L'Hopital's Rule in Chemistry: Irreversible Morphing into Reversible Isothermal Expansions

L'Hopital's Rule is discussed in the cvase of an irreversible isothermal expansion.

Lee O Case's "Elements of the Phase Rule", Chapter 2

The second chapter of the Case text on the phase rule, this time dealing with two component systems, added to by the author, is presented here.

Does the Federal Reserve Follow a Non-Linear Taylor Rule?

The Taylor rule has become one of the most studied strategies for monetary policy. Yet, little is known whether the Federal Reserve follows a non-linear Taylor rule. This paper employs the smooth transition regression model and asks the question: does the Federal Reserve change its policy-rule according to the level of inflation and/or the output gap? I find that the Federal Reserve does follow a non-linear Taylor rule and, more importantly, that the Federal Reserve followed a non-linear Taylor rule during the golden era of monetary policy, 1985-2005, and a linear Taylor rule throughout the dark age of monetary policy, 1960-1979. Thus, good monetary policy is associated with a non-linear Taylor rule: once inflation approaches a certain threshold, the Federal Reserve adjusts its policy-rule and begins to respond more forcefully to inflation.

Lee O. Case's "Elements of the Phase Rule", Chapter 1, One component systems

One component systems are treated from the point of view of the Gibbs' phase rule.

Lee O Case's "Elements of the Phase Rule", Introduction and Explanation

This out of print 1939 manuscript, updated, is added to the literature with slight additions

Lee O Case's "Elements of the Phase Rule", Chapter 3

This is the last (third) chapter of the phase rule text, again altered by the author, addressing 3 and 4 compnent systems.

Rule a wife and have a wife : a comedy

by Beaumont and Fletcher. Adapted for theatrical representation, as performed at the Theatres-Royal Drury-Lane and Covent-Garden. Regulated from the prompt-books, by permission of the managers

The new African slavery; or, King Leopold's rule in Africa

by E. D. Morel

Forebrain-cerebellum interactions revealed by trace eyelid conditioning

While it is commonly assumed that brain systems receive and process information from other brain systems, there are few examples of tractable behaviors that allow such interactions to be studied. With the experiments presented in this dissertation we provide evidence that trace eyelid conditioning, a simple form of associative learning, is mediated by cerebellar learning in response to the output of persistent neural activity in the prefrontal cortex (PFC) and thus may be useful in analyses of PFC-cerebellar interactions. In a series of stimulation and reversible inactivation experiments we provide evidence that trace eyelid conditioning is mediated by cerebellar learning in response to a learned forebrain-driven input. Specifically, we provide evidence that this input is driven by the medial PFC and persists through the stimulus free trace interval of trace eyelid conditioning. In the next set of experiments we show that directly presenting the cerebellum with a pattern of input that mimics the classic persistent activity of PFC neurons reconstitutes trace eyelid conditioning, as assessed by a number of stringent tests. Finally, in set of reversible inactivation experiments, we provide evidence that bidirectional learning during trace eyelid conditioning involves the omission of the persistent, PFC-driven input that the cerebellum learns and responds to during trace eyelid conditioning. Given that persistent activity in PFC is often associated with working memory, these experiments suggest that trace eyelid conditioning may be useful in analyses of working memory mechanisms, cerebellar information processing and their interaction. To facilitate future analyses, we conclude with a working hypothesis of forebrain-cerebellum interactions during trace eyelid conditioning that addresses how persistent activity in PFC is induced and how the cerebellum decodes and uses PFC-driven input. ^

Reconnaissance survey of Galveston Bay sediments for selective nonresidual trace metals

The nonresidual concentrations of five trace metals were determined for 322 sediments that were the product of a systematic sampling program of the entire Galveston Bay system. The nonresidual component of the trace metal concentration (e.g. that fraction of the metals that can be relatively easily removed from the sediments without complete destruction of the sediment particle) was considered to be more indicative of the anthropogenic metal pollution that has impacted the Galveston Bay ecosystem.^ For spatial analysis of the metal concentrations, the Galveston Bay system was divided into nine bay-areas, based on easily definable geological and geographical characteristics. Isopleth mapping analyses of these metal concentrations indicated a direct relationship with the $<$63$\mu$m fraction of the sediment (%FINE) in all of the bay areas. Covariate regression analyses indicated that position of the sediment within the Galveston Bay system (e.g. bay-area) was a better predictor of metal concentration than %FINE. Analysis of variance of the metals versus the bay-areas indicated that the five metals maintained a relatively constant order and magnitude of concentration for all the bay-areas.^ The major shipping channels of the Galveston Bay system, with their associated vessels and transported materials, are a likely source of metal pollution. However, these channels were not depositional corridors of high metal concentration. All metal concentration highs were found to be located away from the channels and associated with %FINE highs in the deeper portions of the bay-areas.^ Disturbance of the sediments, by the proposed widening and deepening of these channels, is not predicted to remobilize the trace metals. A more likely adverse effect on the health of the Galveston Bay ecosystem would come from the increase in turbidity of the water due to the dredging and in an extension of the salt water wedge farther north into the bay system. ^

External validation study of a clinical prediction rule for ambulation outcomes after traumatic spinal cord injury

The main objective of this study was to determine the external validity of a clinical prediction rule developed by the European Multicenter Study on Human Spinal Cord Injury (EM-SCI) to predict the ambulation outcomes 12 months after traumatic spinal cord injury. Data from the North American Clinical Trials Network (NACTN) data registry with approximately 500 SCI cases were used for this validity study. The predictive accuracy of the EM-SCI prognostic model was evaluated using calibration and discrimination based on 231 NACTN cases. The area under the receiver-operating-characteristics curve (ROC) curve was 0.927 (95% CI 0.894 – 0.959) for the EM-SCI model when applied to NACTN population. This is lower than the AUC of 0.956 (95% CI 0.936 – 0.976) reported for the EM-SCI population, but suggests that the EM-SCI clinical prediction rule distinguished well between those patients in the NACTN population who were able to achieve independent ambulation and those who did not achieve independent ambulation. The calibration curve suggests that higher the prediction score is, the better the probability of walking with the best prediction for AIS D patients. In conclusion, the EM-SCI clinical prediction rule was determined to be generalizable to the adult NACTN SCI population.^