We present an algorithm for the two-dimensional translational containment problem: nd translations for k polygons (with up to m vertices each) which place them inside a polygonal container (with n vertices) without overlapping. The polygons and container may be nonconvex. The containment algorithm consists of new algorithms for restriction, evaluation, and subdivision of two-dimensional conngur...

In this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. The stages for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. The model is analyzed by using linear stability analysis to ob...

A new type of composite structure with a metal foam is reinforced by the metal corrugated core, called metal-foam-filled sandwich panel with a corrugated or V-frame core, is modelled, simulated, and studied in this article. All types of samples with different relative densities of the foam are tested and analyzed under the drop hammer load. The sandwich panel included two aluminium face-sheet, ...

In this paper, the effect of angle between predictor and corrector surfaces on the structural analysis is investigated. Two objective functions are formulated based on this angle and also the load factor. Optimizing these functions, and using the structural equilibrium path’s geometry, lead to two new constraints for the nonlinear solver. Besides, one more formula is achieved, which was p...

Man-made objects often have a polyhedral shape. For polyhedral objects it is advantageous to use a line-photogrammetric approach, i.e. lines are observed in the images instead of points. A novel line-photogrammetric mathematical model is presented. This model is built from condition equations with image line observations and object parameters in the form of the coordinates of object points and ...

The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of inform...

The Binary Space Partition (BSP) technique is a simple and efficient method to adaptively partition an initial given domain to match the geometry of a given input function. As such the BSP technique has been widely used by practitioners, but up until now no rigorous mathematical justification to it has been offered. Here we attempt to put the technique on sound mathematical foundations, and we ...