Adjoints of composition operators with rational symbol

Building on techniques developed by Cowen and Gallardo-Guti\'{e}rrez, we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space $H^{2}$. We consider some specific examples, comparing our formula with several results that were previously known.Comment: 14 page

Arkansas Cotton Variety Test 2002

The primary aim of the Arkansas Cotton Variety Test is to provide unbiased data regarding the agronomic performance of cotton varieties and advanced breeding lines in the major cotton-growing areas of Arkansas. This information helps seed dealers establish marketing strategies and assists producers in choosing varieties to plant. In this way, the annual test facilitates the inclusion of new, improved genetic material into Arkansas cotton production. Variety adaptation is determined by evaluation of the varieties and lines at four University of Arkansas research stations located near Keiser, Clarkedale, Marianna, and Rohwer. Tests are duplicated in irrigated and non-irrigated culture at the Keiser and Marianna locations. In 2002, 37 entries were evaluated in the main test and 25 were evaluated in the first-year test. This report also includes the Mississippi County Cotton Variety Test (a large-plot, on-farm evaluation of 12 Round-up Ready varieties) and 12 other on-farm cotton variety tests conducted by the University of Arkansas Cooperative Extension Service

Surface observations for monitoring urban fossil fuel CO_2 emissions: Minimum site location requirements for the Los Angeles megacity

The contemporary global carbon cycle is dominated by perturbations from anthropogenic CO_2 emissions. One approach to identify, quantify, and monitor anthropogenic emissions is to focus on intensely emitting urban areas. In this study, we compare the ability of different CO_2 observing systems to constrain anthropogenic flux estimates in the Los Angeles megacity. We consider different observing system configurations based on existing observations and realistic near-term extensions of the current ad hoc network. We use a high-resolution regional model (Stochastic Time-Inverted Lagrangian Transport-Weather Research and Forecasting) to simulate different observations and observational network designs within and downwind of the Los Angeles (LA) basin. A Bayesian inverse method is employed to quantify the relative ability of each network to improve constraints on flux estimates. Ground-based column CO_2 observations provide useful complementary information to surface observations due to lower sensitivity to localized dynamics, but column CO_2 observations from a single site do not appear to provide sensitivity to emissions from the entire LA megacity. Surface observations from remote, downwind sites contain weak, sporadic urban signals and are complicated by other source/sink impacts, limiting their usefulness for quantifying urban fluxes in LA. We find a network of eight optimally located in-city surface observation sites provides the minimum sampling required for accurate monitoring of CO_2 emissions in LA, and present a recommended baseline network design. We estimate that this network can distinguish fluxes on 8 week time scales and 10 km spatial scales to within ~12 g C m^(–2) d^(–1) (~10% of average peak fossil CO_2 flux in the LA domain)

Glory Oscillations in the Index of Refraction for Matter-Waves

We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and nitrogen over a wide range of sodium velocities. We observe glory oscillations -- a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Definition, Capabilities, and Components of a Terrestrial Carbon Monitoring System

Research efforts for effectively and consistently monitoring terrestrial carbon are increasing in number. As such, there is a need to define carbon monitoring and how it relates to carbon cycle science and carbon management. There is also a need to identify capabilities of a carbon monitoring system and the system components needed to develop the capabilities. Capabilities that enable the effective application of a carbon monitoring system for monitoring and management purposes may include: reconciling carbon stocks and fluxes, developing consistency across spatial and temporal scales, tracking horizontal movement of carbon, attribution of emissions to originating sources, cross-sectoral accounting, uncertainty quantification, redundancy and policy relevance. Focused research is needed to integrate these capabilities for sustained estimates of carbon stocks and fluxes. Additionally, if monitoring is intended to inform management decisions, management priorities should be considered prior to development of a monitoring system

Approximate resonance states in the semigroup decomposition of resonance evolution

The semigroup decomposition formalism makes use of the functional model for $C_{.0}$ class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.Comment: LaTex 22 pages 3 figure