The objective of this paper is to investigate a multi-objective linear quadratic Gaussian (LQG) control problem. Specifically, we examine an optimal problem that minimizes cost over finite time horizon for stochastic systems subject energy constraints. To tackle problem, propose efficient bisection line search algorithm outperforms other approaches such as semidefinite programming in terms comp...

1 Classical Lie algebras A Lie algebra is a vector space g with a bilinear map [, ] : g× g → g such that (a) [x, y] = −[y, x], for x, y ∈ g, and (b) (Jacobi identity) [x, [y, z]] + [z, [x, y]] + [y, [z, x]] = 0, for all x, y, z ∈ g. A bilinear form 〈, 〉 : g× g → C is ad-invariant if, for all x, y, z ∈ g, 〈adx(y), z〉 = −〈y, adx(z)〉, where adx(y) = [x, y], (1.1) for x, y,∈ g. The Killing form is ...

Throughout the 1980’s, Kudla and the second named author studied integral transforms Λ from closed differential forms on arithmetic quotients of the symmetric spaces of orthogonal and unitary groups to spaces of classical Siegel and Hermitian modular forms ([11, 12, 13, 14]). These transforms came from the theory of dual reductive pairs and the theta correspondence. In [14] they computed the Fo...

We study the potential between a static center monopole and antimonopole in 4d SU(2) Yang–Mills theory. Using a new numerical method, we show that the ’t Hooft loop is a dual order parameter with respect to the Wilson loop, for the deconfinement phase transition. We observe a 3d Ising–like critical behaviour for the dual string tension related to the spatial ’t Hooft loop as a function of the t...

The steady boundary layer flow and heat transfer of a viscous fluid on a moving flat plate in a parallel free stream with variable fluid properties are studied. Two special cases, namely, constant fluid properties and variable fluid viscosity, are considered. The transformed boundary layer equations are solved numerically by a finite-difference scheme known as Keller-box method. Numerical resul...

We derive a stable technique, based upon matrix pencils, for the reconstruction of (or approximation by) polygonal shapes from moments. We point out that this problem can be considered the dual of 2 D numerical quadrature over polygonal domains. An analysis of the sensitivity of the problem is presented along with some numerical examples illustrating the relevant points. Finally, an application...

In this paper we propose a new decomposition method for large scale linear programming. This method dualizes an (arbitrary) subset of the constraints and then maximizes the resulting dual functional by dual ascent. The ascent directions are chosen from a finite set and are generated by a truncated version of the painted index algorithm [13]. Central to this method is the novel notion of (e,8)co...