objective: in recent years, farmers have shown great interest to using native drill planter rather than complex planters to grow vegetables. methods: in this study, we tested a native planter independent variables were the two types of substrate surface (asphalt and plowed field), three ground speed (3, 5 and 7 kph) and four types of seeds (tomatoes, onions, radishes and lettuce). dependent var...

INTRODUCTION Recently, a milling for die using a small end mill of diameter less than 1 mm is increased, because sizes of plastic mold parts such as connectors for an IT and an electronics becomes micro extremely. In general, a tool life is long and a good cut surface is obtained as a cutting speed is high. A speed-increasing spindle, which is attached to a shank may be used to increase the cut...

This paper finds and analyzes a formula for the total variation distance between iterations of riffle shuffles and iterations of “cut and then riffle shuffle”. This allows one to obtain information about the convergence rate of permutation statistics (such as the length of the longest increasing subsequence or position of a given card) under these processes. Similar results are given for affine...

Abstract. We compute the limit distribution for (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 two–colored case our method provides a different proof of a similar result by Tracy and Widom about...

We prove a formula for the number of permutations in Sn such that their first n−k entries are increasing and their longest increasing subsequence has length n − k. This formula first appeared as a consequence of character polynomial calculations in the work of Adriano Garsia, [2]. We give an elementary proof of this result and also of its q-analogue. In [2], Adriano Garsia derived as a conseque...