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

On-grid location-by-location variations of transmission electron microscope imaged in-flame soot particles in a small-bore diesel engine

In a small-bore diesel engine, soot particles are sampled directly from the flames by placing a transmission electron microscope (TEM) grid inside the cylinder. The TEM images are taken from multiple on-grid locations to ensure enough number of soot particles are post-processed for statistically meaningful data of morphology parameters. This study presents variations in the soot TEM images and sizes of soot aggregates and primary particles from 30 different on-grid locations for each of jet-wall impingement and jet-jet interaction regions of the diesel flames. The TEM images show significant variations in soot aggregate size and structures for the two different sampling regions with overall larger and more complex soot for the jet-jet interaction region. The statistical results show that the difference in soot primary particle diameter is measurable after five images were processed. For soot aggregate radius of gyration, the two samples show no apparent variations until 25 images were processed, and the mean values levelled only when more than 27 images were processed. As the enough number of TEM images were processed, the larger sizes in both soot aggregates and primary particles were confirmed for the jet-jet interaction region

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

Copper(II) Can Kinetically Trap Arctic and Italian Amyloid‑β40 as Toxic Oligomers, Mimicking Cu(II) Binding to Wild-Type Amyloid‑β42: Implications for Familial Alzheimer’s Disease

The self-association of amyloid-β (Aβ) peptide into neurotoxic oligomers is believed to be central to Alzheimer’s disease (AD). Copper is known to impact Aβ assembly, while disrupted copper homeostasis impacts phenotype in Alzheimer’s models. Here we show the presence of substoichiometric Cu(II) has very different impacts on the assembly of Aβ40 and Aβ42 isoforms. Globally fitting microscopic rate constants for fibril assembly indicates copper will accelerate fibril formation of Aβ40 by increasing primary nucleation, while seeding experiments confirm that elongation and secondary nucleation rates are unaffected by Cu(II). In marked contrast, Cu(II) traps Aβ42 as prefibrillar oligomers and curvilinear protofibrils. Remarkably, the Cu(II) addition to preformed Aβ42 fibrils causes the disassembly of fibrils back to protofibrils and oligomers. The very different behaviors of the two Aβ isoforms are centered around differences in their fibril structures, as highlighted by studies of C-terminally amidated Aβ42. Arctic and Italian familiar mutations also support a key role for fibril structure in the interplay of Cu(II) with Aβ40/42 isoforms. The Cu(II) dependent switch in behavior between nonpathogenic Aβ40 wild-type and Aβ40 Arctic or Italian mutants suggests heightened neurotoxicity may be linked to the impact of physiological Cu(II), which traps these familial mutants as oligomers and curvilinear protofibrils, which cause membrane permeability and Ca(II) cellular influx

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

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