This paper presents the exponential stability of a one-dimensional wave equation with viscoelastic damping. Using the asymptotic analysis technique, we prove that the spectrum of the system operator consists of two parts: the point and continuous spectrum. The continuous spectrum is a set of N points which are the limits of the eigenvalues of the system, and the point spectrum is a set of three classes of eigenvalues: one is a subset of N isolated simple points, the second is approaching to a vertical line which parallels to the imagine axis, and the third class is distributed around the continuous spectrum. Moreover, the Riesz basis property of the generalized eigenfunctions of the system is verified. Consequently, the spectrum-determined growth condition holds true and the exponential stability of the system is then established. (C) 2013 Elsevier Inc. All rights reserved.

Cathepsin G (CatG), a serine protease present in mast cells and neutrophils, can produce angiotensin-II (Ang-II) and degrade elastin. Here we demonstrate increased CatG expression in smooth muscle cells (SMCs), endothelial cells (ECs), macrophages, and T cells from human atherosclerotic lesions. In low-density lipoprotein (LDL) receptor-deficient (Ldlr(-/-)) mice, the absence of CatG reduces arterial wall elastin degradation and attenuates early atherosclerosis when mice consume a Western diet for 3 months. When mice consume this diet for 6 months, however, CatG deficiency exacerbates atherosclerosis in aortic arch without affecting lesion inflammatory cell content or extracellular matrix accumulation, but raises plasma total cholesterol and LDL levels without affecting high-density lipoprotein (HDL) or triglyceride levels. Patients with atherosclerosis also have significantly reduced plasma CatG levels that correlate inversely with total cholesterol (r = -0.535, P < 0.0001) and LDL cholesterol (r = -0.559, P < 0.0001), but not with HDL cholesterol (P = 0.901) or triglycerides (P = 0.186). Such inverse correlations with total cholesterol (r = -0.504, P < 0.0001) and LDL cholesterol (r = -0.502, P < 0.0001) remain significant after adjusting for lipid lowering treatments among this patient population. Human CatG degrades purified human LDL, but not HDL This study suggests that CatG promotes early atherogenesis through its elastinolytic activity, but suppresses late progression of atherosclerosis by degrading LDL without affecting HDL or triglycerides. (C) 2014 Elsevier B.V. All rights reserved.