Optimal design methods involving the solution of an adjoint system of equations are an active area of research in computational fluid dynamics, particularly for aeronautical applications. This paper presents an introduction to the subject, emphasising the simplicity of the ideas when viewed in the context of linear algebra. Detailed discussions also include the extension to p.d.e.’s, the constr...

Transformations of dynamical systems are discussed in terms of adjoint, simple adjoint and weak adjoint functors. The relevance of this approach to interpretations of nuclear transplant experiments is suggested, and three new theorems concerning the development of biological systems are presented. Another three theorems concerning adjoint dyna-mical systems are proved. The connection of these r...

The standard approach to the solution of the adjoint equations stresses the similarity of direct and adjoint equations and implies the use of similar methods for their solution. Nevertheless, the adjoint equations have significant peculiarities in comparison with the direct problem equations at least for compressible flows. From a numerical viewpoint these features concern the existence of the ...

Examples of symmetric quantum semimartingales are easy to find, but essentially self-adjoint quantum semimartingales have, in general, proved elusive. This is not unexpected since a quantum semimartingale is in some sense an indefinite integral of a family of unbounded operators, and strong conditions are required to ensure that the sum of even two unbounded self-adjoint operators is self-adjoi...

For a class of singular potentials, including the Coulomb potential and V (x) = g/x with the coefficient g in a certain range, the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the selfadjoint version chosen. The talk discusses ...

The effect of topology on the thermodynamics of a gas of adjoint representation charges interacting via 1+1 dimensional SU (N) gauge fields is investigated. We demonstrate explicitly the existence of multiple vacua parameterized by the discrete superse-lection variable k = 1, · · · , N. In the low pressure limit, the k dependence of the adjoint gas equation of state is calculated and shown to b...

In this paper, we consider the forgetful functor from the category LDcpo of local dcpos (respectively, Dcpo of dcpos) to the category Pos of posets (respectively, LDcpo of local dcpos), and study the existence of its left and right adjoints. Moreover, we give the concrete forms of free and cofree S-ldcpos over a local dcpo, where S is a local dcpo monoid. The main results are: (1) The forgetful...

We consider one-dimensional steady-state balance laws with discontinuous solutions. Giles and Pierce [J. Fluid Mech., 426 (2001), pp. 327–345] realized that a shock leads to a new term in the adjoint error representation for target functionals. This term disappears if and only if the adjoint solution satisfies an internal boundary condition. Curiously, most computer codes implementing adjoint e...

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. The following paper presents a new method for sensitivity ana...

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of analytic integrals. We also consider the potential systems on adjoint orbits, wh...