Codebooks with small inner-product correlation are applied in many practical applications including direct spread code division multiple access communications, space-time codes and compressed sensing. It is extremely difficult to construct codebooks achieving the Welch or Levenshtein bound. In this paper, we firstly generalize Jacobi sums over finite fields and secondly obtain asymptotically op...

In this chapter we consider optimal control problems with additional inequality constraints imposed on the control unknown u and for their efficient solution we combine a primal-dual active-set strategy with the multigrid method developed in the previous chapter. Control-constraints are specified by the condition u ∈ Uad, where the set of admissible controls Uad ⊂ L(Ω) is a proper subset of L(Ω...

pressurized injection operation means the pressurized injection of a liquid or solution into pore of a mass of soil or stone and/ or cavity between them and built structures. the injected mortar mustconstitute a soil and/ or jel- like matter inside the cavites, and/ or the operations of the injection must cause sedimentation of the solid matter suspending in these cavites. the primary purpose o...

We formulate a discrete time model to identify and evaluate the role of optimal control strategies on influenza transmission. We divide the population in two subgroups defined according to the contact activity or susceptibility levels. The individuals are identified as susceptible, infectious, treated, and recovered. The potential effect of antiviral treatment considering unlimited and limited ...

For optimal control problems satisfying convexity conditions in the state as well as the velocity, the optimal value is studied as a function of the time horizon and other parameters. Conditions are identified in which this optimal value function is locally Lipschitz continuous and semidifferentiable, or even differentiable. The Hamilton-Jacobi theory for such control problems provides the fram...

Abstract. We show a large time behavior result for class of weakly coupled systems of first-order Hamilton-Jacobi equations in the periodic setting. We use a PDE approach to extend the convergence result proved by Namah and Roquejoffre (1999) in the scalar case. Our proof is based on new comparison, existence and regularity results for systems. An interpretation of the solution of the system in...

In this paper, we investigate the L∞-error estimates for the solutions of general optimal control problem by mixed finite element methods. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive L∞-error estimates of optimal order both for the state variables and the control...

Human head movement can be looked at, as a rotational dynamics on the space SO(3) with constraints that have to do with the axis of rotation. Typically the axis vector, after a suitable scaling, is assumed to lie in a surface called Donders’ surface. Various descriptions of Donders’ surface are in the literature and in this paper we assume that the surface is described by a quadratic form. We p...

This article deals with the problem of computing energy-minimal trajectories between the invariant manifolds in the neighborhood of the equilibrium point L1 of the restricted 3-body problem. Initializing a simple shooting method with solutions of the corresponding linear optimal control problem, we numerically compute energy-minimal extremals from the Pontryagin’s Maximum principle, whose optim...