Conformal Symmetry on the Instanton Moduli Space

The conformal symmetry on the instanton moduli space is discussed using the ADHM construction, where a viewpoint of "homogeneous coordinates" for both the spacetime and the moduli space turns out to be useful. It is shown that the conformal algebra closes only up to global gauge transformations, which generalizes the earlier discussion by Jackiw et al. An interesting 5-dimensional interpretation of the SU(2) single-instanton is also mentioned.Comment: 7 pages, LaTeX, version to appear in J. Phys. A: Math. Ge

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

Log canonical thresholds of Del Pezzo Surfaces in characteristic p

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's connectedness principle and other results relying on vanishing theorems of Kodaira type, not known to be true in finite characteristic. We compute the global log canonical threshold of non-singular del Pezzo surfaces over an algebraically closed field. We give algebraic proofs of results previously known only in characteristic $0$. Instead of using of the connectedness principle we introduce a new technique based on a classification of curves of low degree. As an application we conclude that non-singular del Pezzo surfaces in finite characteristic of degree lower or equal than $4$ are K-semistable.Comment: 21 pages. Thorough rewrite following referee's suggestions. To be published in Manuscripta Mathematic

On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces

We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces X and vector fields v which are K-stable in the sense of Berman-Nystrom and therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor correction

Trends and driving forces of China's virtual land consumption and trade

Land resources are important for China’s rapid economic development, especially for food and construction. China’s land resources are under tremendous pressures, and therefore land use is increasingly displaced to other parts of the world. This study analyses the evolution and driving forces of China’s land consumption from 1995 to 2015. The main results show that China’s land footprint increased from 8.8% of the global land resources under human use in 1995 to 15.7% in 2015. China’s domestic land resources are mainly used for serving domestic consumption. Moreover, China needs to import virtual land from foreign countries to satisfy 30.8% of its land demand. Among the three land use types of cropland, grassland and forests, grassland had the largest fraction in China’s land footprint from 1995 to 2000, while forest has become the largest one since 2000. China’s virtual land trade experienced a sharp increase in net imports from 9.4E + 04 km2 in 1995 to 3.4E + 06 km2 in 2015. Observing China’s virtual land network by a cluster analysis, this study concludes that China keeps tight relationships with Australia, Japan, Brazil and Korea for its cropland consumption, and Canada, USA, Mexico, Australia, Korea and Japan are relevant for its grassland consumption. In addition, decomposition analysis results show that affluence is the major driving factor for China’s land consumption, while changes in land use intensity could mitigate some of the related effects. Lastly, policy recommendations are proposed so that China can move toward sustainable land management

Dyson processes on the octonion algebra

We consider Brownian motion on symmetric matrices of octonions, and study the law of the spectrum. Due to the fact that the octonion algebra is nonassociative, the dimension of the matrices plays a special role. We provide two specific models on octonions, which give some indication of the relation between the multiplicity of eigenvalues and the exponent in the law of the spectrum

A general equilibrium analysis on the impacts of regional and sectoral emission allowance allocation at carbon trading market

It is critical to adapt to climate change and reduce the overall carbon emissions. China announced its Nationally Determined Contributions (NDC) at the Paris climate conference in 2015. The carbon cap-and trade scheme, which plays a key role in carbon emissions abatement, is an effective policy for China to achieve its NDC. This study focuses on the allocation of regional and sectoral initial carbon emission allowances in Shanghai. An impact evaluation on the macro-economy, carbon trading markets and participating sectors for the year 2030 was conducted by applying a computable general equilibrium (CGE) model. The results show that the carbon cap-and-trade scheme would cause a 3.4% GDP loss and an 8.9% welfare loss in 2030. The carbon price would be 161.2 USD/t and 147.2 USD/t under the two representative scenarios. The allocation of initial allowances would have a significant impact on both carbon market scale and sectoral trading behaviors. The power generation sector and the petrol oil sector would undertake the greatest output loss, while the metal smelting sector would become the main seller. Furthermore, the initial allowances allocation under a certain abatement target would hardly affect sectoral production but remarkably affect trade behaviors at the carbon trading markets

Examining the role of BRICS countries at the global economic and environmental resources nexus

The BRICS countries (Brazil, Russia, India, China and South Africa) are central to future global economic development. However, they are facing both environmental and natural resource stresses due to their rapid economic growth. This study examines the balance between economic benefits and cost of environmental emissions and resource usage in BRICS countries so that future sustainable development insights can be provided. The historical trends of carbon dioxide (CO2), sulfur dioxide (SO2), water, land, energy and material footprints of these countries from 1995 to 2015 are evaluated with a multi-regional input-output model. Also, whether a decoupling relationship exists between economic development, environmental emissions and resources consumption, is examined. In addition, whether environmental emissions and resource usage costs to obtain identical economic gains of these countries in global trade are explored. The major results show that in congruence with economic development, the average annual growth rates of footprint indicators ranged from 0.2% in 1995 to 9.8% in 2015. A decoupling effect did not occur for CO2 emissions or water consumption but did exist for other indicators. Global trade across the supply chain shows to achieve a unit of USD economic benefit from trade, BRICS countries tend to use relatively greater environmental emissions and resource consumption to high income countries, when compared to other income level countries. These emergent economies did receive relatively greater benefits per environmental emissions and resource usage cost from lower-middle and low-income countries