Purpose: Due to the paucity of the information regarding the lower limb biomechanics in slow speeds running as well as  concentration of the majority of previous studies in a single movement plane, aim of the present study was investigation on a kinetic based analysis of lower limb’ joints with increasing running speed. Methods: 28 runners asked to stay on the belt speed of treadmill that was ...

surface roughness is a significant parameter which determines the efficiency of optical components. surface damages induced by grinding strongly influence the mechanical strength and optical quality of optical glasses. it is meaningful to rapid evaluate the surface roughness through the measurement of different grinding parameters. in this study, a cup diamond wheel (d64) is used in grinding pr...

We consider the distribution of the length of the longest subsequence avoiding an arbitrary pattern, π, in a random permutation of length n. The well-studied case of a longest increasing subsequence corresponds to π = 21. We show that there is some constant cπ such that as n → ∞ the mean value of this length is asymptotic to 2 √ cπn and that the distribution of the length is tightly concentrate...

Inspired by the results of Stanley and Widom concerning the limiting distribution of the lengths of longest alternating subsequences in random permutations, and results of Deutsch, Hildebrand and Wilf on the limiting distribution of the longest increasing subsequence for pattern-restricted permutations, we find the limiting distribution of the longest alternating subsequence for pattern-restric...

It was recently discovered by Baik, Deift and Johansson [4] that the asymptotic distribution of the length of the longest increasing subsequence in a permutation chosen uniformly at random from Sn, properly centred and normalised, is the same as the asymptotic distribution of the largest eigenvalue of an n × n GUE random matrix, properly centred and normalised, as n → ∞. This distribution had e...

In a famous paper 8] Hammersley investigated the length L n of the longest increasing subsequence of a random n-permutation. Implicit in that paper is a certain one-dimensional continuous-space interacting particle process. By studying a hydrodynamical limit for Hammersley's process we show by fairly \soft" arguments that limn ?1=2 EL n = 2. This is a known result, but previous proofs (Vershik-...

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...

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.

Students’ reading speed in the English Department at a Saudi University is low, which, turn, slows down their general proficiency English. This research aims to show how and what degree using increasing software (the ‘7 Speed Reading’ program) could be decisive factor upgrading of EFL-major students KKU while maintaining former level comprehension. study uses pre-test, post-test quasi-experimen...