663 research outputs found

### The Kato Square Root Problem for Divergence Form Operators with Potential

The Kato square root problem for divergence form elliptic operators with
potential $V : \mathbb{R}^{n} \rightarrow \mathbb{C}$ is the equivalence
statement $\left\Vert (L + V)^{\frac{1}{2}} u\right\Vert_{2} \simeq \left\Vert
\nabla u \right\Vert_{2} + \left\Vert V^{\frac{1}{2}} u \right\Vert_{2}$, where
$L + V := - \mathrm{div} A \nabla + V$ and the perturbation $A$ is an
$L^{\infty}$ complex matrix-valued function satisfying an accretivity
condition. This relation is proved for any potential with range contained in
some positive sector and satisfying $\left\Vert |V|^{\frac{\alpha}{2}}
u\right\Vert_{2} + \left\Vert (-\Delta)^{\frac{\alpha}{2}} \right\Vert_{2}
\lesssim \left\Vert ( |V| - \Delta)^{\frac{\alpha}{2}}u \right\Vert_{2}$ for
all $u \in D(|V| -\Delta)$ and some $\alpha \in (1,2]$. The class of potentials
that will satisfy such a condition is known to contain the reverse H\"{o}lder
class $RH_{2}$ and $L^{\frac{n}{2}}(\mathbb{R}^{n})$ in dimension $n > 4$. To
prove the Kato estimate with potential, a non-homogeneous version of the
framework introduced by A. Axelsson, S. Keith and A. McIntosh for proving
quadratic estimates is developed. In addition to applying this non-homogeneous
framework to the scalar Kato problem with zero-order potential, it will also be
applied to the Kato problem for systems of equations with zero-order potential.Comment: arXiv admin note: text overlap with arXiv:1902.0110

### High School Student Athletes: If Stress is the “Lock” is Communication the “Key”

The focus of this Capstone Project was meant to analyze the possible issues high school student-athletes may face academically as well as mentally while in school. This issue is important to note because there is an increase in students participating in sports and the offered school support should reflect the growing population. An argument that was found was the possible overlook of the mental well-being of the student-athletes if they are academically succeeding or are accomplished athletes. The primary stakeholder\u27s perspectives chosen were current high school student-athletes because they can provide insight into the current issues that student-athletes face. Three themes emerged from an analysis of the data: 1) Providing student-athletes with tutors, study programs, and other resources for academic support. 2) Seasonal mental health and time management training for teachers. 3) The creation of an online platform where teachers and coaches can keep track of the student\u27s grades, homework, tests, and schedules. Three action options have suggested the creation of an online platform for the streamlining of communication between teachers, coaches, and students. is argued to be the most effective way to achieve the goals of supporting high school student-athletes

### “Faith, Hope, and Charity”: The Role of Good Faith in Construction – a Common Law Perspective

Los conflictos respecto a la “buena fe” en el desarrollo de contratos de construcción e ingeniería son comunes. Más aún, los conflictos surgen en la mayoría de jurisdicciones del mundo, tanto de common law como civil law. Este artículo aborda el enfoque asumido por el common law británico respecto al concepto legal de “buena fe”. Toma en cuenta las consecuencias de que el Derecho inglés no acepte el concepto de “buena fe” en el Derecho Comercial en general, incluso en relación con los contratos de construcción e ingeniería, y algunas de las doctrinas desarrolladas por el Derecho inglés para aminorar las potenciales graves consecuencias de que una parte ejerza sus derechos contractuales de manera abusiva. También se aborda el New Engineering Contract y otras formas contractuales que requieren expresamente a las partes actuar de buena fe.Issues of “good faith” in the performance of construction and engineering contracts are common. Moreover, “good faith” issues arise in most jurisdictions of the world, including common law and civil law jurisdictions. This paper considers the approach taken by English common law to the legal concept of “good faith”. It considers the consequences of English law not embracing “good faith” in commercial law in any general way, including in relation to construction and engineering contracts, and some of the doctrines developed by English law to ameliorate the potentially harsh consequences of a party exercising its contractual rights in an unfair manner. Consideration is also given to the New Engineering Contract and other forms of contract which expressly require parties to act in good faith

