Schwarzian Derivative Criteria for Valence of Analytic and Harmonic Mappings

For analytic functions in the unit disk, general bounds on the Schwarzian derivative in terms of Nehari functions are shown to imply uniform local univalence and in some cases finite and bounded valence. Similar results are obtained for the Weierstrass--Enneper lifts of planar harmonic mappings to their associated minimal surfaces. Finally certain classes of harmonic mappings are shown to have finite Schwarzian norm

On the number of solutions of a transcendental equation arising in the theory of gravitational lensing

The equation in the title describes the number of bright images of a point source under lensing by an elliptic object with isothermal density. We prove that this equation has at most 6 solutions. Any number of solutions from 1 to 6 can actually occur.Comment: 26 pages, 12 figure

Nondestructive testing of bond integrity in foam insulation/aluminum composites

Nondestructive test methods are used for evaluating bond integrity of low-density polyurethane spray-on foam used as cryogenic insulation on aluminum alloy surfaces

Evaluation of ultrasonics and optimized radiography for 2219-T87 aluminum weldments

Ultrasonic studies are described which are specifically directed toward the quantitative measurement of randomly located defects previously found in aluminum welds with radiography or with dye penetrants. Experimental radiographic studies were also made to optimize techniques for welds of the thickness range to be used in fabricating the External Tank of the Space Shuttle. Conventional and innovative ultrasonic techniques were applied to the flaw size measurement problem. Advantages and disadvantages of each method are discussed. Flaw size data obtained ultrasonically were compared to radiographic data and to real flaw sizes determined by destructive measurements. Considerable success was achieved with pulse echo techniques and with 'pitch and catch' techniques. The radiographic work described demonstrates that careful selection of film exposure parameters for a particular application must be made to obtain optimized flaw detectability. Thus, film exposure techniques can be improved even though radiography is an old weld inspection method

Injectivity of sections of convex harmonic mappings and convolution theorems

In the article the authors consider the class ${\mathcal H}_0$ of sense-preserving harmonic functions $f=h+\overline{g}$ defined in the unit disk $|z|<1$ and normalized so that $h(0)=0=h'(0)-1$ and $g(0)=0=g'(0)$, where $h$ and $g$ are analytic in the unit disk. In the first part of the article we present two classes $\mathcal{P}_H^0(\alpha)$ and $\mathcal{G}_H^0(\beta)$ of functions from ${\mathcal H}_0$ and show that if $f\in \mathcal{P}_H^0(\alpha)$ and $F\in\mathcal{G}_H^0(\beta)$, then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters $\alpha$ and $\beta$ are satisfied. In the second part we study the harmonic sections (partial sums) $$s_{n, n}(f)(z)=s_n(h)(z)+\overline{s_n(g)(z)},$$ where $f=h+\overline{g}\in {\mathcal H}_0$, $s_n(h)$ and $s_n(g)$ denote the $n$-th partial sums of $h$ and $g$, respectively. We prove, among others, that if $f=h+\overline{g}\in{\mathcal H}_0$ is a univalent harmonic convex mapping, then $s_{n, n}(f)$ is univalent and close-to-convex in the disk $|z|< 1/4$ for $n\geq 2$, and $s_{n, n}(f)$ is also convex in the disk $|z|< 1/4$ for $n\geq2$ and $n\neq 3$. Moreover, we show that the section $s_{3,3}(f)$ of $f\in {\mathcal C}_H^0$ is not convex in the disk $|z|<1/4$ but is shown to be convex in a smaller disk.Comment: 16 pages, 3 figures; To appear in Czechoslovak Mathematical Journa

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)

Growth of fat slits and dispersionless KP hierarchy

A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit parameterized by harmonic moments of the latter and show that they obey an infinite set of Lax equations for the dispersionless KP hierarchy. Deformation of a fat slit under changing a particular harmonic moment can be treated as a growth process similar to the Laplacian growth of domains in the whole plane. This construction extends the well known link between solutions to the dispersionless KP hierarchy and conformal maps of slit domains in the upper half plane and provides a new, large family of solutions.Comment: 26 pages, 6 figures, typos correcte