A new method due to Fokas for explicitly solving boundary-value problems for linear partial differential equations is extended to equations with mixed partial derivatives. The Benjamin-Bona-Mahony equation is used as an example: we consider the Robin problem for this equation posed both on the half line and on the finite interval. For specific cases of the Robin boundary conditions the boundary...

The n-card problem is to determine the minimal intervals [u, v] such that for every n×n stochastic matrix A there is an n×n permutation matrix P (depending on A) such that tr(PA) ∈ [u, v]. This problem is closely related to classical mathematical problems from industry and management, including the linear assignment problem and the travelling salesman problem. The minimal intervals for the n-ca...

1 Although the bottleneck traveling salesman problem has not apparently been discussed before, the closely related bottleneck assignment problem has been discussed and solved by 0. Gross, "The bottleneck assignment problem," the RAND Corporation P-1630, March 6, 1959. 2 See Kruskal, J. B., "On the shortest spanning subtree of a graph and the travelling salesman problem," Proc. Amer. Math. Soc.,...

In this paper we will deal with the sequencing and routing problem of order pickers in conventional multi-parallel-aisle warehouse systems. For this NP-hard Steiner Travelling Salesman Problem exact algorithms only exist for warehouses with at most three cross aisles. We propose a new approach were the problem of routing order pickers in multiple-block warehouses is translated into a classical ...

Genetic Algorithms are the population based search and optimization technique that mimic the process of natural evolution. Different crossover and mutation operators exist to solve the problem that involves large population size. Example of such a problem is travelling sales man problem, which is having a large set of solution. In this paper we will discuss different mutation operators that hel...