Mean Rational Approximation for Compact Subsets with Thin Boundaries

In 1991, J. Thomson obtained a celebrated decomposition theorem for $P^t(\mu),$ the closed subspace of $L^t(\mu)$ spanned by the analytic polynomials, when 1 \le t < \i. In 2008, J. Brennan \cite{b08} generalized Thomson's theorem to $R^t(K, \mu),$ the closed subspace of $L^t(\mu)$ spanned by the rational functions with poles off a compact subset $K$ containing the support of $\mu,$ when the diameters of the components of $\mathbb C\setminus K$ are bounded below. We obtain a necessary and sufficient condition for $R^t(K, \mu)$ to ensure such a decomposition theorem holdsComment: arXiv admin note: text overlap with arXiv:1904.06446, arXiv:2212.0539

Mean Rational Approximation for Some Compact Planar Subsets

In 1991, J. Thomson obtained celebrated structural results for $P^t(\mu).$ Later, J. Brennan (2008) generalized Thomson's theorem to $R^t(K,\mu)$ when the diameters of the components of $\mathbb C\setminus K$ are bounded below. The results indicate that if $R^t(K,\mu)$ is pure, then $R^t(K,\mu) \cap L^\infty (\mu)$ is the "same as" the algebra of bounded analytic functions on \mbox{abpe}(R^t(K, \mu)), the set of analytic bounded point evaluations. We show that if the diameters of the components of $\mathbb C\setminus K$ are allowed to tend to zero, then even though \text{int}(K) = \mbox{abpe}(R^t(K, \mu)) and $K =\overline {\text{int}(K)},$ the algebra $R^t(K,\mu) \cap L^\infty (\mu)$ may "be equal to" a proper sub-algebra of bounded analytic functions on $\text{int}(K),$ where functions in the sub-algebra are "continuous" on certain portions of the inner boundary of $K.$Comment: arXiv admin note: text overlap with arXiv:1904.0644

Effects of Buoyancy on Laminar, Transitional, and Turbulent Gas Jet Diffusion Flames

Gas jet diffusion flames have been a subject of research for many years. However, a better understanding of the physical and chemical phenomena occurring in these flames is still needed, and, while the effects of gravity on the burning process have been observed, the basic mechanisms responsible for these changes have yet to be determined. The fundamental mechanisms that control the combustion process are in general coupled and quite complicated. These include mixing, radiation, kinetics, soot formation and disposition, inertia, diffusion, and viscous effects. In order to understand the mechanisms controlling a fire, laboratory-scale laminar and turbulent gas-jet diffusion flames have been extensively studied, which have provided important information in relation to the physico-chemical processes occurring in flames. However, turbulent flames are not fully understood and their understanding requires more fundamental studies of laminar diffusion flames in which the interplay of transport phenomena and chemical kinetics is more tractable. But even this basic, relatively simple flame is not completely characterized in relation to soot formation, radiation, diffusion, and kinetics. Therefore, gaining an understanding of laminar flames is essential to the understanding of turbulent flames, and particularly fires, in which the same basic phenomena occur. In order to improve and verify the theoretical models essential to the interpretation of data, the complexity and degree of coupling of the controlling mechanisms must be reduced. If gravity is isolated, the complication of buoyancy-induced convection would be removed from the problem. In addition, buoyant convection in normal gravity masks the effects of other controlling parameters on the flame. Therefore, the combination of normal-gravity and microgravity data would provide the information, both theoretical and experimental, to improve our understanding of diffusion flames in general, and the effects of gravity on the burning process in particular

Detection of DC currents and resistance measurements in longitudinal spin Seebeck effect experiments on Pt/YIG and Pt/NFO

In this work we investigated thin films of the ferrimagnetic insulators YIG and NFO capped with thin Pt layers in terms of the longitudinal spin Seebeck effect (LSSE). The electric response detected in the Pt layer under an out-of-plane temperature gradient can be interpreted as a pure spin current converted into a charge current via the inverse spin Hall effect. Typically, the transverse voltage is the quantity investigated in LSSE measurements (in the range of \mu V). Here, we present the directly detected DC current (in the range of nA) as an alternative quantity. Furthermore, we investigate the resistance of the Pt layer in the LSSE configuration. We found an influence of the test current on the resistance. The typical shape of the LSSE curve varies for increasing test currents.Comment: 4 pages, 2 figure

