Convexity criteria and uniqueness of absolutely minimizing functions

We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in $L^\infty.$Comment: 34 page

A new representation for non--local operators and path integrals

We derive an alternative representation for the relativistic non--local kinetic energy operator and we apply it to solve the relativistic Salpeter equation using the variational sinc collocation method. Our representation is analytical and does not depend on an expansion in terms of local operators. We have used the relativistic harmonic oscillator problem to test our formula and we have found that arbitrarily precise results are obtained, simply increasing the number of grid points. More difficult problems have also been considered, observing in all cases the convergence of the numerical results. Using these results we have also derived a new representation for the quantum mechanical Green's function and for the corresponding path integral. We have tested this representation for a free particle in a box, recovering the exact result after taking the proper limits, and we have also found that the application of the Feynman--Kac formula to our Green's function yields the correct ground state energy. Our path integral representation allows to treat hamiltonians containing non--local operators and it could provide to the community a new tool to deal with such class of problems.Comment: 9 pages ; 1 figure ; refs added ; title modifie

Modeling and Mapping Urban Evapotranspiration in the Lower Boise River Basin

Surface water demand is primarily controlled by the evapotranspiration (ET) rate, but ET rates are not regularly measured in urban environments. This complicates crucial aspects of efficient water management. I hypothesize the average annual urban ET rate is significantly lower than the surrounding agricultural ET rate, which is commonly used interchangeably with the urban rate. To test this hypothesis, I will map, model, and compare ET of urban and adjacent agricultural landscapes. Using a locally calibrated model and remote sensing data, satellite imagery will be used to create a spatially and temporally distributed ET dataset to analyze the regional ET rates

Events Indicating the Start of Behavioral Momentum in Men\u27s Division I-A Intercollegiate Basketball Games

The purpose of this study was to determine which events indicate the start of behavioral momentum in men\u27s Division I-A intercollegiate basketball games. The researcher videotaped 15 televised games, and recorded offensive and defensive events for both teams in sequence on a frequency chart. Each event was assigned a specific momentum point value. Defensive events began a period of momentum 50% of the time, and offensive events began a period of momentum 50% of the time. A chi-square analysis indicated that there was no significant difference between a defensive event and an offensive event in relation to the start of a period of behavioral momentum. Once a period of momentum was established, the team with momentum outscored the opponent 94. 7% of the time during the given momentum period. However, there was no evidence to indicate the team that established more momentum periods during a game had a better chance of winning the contest. The use of a time-out called by the non-momentum team was determined to be an effective intervention to end the period of momentum. The instrument used in this study was found to be more objective and sensitive than previously used instruments, but future research is necessary to further develop and validate an instrument to reliably measure periods of momentum

An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions

We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.Comment: 4 pages; comments added, proof simplifie

Magmatic Intrusions into the Sulfur-Rich Carmel Formation on the Colorado Plateau, USA: Implications for the Mars 2020 Mission

We report on basaltic dikes in the Colorado Plateau, which crosscut sulfate bearing sediments and compare this to Martian basalts and basaltic sediments in contact with sulfate mineralizations

An overview of Viscosity Solutions of Path-Dependent PDEs

This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations. In partic- ular, we provide a simple presentation of the current existence and uniqueness arguments in the semilinear case. We also review the stability property of this notion of solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme approximation method. Our results rely crucially on the theory of optimal stopping under nonlinear expectation. In the dominated case, we provide a self-contained presentation of all required results. The fully nonlinear case is more involved and is addressed in [12]