Let R be a pseudo-valuation domain with associated valuation domain V and I a nonzero proper ideal of R. Let R̂ (resp., V̂ ) be the I-adic (resp., IV -adic) completion of R (resp., V ). We show that R̂ is a pseudo-valuation domain (which may be a field); and that if I 6= I2, then V̂ is the associated valuation domain of R̂. Let R be an SFT globalized pseudo-valuation domain with associated Prüfer do...

Consider an under-determined system of nonlinear equations F (x) = 0, F : IR → IR, where F is continuously differentiable and m > n. This system appears in a variety of applications, including parameter–dependent systems, dynamical systems with periodic solutions, and nonlinear eigenvalue problems. Robust, efficient numerical methods are often required for the solution of this system. Newton’s ...

With the increasing use of cyberinfrastructure and popularity of e-Science initiatives, science is becoming truly globalized, reducing barriers to entry and enabling formation of open and global networked innovation communities. Yet, relatively little is known about the mechanisms that govern such globalized communities. Meanwhile, creative artificial ecosystem metaphors and interaction process...