Mathematical Foundations of Hypergraph

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...

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...

Foundations for Mathematical Structuralism∗

We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematic...