This paper presents a numerical method for one-dimensional Burgers'equation by the Hopf-Cole transformation and a reproducing kernel function, abbreviated as RKF. The numerical solution is given as explicit integral expressions with the RKF at each time step, so that the computation is fully parallel. The stability and error estimates are derived. Numerical results for some test problems are presented and compared with the exact solutions. Some numerical results are also compared with the results obtained by other methods. The present method is easily implemented and effective.

The solution of the interface problem is only in H 1+α (Ω) with α > 0 possibly close to zero and, hence, it is difficult to be approximated accurately. This paper studies an accurate numerical method on quasi-uniform grids for two-dimensional interface problems. The method makes use of a singular function representation of the solution, dual singular functions, and an extraction formula for stress intensity factors. Using continuous piecewise linear elements on quasi-uniform grids, our finite element approximation is shown to be optimal, O(h), accurate in the H 1 norm. This is confirmed by numerical experiments for interface problems with α < 0.1. An O(h 1+α ) error bound in the L 2 norm is also established by the standard duality argument. For small α, this improvement over the H 1 error bound is negligible. However, numerical tests presented in this paper indicate that the L 2 norm accuracy is much better than the theoretical error bound.

Background: Asthma is a life-threatening immediate-type allergic disease. B cell-activating factor (BAFF) is a key regulator of B lymphocyte development and is required to generate and maintain the mature B cell pool. Objectives: To investigate the level of BAFF in the serum of asthma patients and the role of BAFF on T cells. Methods: The BAFF level was measured by enzyme-linked immunosorbent assay. Peripheral blood mononuclear cells (PBMC) from asthma patients were analyzed by flow cytometry. T8.1 cells were used to test the role of BAFF on T cell-antigen-presenting cell (APC) conjugate formation. Results: The BAFF level in patient serum was elevated relative to normal serum. Immunoglobulin E (IgE) concentration and the percentage of CD3+ T and CD19+ B cells vary according to the serum BAFF level. Patients with high BAFF and high IgE (group II) and those with high BAFF and low IgE (group III) show a high ratio of CD3+ T to CD19+ B cells, and the opposite is seen for patients with low BAFF and high IgE (group I) and those with low BAFF and low IgE (group IV). The addition of BAFF increased PBMC proliferation and T cell-APC conjugate formation. BAFF concentration in serum decreased after treatment with antiasthmatic drugs including glucocorticoids and immunosuppressants. Conclusion: These findings suggest that the serum BAFF level is high in both IgE-mediated asthma and non-IgE-mediated asthma and extend our knowledge about the fact that BAFF may play a stimulatory role on the proliferation of T cells. Thus, BAFF could be a parameter to monitor the severity of asthma symptoms.

Levuglandin (LG) E2 is rapidly sequestered by covalent binding with proteins. The reaction of LGE2 with a protein in neutral aqueous solution exhibits two phases. A metastable adduct rapidly accumulates initially. In the second phase, a protein-bound pyrrole is generated. Pyrrole formation and stability were monitored with an immunoassay using antibodies that were raised against a stable isostere. That LG-derived pyrroles are the major products (> 76%) of the LGE2-protein reaction is suggested by the level of antibody binding found for LG-protein adducts compared with that found for a pyrrole derived from LGE2 and 6-amino-1-hexanol. Because the initial metastable LG-protein adduct is a reactive electrophile, it can be trapped with amines, such as glycine, to give stable ternary adducts that do not cross-react with the antibodies. Although highly alkylated pyrroles are chemically sensitive compounds, the protein-bound LG-derived pyrrole appears to be stable in aqueous solution at pH 7.4. Thus, it shows no decrease in immunoreactivity over several weeks. This discovery leads to the expectation that such pyrroles will accumulate in vivo, especially in proteins that do not turn over rapidly. Thus, the LG-derived protein-bound pyrrole may be a useful marker of oxidative lipid damage, and an immunoassay for this post-translational protein modification can be exploited as a mild, sensitive method for detecting and quantifying the generation of LGs in chronic inflammatory states.

a b s t r a c tIn this paper, we propose some least-squares finite element procedures for linear and nonlinear parabolic equations based on first-order systems. By selecting the least-squares functional properly each proposed procedure can be split into two independent symmetric positive definite sub-procedures, one of which is for the primary unknown variable u and the other is for the expanded flux unknown variable σ . Optimal order error estimates are developed. Finally we give some numerical examples which are in good agreement with the theoretical analysis.

No abstract

No abstract

No abstract