The singularity categories of the Cluster-tilted algebras of Dynkin type

In this paper, we use the stable categories of some selfinjective algebras to describe the singularity categories of the cluster-tilted algebras of Dynkin type. Furthermore, in this way, we settle the problem of singularity equivalence classification of the cluster-tilted algebra of type $A$, $D$ and $E$ respectively.Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1012.4661 by other author

Impacts of the U.S.-Central America-Dominican Republic Free Trade Agreement (CAFTA-DR) on U.S. Fruit Exports - the Apple Case

The U.S.-Central America-Dominican Republic Free Trade Agreement (CAFTA-DR) levels the playing field of trade between the United States and the six CAFTA-DR partner countries. Half of U.S. farm products gain immediate tariff-free access to the markets of the CAFTA-DR region. All Tariffs will be eliminated in 20 years. Under CAFTA-DR, tariffs on an important U.S. fresh fruit export to the region, fresh apples, declined from an initial base of 15%-25% in CAFTA-DR countries to zero immediately upon enforcement. The specific objective of this research is to analyze the impact of tariff elimination under CAFTA-DR on the trade of U.S. fresh apples. Generalized Method of Moments (GMM) is used for the analysis involving an excess-supply-excess-demand model with monthly trade data from January 2000 to December 2010. The more telling empirical results indicate that for each of the six CAFTA-DR countries, tariff elimination positively promotes U.S. apple exports to this region.CAFTA-DR, trade liberalization, tariff elimination, Generalized Method of Moments(GMM), Agricultural and Food Policy, International Relations/Trade, Q17, F13, F15,

Exchange graphs of cluster algebras have the non-leaving-face property

The claim in the title is proved