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.

This paper examines the inter-relationship of three major phenomena- population growth, uncontrolled urban expansion and urban development in Ado Ekiti, Nigeria. Uncontrolled urban expansion has a resultant effect on the urban development of a city whereas uncontrolled urban development is caused by uncontrolled population increase is caused by Migration. This work encapsulates how population g...

The population growth, is increase in the number of individuals in population and it depends on some random environment effects. There are several different mathematical models for population growth. These models are suitable tool to predict future population growth. One of these models is logistic model. In this paper, by using Feynman-Kac formula, the Adomian decomposition method is applied to ...

Shortage of water resources and increasing demand to consumption of this scarce resource, leads to somenoticeable limitations. On the other hand, population growth and consequently, increasing demand for water in aridand semi arid regions , needs production in exchange of little amount of water consumption. To approach thisobjective, an experiment in the complete randomized blocks carried out i...