In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...

We consider a Poisson problem and its functional a posteriori estimate derived in [20]. The estimate majorizes the L2 norm of the error of the discrete solution computed by FEM method and contains a free variable from a H(div) space. In order to keep the estimate sharp, the majorant term is minimized with respect to the free variable. A minimization procedure is introduced, containing a solutio...

We give exact estimations of certain weighted L2-norms of the derivative of polynomial, which have a curved majorant. They are all obtained as applications of special quadrature formulae. 2000 Mathematical Subject Classification: 41A17, 41A05, 41A55, 65D30

Using the concept of majorant sequences (see [4, ch. XXI], [5], [7], [8]) some new inequalities for Walsh polynomials with complex semi-monotone, complex semi-convex, complex monotone and complex convex coefficients are given.

Using the concept of majorant functions, we prove the existence and uniqueness of holomorphic solutions to nonlinear fractional diffusion problems. The analytic continuation of these solutions is studied and the singularity for two cases are posed.

We present a parallel algorithm for the Huuman Coding problem. We reduce the Huuman Coding problem to the Concave Least Weight Subsequence problem and give a parallel algorithm that solves the latter problem in O(p n log n) time with n processors on a CREW PRAM. This leads to the rst sublinear time o(n 2)-total work parallel algorithm for Huuman Coding. This reduction of the Huuman Coding probl...

Approximation theorems were formulated for function continuous in the neighborhood of some point x, -∞< x < ∞. Namely, upper bounds obtained approximations by their Gauss-Weierstrass singular operators terms a majorant first- and second-order continuity moduli relevant functions.

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly st...