About Strictly Hyperbolic Operators with Non-Regular Coefficients

2002 Mathematics Subject Classification: 35L15, 35L80, 35S05, 35S30

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Determination of quenching coefficients in a hydrogen RF discharge by time-resolved optical emission spectroscopy

In gas discharges at elevated pressure, radiation-less collisional de-excitation (quenching) has a strong influence on the population of excited states. The knowledge of quenching coefficients is therefore important for plasma diagnostics and simulations. A novel time-resolved optical emission spectroscopic (OES) technique allows the measurement of quenching coefficients for emission lines of various species, particularly of noble gases, with molecular hydrogen as collision partner. The technique exploits the short electron impact excitation during the field reversal phase within the sheath region of a hydrogen capacitively coupled RF discharge at 13.56 MHz. Quenching coefficients can be determined subsequent to this excitation from the effective lifetime of the fluorescence decay at various hydrogen pressures. The measured quenching coefficients agree very well with results obtained by means of laser excitation. The time-resolved OES technique based on electron impact excitation is not limited - in contrast to laser techniques - by optical selection rules and the energy gap between the ground state and the observed excited level.

Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series

We consider the problem of testing whether the observations X1, ..., Xn of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry-Esséen-Zolotarev bounds. The bounds are exact in finite samples, distribution-free and easy to compute. The performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment. The procedures proposed are applied to U.S. data on interest rates (commercial paper rate).

Time-varying coefficients in the almost ideal demand system: An empirical appraisal

This paper provides a generalisation of the structural time series version of the Almost Ideal Demand System (AIDS) that allows for time-varying coefficients (TVC/AIDS) in the presence of cross-equation constraints. An empirical appraisal of the TVC/AIDS is made using a dynamic AIDS with trending intercept as the baseline model with a data set from the Italian Household Budget Survey (1986-2001). The assessment is based on four criteria: adherence to theoretical constraints, statistical diagnostics on residuals, forecasting performance and economic meaningfulness. No clear evidence is found for superior performance of the TVC/AIDS, apart from improved short-term forecasts.

Solving the non-convexity problem in some shopping-time and human-capital models

Several works in the shopping-time and in the human-capital literature, due to the nonconcavity of the underlying Hamiltonian, use Örst-order conditions in dynamic optimization to characterize necessity, but not su¢ ciency, in intertemporal problems. In this work I choose one paper in each one of these two areas and show that optimality can be characterized by means of a simple aplication of Arrowís (1968) su¢ ciency theorem.

AN EMPIRICAL ESTIMATION OF MEDICAL AND NON-MEDICAL INPUTS IN THE PRODUCTION OF CARDIO-RESPIRATORY PHYSICAL HEALTH STATUS

The purpose of this study was to examine, in the context of an economic model of health production, the relationship between inputs (health influencing activities) and fitness.^ Primary data were collected from 204 employees of a large insurance company at the time of their enrollment in an industrially-based health promotion program. The inputs of production included medical care use, exercise, smoking, drinking, eating, coronary disease history, and obesity. The variables of age, gender and education known to affect the production process were also examined. Two estimates of fitness were used; self-report and a physiologic estimate based on exercise treadmill performance. Ordinary least squares and two-stage least squares regression analyses were used to estimate the fitness production functions.^ In the production of self-reported fitness status the coefficients for the exercise, smoking, eating, and drinking production inputs, and the control variable of gender were statistically significant and possessed theoretically correct signs. In the production of physiologic fitness exercise, smoking and gender were statistically significant. Exercise and gender were theoretically consistent while smoking was not. Results are compared with previous analyses of health production. ^

Non-Maxwellian electron distributions in time-dependent simulations of low-Z materials illuminated by a high-intensity X-ray laser

The interaction of high intensity X-ray lasers with matter is modeled. A collisional-radiative timedependent module is implemented to study radiation transport in matter from ultrashort and ultraintense X-ray bursts. Inverse bremsstrahlung absorption by free electrons, electron conduction or hydrodynamic effects are not considered. The collisional-radiative system is coupled with the electron distribution evolution treated with a Fokker-Planck approach with additional inelastic terms. The model includes spontaneous emission, resonant photoabsorption, collisional excitation and de-excitation, radiative recombination, photoionization, collisional ionization, three-body recombination, autoionization and dielectronic capture. It is found that for high densities, but still below solid, collisions play an important role and thermalization times are not short enough to ensure a thermal electron distribution. At these densities Maxwellian and non-Maxwellian electron distribution models yield substantial differences in collisional rates, modifying the atomic population dynamics.

Laminar heat transfer to non-Newtonian fluids in pipes with abrupt changes in diameter

In this thesis the results of experimental work performed to determine local heat transfer coefficients for non-Newtonian fluids in laminar flow through pipes with abrupt discontinuities are reported. The fluids investigated were water-based polymeric solutiorrs of time-indpendent, pseudoplastic materials, with flow indices "n" ranging from 0.39 to 0.9.The tube configurations were a 3.3 :1 sudden convergence, and a 1: 3.3 sudden divergence.The condition of a prescribed uniform wall heat flux was considered, with both upstream and downstream tube sections heated. Radial temperature traverses were also under­ taken primarily to justify the procedures used in estimating the tube wall and bulk fluid temperatures and secondly to give further insight into the mechanism of heat transfer beyond a sudden tube expansion. A theoretical assessment of the influence of viscous dissipation on a non-Newtonian pseudoplastic fluid of' arbitrary index "n" was carried out. The effects of other secondary factors such as free convection and temperature-dependent consistency were evaluated empirically. In the present investigations, the test conditions were chosen to minimise the effects of natural convection and the estimates of viscous heat generation showed the effect to be insignificant with the polymeric concentrations tested here. The final results have been presented as the relationships between local heat transfer coef'ficient and axial distance downstream of the discontinuities and relationships between dimensionless wall temperature and reduced radius. The influence of Reynolds number, Prandtl number, non-Newtonian index and heat flux have been indicated.

A qualitative study of the determinants of dieting and non-dieting approaches in overweight/obese Australian adults.

Background Dieting has historically been the main behavioural treatment paradigm for overweight/obesity, although a non-dieting paradigm has more recently emerged based on the criticisms of the original dieting approach. There is a dearth of research contrasting why these approaches are adopted. To address this, we conducted a qualitative investigation into the determinants of dieting and non-dieting approaches based on the perspectives and experiences of overweight/obese Australian adults. Methods Grounded theory was used inductively to generate a model of themes contrasting the determinants of dieting and non-dieting approaches based on the perspectives of 21 overweight/obese adults. Data was collected using semi-structured interviews to elicit in-depth individual experiences and perspectives. Results Several categories emerged which distinguished between the adoption of a dieting or non-dieting approach. These categories included the focus of each approach (weight/image or lifestyle/health behaviours); internal or external attributions about dieting failure; attitudes towards established diets, and personal autonomy. Personal autonomy was also influenced by another category; the perceived knowledge and self-efficacy about each approach, with adults more likely to choose an approach they knew more about and were confident in implementing. The time perspective of change (short or long-term) and the perceived identity of the person (fat/dieter or healthy person) also emerged as determinants of dieting or non-dieting approaches respectively. Conclusions The model of determinants elicited from this study assists in understanding why dieting and non-dieting approaches are adopted, from the perspectives and experiences of overweight/obese adults. Understanding this decision-making process can assist clinicians and public health researchers to design and tailor dieting and non-dieting interventions to population subgroups that have preferences and characteristics suitable for each approach.