The most important result of Shaw et al. [1969] is the representation of each component of the vertical-deflection vector as a homogeneous nonisotropic random process when starting from a homogeneous and isotropic random process of gravity anomaly via the fiat Vening-Meinesz formula. Here our purpose is to show that all formulas of Shaw et al. are correct but that the

In general, vertical deflections are obtained either by astrogeodetic methods or by gravimetric methods. In the latter approach, gravity anomaly measurements are processed by using the so‐called Vening Meinesz equations to yield the vertical deflections. These calculated values of vertical deflections differ from the true values for two reasons: the measurements of the gravity anomalies are subject to error, and a numerical algorithm must be used to approximate the Vening Meinesz equations. In this paper, the autocorrelation functions of the deflection errors arising from these two sources are determined under the assumption that the anomalies and the error in measuring the anomalies are random processes.

No abstract

Patients with diabetes are predisposed to microvascular disease. In the retina and brain, this is characterized by neovascularization and new capillary formation. Because of the potential importance of plasmin generation in these processes, we evaluated the effect of elevated glucose concentrations on expression of plasminogen activator inhibitor‐1 (PAI‐1), tissue plasminogen activator (tPA), and urokinase (uPA) in cultured bovine brain endothelial cells (BBEC) versus cultured bovine aortic endothelial cells (BAEC). We observed that BBEC PAI‐1 mRNA levels were decreased fivefold in cells cultured in media containing 20 mM glucose compared with BBEC cultured in media with 5.5 mM glucose, whereas expression of PAI‐1 mRNA in BAEC, bovine mesenteric endothelial cells, and human umbilical vein endothelial cells was not modulated under these conditions. Expression of PAI‐1 protein was also inhibited by growth of BBEC in elevated glucose, but the effect was less marked than at the mRNA level. Elevated glucose did not decrease expression of PAI‐1 protein by BAEC. Withdrawal of acidic fibroblast growth factor enhanced expression of PAI‐1 mRNA and protein in BBEC. Expression of tPA mRNA was not affected by the glucose concentration of the medium, and uPA mRNA was not detected in our BBEC cultures. A decrease in the local tissue activity of PAI‐1 by elevated glucose concentrations, with no effect on tPA or uPA expression, would lead to an increase in the plasmin activity and thereby predispose neural tissues, such as the cerebrum and retina, of diabetic patients to neovascularization.