Related papers: Notes on the log minimal model program

This paper has been withdrawn by the authors, because it has been made obsolete by the detailed expositions in our papers in arXiv:0812.4885 (the mathematics part) and arXiv:0812.4737 (the economics part).

This paper has been withdrawn by the author due to extremely unscientific errors.

This paper has been withdrawn

This paper has been withdrawn since we combine this paper with math.AC/0503685. All contents of the paper have been moved to math.AC/0503685.

This paper has been withdrawn by the author.

This paper has been withdrawn. A more satisfactory account of the results it was supposed to present will appear in a series of papers starting with hep-th/9712256 and hep-th/9712258

This paper has been withdrawn by the author.

This paper has been withdrawn.

This paper has been withdrawn by the author. It will be replaced, substantially modified, by sections of the author's completed PhD thesis.

Title: An unlikely result Authors: T.M. Other Comments: This paper has been withdrawn Abstract: This paper has been withdrawn by the author due to the fact that some of the results turned out to be known.

This paper has been withdrawn.

This paper has been withdrawn by the authors. It has been superseded by hep-th/0309154

This paper has been withdrawn by the author because there are some typos in proofs.

The paper has been withdrawn by the author.

There have been comments on this paper which point out unclear motivation and definitions on noncommutative momentum introduced. Therefore, this paper is withdrawn by the author for more clear presentation.

This paper has been withdrawn by the author,due a immature idea.

This paper has been withdrawn by the authors, due a gap in the proof of the main Theorem.

This paper has been withdrawn by the author due to a crucial sign error.

Due to a computational mistake this paper has been withdrawn.

This paper has been withdrawn.