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The infinite series solution to the boundary-value problems of Laplace's equation with discontinuous Dirichlet boundary conditions was found by using the basic method of separation of variables. The merit of this paper is that the closed-form solution, or the singular similarity solution in the semi-infinite strip domain and the first-quadrant domain, can be generated from the basic infinite series solution in the rectangular domain. Moreover, based on the superposition principle, the infinite series solution in the rectangular domain can be related to the singular similarity solution in the semi-infinite strip domain. It is proven that the analytical source-type singular behavior in the infinite series solution near certain singular points in the rectangular domain can be revealed from the singular similarity solution in the semi-infinite strip domain. By extending the boundary of the rectangular domain, the infinite series solution to Laplace's equation in the first-quadrant domain can be derived to obtain the analytical singular similarity solution in a direct and much easier way than by using the methods of Fourier transform, images, and conformal mapping. [ABSTRACT FROM AUTHOR]

Abstract Background Although low back pain (LBP) among nursing staff, especially in nursing aides (NAs), has been a major health problem around the world, there is limited information on its prevalence in Taiwan. In addition, various measurements have been used to determine LBP; understanding the risk factors for each measurement of LBP is essential for prevention. This study aimed to assess the prevalence of and risk factors for different measures of LBP among NAs in Taiwan. Methods A cross-sectional study was conducted among 244 female NAs from 31 nursing homes in central Taiwan. A self-administered questionnaire, including the Nordic questionnaire and the Karasek's job content questionnaire, was used to collect data regarding five different measures of LBP and about demographic, physical and psychosocial factors. Also, on-site observation at the workplace was conducted to measure the frequency of five high risk patient-handling tasks. Results Based on the subjects' reports on the previous twelve months, the prevalence rates for pain lasting for at least one day, seeking of medical care, intense pain, sick leave, and chronic pain were 66.0%, 43.9%, 38.1%, 10.7%, and 8.6%, respectively. While multiple logistic regression analyses indicated that the risk factors varied with different measures of LBP, at least one high risk patient-handling task and one psychosocial factor were observed to be associated each LBP related measure. Three risk factors, including manual transfer of patients between bed/wheelchair and bath cart, perceived physical exertion, and psychological demands, were consistently associated with different measures of LBP. Besides, age was found to be associated with an increased risk of only chronic pain. Conclusion The prevalence of LBP among NAs in Taiwan is high and should be actively addressed. Certain manual patient-transfer tasks and psychological demands seemed to play more important roles in severe LBP (such as care seeking, intense pain, and sick leave) than in minor LBP (pain lasting for at least one day). Because different LBP related measures might be involved with different etiological risk factors, any LBP reduction interventions that aim to improve ergonomic and psychosocial work environments for NAs should take this information into consideration.