Non-linear Cyclic Codes that Attain the Gilbert-Varshamov Bound

We prove that there exist non-linear binary cyclic codes that attain the Gilbert-Varshamov bound

An optimal mechanism charging for priority in a queue

We derive a revenue-maximizing scheme that charges customers who are homogeneous with respect to their waiting cost parameter for a random fee in order to become premium customers. This scheme incentivizes all customers to purchase priority, each at his/her drawn price. We also design a revenue-maximizing scheme for the case where customers are heterogeneous with respect to their waiting cost parameter. Now lower cost parameter customers are encouraged to join the premium class at a low price: Given that, those with high cost parameter would be willing to pay even more for this privilege

Bounds on distances between eigenvalues

AbstractExplicit (computable) lower and upper bounds on the distances between a given real eigenvalue of a real square matrix and the remaining (not necessarily real) eigenvalues of the matrix are developed

Perturbation of null spaces with application to the eigenvalue problem and generalized inverses

AbstractWe consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of Laurent series expansions for the perturbed group inverse and pseudoinverse matrices