A frequently encountered problem in peer review systems is to facilitate pairwise comparisons of a given set of proposals by as few as referees as possible. In [8], it was shown that, if each referee is assigned to review k proposals then n(n-1)/k(k-1) referees are necessary and n(2n-k)/k referees are sufficient to cover all n(n-1)/2 pairs of n proposals. While the upper bound remains withi...

The upper bound and the lower bound of average numbers of divisors of Euler Phi function and Carmichael Lambda function are obtained by Luca and Pomerance (see [LP]). We improve the lower bound and provide a heuristic argument which suggests that the upper bound given by [LP] is indeed close to the truth.

in this paper, we considered solving approaches to flexible job shop problems. makespan is not a good evaluation criterion with overlapping in operations assumption. accordingly, in addition to makespan, we used total machine work loading time and critical machine work loading time as evaluation criteria. as overlapping in operations is a practical assumption in chemical, petrochemical, and gla...

The aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. Several characterizations and properties of these multifunctions along with their mutual relationships are established in $L$-fuzzy topological spaces

Pudlák shows that bounded arithmetic (Buss’ S2) proves an upper bound on the Ramsey number Rr(k) (the r refers to the number of colors, assigned to edges; the k refers to the size of the monochromatic set). We will strengthen this result by improving the bound. We also investigate lower bounds, obtaining a non-constructive lower bound for the special case of 2 colors (i.e. r = 2), by formalizin...

Pudlák shows that bounded arithmetic (Buss’ S2) proves an upper bound on the Ramsey number Rr(k) (the r refers to the number of colors, assigned to edges; the k refers to the size of the monochromatic set). We will strengthen this result by improving the bound. We also investigate lower bounds, obtaining a non-constructive lower bound for the special case of 2 colors (i.e. r = 2), by formalizin...

We compute the pressure of the random energy model (REM) and generalized random energy model (GREM) by establishing variational upper and lower bounds. For the upper bound, we generalize Guerra’s “broken replica symmetry bounds”, and identify the random probability cascade as the appropriate random overlap structure for the model. For the REM the lower bound is obtained, in the high temperature...