The fundamental group of period domains over finite fields

We determine the fundamental group of period domains over finite fields. This answers a question of M. Rapoport raised in [M. Rapoport, Period domains over finite and local fields, in: Proc. Sympos. Pure Math., vol. 62, part 1, 1997, pp. 361-381].     

On {\alpha }-roughly weighted games

Gvozdeva et al. (Int J Game Theory, doi:10.1007/s00182-011-0308-4, 2013) have introduced three hierarchies for simple games in order to measure the distance of a given simple game to the class of (roughly) weighted voting games. Their third class \({\mathcal {C}}_\alpha \) consists of all simple games permitting a weighted representation such that each winning coalition has a weight of at least \(1\) and each losing coalition a weight of at most \(\alpha \) . For a given game the minimal possible value of \(\alpha \) is called its critical threshold value. We continue the work on the critical threshold value, initiated by Gvozdeva et al., and contribute some new results on the possible values for a given number of voters as well as some general bounds for restricted subclasses of games. A strong relation between this concept and the cost of stability, i.e. the minimum amount of external payment to ensure stability in a coalitional game, is uncovered.     

A note on elliptic type boundary value problems with maximal monotone relations

In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as “coefficients”. A reformulation of the respective problems is constructed such that they turn out to be unitarily equivalent to inverting a maximal monotone relation in a Hilbert space. The method is based on the idea of “tailor‐made” distributions as provided by the construction of extrapolation spaces, see e.g. [Picard, McGhee: Partial Differential Equations: A unified Hilbert Space Approach (De Gruyter, 2011)]. The abstract framework is illustrated by various examples.     

Dynamical Gibbs–Non-Gibbs Transitions in Lattice Widom–Rowlinson Models with Hard-Core and Soft-Core Interactions

Journal of Statistical Physics - We consider the Widom–Rowlinson model on the lattice $${\mathbb {Z}}^d$$ in two versions, comparing the cases of a hard-core repulsion and of a soft-core...     

Closing the green gap of photosystem I with synthetic fluorophores for enhanced photocurrent generation in photobiocathodes

One restriction for biohybrid photovoltaics is the limited conversion of green light by most natural photoactive components. The present study aims to fill the green gap of photosystem I (PSI) with covalently linked fluorophores, ATTO 590 and ATTO 532. Photobiocathodes are prepared by combining a 20 μm thick 3D indium tin oxide (ITO) structure with these constructs to enhance the photocurrent density compared to setups based on native PSI. To this end, two electron transfer mechanisms, with and without a mediator, are studied to evaluate differences in the behavior of the constructs. Wavelength-dependent measurements confirm the influence of the additional fluorophores on the photocurrent. The performance is significantly increased for all modifications compared to native PSI when cytochrome c is present as a redox-mediator. The photocurrent almost doubles from −32.5 to up to −60.9 μA cm⁻². For mediator-less photobiocathodes, interestingly, drastic differences appear between the constructs made with various dyes. While the turnover frequency (TOF) is doubled to 10 e⁻/PSI/s for PSI-ATTO590 on the 3D ITO compared to the reference specimen, the photocurrents are slightly smaller since the PSI-ATTO590 coverage is low. In contrast, the PSI-ATTO532 construct performs exceptionally well. The TOF increases to 31 e⁻/PSI/s, and a photocurrent of −47.0 μA cm⁻² is obtained. This current is a factor of 6 better than the reference made with native PSI in direct electron transfer mode and sets a new record for mediator-free photobioelectrodes combining 3D electrode structures and light-converting biocomponents.

Dyes are covalently bound to photosystem I to close its green gap, and the constructs'' photocurrent densities on 3D ITO are determined in direct and mediated electron transfer. Photocurrent generation is enhanced by the presence of fluorophores.     

Front Cover: Method development for the investigation of Mn2+/3+, Cu2+, Co2+, and Ni2+ with capillary electrophoresis hyphenated to inductively coupled plasma–mass spectrometry

The lifetime of lithium ion batteries (LIBs) decreases under continuous cycling due to various degradation processes, such as dissolution of transition metals (TMs) from the electrodes. Therefore, suitable methods to analyze the oxidation states of TMs are mandatory to better understand the dissolution mechanisms of TMs from positive and negative electrodes (LIBs). To investigate the dissolution of Mn²⁺ and Mn³⁺ in electrolytes of LIBs, a previously implemented capillary electrophoresis (CE) method with UV/Vis spectroscopy detection was further developed with the aim of higher sensitivities and additional detection of other dissolved divalent TMs such as Co²⁺, Ni²⁺, and Cu²⁺. Therefore, inductively coupled plasma–mass spectrometry was applied instead of UV/Vis for detection. This also allows the use of Ga³⁺ instead of the previously used Cu²⁺ as an internal standard, which solves the limitation of this method for cycled LIBs due to copper dissolution from the copper-based current collector. The CE buffer based on sodium diphosphate as complexing agent for the stabilization of Mn³⁺ and cetyltrimethylammonium bromide as dynamic capillary wall modifier was optimized in terms of concentrations and pH. Finally, both manganese species and Co²⁺, Ni²⁺, and Cu²⁺ could be analyzed within 15 min. With this improved method, the dissolution of TMs in LIBs for positive electrode materials such as LiNi_0.5Mn_1.5O₄ (LNMO) or LiNi_xCo_yMn_zO₂ (NCM, x + y + z = 1) can be studied in future in more detail.