Adjoint state method is a well-known method to efficiently compute the gradient of a cost or objective function for a simulation-driven optimization problem. Essentially, it computes the adjoint action of Born operator (the linearized forward map) on any given vector. This report presents a derivation of adjoint state algorithm for an acoustic system discretized by staggered grid finite differe...

in this paper, some categorical properties of the category ${bf cpo}_{{bf act}text{-}s}$ of all {cpo $s$-acts}, cpo's equipped with actions of a monoid $s$ on them, and strict continuous action-preserving maps between them is considered. in particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. also, we show that the forgetful functor from...

The notion of “Weierstrass Section”, comes from Weierstrass canonical form for elliptic curves. In celebrated work Kostant (1963) [26] constructed such a section the action semisimple Lie algebra on its dual using principal s-triple. Actually it is enough to have an “adapted pair” and indeed construction in Joseph Shafrir (2010) [25] works rather well co-adjoint algebraic, but not necessarily r...

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over F(2(n)). Let G be an adjoint algebraic group of type B, C, or D defined over an algebraically closed field of characteristic 2. We construct the Springer correspondence for the nilpotent variety in the Lie algebra of G.

The effect of Z2 magnetic monopoles and vortices on the finite temperature deconfinement phase transition in the fundamental-adjoint Villain form of SU(2) lattice gauge theory has been investigated. A complete suppression of the Z2 monopoles has been shown to lead to an action for the theory which is self-dual under the exchange of the fundamental and adjoint couplings. By further suppressing t...

The general linear group $\mathrm{GL}(n)$ acts on the direct sum of $m$ copies $\mathrm{Mat}(n)$ by adjoint action. action induces unitriangular subgroup $U$. We present system free generators field $U$-invariants.

We consider the totally nonfree (TNF) action of a groups and the corresponding adjoint invariant (AD) measures on the lattices of the subgroups of the given group. The main result is the description of all adjoint-invariant and TNF-measures on the lattice of subgroups of the infinite symmetric group SN. The problem is closely related to the theory of characters and factor representations of gro...