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We propose a preconditioned variant of the modified HSS (MHSS) iteration method for solving a class of complex symmetric systems of linear equations. Under suitable conditions, we prove the convergence of the preconditioned MHSS (PMHSS) iteration method and discuss the spectral properties of the PMHSS-preconditioned matrix. Numerical implementations show that the resulting PMHSS preconditioner leads to fast convergence when it is used to precondition Krylov subspace iteration methods such as GMRES and its 298 Numer Algor (2011) 56:297-317 restarted variants. In particular, both the stationary PMHSS iteration and PMHSS-preconditioned GMRES show meshsize-independent and parameterinsensitive convergence behavior for the tested numerical examples.

We construct a preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration scheme for solving and preconditioning a class of block two-by-two linear systems arising from the Galerkin finite element discretizations of a class of distributed control problems. The convergence theory of this class of PMHSS iteration methods is established and the spectral properties of the PMHSSpreconditioned matrix are analysed. Numerical experiments show that the PMHSS preconditioners can be quite competitive when used to precondition Krylov subspace iteration methods such as GMRES.

Deep or chronic skin wounds are difficult to heal spontaneously due to the lack of scaffold to guide cell growth and reduced levels and activities of endogenous growth factors. Emulsion electrospinning process integrated with DNA condensation techniques indicated potentials to gradually release DNA, but no attempt has been made to clarify the advantages in promoting tissue regeneration and wound recovery. In this study, polyplexes of basic fibroblast growth factor-encoding plasmid (pbFGF) with poly(ethylene imine) were incorporated into electrospun fibers with a core-sheath structure, and poly(ethylene glycol) was included into the fiber sheath to allow a sustained release of pbFGF for 4 weeks. In vitro tests on mouse embryo fibroblasts indicated that pbFGF-loaded fibrous mats enhanced cell proliferation by the autocrine bFGF, and an effective cell transfection proceeded for over 28 days. Skin wounds were created in the dorsal area of diabetic rats for in vivo evaluation of skin regeneration after being covered with pbFGF-loaded fibrous mats. The gradual pbFGF release revealed significantly higher wound recovery rate with improved vascularization, enhanced collagen deposition and maturation, complete re-epithelialization and formation of skin appendages. The above results demonstrate the potential use of pbFGF-loaded electrospun fibrous mats to accelerate the healing of skin ulcers for patients with diabetic mellitus.

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