We formulate three slightly di erent notions of oriented singular chain complexes and show that all three are naturally homotopic to ordinary singular chain complexes

It is shown that the comment by Costa and Meneses [1] did not point any technical or conceptual flaw in our paper titled " Conservative Force Fields in the application of the nonextensive distribution to the historical problem of the unbounded isothermal atmosphere under constant gravity is theoretically correct. It should be stressed that our solution is somewhat connected with a similar solut...

We study the porous medium equation   = , 0 < < , > m t x t  0 t xx . We prove finite time quenching for the solution at the boundary . We also estabu u with a singular boundary condition       0, = 0, m x u t u   = 0 x lish the quenching rate and asymptotic behavior on the quenching point.

The main result is that for λ strong limit singular failing the continuum hypothesis (i.e. 2 > λ+), a polarized partition theorem holds.

This paper establishes a refinement of the classical LöwenheimSkolem theorem. The main result shows that any first order structure has a countable elementary substructure with strong second order properties. Several consequences for Singular Cardinals Combinatorics are deduced from this.