Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings

The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider several aspects of these groups: First, their systematic construction from associative algebras, secondly, their suitability for the characterization of wavefront sets, and finally, the question of constructing embeddings into the symplectic group in a way that intertwines the quasi-regular representation with the metaplectic one. For all questions, it is possible to treat the full class of generalized shearlet groups in a comprehensive and unified way, thus generalizing known results to an infinity of new cases. Our presentation emphasizes the interplay between the algebraic structure underlying the construction of the shearlet dilation groups, the geometric properties of the dual action, and the analytic properties of the associated shearlet transforms.Comment: 28 page

A Probabilistic proof of the breakdown of Besov regularity in LL-shaped domains

{We provide a probabilistic approach in order to investigate the smoothness of the solution to the Poisson and Dirichlet problems in $L$-shaped domains. In particular, we obtain (probabilistic) integral representations for the solution. We also recover Grisvard's classic result on the angle-dependent breakdown of the regularity of the solution measured in a Besov scale

Distillation column dynamics and control

A pilot plant scale, atmospheric pressure, sieve plate distillation column was constructed and fully instrumented. Novel speed controllable pumps were used to control liquid flows. A microcomputer was constructed to provide local and hierarchical control of the column. The microcomputer included an operator console, a 16 channel data acquisition unit, a 4 channel control output unit, and a hardware arithmetic processor. A software development system was assembled by linking the microcomputer to a minicomputer. Software written for the development system included a cross-assembler, a transfer program, and a microcomputer control program. A binary steady state distillation column model was developed, solved on a digital computer, and verified against experimental data using a binary mixture of methanol and water. Two control schemes were investigated using only the microcomputer resources. A multi-loop system using digital PI controllers was found to give excellent control within the accuracy of the instrumentation. An adaptive feedforward controller was proposed and verified using a steady state model, and experiments. The results were good, but because of the relatively simple dynamics of the experimental column, the feedforward controller was no better than the feedback controllers. A microcomputer control system has been shown to be an effective replacement for conventional analog control on a distillation column. The computing power of the microcomputer has enabled a sophisticated control scheme to be implemented at low cost

Integration of Pasturing Systems for Cattle Finishing Programs—A Progress Report

This progress report is an introduction to a study to evaluate the incorporation of rotational pasturing systems into cattle finishing programs. Because the first year is still in progress and the first trial is not complete, few data are available. However, there is a suggestion that feeding an ionophore to young calves on pasture may result in improved daily gains

Early life stages of an arctic keystone species (Boreogadus saida) show high sensitivity to a water-soluble fraction of crude oil

Source: doi: 10.1016/j.envpol.2016.07.044Increasing anthropogenic activities in the Arctic represent an enhanced threat for oil pollution in a marine environment that is already at risk from climate warming. In particular, this applies to species with free-living pelagic larvae that aggregate in surface waters and under the sea ice where hydrocarbons are likely to remain for extended periods of time due to low temperatures. We exposed the positively buoyant eggs of polar cod (Boreogadus saida), an arctic keystone species, to realistic concentrations of a crude oil water-soluble fraction (WSF), mimicking exposure of eggs aggregating under the ice to oil WSF leaking from brine channels following encapsulation in ice. Total hydrocarbon and polycyclic aromatic hydrocarbon levels were in the ng/L range, with most exposure concentrations below the limits of detection throughout the experiment for all treatments. The proportion of viable, free-swimming larvae decreased significantly with dose and showed increases in the incidence and severity of spine curvature, yolk sac alterations and a reduction in spine length. These effects are expected to compromise the motility, feeding capacity, and predator avoidance during critical early life stages for this important species. Our results imply that the viability and fitness of polar cod early life stages is significantly reduced when exposed to extremely low and environmentally realistic levels of aqueous hydrocarbons, which may have important implications for arctic food web dynamics and ecosystem functioning

A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.Comment: 32 page

A wavelet based numerical method for nonlinear partial differential equations

The purpose of this paper is to present a wavelet–Galerkin scheme for solving nonlinear elliptic partial differential equations. We select as trial spaces a nested sequence of spaces from an appropriate biorthogonal multiscale analysis. This gives rise to a nonlinear discretized system. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets to obtain knot oriented quadrature rules. Finally, Newton’s method is applied to approximate the solution in the given ansatz space. The results of some numerical experiments with different biorthogonal systems, confirming the applicability of our scheme, are presented.Instituto de Cooperação Científica e Tecnológica Internacional - Acções Integradas Luso-Alemãs (DAAD/ICCTI) - Projecto DAAD/ICCTI nº 01141

Induced Crystallization of Polyelectrolyte-Surfactant Complexes at the Gas-Water Interface

Synchrotron-X-ray and surface tension studies of a strong polyelectrolyte (PE) in the semi-dilute regime (~ 0.1M monomer-charges) with varying surfactant concentrations show that minute surfactant concentrations induce the formation of a PE-surfactant complex at the gas/solution interface. X-ray reflectivity and grazing angle X-ray diffraction (GIXD) provide detailed information of the top most layer, where it is found that the surfactant forms a two-dimensional liquid-like monolayer, with a noticeable disruption of the structure of water at the interface. With the addition of salt (NaCl) columnar-crystals with distorted-hexagonal symmetry are formed.Comment: 4 pages, 5 eps figure

Additional Laparotomy Sponges Requested During Cesarean Delivery: \u27Early Warning\u27 Associated with Postpartum Hemorrhage

https://digitalcommons.unmc.edu/emet_posters/1015/thumbnail.jp

Using Real-Time Ultrasound During the Feeding Period to Predict Cattle Composition.

A feedlot trial to monitor ribeye area growth, 12th rib backfat, and intramuscular fat accretion was conducted. Data were collected using 112 yearling beef steers. The steers were fed at three intake levels (ad libitum, 95% of ad libitum, or 90% of ad libitum), which when combined with three feeding times (once daily in the morning, once daily in the afternoon, or twice daily), produced nine dietary treatments. Feedlot performance and carcass composition of beef steers was also determined. After analysis of ultrasound measures and animal performance data, equations were developed that described the ribeye area development (R2 = .97), 12th rib fat accretion (R2 = .81), and changes in intramuscular fat percentage (R2 = .79)