Mathematical Foundations of Elasticity

Mathematical Foundations of Photogrammetry

Photogrammetry uses photographic cameras to obtain information about the 3D world. The basic principle of photogrammetric measurement is straightforward: recording a light ray in a photographic image corresponds to observing a direction from the camera to the 3D scene point where the light was reflected or emitted. From this relation, procedures have been derived to orient cameras relative to e...

Mathematical Foundations of Supersymmetry

Mathematical Foundations of Randomness

Thus there are a finite number of possible outcomes, say ω1, ω2, . . . , ωn, and each outcome ωi has a fixed non-trivial probability pi, so that P (ωi) = pi with 0 < pi < 1 for i = 1, 2, . . . , n, and ∑n i=1 pi = 1. The outcomes may be generated either automatically from a continuously running process, or on demand, say by pressing a button on the blackbox. We think of this as an abstract mode...

On the microscopic foundations of elasticity.

The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which microscopically based derivations of elasticity are documented are (nearly) uniformly strained lattices. A microscopic approach to elasticity is proposed. As a first...

Astrogeometry: towards Mathematical Foundations

In image processing (e.g., in astronomy), the desired black-and-white image is, from the mathematical viewpoint, a set. Hence, to process images, we need to process sets. To deene a generic set, we need innnitely many parameters; therefore, if we want to represent and process sets in the computer, we must restrict ourselves to nite-parametric families of sets that will be used to approximate th...