Exactness of the lowest order supersymmetric WKB (SWKB) quantization condition x 2 x 1 E − ω 2 (x)dx = n¯ hπ, for certain potentials, is examined, using complex integration technique. Comparison of the above scheme with a similar , but exact quantization condition, c p(x, E)dx = 2πn¯ h, originating from the quantum Hamilton-Jacobi formalism reveals that, the locations and the residues of the po...

The paper centers around a pair of sequences of linear positive operators. The former has the degree of exactness one and the latter has its degree of exactness null, but, as a novelty, it reproduces the third test function of Korovkin theorem. Quantitative estimates of the rate of convergence are given in different function spaces traveling from classical approximation to approximation in abst...

The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact constraint and as such, is a convex problem with polynomial time complexity. Moreover, as a main pratical advantage of this relaxation over the standard Sem...

The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact constraint and as such, is a convex problem with polynomial time complexity. Moreover, as a main pratical advantage of this relaxation over the standard Sem...

Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of “homotopical exactness”, appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be given for very general “categories with homotopies” having homotopy kernels and cokernels, but become more interesting under suitable “stability” hypotheses, sa...