Related papers: Notes on the log minimal model program

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This paper has been withdrawn by the authors. Significantly revised versions of the results of this paper are now available in arXiv:0707.0487v2 and arXiv:0808.3169v1.

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This manuscript has been withdrawn at 17 April, 2007.

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This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.

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This paper has been withdrawn as it has been superseded by 0808.2697

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this is a duplicate submission(original is arXiv:1612.02141). Hence want to withdraw it

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This paper has been withdrawn. The contents of this paper can now be found in 0907.3000, which combines the erstwhile 0901.2981 and 0901.2982 in a somewhat compact form.

This paper has been withdrawn by the author, due to the insecurity against attacks received in quant-ph/0605027v5.

This paper has been withdrawn because the models on which it was based have undergone significant changes and improvements. A new paper with the same title, based on the improved models, is accepted for publication in MNRAS and is available…

This paper has been withdrawn by the author due to rewritting and skipping crucial sign errors.

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This paper has been withdrawn by the authors as requested by the journal.

This submission has been withdrawn by arXiv administrators because it is a duplicate of 0704.2182.

This article was withdrawn because (1) it was uploaded without the co-authors' knowledge or consent, and (2) there are allegations of plagiarism.