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[2] viXra:1212.0124 [pdf] replaced on 2012-12-21 04:13:24
Authors: Deepak Ponvel Chermakani
Comments: There are 6 Pages, 6 Theorems, 7 Figures. I also made a small correction that in Theorem-1, the correct word is "NP-Hard" and not "NP-Complete".
We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants in the real-variable problem are 0, 1, -1, K, or -K, where K is the time parameter that tends to positive infinity. The number of variables, constraints, and rational linear functions in the objective, of the real-variable problem is bounded by a polynomial function of the size of the NP-Complete Problem. The NP-Complete Problem has a feasible solution, if-and-only-if, the real-variable problem has a feasible optimal objective equal to zero. We thus show the strong NP-hardness of this real-variable optimization problem.
Category: Algebra
[1] viXra:1212.0018 [pdf] submitted on 2012-12-03 12:30:39
Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 200 Pages.
The authors introduce the concept of neutrosophic super matrices and the new notion of quasi super matrices. This new notion of quasi super matrices contains the class of super matrices. The larger class contains more partitions of the usual simple matrices. Studies in this direction are interesting and find more applications in fuzzy models. The authors also suggest in this book some open problems.
Category: Algebra
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