Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity

In this paper, we establish the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy on $\mathbb{R}^d$ in a low regularity Sobolev type space. More precisely, we reduce the regularity $s$ down to the currently known regularity requirement for unconditional uniqueness of solutions to the cubic nonlinear Schr\"odinger equation ($s\ge\frac{d}{6}$ if $d=1,2$ and $s>s_c=\frac{d-2}{2}$ if $d\ge 3$). In such a way, we extend the recent work of Chen-Hainzl-Pavlovi\'c-Seiringer.Comment: 26 pages, 1 figur

The dynamics of bose gases

textWe study the Gross-Pitaevskii (GP) hierarchy, which is an infinite sequence of coupled partial differential equations that models the dynamics of Bose gases and arises in the derivation of the cubic and quintic nonlinear Schrödinger equations from an N-body linear Schrödinger equation. In Chapter 2, we consider the cubic case in R³ and derive the GP hierarchy in the strong topology corresponding to the spaces used by Klainerman and Machedon in (82). We also prove that positive semidefiniteness of solutions is preserved over time and use this result to prove global well-posedness of solutions to the GP hierarchy. This is based on a joint work with Thomas Chen (24). In Chapters 3 and 4, we prove uniqueness of solutions to the GP hierarchy in R[superscript d] in a low regularity Sobolev type space in the cubic and quintic cases, respectively. These chapters are an extension of the work of Chen-Hainzl-Pavlović-Seiringer (17) and are based on joint works with Younghun Hong and Zhihui Xie (70,71).Mathematic

Uniqueness of solutions to the 3D quintic Gross-Pitaevskii Hierarchy

In this paper, we study solutions to the three-dimensional quintic Gross-Pitaevskii hierarchy. We prove unconditional uniqueness among all small solutions in the critical space $\mathfrak{H}^1$ (which corresponds to $H^1$ on the NLS level). With slight modifications to the proof, we also prove unconditional uniqueness of solutions to the Hartree hierarchy without smallness condition. Our proof uses the quantum de Finetti theorem, and is an extension of the work by Chen-Hainzl-Pavlovi\'c-Seiringer \cite{CHPS}, and our previous work \cite{UniqueLowReg}.Comment: 1 figure, 24 page

Latitudinal Adaptation of Switchgrass Populations

Switchgrass (Panicum virgatum L.) is a widely adapted warm-season perennial that has considerable potential as a biofuel crop. Evolutionary processes and environmental factors have combined to create considerable ecotypic differentiation in switchgrass. The objective of this study was to determine the nature of population x location interaction for switchgrass, quantifying potential differences in latitudinal adaptation of switchgrass populations. Twenty populations were evaluated for biofuel and agronomic traits for 2 yr at five locations ranging from 36 to 46° N lat. Biomass yield, survival, and plant height had considerable population x location interaction, much of which (53-65%) could be attributed to the linear effect of latitude and to germplasm groups (Northern Upland, Southern Upland, Northern Lowland, and Southern Lowland). Differences among populations were consistent across locations for maturity, dry matter, and lodging. Increasingly later maturity and the more rapid stem elongation rate of more southern-origin ecotypes (mainly lowland cytotypes) resulted in high biomass yield potential, reduced dry matter concentration, and longer retention of photosynthetically active tissue at more southern locations. Conversely, increasing cold tolerance of more northern-origin ecotypes (mainly upland cytotypes) resulted in higher survival, stand longevity, and sustained biomass yields at more northern locations, allowing switchgrass to thrive at cold, northern latitudes. Although cytotype explained much of the variation among populations and the population x location interaction, ecotypic differentiation within cytotypes accounted for considerable variation in adaption of switchgrass populations

Latitudinal and Longitudinal Adaptation of Switchgrass Populations

Switchgrass (Panicum virgatum L.) is a warmseason native grass, used for livestock feed, bioenergy, soil and wildlife conservation, and prairie restoration in a large portion of the USA. The objective of this research was to quantify the relative importance of latitude and longitude for adaptation and agronomic performance of a diverse group of switchgrass populations. Six populations, chosen to represent remnant prairie populations on two north–south transects, were evaluated for agronomic traits at 12 locations ranging from 36 to 47°N latitude and 88 to 101°W longitude. Although the population × location interactions accounted for only 10 to 31% of the variance among population means, many significant changes in ranking and adaptive responses were observed. Ground cover was greater for northern-origin populations evaluated in hardiness zones 3 and 4 and for southern-origin populations evaluated in hardiness zones 5 and 6. There were no adaptive responses related to longitude (ecoregion). Switchgrass populations for use in biomass production, conservation, or restoration should not be moved more than one hardiness zone north or south from their origin, but some can be moved east or west of their original ecoregion, if results from field tests support broad longitudinal adaptation

