| The problem of initial probability assignment consistent with the available information about a probabilis-tic system is called a direct problem. Jaynes' maximum en-tropy principle (MaxEnt) provides a method for solving direct problems when the available information is in the form of moment constraints. On the other hand, given a probability distribution, the problem of nding a set of constra...

We present a precise fully relativistic numerical solution of the two-center Coulomb problem. The special case unit nuclear charges is relevant for accurate description ${\rm H}_2^+$ molecular ion and its isotopologues, systems that are an active experimental topic. computation utilizes 2-spinor minmax approach finite-element method. computed total energies have estimated fractional uncertainti...

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are ...

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference ap...

The relation between L 2 ?gain and nite dimensional nonlinear observers is investigated. It is shown that suitable choices of supply rates render nite dimensional minimum energy, minimum energy certainty-equivalence, and minmax observers for nonlinear systems. The gains of these observers are analogous of the error covariance of the Kalman-Filter. They are derived by solving explicitly Hamilton...

The asymptotic behavior of the solution of a differential inclusion provides a simple proof of a minmax theorem.

This paper considers the shortest path problem on directed acyclic graphs, where the uncertainty of input data (lengths of arcs) is modeled in the form of intervals. In order to handle the interval data the minmax criterion to the regret values is applied, where the original objective function with interval coefficients is transformed into that of finding the least maximum worst-case regret, wh...

This paper focuses on tractable instances of interval data minmax regret graph problems. More precisely, we provide polynomial and pseudopolynomial algorithms for sets of particular instances of the interval data minmax regret versions of the shortest path, minimum spanning tree and weighted (bipartite) perfect matching problems. These sets are defined using a parameter that measures the distan...