<p style='text-indent:20px;'>We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In case multiplicative noise, existence optimal controls and necessary conditions for optimality are derived. additive we obtain a representation gradient cost functional adjoint calculus. The restriction to noise avoids necessity introducing bac...

This work presents and analyzes space-time finite element methods on fully unstructured simplicial meshes for the numerical solution of parabolic optimal control problems. Using Babuška's theorem, we show well-posedness first-order optimality systems a typical model problem with linear state equations, but without constraints. is done both continuous discrete levels. Based these results, derive...

A temperature-resistant organic phosphate with a photolabile o-nitrobenzyl protecting group is introduced in visible light curable thiol-click photopolymer, as reported by Sandra Schlögl, Thomas Griesser et al. their Communication (e202215525). The sequence-dependent λ-orthogonality of the curing and cleavage enables an efficient network formation at 451 nm, without premature release catalyst. ...

Noyes [Noyes, R. M. (1981) Proc. Natl. Acad. Sci. USA 78, 7248-7249] has obtained a result for the Gibbs free energy per unit mass in a continuous flow stirred tank reactor, which states that the steady-state free energy increases monotonically with decreasing residence time for any stable stationary point. We show that his derivation is based on an erroneous stability criterion. We further inv...

Given an original distribution, its statistical and probabilistic attributes may be scanned using the associated escort distribution introduced by Beck and Schlögl and employed in the formulation of nonextensive statistical mechanics. Here, the geometric structure of the one-parameter family of the escort distributions is studied based on the Kullback-Leibler divergence and the relevant Fisher ...