Different Public Health Interventions have Varying Effects

Objective: To compare performance of one-time health interventions to those that change the probability of transitioning from one health state to another. Study Design and Setting: We used multi-state life table methods to estimate the impact of eight types of interventions on several outcomes. Results: In a cohort beginning at age 65, curing all the sick persons at baseline would increase life expectancy by 0.23 years and increase years of healthy life by .54 years. An equal amount of improvement could be obtained with a 12% decrease in the probability of getting sick, a 16% increase in the probability of a sick person recovering, a 15% decrease in the probability that a sick person dies, or a 14% decrease in the probability that a healthy person dies. Interventions aimed at keeping persons healthy increased longevity and years of healthy life, while decreasing morbidity and medical expenditures. Interventions focusing on lowering mortality had a greater effect on longevity, but increased morbidity and future medical expenditures. Results differed by the age at baseline and the relative value of a year of sick life. Conclusions: Some, but not all, interventions can improve survival while reducing morbidity and medical expenditures

Moderate joint loading reduces degenerative actions of matrix metalloproteinases in the articular cartilage of mouse ulnae

Joint loading is a recently developed loading modality, which can enhance bone formation and accelerate healing of bone fracture. Since mechanical stimulation alters expression of matrix metalloproteinases (MMPs) in chondrocytes, a question addressed herein was, does joint loading alter actions of MMPs in the articular cartilage? We hypothesized that expression and activity of MMPs are regulated in a load-intensity-dependent manner and that moderate load scan downregulates MMPs. To test this hypothesis, a mouse elbow-loading model was employed. In the articular cartilage of an ulna, the mRNA levels of a group of MMPs as well as their degenerative activities were determined. The result revealed that elbow loading altered the expression and activities of MMPs depending on its loading intensity. Collectively, the data in this study indicate that 0.2 and 0.5 N joint loading significantly reduced the expression of multiple MMPs, that is, MMP-1, MMP-3, MMP-8, and MMP-13, and overall activities of collagenases or gelatinases in articular cartilage, while higher loads increased the expression and activity of MMP-1 and MMP-13. Furthermore, moderate loads at 1 N elevated the mRNA level of CBP/p300-interacting transactivator with ED-rich tail 2 (CITED2), but higher loads at 4 N did not induce a detectable amount of CITED2 mRNA. Since CITED2 is known to mediate the downregulation of MMP-1 and MMP-13, the result indicates that joint loading at moderate intensity reduces MMP activities through potential induction of CITED2. MMPs such as MMP-1 and MMP-13 are predominant collagenases in the pathology of osteoarthritis. Therefore, joint loading could offer an interventional regimen for maintenance of joint tissues

The effect of different public health interventions on longevity, morbidity, and years of healthy life

BACKGROUND: Choosing cost-effective strategies for improving the health of the public is difficult because the relative effects of different types of interventions are not well understood. The benefits of one-shot interventions may be different from the benefits of interventions that permanently change the probability of getting sick, recovering, or dying. Here, we compare the benefits of such types of public health interventions. METHODS: We used multi-state life table methods to estimate the impact of five types of interventions on mortality, morbidity (years of life in fair or poor health), and years of healthy life (years in excellent, very good, or good health). RESULTS: A one-shot intervention that makes all the sick persons healthy at baseline would increase life expectancy by 3 months and increase years of healthy life by 6 months, in a cohort beginning at age 65. An equivalent amount of improvement can be obtained from an intervention that either decreases the probability of getting sick each year by 12%, increases the probability of a sick person recovering by 16%, decreases the probability that a sick person dies by 15%, or decreases the probability that a healthy person dies by 14%. Interventions aimed at keeping persons healthy increased longevity and years of healthy life, while decreasing morbidity and medical expenditures. Interventions focused on preventing mortality had a greater effect on longevity, but had higher future morbidity and medical expenditures. Results differed for older and younger cohorts and depended on the value to society of an additional year of sick life. CONCLUSION: Interventions that promote health and prevent disease performed well, but other types of intervention were sometimes better. The value to society of interventions that increase longevity but also increase morbidity needs further research. More comprehensive screening and treatment of new Medicare enrollees might improve their health and longevity without increasing future medical expenditures