In many practical situations, e.g., in aerospace applications and in mammography, it is important to test the structural integrity of material structures. We show that interval methods can help.
The ideal design of an airplane should include built-in sensors that are pre-blended in the perfect aerodynamic shape. Each built-in sensor is expensive to blend in and requires continuous maintenance and data processing, so we would like to use as few sensors as possible. The ideal formulation of the corresponding optimization problem is, e.g., to minimize… (More)
One of the most important characteristics of the plane is its weight: every pound shaved oo the plane means a pound added to the carrying ability of this plane. As a result, planes are made as light as possible , with its \skin" as thin as possible. However, the thinner the layer, the more vulnerable is the resulting structure to stresses and faults, and a… (More)
Flight is a very stressful experience for materials and structures. As a result, even small faults in aerospace structures can lead to catastrophic results. It is therefore desirable to test the structural integrity of an airplane and/or a space structure before the ight (and ideally, in-ight as well) and detect potential faults. In this paper, we show that… (More)
Celestial bodies such as galaxies, stellar clusters, planetary systems, etc., have diierent geometric shapes (e.g., galaxies can be spiral or circular, etc.). Usually, complicated physical theories are used to explain these shapes; for example, several dozen diierent theories explain why many galaxies are of spiral shape. Some rare shapes are still diicult… (More)
The inverse problem is usually diicult because the signal (image) that we want to reconstruct is weak. Since it is weak, we can usually neglect quadratic and higher order terms, and consider the problem to be linear. Since the problem is linear, methods of solving this problem are also, mainly, linear (with the notable exception of the necessity to take… (More)
– This paper treats computation as a game process. We place an algorithm within a single computational domain. The domain structure is a graphical structure with the moves of the game representing vertices. The algorithmic process evolves through these moves. The noise of the physical computing device manifests a mesoscopic system. The algorithmic process… (More)
| The ideal design of an airplane should include built-in sensors that are pre-blended in the perfect aerodynamic shape. Each built-in sensor is expensive to blend in and requires continuous maintenance and data processing, so we would like to use as few sensors as possible. The ideal formulation of the corresponding optimization problem is, e.g., to… (More)