Non-symmetric Jacobi and Wilson type polynomials

Consider a root system of type $BC_1$ on the real line $\mathbb R$ with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an $L^2$-space on $\mathbb R$ to a $L^2$-space of $\mathbb C^2$-valued functions on $\mathbb R^+$ with the Harish-Chandra measure |c(\lam)|^{-2}d\lam. By introducing a weight function of the form \cosh^{-\sig}(t)\tanh^{2k} t on $\mathbb R$ we find an orthogonal basis for the $L^2$-space on $\mathbb R$ consisting of even and odd functions expressed in terms of the Jacobi polynomials (for each fixed \sig and $k$). We find a Rodrigues type formula for the functions in terms of the Cherednik operator. We compute explicitly their Cherednik-Opdam transforms. We discover thus a new family of $\mathbb C^2$-valued orthogonal polynomials. In the special case when $k=0$ the even polynomials become Wilson polynomials, and the corresponding result was proved earlier by Koornwinder

Three Essays in Health Economics

This dissertation consists of three essays. The first essay examines the unintended consequence of Medicare pay-for-performance programs. I find evidence that the CMS case mix adjustment formula for patient experience measures in the Hospital Value-based Purchasing Program (HVBP) over-corrects (under-corrects) for the effect of patient health status on favorable survey responses for surgical (obstetric) patients, which creates scope for hospital to risk select patients on the basis of health status. Using inpatient discharge data from Pennsylvania and Maryland, I find that average patient severity increased among surgical patients and decreased among obstetric patients after the HVBP took effect. In addition, I find weak evidence of an increase in patient experience measures as a result of the HVBP, but no such effect is found for clinical process measures. In the second essay, I estimate the short-term effect of depression on labor market outcomes using data from the 2004-2009 Medical Expenditure Panel Survey. After accounting for the endogeneity of depression through a correlated random effects panel data specification, I find that depression reduces the contemporaneous probability of employment by 2.6 percentage points. I do not find evidence of a causal relationship between depression and hourly wages or weekly hours worked. In addition, I examine the effect of depression on work impairment and found that depression increases annual work loss days by about 1.4 days (33 percent), which implies that the annual aggregate productivity loses due to depression range from \$700 million to 1.4 billion in 2009 USD. In the third essay, I investigate the health impacts of unconventional natural gas development of Marcellus shale in Pennsylvania between 2001 and 2013. Through a multivariate regression analysis that compares changes in hospitalization rates over time for air pollution-sensitive disease in counties with unconventional gas wells to changes in hospitalization rates in non-well counties, I find significant associations between shale gas development and hospitalizations for acute myocardial infarction (AMI), chronic obstructive pulmonary disease (COPD), asthma, pneumonia, and upper respiratory infections (URI). These adverse effects on health are consistent with higher levels of air pollution resulting from unconventional natural gas development

Biorthogonal radial multiresolution in dimension three

AbstractIn this paper, we present the definition and the relative theorems of the biorthogonal radial multiresolution in dimension three. Unlike the orthogonal case, there exist real-valued dual radial scaling functions with compact support in the biorthogonal case. The associated Mallat algorithm can be simply performed in terms of classical biorthogonal filters

Electromechanical coupled nonlinearity and critical velocity for electromagnetic railgun

The nonlinear electromagnetic force can change the critical velocity of the projectile for a railgun. It corresponds to the resonance state in railgun. Here, the nonlinear electromechanical coupled dynamics equations for the railgun are proposed. Based on it, the equation of the nonlinear critical velocity of the projectile is given and the effects of the electromagnetic nonlinearity on the critical velocity of the projectile are investigated. Besides it, the effects of the fire velocity on the nonlinear critical velocity are studied as well. Results show that the critical velocity of the railgun system increases when the electromagnetic nonlinearity is considered, and the nonlinear critical velocity is influenced by the system parameters such as rail current, rail thickness, rail distance, etc. A FEM analysis package, ANSYS, is used to simulate dynamics performance of the railgun system and illustrate the analytical results about critical velocities of the railgun system. The results can be used to design dynamics performance of the railgun system

Metabolic engineering of yeast for increased production of cyclopropane fatty acids

