Backward stability for polynomial maps with locally connected Julia sets

We study topological dynamics on unshielded planar continua with weak expanding properties at cycles for which we prove that the absence of wandering continua implies backward stability. Then we deduce from this that a polynomial with a locally connected Julia set is backward stable outside any neighborhood of its attracting and neutral cycles. For a conformal measure this easily implies that one of the following holds: 1. for -a.e. , ; 2. for -a.e. , for a critical point depending on .

     

Using ultrasonic attenuation to monitor slurry mixing in real time

Staff at Pacific Northwest National Laboratory have developed and applied a simple ultrasonic attenuation measurement to measure slurry concentration in real time during suspension of solids settled in a large tank. This paper presents a simple single frequency ultrasonic measurement technique that demonstrates the ability of ultrasonic sensors to measure slurry concentration. Sensor calibration data show that in this attenuation regime ultrasonic signal attenuation is proportional to the applied frequency and to the slurry volume fraction. Real-time measurements of ultrasonic signal attenuation were used to track the process of slurry mixing using single sensors and sensor arrays. Results from two experiments show the use of real-time measurements of ultrasonic signal attenuation to track the process of slurry mixing in situ and to track the ability to maintain a well-mixed steady state condition. Comparison of concentration means of the ultrasonic measurements with concentration means obtained from discrete extractive measurements show that the distributions overlap and cannot be statistically distinguished. The real-time ultrasonic sensor can be used as a primary measurement method or to reduce reliance upon extractive methods to measure slurry density and solids concentration.     

Ball lens coupled fiber-optic probe for depth-resolved spectroscopy of epithelial tissue

A ball lens coupled fiber-optic probe design is described for depth-resolved measurements of the fluorescence and reflectance properties of epithelial tissue. A reflectance target, fluorescence targets, and a two-layer tissue phantom consisting of fluorescent microspheres suspended in collagen are used to characterize the performance of the probe. Localization of the signal to within 300 microm of the probe tip is observed by use of reflectance and fluorescence targets in air. Differential enhancement of the fluorescence signal from the top layer of the two-layer tissue phantom is observed.     

Correlation dimension and integral do not predict epileptic seizures

Reports in the literature have indicated potential value of the correlation integral and dimension for prediction of epileptic seizures up to several minutes before electrographic onset. We apply these measures to over 2000 total hours of continuous electrocortiogram, taken from 20 patients with epilepsy, examine their sensitivity to quantifiable properties such as the signal amplitude and autocorrelation, and investigate the influence of embedding and filtering strategies on their performance. The results are compared against those obtained from surrogate time series. Our conclusion is that neither the correlation dimension nor the correlation integral has predictive power for seizures.     

Second-generation organocatalysts for the highly enantioselective dynamic kinetic resolution of azlactones

Bifunctional organocatalysts of the thiourea-tert-amine type, carrying two "matched" elements of chirality, effect the alcoholytic dynamic kinetic resolution of a variety of azlactones with up to 95% ee.     

Linear Discrepancy and Weak Discrepancy of Partially Ordered Sets

The linear discrepancy of a partially ordered set P=(X,) is the least integer k for which there exists an injection f: XZ satisfying (i) if xy then f(x)<f(y) and (ii) if xy then |f(x)–f(y)|k. This concept is closely related to the weak discrepancy of P studied previously. We prove a number of properties of linear and weak discrepancies and relate them to other poset parameters. Both parameters have applications in ranking the elements of a partially ordered set so that the difference in rank of incomparable elements is minimized.