One of the fundamental topics on the area of combinatorial algorithms is the efficient generation of all objects in a specific combinatorial class in such a way that each item is generated exactly once, hence producing a listing of all objects in the considered class. A common approach to this problem has been the generation of the objects of a combinatorial class in such a way that two consecu...

This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar to the transformation used to relate the classical Hamilton-Jacobi equation to the Schrödinger equation. As a re...

We present serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type. A vehicle starts at a prespecified point zo and follows a unit speed trajectory ~ ( t ) inside a region in P. until an unspecified time T that the region is exited. A trajectory mini...

This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar to the transformation used to relate the classical Hamilton-Jacobi equation to the Schrödinger equation. As a re...

Dirac’s classic theorem asserts that if G is a graph on n vertices, and δ(G) ≥ n/2, then G has a hamilton cycle. As is well known, the proof also shows that if deg(x) + deg(y) ≥ (n− 1), for every pair x, y of independent vertices in G, then G has a hamilton path. More generally, S. Win has shown that if k ≥ 2, G is connected and ∑ x∈I deg(x) ≥ n− 1 whenever I is a k-element independent set, the...

This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar to the transformation used to relate the classical Hamilton-Jacobi equation to the Schrödinger equation. As a re...

objective : patients with chronic physical diseases sometimes show increased loss of function; such patients need more care. anxiety is a well-known symptom that is prevalent among chronic obstructive pulmonary disease patients that can prolong and increase the risk of hospitalization. the purpose of this study was to evaluate the severity of anxiety in the mentioned patients and to examine the...

A graph is called homogeneously traceable if every vertex an endpoint of a Hamilton path. In 1979 Chartrand, Gould and Kapoor proved that for integer n≥9, there exists nonhamiltonian order n. The graphs they constructed are irregular. Thus it natural to consider the existence problem regular graphs. We prove two results: (1) For even n≥10, cubic n; (2) p≥18, 4-regular p circumference p−4. Unsol...