### Schrodinger Operators and the Kato Square Root Problem

The general theme of this thesis is the harmonic analysis of Schrodinger operators and its applications. We will focus on two distinct but related open problems in this field.
The first problem is the construction of potential dependent averaging operators and will be primarily considered in the first part of this thesis. Here, a Hardy-Littlewood type maximal operator adapted to the Schrodinger operator $\mathcal{L} :=-\Delta + |x|^{2}$ and acting on $L^{2}(\mathbb{R}^{n})$ is constructed. This is achieved through the use of the Gaussian grid $\Delta^{\gamma}_{0}$, constructed by J. Maas, J. van Neerven and P. Portal with the Ornstein-Uhlenbeck operator in mind. At the scale of this grid, the maximal operator will resemble the classical Hardy-Littlewood operator. At a larger scale, the constituent averaging operators of the maximal function are decomposed over the cubes from $\Delta^{\gamma}_{0}$ and weighted appropriately. Through this maximal function, a new class of weights is defined, $A_{p}^{+}$, with the property that for any $w \in A_{p}^{+}$ the heat maximal operator associated with $\mathcal{L}$ is bounded from $L^{p}(w)$ to itself. This class contains any other known class that possesses this property and contains weights of exponential growth. In particular, it is strictly larger than $A_{p}$.
The second problem that we consider is the Kato square root problem for divergence form elliptic operators with potential $V : \mathbb{R}^{n} \rightarrow \mathbb{C}$. This is the equivalence statement $\left\Vert (L + V)^{1/2} u \right\Vert \simeq \left\Vert \nabla u \right\Vert + \left\Vert V^{1/2} u \right\Vert$, where $L + V := - div (A \nabla) + V$ and the perturbation $A$ is an $L^{\infty}$ complex matrix-valued function satisfying an ellipticity condition. One possible path to a solution for this problem is by proving square function estimates for perturbations of associated non-homogeneous Dirac-type operators. At present, there is no general method to obtain such square function estimates other than for potentials bounded both from above and below. We develop such a method by adapting the homogeneous framework introduced by A. Axelsson, S. Keith and A. McIntosh. Two distinct approaches will be considered when adapting this framework. The second such approach will yield a satisfying solution to the potential dependent Kato problem for a large class of potentials with range contained in the right-half of the complex plane

### Behavioural simulation of biological neuron systems using VHDL and VHDL-AMS

The investigation of neuron structures is an incredibly difficult and complex task that yields relatively low rewards in terms of information from biological forms (either animals or tissue). The structures and connectivity of even the simplest invertebrates are almost impossible to establish with standard laboratory techniques, and even when this is possible it is generally time consuming, complex and expensive. Recent work has shown how a simplified behavioural approach to modelling neurons can allow “virtual” experiments to be carried out that map the behaviour of a simulated structure onto a hypothetical biological one, with correlation of behaviour rather than underlying connectivity. The problems with such approaches are numerous. The first is the difficulty of simulating realistic aggregates efficiently, the second is making sense of the results and finally, it would be helpful to have an implementation that could be synthesised to hardware for acceleration. In this paper we present a VHDL implementation of Neuron models that allow large aggregates to be simulated. The models are demonstrated using a system level VHDL and VHDL-AMS model of the C. Elegans locomotory system

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### Towards a method for the economic evaluation of environmental indicators in UK Integrated Arable Farming Systems

Integrated Arable Farming Systems (IAFS), which involve a reduction in the use of off-farm inputs, are attracting considerable research interest in the UK. The objectives of these systems experiments are to compare their financial performance with that from conventional or current farming practices. To date, this comparison has taken little account of any environmental benefits (or disbenefits) of the two systems. The objective of this paper is to review the assessment methodologies available for the analysis of environmental impacts. To illustrate the results of this exercise, the methodology and environmental indicators chosen are then applied to data from one of the LINK - Integrated Farming Systems experimental sites. Data from the Pathhead site in Southern Scotland are used to evaluate the use of invertebrates and nitrate loss as environmental indicators within IAFS. The results suggest that between 1992 and 1995 the biomass of earthworms fell by 28 kg per hectare on the integrated rotation and rose by 31 kg per hectare on the conventional system. This led to environmental costs ranging between £2.24 and £13.44 per hectare for the integrated system and gains of between £2.48 and £14.88 for the conventional system. In terms of nitrate, the integrated system had an estimated loss of £72.21 per hectare in comparison to £149.40 per hectare on the conventional system. Conclusions are drawn about the advantages and disadvantages of this type of analytical framework.
Keywords: Farming systems; IAFS; Environmental valuation; Economics; Earthworms; Nitrates; Soil faun

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### Integrated Arable Farming Systems and their potential uptake in the UK

Integrated Arable Farming Systems are examined from the perspective of the farmer considering the use of such techniques, and data are presented which suggest that the uptake of the approach may expose the manager to a greater degree of risk. Observations are made about the possible uptake of such systems in the UK and the implications this may have for agricultural and environmental policy in general

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### UPenn Green Living Certification

In 2013, the University of Pennsylvania launched a new sustainability certification for on-campus residents called “Green Living.” The program offers students the opportunity to receive a certification and earn rewards for making choices that reduce their environmental footprint and contribute to Penn’s Climate Action Plan goals. In order to become certified, students are asked to fill out an online survey about their habits, which gives them a gold, silver, or bronze score based on their responses. The point values assigned to each of the habits in the survey vary, similar to USGBC’s LEED certification for buildings. The certification includes actions related to waste, energy, water, transportation, purchasing, and community involvement.
In addition to giving certified students a sticker acknowledging their accomplishment, the program also includes prize incentives. Prizes for becoming certified depend on the level of certification and include coupons from local businesses and a reusable ceramic mug. Several local restaurants engaged in purchasing and operational sustainability initiatives have partnered with the university to provide coupons to certified students.
150 students were certified in the program’s first year, and in the second year, the number of certified students rose to 260, an increase of 73%. The growth of the program can be attributed to improvements to the program’s branding and marketing efforts and prize distribution methods.
Analysis of the program over the past year and a half has revealed many successes and possible improvements. This presentation will focus on the Green Living program’s development, implementation, logistics, results, and lessons learned. This presentation will be informative for other schools interested in resident engagement or creating a similar program on their campus.
Program website: http://www.upenn.edu/sustainability/get-involved/green-living-certificatio

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