The State Space of Perturbative Quantum Field Theory in Curved Spacetimes

The space of continuous states of perturbative interacting quantum field theories in globally hyperbolic curved spacetimes is determined. Following Brunetti and Fredenhagen, we first define an abstract algebra of observables which contains the Wick-polynomials of the free field as well as their time-ordered products, and hence, by the well-known rules of perturbative quantum field theory, also the observables (up to finite order) of interest for the interacting quantum field theory. We then determine the space of continuous states on this algebra. Our result is that this space consists precisely of those states whose truncated n-point functions of the free field are smooth for all n not equal to two, and whose two-point function has the singularity of a Hadamard fundamental form. A crucial role in our analysis is played by the positivity property of states. On the technical side, our proof involves functional analytic methods, in particular the methods of microlocal analysis.Comment: 24 pages, Latex file, no figure

A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society

This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application

Optimal Strategies of Critical Mineral Depletion and Recycling

peer reviewedCritical minerals play a crucial role in making eco-friendly and sustainable technology a reality. Yet, these essential minerals face challenges such as disruptions in their supply chain, dwindling availability, limited recycling methods, and uncertain demand, which may increase in the short term. In this study, we explore how we can better extract and recycle these important minerals through international cooperation and precommitment among different countries. Our findings highlight a few key points: (1)While recycling technology can help reduce reliance on virgin minerals, it cannot fully replace the need for them, as recycling still depends on limited resources. (2) When deciding how to distribute these minerals in the market, international cooperation should consider both virgin and recyclable sources, prioritizing the more globally desirable option. (3) If the recyclable sources are being used up, it becomes challenging for a supranational decision-maker to decide how to best use the remaining virgin minerals. (4) With precommitment from both virgin resource 18 suppliers and recyclers, both recycled and virgin resources can be used together until the virgin ones are completely used up. In simpler terms, securing these crucial minerals for sustainable technology involves complex decisions about recycling, resource allocation, and cooperation among nations

The Irreversible Pollution Game

We study a 2-country differential game with irreversible pollution. Irresability is of a hard type: above a certain threshold level of pollution, the self-cleaning capacity of Nature drops to zero. Accordingly, the game includes a non-concave feature, and we characterize both the cooperative and non-cooperative versions with this general non-LQ property. We deliver full analytical results for the existence of Markov Perfect Equilibria. We first demonstrate that when pollution costs are equal across players (symmetry), irreversible pollution regimes are more frequently reached than under cooperation. Second, we study the implications of asymmetry in the pollution cost. We find far nontrivial results on the reachability of the irreversible regime. However, we unambiguously prove that, for the same total cost of pollution, provided the irreversible regime is reached in both the symmetric and asymmetric cases, long-term pollution is larger in the symmetric case, reflecting more intensive free-riding under symmetry

Optimal behavior under pollution irreversibility risk and distance to the irreversibility thresholds: A global approach

We study optimal behavior under irreversible pollution risk. Irreversibility comes from the decay rate of pollution sharply dropping (possibly to zero) above a threshold pollution level. In addition, the economy can instantaneously move from a reversible to an irreversible pollution mode, following a Poisson process, the irreversible mode being an absorbing state. The resulting non-convex optimal pollution control is therefore piecewise deterministic. First, we are able to characterize analytically and globally the optimal emission policy using dynamic programming. Second, we prove that for any value of the Poisson probability, the optimal emission policy leads to more pollution with the irreversibility risk than without in a neighborhood of the pollution irreversibility threshold. Third, we find that this local result does not necessarily hold if actual pollution is far enough from the irreversibility threshold. Our results enhance the importance of the avoidability of the latter threshold in the optimal economic behavior under the irreversibility risk

RAB18, a protein associated with Warburg Micro syndrome, controls neuronal migration in the developing cerebral cortex

There is no apparently changed after overexpression of RAB18 in cortical neuronal migration. A Representative coronal section showing migration of transfected neurons 4 d after electroporated at E14.5 with GFP plasmid together with indicated constructs. Scale bar: 100 μm. B Quantitative analysis of GFP positive neurons in different cortical regions in A. Data represent the mean ± SEM (n = 3). (PDF 76 kb

Salesperson human capital investment and heterogeneous export enterprises performance

This paper aims to study the impact of salesperson human capital investment on the export performance of heterogeneous enterprises in China. To distinguish the different effects on the staff level and the management level, we define the human capital investment for the overall salespersons as human capital investment I and the human capital investment for the sales managers as human capital investment II, respectively measured by the salary of the ordinary salespersons and the ratio of expenses to sales. We find that human capital investment I has a significant positive effect on export performance, while human capital investment II shows a “positive U-shaped” relationship with export performance. Considering the heterogeneity of enterprise, the positive effect of human capital investment I is more significant than that of human capital investment II in enterprises with high R&D intensity. Moreover, with the improvement of technology intensity, both the promotion of human capital investment I and human capital investment II would generate greater influence on export performance