On the topology of conformally compact Einstein 4-manifolds

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that the renormalized volume is relatively large, we conclude that the conformally compact Einstein 4-manifold is diffeomorphic to $B^4$ and its conformal infinity is diffeomorphic to $S^3$.Comment: 16 page

Limit of Fractional Power Sobolev Inequalities

We derive the Moser-Trudinger-Onofri inequalities on the 2-sphere and the 4-sphere as the limiting cases of the fractional power Sobolev inequalities on the same spaces, and justify our approach as the dimensional continuation argument initiated by Thomas P. Branson.Comment: 17 page

On fractional GJMS operators

We describe a new interpretation of the fractional GJMS operators as generalized Dirichlet-to-Neumann operators associated to weighted GJMS operators on naturally associated smooth metric measure spaces. This gives a geometric interpretation of the Caffarelli--Silvestre extension for $(-\Delta)^\gamma$ when $\gamma\in(0,1)$, and both a geometric interpretation and a curved analogue of the higher order extension found by R. Yang for $(-\Delta)^\gamma$ when $\gamma>1$. We give three applications of this correspondence. First, we exhibit some energy identities for the fractional GJMS operators in terms of energies in the compactified Poincar\'e--Einstein manifold, including an interpretation as a renormalized energy. Second, for $\gamma\in(1,2)$, we show that if the scalar curvature and the fractional $Q$-curvature $Q_{2\gamma}$ of the boundary are nonnegative, then the fractional GJMS operator $P_{2\gamma}$ is nonnegative. Third, by assuming additionally that $Q_{2\gamma}$ is not identically zero, we show that $P_{2\gamma}$ satisfies a strong maximum principle.Comment: 38 pages. Final version, to appear in Communications on Pure and Applied Mathematic

Would You Like It Hot or Cold? An Analysis of U.S.-China Climate Policy

As the world’s largest emitters and economies, the United States and China play a critical role in global climate mitigation. Using Putnam’s two-level game showcases how the domestic political context of each country impacts their international policies. However, Putnam’s framework does not differentiate between bilateral and multilateral circumstances. The clarity and concentration of perceived costs and benefits for the United States and China from climate policies lead to differing outcomes on the multilateral and bilateral stage. Fear of the free-rider effect makes players assume payoffs that resemble the Prisoner’s Dilemma during multilateral climate negotiations, whereas bilateral negotiations usually result in more cooperative outcomes. These contrasting policy outcomes reflect the hot and cold relationship between the United States and China. The additional expediency and effectiveness of bilateral agreements suggest that substantial climate action will likely originate from strong bilateral agreements. In an optimal scenario, increased U.S.-China climate collaboration translates into a stronger relationship between the two global superpowers and provides other nations with the confidence and certainty to invest in abatement in a renewed global climate regime

The Politics and Future of Carbon Cap-and-Trade: Lessons from the European Union

Economists and policy analysts recognize a well-designed cap-and-trade scheme as the premier approach to effectively reduce carbon emissions. However, politics is bound to play a major role in the policymaking process—more so with carbon dioxide emissions than other pollutants like sulfur dioxide. This paper examines the political climate in which the major trading scheme in the European Union was proposed in order to explore how politics affects the programs’ environmental integrity and ultimate policy outcome. Based on an analysis of the EU’s program, many pieces need to align within the political landscape for a cap-and-trade system to pass the policymaking body, let alone an ambitious one

Biosynthesis and axoplasmic transport of neurophysin in the hypothalamo-neurohypophysial system of the grass frog Rana pipiens

Neurons of the preoptic nucleus (PON) are capable of synthesizing cysteine-rich proteins. The time course study reveals the presence in the neural lobe of a (\u2735)S-cysteine labeled protein (Np), which first appeared at 4 hours after the isotope injection and persisted throughout the entire observation period of 5 days. The Np protein is tentatively identified as the neurophysin protein of Rana pipiens. The minimum rate of transport for neurophysin is calculated as 0.9 mm/hr (22 mm/day). The Np protein can be further resolved by SDS-PAGE into 2 proteins, Np I (M.W. 23,000) and Np II (M.W. 20,100); or by isoelectric focusing in polyacrylamide gel into two proteins with pI = 4.9, and pI = 4.6. Also, two (\u2735)S-cysteine labeled proteins (pI = 5.8 and pI = 5.2) are present in the preoptic nucleus and infundibulum within one hour isotope injection. Preliminary evidence suggests a putative precursor role for the pI = 5.2 protein;Axoplasmic transport in the hypothalamo-neurohypophysial system of the frog has been effectively blocked by microiontophoretic ejection of vinblastine into the median eminence. Paracrystalline structures, presumably formed by the binding of vinblastine to tubulin, fill many of the neurosecretory axons in the median eminence 1 and 3 days after the ejection. These paracrystals are thought to be the major cause for the blockade. Large axon dilatations (Herring bodies) are induced proximal to the ejection site at day 3, local disposal of NGVs by lysosomes is seen within these Herring bodies at day 8, and to a lesser extent at day 15. Herring bodies are no longer seen at day 30 after the ejection. The sequence of fine structural changes observed suggests that the blockade is reversible. The early (day 3-8) responses in the distal neural lobe are marked by the degeneration of some neurosecretory axons. Whereas fine structure recovery in both the hypothalamo-neurohypophysial tract and the neural lobe at later stages (day 15-30) imply a functional recovery;Microtubule protein, tubulin was purified to apparent homogeneity from porcine brain. The purity of the PC-tubulin was checked by SDS-PAGE and the molecular weight was determined to be about 52,000. PC-tubulin was unable to assemble into microtubules under conditions where in vitro assembly from 2xMT is readily accomplished. However, the addition of the MAP fraction to the PC-tubulin greatly facilitate in vitro assembly of the latter into microtubules with an average diameter of 21 nm. Monospecific antisera against glutaraldehyde cross-linked PC-tubulin or SDS-PAGE purified tubulin were obtained and used to stain the in vitro assembled microtubules by the unlabeled peroxidase-anti-peroxidase (PAP) method. The resulting PAP complex-decorated microtubules attain an average diameter of 53 nm