Value functions propagated from initial or terminal costs and constraints by way of a differential inclusion, or more broadly through a Lagrangian that may take on∞, are studied in the case where convexity persists in the state argument. Such value functions, themselves taking on ∞, are shown to satisfy a subgradient form of the Hamilton-Jacobi equation which strongly supports properties of loc...

The quantization of the giant magnon away from the infinite size limit is discussed. We argue that this quantization inevitably leads to string theory on a ZM -orbifold of S . This is shown explicitly and examined in detail in the near plane-wave limit. A significant amount of work on the AdS/CFT correspondence [1],[2],[3] has been inspired the idea that the planar limit of N = 4 Yang-Mills the...

When using the original slope-intercept parameter-isation for the Hough transform, the resulting parameter space actually corresponds to the dual space. Indeed , lines are transformed into points, and for every point there is also a corresponding line. This paper presents a way of exploiting this special property, by the introduction of the Cascaded Hough Transform, or CHT for short. This allow...

In this paper we deal with a utility maximization problem at finite horizon on a continuous-time market with conical (and time varying) constraints (particularly suited to model a currency market with proportional transaction costs). In particular, we extend the results in [CO10] to the situation where the agent is initially endowed with a random and possibly unbounded quantity of assets. We st...

It is a standard remark that the group Aut(C) of abstract field automorphisms of C has uncountably many elements but only two that are are continuous. One consequence is that the analytic properties of a Dirichlet series ∑ n>1 a(n)n −s do not usually carry over to ∑ n>1 ι(a(n))n −s for ι ∈ Aut(C). Silly counterexamples abound: for instance, take a(n) = (1 − √ 2) and choose ι so that ι( √ 2) = −...

A generalized star-triangle transformation and a concept of triangle-duality have been introduced recently in the physics literature to predict exact percolation threshold values of several lattices. We investigate the mathematical conditions for the solution of bond percolation models, and identify an infinite class of lattice graphs for which exact bond percolation thresholds may be rigorousl...

A primal interior point method for control constrained optimal control problems with PDE constraints is considered. Pointwise elimination of the control leads to a homotopy in the remaining state and dual variables, which is addressed by a short step pathfollowing method. The algorithm is applied to the continuous, infinite dimensional problem, where discretization is performed only in the inne...

We apply the recently developed duality methods based on information relaxations to the classic linear quadratic (LQ) control problem. We derive two dual optimal penalties for the LQ problem when the control space is unconstrained. These two penalties, which are derived using value function and gradient methods, respectively, may be used to evaluate sub-optimal policies for constrained LQ probl...

K. Larsen, M. Soner, and G. Zitkovic kindly pointed out to us an error in our paper [1] which appeared in 2001 in this journal. They also provide an explicit counter-example in [4]. In Theorem 3.1 of [1] it was incorrectly claimed (among several other correct assertions) that the value function u(x) is continuously differentiable. The erroneous argument for this assertion is contained in Remark...

Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds. Using the geome...