Particular solutions of singularly perturbed partial differential equations with constant coefficients in rectangular domains, Part I. Convergence analysis

AbstractThe technique of separation of variables is used to derive explicit particular solutions for constant coefficient, singularly perturbed partial differential equations (PDEs) on a rectangular domain with Dirichlet boundary conditions. Particular solutions and exact solutions in closed form are obtained. An analysis of convergence for the series solutions is performed, which is useful in numerical solution of singularly perturbed differential equations for moderately small values of ε (e.g., ε=0.1–10−4). Two computational models are designed deliberately: Model I with waterfalls solutions and Model II with wedding-gauze solutions. Model II is valid for very small ε (e.g., ε=10−7), but Model I for a moderately small ε(=0.1–10−4). The investigation contains two parts. The first part, reported in the present paper, focuses on the convergence analysis and some preliminary numerical experiments for both of the models, while the second part, to be reported in a forthcoming paper, will illustrate the solutions near the boundary layers

Functional Characterization of a Chicken Major Histocompatibility Complex Class II B Gene Promoter

A 0.7 kilobase (kb) DNA fragment from the 5\u27 flanking region of a chicken major histocompatibility complex (MHC) class II B gene was cloned into chloramphenicol acetyltransferase (CAT) reporter vectors and was transfected into a chicken macrophage cell line that expresses a low level of MHC class II antigens. Positive orientation-dependent promoter activity of the chicken DNA was evident in a reporter construct containing an SV40 enhancer. Deletion analysis of this 0.7 kb DNA fragment revealed a short fragment in the 3\u27 end that was crucial for the promoter function and negative regulatory elements (NRE) located further upstream. The conserved MHC class II X and Y boxes did not have a significant effect on promoter activity. Sequence analysis of the 0.7 kb class II B gene upstream region suggests possible involvement of interferon (IFN), E twenty-six specific (ETS)-related proteins, and other factors in regulating this promoter. A chicken T-cell line culture supernatant increased surface expression of MHC class II antigens, as well as class II promoter activity, in this macrophage cell line. This first functional characterization of a chicken MHC class II B gene promoter will aid in understanding the regulatory mechanisms that control the expression of these genes

Clinical Study The Clinical Investigation of Disparity of Utility Values Associated with Gallstone Disease: A Pilot Study

. Purpose. The utility evaluation was an effective method to incorporate all of the contributing variables for multiple diseases into one outcome measure. A cross-sectional study was conducted to assess the utility values associated with varying states of gallstone disease among outpatient clinics participants at a teaching hospital in Taipei, Taiwan. Methods. The utility values were measured by using time trade-off method. A total of 120 outpatient clinics participants (30 subjects with no gallstone disease, 30 subjects with single stone, 30 subjects with multiple stones, and 30 subjects with cholecystectomy) evaluated utility values from January 1, 2006 to December 31, 2006. The diagnosis of gallstone disease was performed by a panel of specialists using ultrasound sonography. Results. The overall mean utility value was 0.89 ± 0.13 (95% CI: 0.87-0.91) indicating that study participants were willing to trade about 11% (95% CI: 9-13%) of their remaining life in return for being free of gallstone disease perpetually. The significant associated factors of utility values based on the multiple linear regression analysis were older age and different degrees of gallstone disease. Conclusion. Our results found that in addition to older age, multiple stones and cholecystectomy could influence utility values from the patient's preference-based viewpoint

The Clinical Investigation of Disparity of Utility Values Associated with Gallstone Disease: A Pilot Study

Purpose. The utility evaluation was an effective method to incorporate all of the contributing variables for multiple diseases into one outcome measure. A cross-sectional study was conducted to assess the utility values associated with varying states of gallstone disease among outpatient clinics participants at a teaching hospital in Taipei, Taiwan. Methods. The utility values were measured by using time trade-off method. A total of 120 outpatient clinics participants (30 subjects with no gallstone disease, 30 subjects with single stone, 30 subjects with multiple stones, and 30 subjects with cholecystectomy) evaluated utility values from January 1, 2006 to December 31, 2006. The diagnosis of gallstone disease was performed by a panel of specialists using ultrasound sonography. Results. The overall mean utility value was 0.89±0.13 (95% CI: 0.87–0.91) indicating that study participants were willing to trade about 11% (95% CI: 9–13%) of their remaining life in return for being free of gallstone disease perpetually. The significant associated factors of utility values based on the multiple linear regression analysis were older age and different degrees of gallstone disease. Conclusion. Our results found that in addition to older age, multiple stones and cholecystectomy could influence utility values from the patient’s preference-based viewpoint