Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat’s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Low-dimensional modeling of streaks in a wedge flow boundary layer

This paper is concerned with the low dimensional structure of optimal streaks in a wedge flow boundary layer, which have been recently shown to consist of a unique (up to a constant factor) three-dimensional streamwise evolving mode, known as the most unstable streaky mode. Optimal streaks exhibit a still unexplored/unexploited approximate self-similarity (not associated with the boundary layer self-similarity), namely the streamwise velocity re-scaled with their maximum remains almost independent of both the spanwise wavenumber and the streamwise coordinate; the remaining two velocity components instead do not satisfy this property. The approximate self-similar behavior is analyzed here and exploited to further simplify the description of optimal streaks. In particular, it is shown that streaks can be approximately described in terms of the streamwise evolution of the scalar amplitudes of just three one-dimensional modes, providing the wall normal profiles of the streamwise velocity and two combinations of the cross flow velocity components; the scalar amplitudes obey a singular system of three ordinary differential equations (involving only two degrees of freedom), which approximates well the streamwise evolution of the general streaks.

Lithologic Control on the Scaling Properties of the First-Order Streams of Drainage Networks: A Monofractal Analysis

The movement of water through the landscape can be investigated at different scales. This study dealt with the interrelation between bedrock lithology and the geometry of the overlying drainage systems. Parameters of fractal analysis, such as fractal dimension and lacunarity, were used to measure and quantify this relationship. The interrelation between bedrock lithology and the geometry of the drainage systems has been widely studied in the last decades. The quantification of this linkage has not yet been clearly established. Several studies have selected river basins or regularly shaped areas as study units, assuming them to be lithologically homogeneous. This study considered irregular distributions of rock types, establishing areas of the soil map (1:25,000) with the same lithologic information as study units. The tectonic stability and the low climatic variability of the study region allowed effective investigation of the lithologic controls on the drainage networks developed on the plutonic rocks, the metamorphic rocks, and the sedimentary materials existing in the study area. To exclude the effect of multiple in- and outflows in the lithologically homogeneous units, we focused this study on the first-order streams of the drainage networks. The geometry of the hydrologic features was quantified through traditional metrics of fluvial geomorphology and scaling parameters of fractal analysis, such as the fractal dimension, the reference density, and the lacunarity. The results demonstrate the scale invariance of both the drainage networks and the set of first-order streams at the study scale and a relationship between scaling in the lithology and the drainage network.

New systems of management to improve the health and welfare of rabbits in farm conditions = Nuevos sistemas de cría y manejo para mejorar la salud y bienestar de conejos de granja

