A new characterization of excessive functions for arbitrary one–dimensional regular diffusion processes is provided, using the notion of concavity. It is shown that excessivity is equivalent to concavity in some suitable generalized sense. This permits a characterization of the value function of the optimal stopping problem as “the smallest nonnegative concave majorant of the reward function” a...

This article discusses the generation of temperature majorant cross sections, the type of cross sections required by two separate techniques related to Monte Carlo neutron tracking, namely the Doppler-broadening rejection correction (DBRC) and Target Motion Sampling (TMS) temperature treatment methods. In the generation of these cross sections the theoretically infinite range of thermal motion ...

We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above ...

In this paper new fundamental theorems are stated, which allow to easily determine a first-order majorant system of a pseudo-quadratic uncertain MIMO discrete-time system. For the above class of systems, some results and systematic methods are provided, which allow to solve, “via majorant system”, several analysis problems of robust stability, stabilization and tracking of a generic reference s...

We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with ...

Let α ∈ C in the upper half-plane and let I be an interval. We construct an analogue of Selberg’s majorant of the characteristic function of I that vanishes at the point α. The construction is based on the solution to an extremal problem with positivity and interpolation constraints. Moreover, the passage from the auxiliary extremal problem to the construction of Selberg’s function with vanishi...

This paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎With the help of the Nehari manifold and Palais-Smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a c...