

Crank-Nicholson method for rate equations in powder random lasers

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2014)

Processos estocásticos em teoria de campos e aplicação ao universo inflacionário

É conhecido que derivações microscópicas obtidas através de métodos de teoria quântica de campos (TQC) podem conduzir a complicadas equações de movimento (EdM) que possuem um termo dissipativo com memória e um termo de ruído colorido. Um caso particularmente interessante é o modelo que escreve a interação entre um sistema e um banho térmico a temperatura T. Motivado por isso, usamos uma prescrição que nos permite reescrever EdMs não-markovianas semelhantes as obtidas em TQC em termos de um sistema de equações locais, para então confrontarmos a solução desse sistema com a solução aproximada usada correntemente na literatura, a chamada aproximação markoviana. A pergunta chave a qual se pretende responder aqui é: dado um conjunto de parâmetros que descrevem o modelo, a aproximação markoviana é suficientemente boa para descrever a dinâmica do sistema se comparada a dinâmica obtida atravéS da EdM não-markoviana? Além disso, consideramos uma versão linear da ELG de forma que pudéssemos determinar o nível de confiança da nossa metodologia numérica, procedimento este realizado comparando-se a solução analítica com a solução numérica. Como exemplo de aplicação prática do tema discutido aqui, comparamos a evolução não-markoviana do inflaton com a evolução markoviana do mesmo num modelo de universo primordial denominado inflação não-isentrópica (warm inflation).

Beverton and Holt equations: spreadsheet functions and uncertainty

This contribution illustrates how modern spreadsheets aid the calculation and visualization of yield models and how the effects of uncertainties may be incorporated using Monte Carlo simulation. It is argued that analogous approaches can be implemented for other assessment models of simple to medium complexity justifying wider use of spreadsheets in fisheries analysis and training.