El objetivo general de esta Tesis Doctoral fue evaluar nuevos sistemas de alojamiento y cría de conejos de granja, estudiando tanto parámetros comportamentales (experimento 1) como productivos y reproductivos (experimento 3). Además, se evaluaron diferentes técnicas de muestreo con el fin de optimizar el tiempo empleado para el estudio del comportamiento animal (experimento 2). En el experimento 1, se estudió el comportamiento de conejas alojadas en dos tipos de jaulas (TJ), convencionales vs. alternativas con una plataforma elevada, en distintos estados fisiológicos (EF), lactantes y gestantes. Se observó el comportamiento de 12 conejas reproductoras con grabaciones de una duración de 24 h continuas. Independientemente del EF y TJ, las conejas pasaron gran parte de su tiempo sobre el reposapatas (57,7 %, de media). Sin embargo, debido al uso de la plataforma (23,0% del tiempo, de media), las conejas lactantes permanecieron un 36,6 % menos de tiempo (P<0,001) sobre el reposapatas y las gestantes un 27,0% menos (P<0,001) sobre el enrejillado en jaulas alternativas que en convencionales. En las jaulas alternativas, las conejas podían adoptar la postura “levantada”, sin embargo ésta fue observada solamente en conejas gestantes una media de 4,6 veces al día. Las conejas bebieron con mas frecuencia en jaulas convencionales que en alternativas (24,6 vs 19,1 veces al día; P<0,05). Se observó una mayor duración y frecuencia del comportamiento “interactuando con compañeras” en conejas gestantes alojadas en jaulas convencionales (276 s/d y 4,6 veces/d; P<0,05). La frecuencia de “interactuando con gazapos” fue menor en jaulas alternativas que en convencionales (2,4 vs 8,6 veces al día; P<0,01). La hora del día afectó al comportamiento de las conejas, teniendo un comportamiento menos activo durante las horas centrales del día. Durante las horas de oscuridad, las conejas estuvieron más inquietas realizando comportamientos como ‘encabritarse’ o amamantar, coincidiendo éstos en el tiempo en el cual las conejas pasaron más tiempo en la plataforma. Las conejas utilizaron frecuentemente la plataforma, independientemente del estado fisiológico. En la fase de lactación, las conejas utilizaron la plataforma para huir de los intentos de mamar por parte de los gazapos cuando éstas no estaban receptivas. El uso de la plataforma puede dar lugar a problemas higiénicos debidos tanto por la acumulación de heces sobre ella como por la caída de heces y orina sobre los animales que están en la parte inferior. La ausencia de estereotipias por parte de las conejas tanto en jaulas alternativas como en convencionales no sugiere una falta de bienestar debida al sistema de alojamiento. En el experimento 2, se compararon distintos métodos de observación simplificada con respecto un método de referencia usando grabaciones continuas de 24 h para la evaluación del comportamiento de conejas en distintos estados fisiológicos (gestantes y lactantes) alojadas en dos tipos de jaulas (convencionales y alternativas). Se analizaron un total de 576 h de grabaciones continuas de 24 h en 12 conejas reproductoras al final del periodo de lactación y en las mismas conejas después del destete. Los comportamientos observados se clasificaron en tres categorías independientes (localización en la jaula, postura y comportamientos funcionales). Se utilizaron grabaciones continuas de 24 h como método de referencia para validar otros cuatro métodos de observación simplificados, utilizando grabaciones de distinta duración y frecuencia a lo largo del día. Métodos regulares: corto y largo con 2.4 y 8 h de observación respectivamente, y métodos irregulares: corto y largo con 6 y 8 h de observación, respectivamente. Como resultado, se observó que independientemente del sistema de alojamiento, el mejor método para reducir el tiempo de observación necesario para evaluar el comportamiento de conejas reproductoras depende del tipo de variable a estudiar y del estado fisiológico de las conejas. En gestantes, los métodos irregulares no fueron adecuados para estimar comportamientos de larga duración tales como tumbada, sentada, descansando y acicalándose. Sin embargo, en ambos estados fisiológicos, los métodos regulares fueron precisos para los comportamientos de los grupos localización y postura y para comportamientos funcionales de larga duración. Por otro lado, los coeficientes de variación de los comportamientos poco frecuentes realizados principalmente durante el periodo de oscuridad fueron muy altos, y el método irregular largo obtuvo los menores errores de estimación para éstos comportamientos. En el experimento 3, se estudió el efecto de un uso combinado de lactaciones largas (hasta 46 días) con jaulas alternativas sobre los parámetros productivos y reproductivos de 104 conejas y sus camadas durante cinco ciclos reproductivos. La mitad de las conejas fueron alojadas en jaulas polivalentes convencionales (39 cm x 100 cm x 30 cm) y la otra mitad en jaulas polivalentes alternativas (39 cm x 100 cm x 60 cm), con una plataforma elevada. Dentro de cada grupo de alojamiento, la mitad de las conejas se destetaron a 32 días y la otra mitad a 46 días tras el parto. Las lactaciones más largas afectaron negativamente al peso (P<0,001), contenido en grasa y energía (P<0,05) de las conejas al final del periodo de lactación, pero éste efecto disminuyó con el número de partos. La fertilidad, prolificidad y la mortalidad de las conejas no fue afectada por la duración de la lactación. El destete tardío dio lugar a un mayor tamaño y peso de la camada al final del periodo de crecimiento (8,9 y 11,3 %, respectivamente) y a un menor índice de conversión por jaula durante el todo el periodo experimental (13,5 %) con respecto al destete convencional (P<0,001). Éstos resultados fueron paralelos a la menor mortalidad global (12,6 vs 17,6 %; P<0,05) observada en gazapos con destete tardío. Las diferencias en los parámetros productivos con las distintas edades al destete sólo fueron observadas en los ciclos con peor estado sanitario (tercer y quinto ciclo), en los cuales el destete tardío redujo la mortalidad. El tipo de jaula no afectó al peso de la coneja, condición corporal, mortalidad, fertilidad ni tamaño de camada durante los cinco primeros ciclos reproductivos. Sin embargo, el peso de la camada y el índice de conversión a los 21 días de edad fueron 4,2% mayor (P<0,001) y 5,0% menor (P<0,005) en animales alojados en jaulas alternativas que en jaulas convencionales. A día 59 las jaulas alternativas dieron lugar a camadas más pesadas (P<0,01); sin embargo, éste efecto fue influenciado por la densidad alcanzada en cada ciclo, ya que cuando la densidad de los animales