Lyapunov stability and its application to systems of ordinary differential equations

An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem

Thermomechanical effects in high-speed seal rubs

The analytical effort was aimed at development of numerical model of thermal and mechanical phenomena which occur during seal rub. Finite element programs were develped for studying the temperatures that result from frictional heating during rubs, and the plastic deformation which is caused by rub forces. The experiment phase was originally intended to aid in verification of the results of the analytical model. Experimental techniques were developed for measuring surface temperatures and deformations during single pass rubs. Modifications were made to the device to permit testing at both high and cryogenic temperatures. The results from the experiments are discussed

Development of freeze-thaw processing technique for disaggregation of indurated mudrocks and enhanced recovery of calcareous microfossils

Microfossil extraction from indurated mudrocks is widely acknowledged as challenging, especially for foraminifera. Here we report development of the freeze–thaw extraction method through the addition of rapid heating, detergent and ultrasound stages. We use indurated mudrock samples from the Toarcian (Early Jurassic) of Yorkshire, UK to assess the effectiveness and develop the freeze–thaw method. We compare our results from freeze–thaw with those from standard foraminifera processing techniques, including the use of hydrogen peroxide. Processing by freeze–thaw increased the degree of mudrock disaggregation and resulted in no damage or dissolution of foraminifera. Following the freeze–thaw method with treatment in white spirit and sodium hexametaphosphate aided the separation of foraminifera from the disaggregated clays and was twice as efficient as pressure washing. Samples processed with hydrogen peroxide contained damaged microfossils and an under representation of delicate calcareous foraminifera. Many other studies of indurated mudrocks have used hydrogen peroxide to extract foraminifera, and this might have resulted in apparently barren intervals. The freeze–thaw method outlined here provides a low-cost, low-risk and successful method of disaggregating and extracting calcareous microfossils from indurated mudrocks. We anticipate our method may be relevant for other fossil groups and merits further development

Regional distribution of type II Ca^(2+)/calmodulin-dependent protein kinase in rat brain

The distribution of type II Ca^(2+)/calmodulin-dependent protein kinase has been mapped in rat brain by immunochemical and immunohistochemical methods using an antibody against its alpha-subunit. The concentration of the kinase, measured by radioimmunoassay, varies markedly in different brain regions. It is most highly concentrated in the telencephalon where it comprises approximately 2% of the total hippocampal protein, 1.3% of cortical protein, and 0.7% of striatal protein. It is less concentrated in lower brain structures, ranging from about 0.3% of hypothalamic protein to 0.1% of protein in the pons/medulla. The gradient of staining intensity observed in brain sections by immunohistochemistry corroborates this distribution. Neurons and neuropil of the hippocampus are densely stained, whereas little staining is observed in lower brain regions such as the superior colliculus. Within the diencephalon and midbrain, dense staining is observed only in thalamic nuclei and the substantia nigra. The skewed distribution of alpha-subunit appears to be due in part to the occurrence in the cerebellum and pons/medulla of forms of the kinase with a high ratio of beta- to alpha-subunits. However, most of the variation is due to the extremely high concentration of the kinase in particular neurons, especially those of the hippocampus, cortex and striatum. The unusually high expression of the kinase in these neurons is likely to confer upon them specialized responses to calcium ion that are different from those of neurons in lower brain regions

Contribution of poor blood pressure control to strokes

No abstract available

More on F versus t tests for unit roots when there is no trend

Rodrigues and Tremayne (2004) interpret a problematic size result in a Monte Carlo study reported in Elder and Kennedy (2001) as arising from Elder and Kennedy's use of an inappropriate testing equation. In expositing their result, Rodrigues and Tremayne inadvertently lead readers to believe that the Elder and Kennedy conclusion is in error. We clarify the Rodrigues and Tremayne contribution, putting the validity of the Elder and Kennedy result in proper perspective and underlining the important role played by the starting value in Monte Carlo analyses.

Investigations into the assembly behaviour of a 'rigidified': P-carboxylatocalix[4]arene

The p-carboxylatocalix[4]arenes have been shown to be versatile supramolecular building blocks capable of forming a range of bi-layers, capsules and nanoscale tubules in the solid state. Here we report the synthesis of a new 'rigidified' analogue, as well as investigations into its self-assembly and related coordination chemistry. These behaviours are reminiscent of other p-carboxylatocalix[4]arenes despite the presence of rigidifying groups at the lower-rim, suggesting that this building block may be further exploited in the assembly of a range of new metal-organic cages and coordination polymers

F versus t tests for unit roots

F tests which test jointly for a unit root and a zero intercept, and so compete against Dickey-Fuller t tests, are shown not to enhance power because they are invariant to the intercept value in the absence of a unit root. Monte Carlo results in the literature that indicate otherwise are shown to have resulted from the use of special starting values. Testing procedures that employ these F tests to enhance power should be revised.Dickey-Fuller