Fuzzy inferring mathematical morphology and optical implementation

Fuzzification is introduced into gray-scale mathematical morphology by using two-input one-output fuzzy rule-based inference systems. The fuzzy inferring dilation or erosion is defined from the approximate reasoning of the two consequences of a dilation or an erosion and an extended rank-order operation. The fuzzy inference systems with numbers of rules and fuzzy membership functions are further reduced to a simple fuzzy system formulated by only an exponential two-input one-output function. Such a one-function fuzzy inference system is able to approach complex fuzzy inference systems by using two specified parameters within it-a proportion to characterize the fuzzy degree and an exponent to depict the nonlinearity in the inferring. The proposed fuzzy inferring morphological operators tend to keep the object details comparable to the structuring element and to smooth the conventional morphological operations. Based on digital area coding of a gray-scale image, incoherently optical correlation for neighboring connection, and optical thresholding for rank-order operations, a fuzzy inference system can be realized optically in parallel. (C) 1996 Society of Photo-Optical Instrumentation Engineers.

Optoelectronic implementation of mathematical morphology

An optoelectronic implementation based on optical neighborhood operations and electronic nonlinear feedback is proposed to perform morphological image processing such as erosion, dilation, opening, closing and edge detection. Results of a numerical simulation are given and experimentally verified.

A mathematical and experimental investigation of microcycle spectral estimates of semiconductor flicker noise

The experimental portion of this thesis tries to estimate the density of the power spectrum of very low frequency semiconductor noise, from 10^-6.3 cps to 1. cps with a greater accuracy than that achieved in previous similar attempts: it is concluded that the spectrum is 1/f^α with α approximately 1.3 over most of the frequency range, but appearing to have a value of about 1 in the lowest decade. The noise sources are, among others, the first stage circuits of a grounded input silicon epitaxial operational amplifier. This thesis also investigates a peculiar form of stationarity which seems to distinguish flicker noise from other semiconductor noise.

In order to decrease by an order of magnitude the pernicious effects of temperature drifts, semiconductor "aging", and possible mechanical failures associated with prolonged periods of data taking, 10 independent noise sources were time-multiplexed and their spectral estimates were subsequently averaged. If the sources have similar spectra, it is demonstrated that this reduces the necessary data-taking time by a factor of 10 for a given accuracy.

In view of the measured high temperature sensitivity of the noise sources, it was necessary to combine the passive attenuation of a special-material container with active control. The noise sources were placed in a copper-epoxy container of high heat capacity and medium heat conductivity, and that container was immersed in a temperature controlled circulating ethylene-glycol bath.

Other spectra of interest, estimated from data taken concurrently with the semiconductor noise data were the spectra of the bath's controlled temperature, the semiconductor surface temperature, and the power supply voltage amplitude fluctuations. A brief description of the equipment constructed to obtain the aforementioned data is included.

The analytical portion of this work is concerned with the following questions: what is the best final spectral density estimate given 10 statistically independent ones of varying quality and magnitude? How can the Blackman and Tukey algorithm which is used for spectral estimation in this work be improved upon? How can non-equidistant sampling reduce data processing cost? Should one try to remove common trands shared by supposedly statistically independent noise sources and, if so, what are the mathematical difficulties involved? What is a physically plausible mathematical model that can account for flicker noise and what are the mathematical implications on its statistical properties? Finally, the variance of the spectral estimate obtained through the Blackman/Tukey algorithm is analyzed in greater detail; the variance is shown to diverge for α ≥ 1 in an assumed power spectrum of k/|f|^α, unless the assumed spectrum is "truncated".

On some new mathematical models for infective diseases: analysis, equilibrium, positivity and vaccination controls

196 p.

Mathematical models for the prediction of temperature distributions resulting from the discharge of heated water into large bodies of water

Mathematical models for heated water outfalls were developed for three flow regions. Near the source, the subsurface discharge into a stratified ambient water issuing from a row of buoyant jets was solved with the jet interference included in the analysis. The analysis of the flow zone close to and at intermediate distances from a surface buoyant jet was developed for the two-dimensional and axisymmetric cases. Far away from the source, a passive dispersion model was solved for a two dimensional situation taking into consideration the effects of shear current and vertical changes in diffusivity. A significant result from the surface buoyant jet analysis is the ability to predict the onset and location of an internal hydraulic jump. Prediction can be made simply from the knowledge of the source Froude number and a dimensionless surface exchange coefficient. Parametric computer programs of the above models are also developed as a part of this study. This report was submitted in fulfillment of Contract No. 14-12-570 under the sponsorship of the Federal Water Quality Administration.

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.

O que há de metafísica na mecânica do século XVIII?

Ao contrário do período precedente de criação da chamada ciência moderna, o século XVIII parece não desempenhar um papel fundamental no desenvolvimento da física. Na visão de muitos autores, o século das luzes é considerado como uma fase de organização da mecânica que teve seu coroamento com as obras de Lagrange, imediatamente precedidas por Euler e dAlembert. Muitos autores afirmam que na formulação da mecânica racional houve uma eliminação gradual da metafísica e também da teologia e que o surgimento da física moderna veio acompanhado por uma rejeição da metafísica aristotélica da substância e qualidade, forma e matéria, potência e ato. O ponto central da tese é mostrar que, no século XVIII, houve uma preocupação e um grande esforço de alguns filósofos naturais que participaram da formação da mecânica, em determinar como seria possível descrever fenômenos através da matemática. De uma forma geral, a filosofia mecanicista exigia que as mudanças observadas no mundo natural fossem explicadas apenas em termos de movimento e de rearranjos das partículas da matéria, uma vez que os predecessores dos filósofos iluministas conseguiram, em parte, eliminar da filosofia natural o conceito de causas finais e a maior parte dos conceitos aristotélicos de forma e substância, por exemplo. Porém, os filósofos mecanicistas divergiam sobre as causas do movimento. O que faria um corpo se mover? Uma força externa? Uma força interna? Força nenhuma? Todas essas posições tinham seus adeptos e todas sugeriam reflexões filosóficas que ultrapassavam os limites das ciências da natureza. Mais ainda: conceitos como espaço, tempo, força, massa e inércia, por exemplo, são conceitos imprescindíveis da mecânica que representam uma realidade. Mas como a manifestação dessa realidade se torna possível? Como foram definidos esses conceitos? Embora não percebamos explicitamente uma discussão filosófica em muitos livros que versam sobre a mecânica, atitudes implícitas dessa natureza são evidentes no tratamento das questões tais como a ambição à universalidade e a aplicação da matemática. Galileu teve suas motivações e suas razões para afirmar que o livro da natureza está escrito em liguagem matemática. No entanto, embora a matemática tenha se tornado a linguagem da física, mostramos com esta tese que a segunda não se reduz à primeira. Podemos, à luz desta pesquisa, falarmos de uma mecânica racional no sentido de ser ela proposta pela razão para organizar e melhor estruturar dados observáveis obtidos através da experimentação. Porém, mostramos que essa ciência não foi, como os filósofos naturais pretendiam que assim fosse, obtidas sem hipóteses e convenções subjetivas. Por detrás de uma representação explicativa e descritiva dos fenômenos da natureza e de uma consistência interna de seus próprios conteúdos confirmados através da matemática, verificamos a presença da metafísica.