Comment on: “Fundamental flows with nonlinear slip conditions: exact solutions”, by R. Ellahi,T. Hayat,F. M. Mahomed and A. Zeeshan,Z. Angew. Math. Phys. 61 (2010) 877–888

In their article (Fundamental flows with nonlinear slip conditions: exact solutions, R. Ellahi, T. Hayat, F. M. Mahomed and A. Zeeshan, Z. Angew. Math. Phys. 61 (2010) 877–888.), the authors considered three simple cases of the steady flow of a third grade fluid between parallel plates with slip conditions; namely, Couette flow, Poiseuille flow, and generalized Couette flow. They obtained exact solutions, which were utilized in a way that did not lead to useful results. Their conclusion that the Couette flow cannot be obtained from the generalized Couette flow, by dropping the pressure gradient, is incorrect. Meaningful results based on their solution are herein presented.     

Comment on: “Fundamental flows with nonlinear slip conditions: exact solutions”, by R. Ellahi, T. Hayat, F. M. Mahomed and A. Zeeshan, Z. Angew. Math. Phys. 61 (2010) 877–888

In their article (Fundamental flows with nonlinear slip conditions: exact solutions, R. Ellahi, T. Hayat, F. M. Mahomed and A. Zeeshan, Z. Angew. Math. Phys. 61 (2010) 877–888.), the authors considered three simple cases of the steady flow of a third grade fluid between parallel plates with slip conditions; namely, Couette flow, Poiseuille flow, and generalized Couette flow. They obtained exact solutions, which were utilized in a way that did not lead to useful results. Their conclusion that the Couette flow cannot be obtained from the generalized Couette flow, by dropping the pressure gradient, is incorrect. Meaningful results based on their solution are herein presented.     

Comment to: Perturbation estimates for the nonlinear matrix equation X−A ∗ X q A=Q (0<q<1) by G. Jia and D. Gao

We show that the perturbation estimate for the matrix equation X?A ^? X ^q A=Q (0<q<1), due to G. Jia and D. Cao, published in this journal, is wrong.     

“Small sample properties of ML,COLS and DEA estimators of frontier models in the presence of heteroscedasticity” by A.N. Bojanic,S.B. Caudill and J.M. Ford,European Journal of Operational Research 108, 1998, 140–148: A comment

This paper comments on the paper by Bojanic et al. (1998) in this Journal.     

Book Review of Introduction to the theory of toeplitz operators with infinite index,Vladimir Dybin and Sergei M. Grudsky (Translated from Russian by Andrei Jacob), operator theory: advances and applications,Birkhäuser Verlag,Basel-Boston-Berlin, 2002, volume 137, 299 pages. ISBN 3-7643-6728-8.

We consider a special class of optimization problems that we call a Mathematical Programme with Vanishing Constraints. It has a number of important applications in structural and topology optimization, but typically does not satisfy standard constraint qualifications like the linear independence and the Mangasarian–Fromovitz constraint qualification. We therefore investigate the Abadie and Guignard constraint qualifications in more detail. In particular, it follows from our results that also the Abadie constraint qualification is typically not satisfied, whereas the Guignard constraint qualification holds under fairly mild assumptions for our particular class of optimization problems.