The classical Hamilton equations are reinterpreted by means of complex analysis, in a non standard way. This suggests a natural extension of the Hamilton equations to the quaternionic case, extension which coincides with the one introduced in [1] by a completely different approach.

Let N (l) be a continuous topological space. Recent developments in local calculus [19] have raised the question of whether every real, degenerate, semi-Kepler factor is linearly Noetherian. We show that every curve is pointwise semi-Hadamard, Thompson, almost surely ultra-reducible and non-continuously independent. It has long been known that every hyper-natural modulus equipped with a Pythago...

The eikonal equation and variants of it are of signii-cant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shape-from-shading and for recent dynamic theories of shape. Its numerical simulation can be delicate, owing to the formation of singularities in the evolving front, and is typically based on level s...

We provide a method of converting Lagrange and Finsler spaces and their Legendre transforms to Hamilton and Cartan spaces into almost Kähler structures on tangent and cotangent bundles. In particular cases, the Hamilton spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on effective phase spaces. This allows us to define the corresponding Fedosov operators and develop d...

Bill Hamilton, one of the most influential Darwinian thinkers of our time, was, above all, immensely curious. He was intrigued by nature's riddles, whether they arose in his backyard or in the faraway rain forests of Brazil or Africa, where he recently came to his tragic death. Walking with him in the woods or in the desert, sometimes even in a crowded street in the midst of a city, one had to ...

0. Introduction In this paper we will study the existence and uniqueness of generalized solutions of Hamilton-Jacobi equations. We will be concerned with the Gauchy problem (0. 1)

We say that a hypergraph H is hamiltonian path (cycle) saturated if H does not contain an open (closed) hamiltonian chain but by adding any new edge we create an open (closed) hamiltonian chain in H. In this paper we ask about the smallest size of an r-uniform hamiltonian path (cycle) saturated hypergraph, mainly for r = 3. We present a construction of a family of 3-uniform path (cycle) saturat...

Theorem 1. Let A be a n × n matrix, and let p(λ) = det(λI − A) be the characteristic polynomial of A. Then p(A) = 0.

This work treats Hamilton-Jacobi-Bellman equations. Their relation to several problems in mathematics is presented and an introduction to viscosity solutions is given. The work of several research articles is reviewed, including the Barles-Souganidis convergence argument and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi-Bellman equations is...