Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page

CD28null CD4 T-cell expansions in autoimmune disease suggest a link with cytomegalovirus infection

Immunosenescence is thought to contribute to the increase of autoimmune diseases in older people. Immunosenescence is often associated with the presence of an expanded population of CD4 T cells lacking expression of CD28 (CD28null). These highly cytotoxic CD4 T cells were isolated from disease-affected tissues in patients with rheumatoid arthritis, systemic lupus erythematosus, multiple sclerosis, or other chronic inflammatory diseases and their numbers appeared to be linked to disease severity. However, we recently demonstrated that the common herpes virus, cytomegalovirus (CMV), not ageing, is the major driver of this subset of cytotoxic T cells. In this review, we discuss how CMV might potentiate and exacerbate autoimmune disease through the expansion of CD28null CD4 T cells