Mathematics and Wave Mechanics.

Rational Mechanics and Natural Mathematics

Chu spaces have found applications in computer science, mathematics, and physics. They enjoy a useful categorical duality analogous to that of lattice theory and projective geometry. As natural mathematics Chu spaces borrow ideas from the natural sciences, particularly physics, while as rational mechanics they cast Hamiltonian mechanics in terms of the interaction of body and mind. This paper a...

Wave Mechanics

1 The Schrödinger equation In classical mechanics the motion of a particle is usually described using the time-dependent position ix(t) as the dynamical variable. In wave mechanics the dynamical variable is a wavefunction. This wavefunction depends on position and on time and it is a complex number – it belongs to the complex numbers C (we denote the real numbers by R). When all three dimension...

From Matrix Mechanics and Wave Mechanics to Unified Quantum Mechanics

T he story I want to tell you begins in March 1926 and ends in April 1926. Early in March two separate theories existed: matrix mechanics and wave mechanics. At the end of April these two had merged into one theory, more powerful than the two parents taken separately. Wave mechanics was based upon three fundamental hypotheses: A. Stationary states are determined by complexvalued wave functions ...

Faculty of Mathematics , Informatics and Mechanics

In this dissertation two models of morphogen transport are studied analytically. Both models are based on the concept of positional signalling as introduced by Wolpert in the late sixties. Positional signalling explains the mechanism of cell differentiation and pattern formation in developing embryo using the process of morphogen gradient formation. Both models couple semilinear parabolic equat...

Mathematics and mechanics of granular materials