Arbitrage and Equilibrium in Economies with Externalities.

We introduce consumption externalities into a general equilibrium model with arbitrary consumption sets. To treat the problem of existence of equilibrium, a condition of no unbounded arbitrage, extending the condition of Page (1987) and Page and Wooders (1993, 1996) is defined. It is proven that this condition is sufficient for the existence of an equilibrium and both necessary and sufficient for compactness of the set of rational allocations.CONSUMPTION ; EXTERNALITIES ; ARBITRAGE

In vivo investigation of hyperpolarized [1,3-13C2]acetoacetate as a metabolic probe in normal brain and in glioma.

Dysregulation in NAD+/NADH levels is associated with increased cell division and elevated levels of reactive oxygen species in rapidly proliferating cancer cells. Conversion of the ketone body acetoacetate (AcAc) to β-hydroxybutyrate (β-HB) by the mitochondrial enzyme β-hydroxybutyrate dehydrogenase (BDH) depends upon NADH availability. The β-HB-to-AcAc ratio is therefore expected to reflect mitochondrial redox. Previous studies reported the potential of hyperpolarized 13C-AcAc to monitor mitochondrial redox in cells, perfused organs and in vivo. However, the ability of hyperpolarized 13C-AcAc to cross the blood brain barrier (BBB) and its potential to monitor brain metabolism remained unknown. Our goal was to assess the value of hyperpolarized [1,3-13C2]AcAc in healthy and tumor-bearing mice in vivo. Following hyperpolarized [1,3-13C2]AcAc injection, production of [1,3-13C2]β-HB was detected in normal and tumor-bearing mice. Significantly higher levels of [1-13C]AcAc and lower [1-13C]β-HB-to-[1-13C]AcAc ratios were observed in tumor-bearing mice. These results were consistent with decreased BDH activity in tumors and associated with increased total cellular NAD+/NADH. Our study confirmed that AcAc crosses the BBB and can be used for monitoring metabolism in the brain. It highlights the potential of AcAc for future clinical translation and its potential utility for monitoring metabolic changes associated with glioma, and other neurological disorders

Laser-induced fluorescence velocimetry for a hypersonic leading-edge separation

Two-dimensional mapping of the velocity distribution for a hypersonic leading-edge separation flowfield generated by a "tick" shaped geometry is presented for the first time. Discrete measurements of two velocity components were acquired at a flow condition having a total specific enthalpy of 3.8 MJ/kg by imaging nitric oxide fluorescence over numerous runs of the hypersonic tunnel at the Australian Defence Force Academy (T-ADFA). The measured freestream velocity distribution exhibited some non-uniformity, which is hypothesized to originate from images acquired using a set of ultraviolet specific mirrors mounted on the shock tunnel deflecting under load during a run of the facility, slightly changing the laser sheet orientation. The flow separation point was measured to occur at 1.4 ± 0.2 mm from the model leading edge, based on the origin of the free shear layer emanating from the expansion surface. Reattachment of this free shear layer on the compression surface occurred at 59.0 ± 0.2 mm from the model vertex. Recirculating the flow bound by the separation and reattachment points contained supersonic reverse flow and areas of subsonic flow aligned with the location of three identified counter-rotating vortices. A comparison of the recirculation flow streamline plots with those computed using Navier-Stokes and direct simulation Monte Carlo (DSMC) codes showed differences in flow structures. At a flow time close to that produced by the facility, flow structures generated by the DSMC solution were seen to agree more favorably with the experiment than those generated by the Navier-Stokes solver due to its ability to better characterize separation by modeling the strong viscous interactions and rarefaction at the leading edge. The primary reason for this is that the no-slip condition used in the Navier-Stokes solution predicts a closer separation point to the leading edge and structures when compared to the DSMC solution, which affects surface shear stress and heat flux, leading to a difference in flow structures downstream of the separation