Biological production of chemicals and fuels using whole cells is an important and growing segment of manufacturing and among the various forms, microorganisms are the most successfully utilized. In particular, yeasts such as Saccharomyces cerevisiae are both widely used production organisms and metabolic models for oleaginous yeasts. Fatty acid-containing lipids are one example of moderate value, highly versatile chemicals produced by yeasts that are used in a broad range of industries for lubrication, cosmetics, fuels and polymers. Production levels of standard fatty acids by yeasts has increased enormously over the past 10 years through the application of metabolic pathway engineering, flux analysis, computational approaches and to a lesser extent, bioprocessing improvements. Combined, these advances have brought yeast-based fatty acid production close to commercial reality. Functionalized fatty acids such as those containing hydroxyl or cyclopropyl groups are more valuable as chemical feedstocks and are an attractive target for yeast production as commercial supply is limited. Cyclopropane fatty acids, possessing a strained 3-membered ring and having a saturated chain, are especially attractive as they have application in cosmetics and specialty lubrication. However, cyclopropyl fatty acids present greater challenges for metabolic engineering as they are not produced naturally by yeast. Please click Additional Files below to see the full abstract

Endpoint Strichartz estimate for the kinetic transport equation in one dimension

In this Note, we consider problems of endpoint Strichartz estimates for the kinetic equation in one dimension. The fundamental result obtained in Theorem 1 is proved using two different methods: in the first we construct an explicit counterexample; in the second uses a duality argument.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000249934800003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)3ARTICLE5253-25634

LpL^p Boundedness of Commutators of Riesz Transforms associated to Schr\"{o}dinger Operator

In this paper we consider $L^p$ boundedness of some commutators of Riesz transforms associated to Schr\"{o}dinger operator $P=-\Delta+V(x)$ on $\mathbb{R}^n, n\geq 3$. We assume that $V(x)$ is non-zero, nonnegative, and belongs to $B_q$ for some $q \geq n/2$. Let $T_1=(-\Delta+V)^{-1}V,\ T_2=(-\Delta+V)^{-1/2}V^{1/2}$and$T_3=(-\Delta+V)^{-1/2}\nabla$. We obtain that$[b,T_j] (j=1,2,3)$are bounded operators on$L^p(\mathbb{R}^n)$when$p$ranges in a interval, where$b \in \mathbf{BMO}(\mathbb{R}^n)$. Note that the kernel of$T_j (j=1,2,3)$ has no smoothness.Comment: 14 pages, 0 figure

The seismically induced failure sequence of multiple components of high-speed railway bridges under different earthquake intensities

Though seismic vulnerability analysis of highway bridges is mature, there is little corresponding research on high-speed railway (HSR) bridges. The seismic vulnerability analysis of HSR bridges is very different to and more difficult than for highway bridges because the multiple components of the track structure are very complex. To fill this research gap, the authors establish a finite element (FE) model of an HSR bridge with the China railway track system II (CRTS II), which includes sliding layers, cement asphalt (CA) layers and fasteners, base plates, track plates and rails. Analytical results show that seismic responses of multiple bridge components have a linear correlation. Thus, the overall track-bridge system can be assumed to operate like a serial system. Here, the seismic response and vulnerability of various bridge components are first analyzed using the incremental dynamic analysis (IDA) method. Afterwards, the failure sequence is found by comparing the seismic vulnerability of critical bridge components. Finally, the seismic vulnerability of the overall track-bridge system is evaluated according to the upper and lower first-bounds. Results illustrate that the system vulnerability of HSR bridges, which is very different to that of highway bridges, is mainly determined by the sliding layers and fixed bearings. In particular, the serious damage of a sliding layer is caused by the uncoordinated deformation of beam ends, and fixed bearings may break down when they are exposed to strong earthquakes. The overall track-bridge system is prone to severe seismic damage when peak ground acceleration (PGA) is larger than 0.2 g

Parameter optimization of damper-friction isolation systems using concave friction distribution

The random friction distribution is an objective phenomenon and always leads to great uncertainty in seismic responses of damper-friction isolation systems. As to optimize the seismic performance, this paper artificially made the friction distribution on a contact surface to be concave. When the damper-friction isolation system was subjected to different ground motions, more regular responses, due to the concave friction distribution, were obtained comparing with the responses of the random friction distribution. The concave friction distribution is always conducive to reducing the structural relative displacement and insignificantly increasing the structural acceleration. An optimization design example of an isolation building was carried out. And the results showed that as for a structure only being sensitive to acceleration or force, significant concave friction distribution and little damping constant would be the best design combination. It resulted in a much less acceleration and an acceptable relative displacement on the structure