Latitudinal Adaptation of Switchgrass Populations

Switchgrass (Panicum virgatum L.) is a widely adapted warm-season perennial that has considerable potential as a biofuel crop. Evolutionary processes and environmental factors have combined to create considerable ecotypic differentiation in switchgrass. The objective of this study was to determine the nature of population x location interaction for switchgrass, quantifying potential differences in latitudinal adaptation of switchgrass populations. Twenty populations were evaluated for biofuel and agronomic traits for 2 yr at five locations ranging from 36 to 46° N lat. Biomass yield, survival, and plant height had considerable population x location interaction, much of which (53-65%) could be attributed to the linear effect of latitude and to germplasm groups (Northern Upland, Southern Upland, Northern Lowland, and Southern Lowland). Differences among populations were consistent across locations for maturity, dry matter, and lodging. Increasingly later maturity and the more rapid stem elongation rate of more southern-origin ecotypes (mainly lowland cytotypes) resulted in high biomass yield potential, reduced dry matter concentration, and longer retention of photosynthetically active tissue at more southern locations. Conversely, increasing cold tolerance of more northern-origin ecotypes (mainly upland cytotypes) resulted in higher survival, stand longevity, and sustained biomass yields at more northern locations, allowing switchgrass to thrive at cold, northern latitudes. Although cytotype explained much of the variation among populations and the population x location interaction, ecotypic differentiation within cytotypes accounted for considerable variation in adaption of switchgrass populations

A multimodal approach to improving human papillomavirus vaccination in a community pharmacy setting

Background: Community pharmacy has become a major access point for several types of vaccinations. Despite the success of vaccination programs like influenza, pneumococcal, and herpes zoster, the rates of human papillomavirus vaccination continue to lag. Objectives: The primary objective is to describe and report on the impact of a multimodal series of pharmacist-led educational interventions on human papillomavirus vaccination rates in a community pharmacy setting. The primary outcome of this study was change in pharmacist-delivered human papillomavirus vaccination throughout a corresponding 8-week period in 2014 and 2015. Methods: A single-center, quasi-experimental interrupted time series mixed-methods pilot study was used to investigate a pharmacist-led, multimodal educational intervention approach to improve human papillomavirus vaccination rates in the community. Results: During the 2014 control period, there were no human papillomavirus vaccines dispensed or administered according to the internal prescription dispensing software. In 2015, a total of 10 patients indicated that they were vaccinated, with 9 patients receiving their first dose and 1 patient receiving his or her second dose at the pharmacy. Pharmacist recommendation was the most reported education method for increasing patient awareness of the human papillomavirus vaccine (n = 10). Conclusion: This study demonstrates pharmacist designed, educational interventions may impact human papillomavirus vaccination rates in the community. Further community-based research with larger sample sizes is warranted to verify these results. Due to the unique barriers to human papillomavirus vaccination, a multimodal and inter-professional approach such as the one presented here is warranted

Latitudinal and Longitudinal Adaptation of Switchgrass Populations

Switchgrass (Panicum virgatum L.) is a warmseason native grass, used for livestock feed, bioenergy, soil and wildlife conservation, and prairie restoration in a large portion of the USA. The objective of this research was to quantify the relative importance of latitude and longitude for adaptation and agronomic performance of a diverse group of switchgrass populations. Six populations, chosen to represent remnant prairie populations on two north–south transects, were evaluated for agronomic traits at 12 locations ranging from 36 to 47°N latitude and 88 to 101°W longitude. Although the population × location interactions accounted for only 10 to 31% of the variance among population means, many significant changes in ranking and adaptive responses were observed. Ground cover was greater for northern-origin populations evaluated in hardiness zones 3 and 4 and for southern-origin populations evaluated in hardiness zones 5 and 6. There were no adaptive responses related to longitude (ecoregion). Switchgrass populations for use in biomass production, conservation, or restoration should not be moved more than one hardiness zone north or south from their origin, but some can be moved east or west of their original ecoregion, if results from field tests support broad longitudinal adaptation