Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Partial regularity of minimizers of a functional involving forms and maps

We discuss the partial regularity of minimizers of energy functionals such as (1)/(p)integral(Omega)[sigma(u)dA(p) + (1)/(2)delu(2p)]dx, where u is a map from a domain Omega is an element of R-n into the m-dimensional unit sphere of Rm+1 and A is a differential one-form in Omega.

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

Ross River virus disease in Australia, 1886-1998, with analysis of risk factors associated with outbreaks

Ross River virus (RE) is a mosquito-borne arbovirus responsible for outbreaks of polyarthritic disease throughout Australia. To better understand human and environmental factors driving such events, 57 historical reports oil RR Outbreaks between 1896 and 1998 were examined collectively. The magnitude, regularity, seasonality, and locality of outbreaks were found to be wide ranging; however, analysis of climatic and tidal data highlighted that environmental conditions let differently ill tropical, arid, and temperate regions. Overall, rainfall seems to be the single most important risk factor, with over 90% of major outbreak locations receiving higher than average rainfall in preceding mouths. Many temperatures were close to average, particularly in tropical populations; however, in arid regions, below average maximum temperatures predominated, and ill southeast temperate regions, above average minimum temperatures predominated. High spring tides preceded coastal Outbreaks, both in the presence and absence of rainfall, and the relationship between rainfall and the Southern Oscillation Index and Lit Nina episodes suggest they may be useful predictive tools, but only ill southeast temperate regions. Such heterogeneity predisposing outbreaks supports the notion that there are different RE epidemiologies throughout Australia but also Suggests that generic parameters for the prediction and control of outbreaks are of limited use at a local level.

A Bayesian approach to imposing curvature on distance functions

The estimated parameters of output distance functions frequently violate the monotonicity, quasi-convexity and convexity constraints implied by economic theory, leading to estimated elasticities and shadow prices that are incorrectly signed, and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels. We show how a Bayesian approach can be used to impose these constraints on the parameters of a translog output distance function. Implementing the approach involves the use of a Gibbs sampler with data augmentation. A Metropolis-Hastings algorithm is also used within the Gibbs to simulate observations from truncated pdfs. Our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time-invariant. Two models-a fixed effects model and a random effects model-are developed and applied to panel data on 17 European railways. We observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed. (c) 2004 Elsevier B.V. All rights reserved.

On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

Seizure detection algorithm for neonates based on wave-sequence analysis

Objective: The description and evaluation of the performance of a new real-time seizure detection algorithm in the newborn infant. Methods: The algorithm includes parallel fragmentation of EEG signal into waves; wave-feature extraction and averaging; elementary, preliminary and final detection. The algorithm detects EEG waves with heightened regularity, using wave intervals, amplitudes and shapes. The performance of the algorithm was assessed with the use of event-based and liberal and conservative time-based approaches and compared with the performance of Gotman's and Liu's algorithms. Results: The algorithm was assessed on multi-channel EEG records of 55 neonates including 17 with seizures. The algorithm showed sensitivities ranging 83-95% with positive predictive values (PPV) 48-77%. There were 2.0 false positive detections per hour. In comparison, Gotman's algorithm (with 30 s gap-closing procedure) displayed sensitivities of 45-88% and PPV 29-56%; with 7.4 false positives per hour and Liu's algorithm displayed sensitivities of 96-99%, and PPV 10-25%; with 15.7 false positives per hour. Conclusions: The wave-sequence analysis based algorithm displayed higher sensitivity, higher PPV and a substantially lower level of false positives than two previously published algorithms. Significance: The proposed algorithm provides a basis for major improvements in neonatal seizure detection and monitoring. Published by Elsevier Ireland Ltd. on behalf of International Federation of Clinical Neurophysiology.