In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.

We study magnetohydrodynamic radiation-convection flow through a porous medium with mass transfer in the presence of a homogeneous first order chemical reaction and surface temperature oscillation. The governing equations are solved analytically using perturbation technique. Detailed computations of the influence of Hartmann number, frequency of the oscillation, radiation parameter, Prandtl num...

The behavior of the Hasse–Schmidt algebra under étale extension is used to show that the Hasse–Schmidt algebra of a smooth algebra of finite type over a field equals the ring of differential operators. These techniques show that the formation of Hasse–Schmidt derivations does not commute with localization, providing a counterexample to a question of Brown and Kuan; their conjecture is reformula...