fue menor que 40kg/m2 (tercer y quinto ciclo), el efecto del tipo de jaula sobre el peso de la camada no fue significativo. De los resultados obtenidos se puede concluir que el uso combinado de lactaciones más largas y jaulas con mayor superficie disponible con una plataforma elevada podría ser una alternativa para mejorar el bienestar animal en determinadas situaciones productivas. ABSTRACT The general aim of this PhD Thesis was to evaluate new housing and husbandry systems of farmed rabbits, studying behavioral (experiment 1), productive and reproductive (experiment 3) parameters. Moreover, different sampling techniques were evaluated in order to optimize the assessment of rabbit behaviour (experiment 2). In experiment 1, the behaviour of rabbit does housed in two different types of cage (TC), conventional vs. alternative with an elevated platform, at different physiological stages (PS), lactation and gestation was to study. Behavioural observations were carried out on 12 commercial rabbit does using continuous 24 hour video recording. Independently of PS and TC, rabbit does spent most of their time on foot mats (57.7 %, as average). However, due to the use of platforms (23.0% of time, as average), lactating does spent 36.6% less time (P<0.001) on foot mats and gestating does spent 27.0% less (P<0.001) time on wire mesh in alternative cages than in conventional cages. Alternative cages allowed for standing posture but this behaviour was only observed in gestating does (4.6 times a day, as average). Frequency of drinking was higher in conventional than in alternative cages (24.6 vs. 19.1 times a day; P<0.05). Gestating does housed in conventional cages reached the highest duration and frequency of interacting with neighbours (276 s/d and 4.6 times/d; P<0.05). The frequency of interacting with kits was lower in alternative than in conventional cages (2.4 vs. 8.6 times a day; P<0.01). Does’ behaviour was influenced by hour of day, being less active at the midday hours. During dark hours rabbit does more frequently performed restless behaviour such as hyperactivity or nursing, matching the time at which rabbit does spent more time on the platform. The platform was frequently used by rabbit does, independent of their physiological state, and during late lactation phase, when mothers were not receptive to nursing, does housed in alternative cages used the platform as a mean to flee from kids trying to suckle. The use of the platform might lead to hygienic problems due to retained faeces on the platform and faeces and urine falling onto animals located in the lower part of the cage. Stereotypies were not observed in any housing system, therefore conventional cages do not suggest lack of animal welfare. In experiment 2, it was compared the results of different simplified sampling methods of behavioural data with respect to reference records of 24-h in order to assess rabbit does behaviours at different physiological stages (gestation and lactation) in animals housed in two types of cages (conventional and alternative). A total of 576 h of continuous video of 12 rabbit does at the end of lactation and on the same females after weaning were analysed. The behavioural observations were studied using three independent categories of classification (location in the cage, posture and functional behaviours). Continuous behavioural recordings of 24 h were considered as the reference method to validate another 4 sampling methods of data collection by aggregated video recordings of different frequency and duration (regular short and long methods with 2.4 and 8 h of observation respectively, and irregular short and long methods with 6 and 8 h of observation, respectively). The current results showed that, independently of housing system, the best method to reduce the total observation time required to assess rabbit does behaviour depends on the trait studied and physiological stage of does. In gestating does, irregular methods were not suitable to estimate behaviours of long duration such as lying, sitting, resting and grooming. However, in both physiological stages, regular methods were accurate for location behaviours, postures and functional behaviours of long duration. Instead, for the study of infrequent behaviours performed mainly during dark period, where coefficients of variation were high, the irregular long method led to the lowest mean estimation errors. In experiment 3, the effects of the combined use of long lactation periods (46 days) with alternative cages on the reproductive and growth performance of 104 rabbit does and their litters during five consecutive reproductive cycles were studied. Half of does were housed in conventional polyvalent cages (39 cm x 100 cm x 30 cm) and the other half in alternative polyvalent cages (39 cm x 100 cm x 60 cm), with a raised platform. Half of the rabbit does in each type of cages were weaned at 32 and the other half at 46 days after parturition. Longer lactations affected negatively to body weight (P<0.001), fat and energy content (P<0.05) of rabbit does at the end of the lactation period, but this effect decreased with the number of parturitions. Fertility, prolificacy and doe mortality were not affected by lactation length. Late weaning led to higher litter size (by 8.9 %) and litter weight (by 11.3 %) at the end of growing period and lower feed conversion ratio per cage during the overall experimental period (13.5 %) than standard weaning (P<0.001). These results were parallels to a lower mortality (12.6 vs 17.6 %; P<0.05) of young rabbit weaned later during the overall experimental period. Differences in performances at different weaning ages were only observed during cycles with worst health status (third and fifth cycles) in which late weaning decreased mortality. Type of cage did not affect doe body weight and body condition, mortality, fertility, prolificacy and litter size during the five firsts reproductive cycles. Nevertheless, at day 21 litter weight and feed conversion ratio were 4.2 % higher (P<0.001) and 5.0 % lower (P<0.005) in animals housed in alternative than in conventional cages. Alternative cages also led to heavier litters at 59 days (P<0.01); however, this effect was influenced by density reached in each cycle, as when the density of animals was lower than 40 kg/m2 (cycles three and five), the difference of litter weight between alternative and conventional cages was not significant. From the results obtained it can be concluded that the combined use of longer lactations and cages with higher available surface with a raised platform could be an alternative to improve animal welfare in some productive situations.

Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

Brain-derived neurotrophic factor is an endogenous modulator of nociceptive responses in the spinal cord

The primary sensory neurons that respond to noxious stimulation and project to the spinal cord are known to fall into two distinct groups: one sensitive to nerve growth factor and the other sensitive to glial cell-line-derived neurotrophic factor. There is currently considerable interest in the ways in which these factors may regulate nociceptor properties. Recently, however, it has emerged that another trophic factor—brain-derived neurotrophic factor (BDNF)—may play an important neuromodulatory role in the dorsal horn of the spinal cord. BDNF meets many of the criteria necessary to establish it as a neurotransmitter/neuromodulator in small-diameter nociceptive neurons. It is synthesized by these neurons and packaged in dense core vesicles in nociceptor terminals in the superficial dorsal horn. It is markedly up-regulated in inflammatory conditions in a nerve growth factor-dependent fashion. Postsynaptic cells in this region express receptors for BDNF. Spinal neurons show increased excitability to nociceptive inputs after treatment with exogenous BDNF. There are both electrophysiological and behavioral data showing that antagonism of BDNF at least partially prevents some aspects of central sensitization. Together, these findings suggest that BDNF may be released from primary sensory nociceptors with activity, particularly in some persistent pain states, and may then increase the excitability of rostrally projecting second-order systems. BDNF released from nociceptive terminals may thus contribute to the sensory abnormalities associated with some pathophysiological states, notably inflammatory conditions.

Dynamics of maize endosperm development and DNA endoreduplication.

