State constrained reachability for stochastic hybrid systems

Many control problems can be formulated as driving a system to reach some target states while avoiding some unwanted states. We study this problem for systems with regime change operating in uncertain environments. Nowadays, it is a common practice to model such systems in the framework of stochastic hybrid system models. In this casting, the problem is formalized as a mathematical problem named state constrained stochastic reachability analysis. In the state constrained stochastic reachability analysis, this probability is computed by imposing a constraint on the system to avoid the unwanted states. The scope of this paper is twofold. First we define and investigate the state constrained reachability analysis in an abstract mathematical setting. We define the problem for a general model of stochastic hybrid systems, and we show that the reach probabilities can be computed as solutions of an elliptic integro-differential equation. Moreover, we extend the problem by considering randomized targets. We approach this extension using stochastic dynamic programming. The second scope is to define a developmental setting in which the state constrained reachability analysis becomes more tractable. This framework is based on multilayer modelling of a stochastic system using hierarchical viewpoints. Viewpoints represent a method originated from software engineering, where a system is described by multiple models created from different perspectives. Using viewpoints, the reach probabilities can be easily computed, or even symbolically calculated. The reach probabilities computed in one viewpoint can be used in another viewpoint for improving the system control. We illustrate this technique for trajectory design.     

Zero-sum problems with congruence conditions

For a finite abelian group G and a positive integer d, let s _dℕ(G) denote the smallest integer ℓ∈ℕ₀ such that every sequence S over G of length |S|≧ℓ has a nonempty zero-sum subsequence T of length |T|≡0 mod d. We determine s _dℕ(G) for all d≧1 when G has rank at most two and, under mild conditions on d, also obtain precise values in the case of p-groups. In the same spirit, we obtain new upper bounds for the Erdős–Ginzburg–Ziv constant provided that, for the p-subgroups G _p of G, the Davenport constant D(G _p ) is bounded above by 2exp  (G _p )−1. This generalizes former results for groups of rank two.     

Abstract capacitary estimates and the completeness and separability of certain classes of non-locally convex topological vector spaces

We are concerned with establishing completeness and separability criteria for large classes of topological vector spaces which are typically non-locally convex, including Lebesgue-like spaces, Lorentz spaces, Orlicz spaces, mixed-normed spaces, tent spaces, and discrete Triebel–Lizorkin and Besov spaces. For vector spaces of measurable functions we also derive pointwise convergence results. Our approach relies on abstract capacitary estimates and works in certain cases of interest even in the absence of a background measure space and/or of a vector space structure.     

Thin-layer chromatography of green leaves extracts: Zinc migrates into pheophytin on TLC silica plates with fluorescence indicator (F254)

JPC – Journal of Planar Chromatography – Modern TLC -     

Front Cover: Twisting versus Delocalization in CAAC- and NHC-Stabilized Boron-Based Biradicals: The Roles of Sterics and Electronics (Chem. Eur. J. 16/2021)

Invited for the cover of this issue is Bernd Engels, Holger Braunschweig, Volker Engel and their coworkers at University of Würzburg. The image depicts bridged boron compounds which possess fascinating relationships between their composition and their geometrical and electronic structures, the latter ranging from closed-shell to biradical triplet or singlet ground state. Read the full text of the article at 10.1002/chem.202004619 .     

Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation

The time evolution of surface defect density and width of space charge region in thin layer of amorphous silicon is observed experimentally by Fourier transform photocurrent spectroscopy. This work reviews the assumption that photocurrent is insensitive to surface defects for samples thinner than 1500 nm. We show that correct evaluation based on simple optical model comprising layers representing surface defects and layers representing space charge region with reduced collection allows obtaining the same results as from photothermal deflection spectroscopy. Our main approach is the comparison of photocurrent or photothermal deflection spectra measured in absorptance/transmittance mode from layer and substrate side of the thin film.     

Heterotrimetallic Coordination Polymers: {CuIILnIIIFeIII} Chains and {NiIILnIIIFeIII} Layers: Synthesis,Crystal Structures,and Magnetic Properties

The use of the [Fe^III(AA)(CN)₄]^? complex anion as metalloligand towards the preformed [Cu^II(valpn)Ln^III]³⁺ or [Ni^II(valpn)Ln^III]³⁺ heterometallic complex cations (AA=2,2′‐bipyridine (bipy) and 1,10‐phenathroline (phen); H₂valpn=1,3‐propanediyl‐bis(2‐iminomethylene‐6‐methoxyphenol)) allowed the preparation of two families of heterotrimetallic complexes: three isostructural 1D coordination polymers of general formula {[Cu^II(valpn)Ln^III(H₂O)₃(μ‐NC)₂Fe^III(phen)(CN)₂ {(μ‐NC)Fe^III(phen)(CN)₃}]NO₃ ? 7 H₂O}_n (Ln=Gd ( 1 ), Tb ( 2 ), and Dy ( 3 )) and the trinuclear complex [Cu^II(valpn)La^III(OH₂)₃(O₂NO)(μ‐NC)Fe^III(phen)(CN)₃] ? NO₃ ? H₂O ? CH₃CN ( 4 ) were obtained with the [Cu^II(valpn)Ln^III]³⁺ assembling unit, whereas three isostructural heterotrimetallic 2D networks, {[Ni^II(valpn)Ln^III(ONO₂)₂(H₂O)(μ‐NC)₃Fe^III(bipy)(CN)] ? 2 H₂O ? 2 CH₃CN}_n (Ln=Gd ( 5 ), Tb ( 6 ), and Dy ( 7 )) resulted with the related [Ni^II(valpn)Ln^III]³⁺ precursor. The crystal structure of compound 4 consists of discrete heterotrimetallic complex cations, [Cu^II(valpn)La^III(OH₂)₃(O₂NO)(μ‐NC)Fe^III(phen)(CN)₃]⁺, nitrate counterions, and non‐coordinate water and acetonitrile molecules. The heteroleptic {Fe^III(bipy)(CN)₄} moiety in 5 – 7 acts as a tris‐monodentate ligand towards three {Ni^II(valpn)Ln^III} binuclear nodes leading to heterotrimetallic 2D networks. The ferromagnetic interaction through the diphenoxo bridge in the Cu^II?Ln^III ( 1 – 3 ) and Ni^II?Ln^III ( 5 – 7 ) units, as well as through the single cyanide bridge between the Fe^III and either Ni^II ( 5 – 7 ) or Cu^II ( 4 ) account for the overall ferromagnetic behavior observed in 1 – 7 . DFT‐type calculations were performed to substantiate the magnetic interactions in 1 , 4 , and 5 . Interestingly, compound 6 exhibits slow relaxation of the magnetization with maxima of the out‐of‐phase ac signals below 4.0 K in the lack of a dc field, the values of the pre‐exponential factor (τ_o) and energy barrier (E_a) through the Arrhenius equation being 2.0×10^?12 s and 29.1 cm^?1, respectively. In the case of 7 , the ferromagnetic interactions through the double phenoxo (Ni^II–Dy^III) and single cyanide (Fe^III–Ni^II) pathways are masked by the depopulation of the Stark levels of the Dy^III ion, this feature most likely accounting for the continuous decrease of χ_M T upon cooling observed for this last compound.