Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X , generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reduc...

We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the...

Using improved mean field and strong coupling expansions we re-analyse the bulk phase diagram of the fundamental-adjoint action of the SU(2) Lattice Gauge Theory. We find that the qualitative features of the bulk phase diagram are robust and unchanged by the inclusion of higher order terms. On the other hand, some of the quantitative features, such as the location of the endpoint of the line of...

An adjoint sensitivity method is presented for parameter-dependent differentialalgebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system (for fully implicit DAEs) is shown. In...

In this article, we consider an optimization problem where the objective function is evaluated at fixed-point of a contraction mapping parameterized by control variable, and takes place over variable. Since derivative with respect to parameter can usually not be exactly, adjoint dynamical system used estimate gradients. Using estimation procedure, algorithm alternates between approximate gradie...

We study the isospectrality problem for a free quantum particle confined in ring with junction, analyzing all self-adjoint realizations of corresponding Hamiltonian terms boundary condition at junction. In particular, by characterizing energy spectrum spectral function, we classify two classes, identifying families isospectral Hamiltonians. These classes turn out to be discerned action parity (...

in this paper, we consider weighted composition operators betweenmeasurable differential forms and then some classic properties of these operators are characterized.

Inspired by Lie algebra expansion, we consider an extension of the introduced in A. Fontanella and S. J. van Tongeren [Coset space actions for nonrelativistic strings, High Energy Phys. 06 (2022) 80.] string coset action ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$. We show that extended admits a nondegenerate inner product which is adjoint invariant under full algebra...