Group Analysis of the Novikov Equation

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions

An examination of cancer-related fatigue through proposed diagnostic criteria in a sample of cancer patients in Taiwan

<p>Abstract</p> <p>Background</p> <p>Fatigue among cancer patients has often been reported in the literature; however, great variations have been documented, ranging from 15% to 90%, probably due to the lack of a widely accepted definition and established diagnostic criteria for cancer-related fatigue. The objective of this study was to evaluate the proposed International Statistical Classification of Diseases and Related Health Problems (10^threvision) (ICD-10) criteria in a sample of cancer patients from a medical center and a regional teaching hospital in northern Taiwan. More accurate prevalence estimates of CRF may result in improved diagnoses and management of one of the most common symptoms associated with cancer and its treatment.</p> <p>Methods</p> <p>Since self-reporting from patients is the most effective and efficient method to measure fatigue, the ICD-10 criteria for fatigue were used. The ICD-10 criteria questionnaire was translated into Chinese and was approved by experts. Patients were recruited from outpatient palliative and oncology clinics and from palliative and oncology inpatient units.</p> <p>Results</p> <p>Of the 265 cancer patients that were interviewed between 21 October 2008 and 28 October 2009, 228 (86%) reported having at least 2 weeks of fatigue in the past month, and further evaluation with the ICD-10 criteria showed that 132 (49.8%) had cancer-related fatigue. Internal consistency was very good, which was indicated by a Cronbach alpha of 0.843.</p> <p>Conclusion</p> <p>The prevalence of diagnosable CRF in the patients in this sample, of whom most were under palliative treatment, was 49.8%, which was probably somewhat lower than in some of the previous reports that have used less-strict criteria. In addition, among the various criteria of the proposed diagnostic criteria, the most frequently reported symptoms in our sample populations were regarding sleep disturbance and physical factors. Although they will require further replication in other samples, these formal diagnostic criteria can serve as a step toward a common language and a better understanding of the severity range of CRF.</p

Describing knowledge encounters in healthcare: a mixed studies systematic review and development of a classification

This review was self-funded

Equivalence group of a fourth-order evolution equation unifying various non-linear models

A fourth-order non-linear evolutionary partial differential equation containing several arbitrary functions of the dependent variable is considered. This equation arises as a generalization of various non-linear models describing a non-linear heat diffusion, the dynamics of thin liquid films, etc. Equivalence transformations give more flexibility to the unified model. We determine the generators of the equivalence group and use them for specifying certain types of arbitrary functions when the model equation has additional symmetries, and hence admits non-trivial group invariant solutions. (c) 2006 Elsevier B.V. All rights reserved.</p

Self-adjoint sub-classes of generalized thin film equations

In this work we consider a class of fourth-order nonlinear partial differential equation containing several tin-specified coefficient functions of the dependent variable which encapsulates various mathematical models used, e.g. for describing the dynamics of thin liquid films. We determine the subclasses of these equations which are self-adjoint. By using a general theorem on conservation laws proved by one of the authors (NHI) we find conservation laws for some of these partial differential equations without Classical Lagrangians.</p

Evaluation of manometric temperature measurement, a process analytical technology tool for freeze-drying: Part I, product temperature measurement

This study examines the factors that may cause systematic errors in the manometric temperature measurement (MTM) procedure used to evaluate product temperature during primary drying. MTM was conducted during primary drying using different vial loads, and the MTM product temperatures were compared with temperatures directly measured by thermocouples. To clarify the impact of freeze-drying load on MTM product temperatures, simulation of the MTM vapor pressure rise was performed, and the results were compared with the experimental results. The effect of product temperature heterogeneity in MTM product temperature determination was investigated by comparing the MTM product temperatures with directly measured thermocouple product temperatures in systems differing in temperature heterogeneity. Both the simulated and experimental results showed that at least 50 vials (5 mL) were needed to give sufficiently rapid pressure rise during the MTM data collection period (25 seconds) in the freeze dryer, to allow accurate determination of the product temperature. The product temperature is location dependent, with higher temperature for vials on the edge of the array and lower temperature for the vials in the center of the array. The product temperature heterogeneity is also dependent upon the freeze-drying conditions. In product temperature heterogeneous systems, MTM measures a temperature close to the coldest product temperature, even, if only a small fraction of the samples have the coldest product temperature. The MTM method is valid even at very low product temperature (−45°C)