Endosperm development in Zea mays is characterized by a period of intense mitotic activity followed by a period in which mitosis is essentially eliminated and the cell cycle becomes one of alternating S and G phases, leading to endoreduplication of the nuclear DNA. The endosperm represents a significant contribution to the grain yield of maize; thus, methods that facilitate the study of cellular kinetics may be useful in discerning cellular and molecular components of grain yield. Two mathematical models have been developed to describe the kinetics of endosperm growth. The first describes the kinetics of mitosis during endosperm development; the second describes the kinetics of DNA endoreduplication during endosperm development. The mitotic model is a modification of standard growth curves. The endoreduplication model is composed of six differential equations that represent the progression of nuclei from one DNA content to another during the endoreduplication process. Total nuclei number per endosperm and the number of 3C, 6C, 12C, 24C, 48C, and 96C nuclei per endosperm (C is the haploid DNA content per nucleus) for inbred W64A from 8 to 18 days after pollination were determined by flow cytometry. The results indicate that the change in number of nuclei expressed as a function of the number of days after pollination is the same from one yearly crop to another. These data were used in the model to determine the endosperm growth rate, the maximum nuclei number per endosperm, and transition rates from one C value to the next higher C value. The kinetics of endosperm development are reasonably well represented by the models. Thus, the models provide a means to quantify the complex pattern of endosperm development.

Método multigrid algébrico: reutilização das estruturas multigrid no transporte de contaminantes

A necessidade de obter solução de grandes sistemas lineares resultantes de processos de discretização de equações diferenciais parciais provenientes da modelagem de diferentes fenômenos físicos conduz à busca de técnicas numéricas escaláveis. Métodos multigrid são classificados como algoritmos escaláveis.Um estimador de erros deve estar associado à solução numérica do problema discreto de modo a propiciar a adequada avaliação da solução obtida pelo processo de aproximação. Nesse contexto, a presente tese caracteriza-se pela proposta de reutilização das estruturas matriciais hierárquicas de operadores de transferência e restrição dos métodos multigrid algébricos para acelerar o tempo de solução dos sistemas lineares associados à equação do transporte de contaminantes em meio poroso saturado. Adicionalmente, caracteriza-se pela implementação das estimativas residuais para os problemas que envolvem dados constantes ou não constantes, os regimes de pequena ou grande advecção e pela proposta de utilização das estimativas residuais associadas ao termo de fonte e à condição inicial para construir procedimentos adaptativos para os dados do problema. O desenvolvimento dos códigos do método de elementos finitos, do estimador residual e dos procedimentos adaptativos foram baseados no projeto FEniCS, utilizando a linguagem de programação PYTHONR e desenvolvidos na plataforma Eclipse. A implementação dos métodos multigrid algébricos com reutilização considera a biblioteca PyAMG. Baseado na reutilização das estruturas hierárquicas, os métodos multigrid com reutilização com parâmetro fixo e automática são propostos, e esses conceitos são estendidos para os métodos iterativos não-estacionários tais como GMRES e BICGSTAB. Os resultados numéricos mostraram que o estimador residual captura o comportamento do erro real da solução numérica, e fornece algoritmos adaptativos para os dados cuja malha retornada produz uma solução numérica similar à uma malha uniforme com mais elementos. Adicionalmente, os métodos com reutilização são mais rápidos que os métodos que não empregam o processo de reutilização de estruturas. Além disso, a eficiência dos métodos com reutilização também pode ser observada na solução do problema auxiliar, o qual é necessário para obtenção das estimativas residuais para o regime de grande advecção. Esses resultados englobam tanto os métodos multigrid algébricos do tipo SA quanto os métodos pré-condicionados por métodos multigrid algébrico SA, e envolvem o transporte de contaminantes em regime de pequena e grande advecção, malhas estruturadas e não estruturadas, problemas bidimensionais, problemas tridimensionais e domínios com diferentes escalas.

Partial differential equations.

Mode of access: Internet.

Existence theorems in partial differential equations.

"Only the material on elliptic equations will appear in these notes."

Differential equations; geometric theory.

Mode of access: Internet.

Partial differential equations,

Mimeographed.

Plane waves and spherical means applied to partial differential equations.

Bibliography: p. 165-170.

Numerical integrators for stiff and highly oscillatory differential equations /

Bibliography: p. 27-28.

VIPTRAN--a programming language and its compiler for Boolean systems or process control equations.

Thesis (M.A.)--University of Illinois at Urbana-Champaign.