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...

The prism over a graph G is the Cartesian product G2K2 of G with the complete graph K2. If G is hamiltonian, then G2K2 is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be an interesting relaxation of being hamiltonian. In this paper, we examine classical problems on hamiltonicity of graphs in the context of having a hamiltonian prism. c © ???...

This document contains a proof of the Cayley-Hamilton theorem based on the development of matrices in HOL/Multivariate Analysis.

The Adams apportionment method is the only divisor method that consistently favors small districts relative to the Hamilton method. The Jefferson method is the only divisor method that favors large districts relative to the Hamilton method. These statements hold for the Balinski and Young [3] interpretation of "favoring small/large districts," and for the partial "majorization ranking" introduc...