Compactness and convergence rates in the combinatorial integral approximation decomposition

The combinatorial integral approximation decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and computing a discrete-valued approximation of the relaxed control. Different algorithms exist for the second step to construct piecewise constant discrete-valued approximants that are defined on given decompositions of the domain. It is known that the resulting discrete controls can be constructed such that they converge to a relaxed control in the \(\hbox {weak}^*\) topology of \(L^\infty \) if the grid constant of this decomposition is driven to zero. We exploit this insight to formulate a general approximation result for optimization problems, which feature discrete and distributed optimization variables, and which are governed by a compact control-to-state operator. We analyze the topology induced by the grid refinements and prove convergence rates of the control vectors for two problem classes. We use a reconstruction problem from signal processing to demonstrate both the applicability of the method outside the scope of differential equations, the predominant case in the literature, and the effectiveness of the approach.

     

Judith R. Goodstein: Einstein’s Italian Mathematicians – Ricci,Levi-Civita,and the Birth of General Relativity

Mathematische Semesterberichte -     

Some geometric inequalities for varifolds on Riemannian manifolds based on monotonicity identities

Annals of Global Analysis and Geometry - Using Rauch’s comparison theorem, we prove several monotonicity inequalities for Riemannian submanifolds. Our main result is a general Li–Yau...     

DABCOnium: An Efficient and High‐Voltage Stable Singlet Oxygen Quencher for Metal–O2 Cells

Singlet oxygen (¹O₂) causes a major fraction of the parasitic chemistry during the cycling of non‐aqueous alkali metal‐O₂ batteries and also contributes to interfacial reactivity of transition‐metal oxide intercalation compounds. We introduce DABCOnium, the mono alkylated form of 1,4‐diazabicyclo[2.2.2]octane (DABCO), as an efficient ¹O₂ quencher with an unusually high oxidative stability of ca. 4.2 V vs. Li/Li⁺. Previous quenchers are strongly Lewis basic amines with too low oxidative stability. DABCOnium is an ionic liquid, non‐volatile, highly soluble in the electrolyte, stable against superoxide and peroxide, and compatible with lithium metal. The electrochemical stability covers the required range for metal–O₂ batteries and greatly reduces ¹O₂ related parasitic chemistry as demonstrated for the Li–O₂ cell.     

Correction to: Quantitative analysis of PET microplastics in environmental model samples using quantitative 1H-NMR spectroscopy: validation of an optimized and consistent sample clean-up method

Analytical and Bioanalytical Chemistry - The original version of this article contained a mistake.     

Influence of weak groups on polyelectrolyte mobilities

The ionization of dissociable groups in weak polyelectrolytes does not occur in a homogenous fashion. Monomer connectivity imposes constraints on the localization of the dissociated (charged) monomers that affect the local electric potential. As a result, the mean bare charge along a weak polyelectrolyte can vary depending on the proximity to topological features (e.g. presence of crosslinks or dangling ends). Using reaction‐ensemble Monte‐Carlo simulations we calculate the dissociation inhomogeneities for a few selected PE configurations, linear, rod‐like, flexible four‐arm star, and a star with stiff arms. An ensemble preaverage is used to obtain the annealed bare charge profile for these different polymer configurations. Using molecular dynamics simulations within a Lattice‐Boltzman fluid, we investigate how the electrophoretic mobility is affected by the bare charge inhomogeneities arising from the annealed weak polyelectrolytes. Surprisingly, the mobility obtained for the situations corresponding to the predicted charge profile for annealed weak polyelectrolytes are not significantly different than the mobility obtained when all the monomers have an identical charge (under the constraint that the total polyelectrolyte bare charge is the same). This is also true for the stiff rod‐like variants where conformational changes induced from the localization of the monomer charges are negligible. In salty solutions, we find that counterions are affected by the electric potential modulations induced by the topological features. Since the counterions crowd in regions where the electric potential caused by the dissociated monomers is highest, they wash‐out the bare charge inhomogeneities and contribute to a more uniform effective backbone charge.     

How to speed up the detection of aerobic microbial contaminations by using isothermal microcalorimetry

Journal of Thermal Analysis and Calorimetry - A sudden expansion is a classical problem which is happened in different industries such as energy conversion, environmental control, and chemical...