Dissipative Quasigeostrophic Dynamics under Random Forcing

The quasigeostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with dissipation under random forcing in bounded domains. We show that global unique solutions exist for appropriate initial data. Unlike the deterministic quasigeostrophic equation whose well-posedness is well-known, there seems no rigorous result on global existence and uniqueness of the randomly forced quasigeostrophic equation. Our work provides such a rigorous result on global existence and uniqueness, under very mild conditions.Comment: LaTeX, 15 page

Nonlocal Dynamics of Passive Tracer Dispersion with Random Stopping

We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion equation with a memory term. We have shown the exponential decay of the passive tracer concentration, under suitable conditions for the velocity field and the probability distribution of random stopping time.Comment: 7 page

Interpretation and Application of Elements of Differential Geometry and Lie Theory

Basic concepts of differential geometry and Lie theory are introduced. Lie transformation groups are applied to linear systems of differential equations and the problem of describing rigid body orientation. Linear Hamiltonian systems are then treated as a Lie system of differential equations. This theory is applied to a particular Hamiltonian system arising from a problem in control theory, the linear state regulator problem

Studies on the Thermodynamics of Ion Association in Aqueous Solutions

Studies have been made on the association in aqueous solution between divalent transition metal ions and the anions of mono-and di-carboxylic acids. The thesis is divided into four parts. In Part I the association between the nickel ion and the malonate and n-butylmalonate anions has been studied using a cell incorporating a pair of glass electrodes and a pair of silver, silver chloride electrodes. In order to determine the best activity coefficient expression to be used, both systems were studied at low concentration, activity coefficients being calculated from the Davies equation, and at constant ionic strengths of 0.03, 0.05, 0.10, 0.15 and 0.20 M. The stability constants have been extrapolated to zero ionic strength and the thermodynamic constants are compared with those determined at low concentration. Part II deals with the study of the association of the divalent nickel, cobalt and manganese ions with the glycinate and beta-alaninate anions over the temperature range of 0° to 45°C using the cell Hg/Pt/HA, NaOH, MCl2,/AgCl/Ag. Activity coefficients were calculated from the equation for various values of beta. A comparison of the results shows that for low ionic strengths consistent association constants are obtained with 0 ≤ beta ≤ 1. The constants determined with beta = 0.2 have been used in the calculation of the thermodynamic properties. The dissociations of beta-alanine have been measured over the same temperature range and the results are compared with those in the literature. Part III describes a calorimetric determination of the heats of formation of the complexes studied in Part II. The heat of solution of potassium chloride has also been determined in order to calibrate the calorimeter. Part IV consists of a general discussion of the results. The heat and entropy data are discussed in relation to ionic sizes and electronic structure and the entropies of ion-pairs have been calculated

1976: Abilene Christian College Bible Lectures - Full Text

FREEDOM IN CHRIST Being the Abilene Christian College Annual Bible Lectures 1976 Published by ABILENE CHRISTIAN COLLEGE Book Store ACC Station Abilene, Texas 7960

A simplified (modified) Duke Activity Status Index (M-DASI) to characterise functional capacity: A secondary analysis of the Measurement of Exercise Tolerance before Surgery (METS) study

Background Accurate assessment of functional capacity, a predictor of postoperative morbidity and mortality, is essential to improving surgical planning and outcomes. We assessed if all 12 items of the Duke Activity Status Index (DASI) were equally important in reflecting exercise capacity. Methods In this secondary cross-sectional analysis of the international, multicentre Measurement of Exercise Tolerance before Surgery (METS) study, we assessed cardiopulmonary exercise testing and DASI data from 1455 participants. Multivariable regression analyses were used to revise the DASI model in predicting an anaerobic threshold (AT) >11 ml kg −1 min −1 and peak oxygen consumption (VO 2 peak) >16 ml kg −1 min −1, cut-points that represent a reduced risk of postoperative complications. Results Five questions were identified to have dominance in predicting AT>11 ml kg −1 min −1 and VO 2 peak>16 ml.kg −1min −1. These items were included in the M-DASI-5Q and retained utility in predicting AT>11 ml.kg −1.min −1 (area under the receiver-operating-characteristic [AUROC]-AT: M-DASI-5Q=0.67 vs original 12-question DASI=0.66) and VO 2 peak (AUROC-VO2 peak: M-DASI-5Q 0.73 vs original 12-question DASI 0.71). Conversely, in a sensitivity analysis we removed one potentially sensitive question related to the ability to have sexual relations, and the ability of the remaining four questions (M-DASI-4Q) to predict an adequate functional threshold remained no worse than the original 12-question DASI model. Adding a dynamic component to the M-DASI-4Q by assessing the chronotropic response to exercise improved its ability to discriminate between those with VO 2 peak>16 ml.kg −1.min −1 and VO 2 peak<16 ml.kg −1.min −1. Conclusions The M-DASI provides a simple screening tool for further preoperative evaluation, including with cardiopulmonary exercise testing, to guide perioperative management

Integration of the Duke Activity Status Index into preoperative risk evaluation: a multicentre prospective cohort study.

BACKGROUND: The Duke Activity Status Index (DASI) questionnaire might help incorporate self-reported functional capacity into preoperative risk assessment. Nonetheless, prognostically important thresholds in DASI scores remain unclear. We conducted a nested cohort analysis of the Measurement of Exercise Tolerance before Surgery (METS) study to characterise the association of preoperative DASI scores with postoperative death or complications. METHODS: The analysis included 1546 participants (≥40 yr of age) at an elevated cardiac risk who had inpatient noncardiac surgery. The primary outcome was 30-day death or myocardial injury. The secondary outcomes were 30-day death or myocardial infarction, in-hospital moderate-to-severe complications, and 1 yr death or new disability. Multivariable logistic regression modelling was used to characterise the adjusted association of preoperative DASI scores with outcomes. RESULTS: The DASI score had non-linear associations with outcomes. Self-reported functional capacity better than a DASI score of 34 was associated with reduced odds of 30-day death or myocardial injury (odds ratio: 0.97 per 1 point increase above 34; 95% confidence interval [CI]: 0.96-0.99) and 1 yr death or new disability (odds ratio: 0.96 per 1 point increase above 34; 95% CI: 0.92-0.99). Self-reported functional capacity worse than a DASI score of 34 was associated with increased odds of 30-day death or myocardial infarction (odds ratio: 1.05 per 1 point decrease below 34; 95% CI: 1.00-1.09), and moderate-to-severe complications (odds ratio: 1.03 per 1 point decrease below 34; 95% CI: 1.01-1.05). CONCLUSIONS: A DASI score of 34 represents a threshold for identifying patients at risk for myocardial injury, myocardial infarction, moderate-to-severe complications, and new disability