Non-probabilistic convex models need to be provided only the changing boundary of parameters rather than their exact probability distributions; thus, such models can be applied to uncertainty analysis of complex structures when experimental information is lacking. The interval and the ellipsoidal models are the two most commonly used modeling methods in the field of non-probabilistic convex mod...

New line generation algorithm is proposed for generating lines over 3D body-centered cubic lattice, a kind of optimal lattice in 3D space. The main contribution in this paper is employing the 3D Bresenham algorithm, a popular algorithm for generating 3D lines on a cubic lattice, to produce the BCC lattice occupied by 3D lines, with the help of the adjunct parallelepiped space, having the same c...

We investigate the problem of finding a minimal volume parallelepiped enclosing a given set of n threedimensional points. We give two mathematical properties of these parallelepipeds, from which we derive two algorithms of theoretical complexity O(n6). Experiments show that in practice our quickest algorithm runs in O(n2) (at least for n 105). We also present our application in structural biolo...

This paper presents a complete end-to-end framework to generate automatic message-passing code for tiled iteration spaces. It considers general parallelepiped tiling transformations and general convex iteration spaces. We aim to address all problems concerning data parallel code generation efficiently by transforming the initial non-rectangular tile to a rectangular one. In this way, data distr...

Fix a choice and ordering of four pairwise non-adjacent vertices of a parallelepiped, and call a motif a sequence of four points in R3 that coincide with these vertices for some, possibly degenerate, parallelepiped whose edges are parallel to the axes. We show that a set of r points can contain at most r2 motifs. Generalizing the notion of motif to a sequence of L points in Rp, we show that the...

Solutions of the diffusion approximation to the radiative transport equation are derived for a turbid (rectangular) parallelepiped using the method of image sources and applying extrapolated boundary conditions. The derived solutions are compared with Monte Carlo simulations in the steady-state and time domains. It is found that the diffusion theory is in good agreement with Monte Carlo simulat...

The present paper deals with an application of Jacobi polynomial and multivariable Aleph-function to solve the differential equation heat conduction in non-homogeneous moving rectangular parallelepiped. temperature distribution parallelepiped, a direction length (x-axis) between limits x = −1 1 has been considered. conductivity velocity have assumed be variables. We shall see two particular case...