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).

Solvability of singular second order m-point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

The impact of computer display height and desk design on 3D posture during information technology work by young adults

Computer display height and desk design to allow forearm support are two critical design features of workstations for information technology tasks. However there is currently no 3D description of head and neck posture with different computer display heights and no direct comparison to paper based information technology tasks. There is also inconsistent evidence on the effect of forearm support on posture and no evidence on whether these features interact. This study compared the 3D head, neck and upper limb postures of 18 male and 18 female young adults whilst working with different display and desk design conditions. There was no substantial interaction between display height and desk design. Lower display heights increased head and neck flexion with more spinal asymmetry when working with paper. The curved desk, designed to provide forearm support, increased scapula elevation/protraction and shoulder flexion/abduction.

Validation and patient acceptance of a computer touch screen version of the WOMAC 3.1 osteoarthritis index

Objectives: To validate the WOMAC 3.1 in a touch screen computer format, which applies each question as a cartoon in writing and in speech (QUALITOUCH method), and to assess patient acceptance of the computer touch screen version. Methods: The paper and computer formats of WOMAC 3.1 were applied in random order to 53 subjects with hip or knee osteoarthritis. The mean age of the subjects was 64 years ( range 45 to 83), 60% were male, 53% were 65 years or older, and 53% used computers at home or at work. Agreement between formats was assessed by intraclass correlation coefficients (ICCs). Preferences were assessed with a supplementary questionnaire. Results: ICCs between formats were 0.92 (95% confidence interval, 0.87 to 0.96) for pain; 0.94 (0.90 to 0.97) for stiffness, and 0.96 ( 0.94 to 0.98) for function. ICCs were similar in men and women, in subjects with or without previous computer experience, and in subjects below or above age 65. The computer format was found easier to use by 26% of the subjects, the paper format by 8%, and 66% were undecided. Overall, 53% of subjects preferred the computer format, while 9% preferred the paper format, and 38% were undecided. Conclusion: The computer format of the WOMAC 3.1 is a reliable assessment tool. Agreement between computer and paper formats was independent of computer experience, age, or sex. Thus the computer format may help improve patient follow up by meeting patients' preferences and providing immediate results.

Global behavior of positive solutions of nonlinear three-point boundary value problems

We investigate the structure of the positive solution set for nonlinear three-point boundary value problems of the form u('') + h(t) f(u) = 0, u(0) = 0, u(1) = lambdau(eta), where eta epsilon (0, 1) is given lambda epsilon (0, 1/n) is a parameter, f epsilon C ([0, infinity), [0, infinity)) satisfies f (s) > 0 for s > 0, and h epsilon C([0, 1], [0, infinity)) is not identically zero on any subinterval of [0, 1]. Our main results demonstrate the existence of continua of positive solutions of the above problem. (C) 2004 Elsevier Ltd. All rights reserved.

Efficient accommodation of local minima in watershed model calibration

The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not, in fact, optimized at all. This can seriously degrade its utility in the calibration of watershed models where local optima abound. Nevertheless, the method also has advantages, chief among these being its model-run efficiency, and its ability to report useful information on parameter sensitivities and covariances as a by-product of its use. It is also easily adapted to maintain this efficiency in the face of potential numerical problems (that adversely affect all parameter estimation methodologies) caused by parameter insensitivity and/or parameter correlation. The present paper presents two algorithmic enhancements to the GML method that retain its strengths, but which overcome its weaknesses in the face of local optima. Using the first of these methods an intelligent search for better parameter sets is conducted in parameter subspaces of decreasing dimensionality when progress of the parameter estimation process is slowed either by numerical instability incurred through problem ill-posedness, or when a local objective function minimum is encountered. The second methodology minimizes the chance of successive GML parameter estimation runs finding the same objective function minimum by starting successive runs at points that are maximally removed from previous parameter trajectories. As well as enhancing the ability of a GML-based method to find the global objective function minimum, the latter technique can also be used to find the locations of many non-global optima (should they exist) in parameter space. This can provide a useful means of inquiring into the well-posedness of a parameter estimation problem, and for detecting the presence of bimodal parameter and predictive probability distributions. The new methodologies are demonstrated by calibrating a Hydrological Simulation Program-FORTRAN (HSPF) model against a time series of daily flows. Comparison with the SCE-UA method in this calibration context demonstrates a high level of comparative model run efficiency for the new method. (c) 2006 Elsevier B.V. All rights reserved.