Let Ln be the length of the longest increasing subsequence of a random permutation of the numbers 1, . . . , n, for the uniform distribution on the set of permutations. We discuss the “hydrodynamical approach” to the analysis of the limit behavior, which probably started with Hammersley (1972), and was subsequently further developed by several authors. We also give two proofs of an exact (non-a...

Two-dimensional Lorentzian geometry has recently found application in some models of nonrelativistic systems, most profitably for the process of boarding an aeroplane. The duration of the boarding process is assumed to be a result of passengers standing in the isle and blocking each others’ way. According to this model, the expected boarding time is equal to the length of the longest timelike g...

New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematic and uses Max-Plus idempotent semiring. Problem of finding longest increasing subsequence is reformulated in a matrix form and solved with linear algebra.

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...

In this paper, Vacuum Assisted Resin Transfer Molding (VARTM) method was simulated by analytical solution. Then the effect of parameters like fiber density, distribution of layer thickness, perform layer thickness, resin viscosity was investigated theoretically. Obtained results show that by selecting optimum distribution layer thickness, increasing fiber volume fraction, reducing viscosity of ...

In this paper, Vacuum Assisted Resin Transfer Molding (VARTM) method was simulated by analytical solution. Then the effect of parameters like fiber density, distribution of layer thickness, perform layer thickness, resin viscosity was investigated theoretically. Obtained results show that by selecting optimum distribution layer thickness, increasing fiber volume fraction, reducing viscosity of ...