We compute the limit distribution for the (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In the two–colored case our method provides a different proof of a similar result by Tracy and Widom about t...

Abstract: Background & Aims of the Study: Textile dyes generally are made of synthetic, organic, and aromatic compounds that may be contain of some heavy metals in their structure. Complex structure and presence of these metals cause toxicity and may be mutagen, teratogen or carcinogen. This study has investigated the ability of peanut shell powder to removal of some reactive dyes (Green 19...

In this work, removal of C. I. Acid Red 14 was investigated by Pumice stone as a low cost adsorbent. Various parameters such as initial dye solution, contact time and pH were studied. Removal of dye were increased by increasing of contact time and initial dye solution and deceased by increasing of pH. Three isotherm models were studied. Linear and non-linear regression analyses were used fo...

conclusions the study results showed that by increasing the initial dye concentration and contact time, the adsorption capacity increased, as well. moreover, the thermodynamic parameters (δh °, δg °, and δs °) revealed the endothermic sorption of rr-198 onto mwcnts. results the rr-198 absorption rates were 33.26 and 222.88 mg/g, respectively for 20, and 200 mg/l dye concentration, at ph of 3, 6...

We study the uctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation. i=1 denote a sequence of i.i.d. random variables with marginal law on the unit square Q = 0; 1] 2. ...

Connections between longest increasing subsequences in random permutations and eigenvalues of random matrices with complex entries have been intensely studied. This note applies properties of random elements of the finite general linear group to obtain results about the longest increasing subsequence in non-uniform random permutations.