The abundances of light elements based on the big bang nucleosynthesis model are calculated using the Tsallis non-extensive statistics. The impact of the variation of the non-extensive parameter q from the unity value is compared to observations and to the abundance yields from the standard big bang model. We find large differences between the reaction rates and the abundance of light elements calculated with the extensive and the non-extensive statistics. We found that the observations are consistent with a non-extensive parameter q = 1 +0.05 −0.12 , indicating that a large deviation from the Boltzmann-Gibbs statistics (q = 1) is highly unlikely. arXiv:1205.4000v2 [nucl-th]

(M.S. Hussein), amt5ld@maths.leeds.ac.uk (D. Lesnic). AbstractIn this paper, we consider the inverse problem of simultaneous determination of time-dependent leading coefficient (thermal diffusivity) and free boundary in the one-dimensional time-dependent heat equation. The resulting inverse problem is recast as a nonlinear regularized least-squares problem. Stable and accurate numerical results are presented and discussed.

(M.S. Hussein), amt5ld@maths.leeds.ac.uk (D. Lesnic), ivanchov@franko.lviv.ua (M.I. Ivanchov). AbstractIn this paper, the determination of time-dependent leading and lower-order thermal coefficients is investigated. We consider the inverse and ill-posed nonlinear problems of simultaneous identification of a couple of these coefficients in the one-dimensional heat equation from Cauchy boundary data. Unique solvability theorems of these inverse problems are supplied and, in one new case where they were not previously provided, are rigorously proved. However, since the problems are still ill-posed the solution needs to be regularized. Therefore, in order to obtain a stable solution, a regularized nonlinear least-squares objective function is minimized in order to retrieve the unknown coefficients. The stability of numerical results is investigated for several test examples with respect to different noise levels and for various regularization parameters. This study will be significant to researchers working on computational and mathematical methods for solving inverse coefficient identification problems with applications in heat transfer and porous media.