Sea f: N → R una función convexa y sea x ∈ Ni, donde N es un convexo en un espacio vectorial real. Se demuestra que, si Df<(x) es no vacío, entonces Df<(x) es el interior algebraico de Df≤(x).
In this paper, we introduce a new class of variational inequality with its weak and split forms to obtain an -optimal solution to the multi-dimensional interval-valued variational problem, which is a wider class of interval-valued programming problem in operations research. Using the concept of (strict) -convexity over the involved interval-valued functionals, we establish equivalence relationships between the solutions of variational inequalities and the (strong) -optimal solutions of the multi-dimensional...
According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value...
The problem considered in this paper is the minimization of the lifetime variance of a complex system subject to its expected life and economic constraints. The example of a bridge network, in which all elements have constant failure rates, illustrates the problem. A numerical algorithm for solving this optimization problem by using exact formulae for system lifetime moments is included. Using this algorithm, we can obtain results better than the solutions known from earlier papers.
This paper proposes a novel approach to reliability evaluation for active Fault Tolerant Control Systems (FTCSs). By introducing a reliability index based on the control performance and hard deadline, a semi-Markov process model is proposed to describe system operation for reliability evaluation. The degraded performance of FTCSs in the presence of imperfect Fault Detection and Isolation (FDI) is reflected by semi-Markov states. The semi-Markov kernel, the key parameter of the process, is determined...
The availability of a system with dependent units is obtained in the case where the system fails when one of the essential units fails. Markov model is assumed. The system considered consists of dependent units of which units are essential units. A unit is said to be essential if its failure causes the system to fail. The mean and variance of time to system failure are given. Unit reliability is also discussed.
The contribution is devoted to computations of the limit load for a perfectly plastic model with the von Mises yield criterion. The limit factor of a prescribed load is defined by a specific variational problem, the so-called limit analysis problem. This problem is solved in terms of deformation fields by a penalization, the finite element and the semismooth Newton methods. From the numerical solution, we derive a guaranteed upper bound of the limit factor. To achieve more accurate results, a local...