In‐Planta Expression: Searching for the Genuine Chromophores of Cryptochrome‐3 from Arabidopsis thaliana

Göbel et al. present in this issue an exemplary study of identification of chromophores from Arabidopsis thaliana cryptochrome‐3. Usually taken for granted, proteins and cofactors, respective chromophores, from heterologous expression are considered identical to material isolated from their genuine host. Cryptochromes carry two chromophores, an antenna cofactor and a functional flavin chromophore, both noncovalently embedded into the protein. In particular the antenna chromophore is loosely bound and often lost during protein purification. The authors identify from plant‐extracted Cry3 unambiguously N⁵,N¹⁰‐methenyltetrahydrofolate as antenna chromophore and flavin adenine dinucleotide as the functional chromophore.     

Probing the Electronic Structure of Bacteriochlorophyll Radical Ions—A Theoretical Study of the Effect of Substituents on Hyperfine Parameters

In reaction centers (RCs) of photosynthesis, a light‐induced charge separation takes place creating radical cations and anions of the participating cofactors. In photosynthetic bacteria, different bacteriochlorophylls (BChl) are involved in this process. Information about the electronic structure of the BChl radical cations and anions can be obtained by measuring the electron spin density distribution via the electron–nuclear hyperfine interaction using EPR and ENDOR techniques. In this communication, we report isotropic hyperfine coupling constants (hfcs) of the BChl b and g radical cations and anions, calculated by density functional theory, and compare them with the more common radical ions of BChl a and with available experimental data. The observed differences in the computed hyperfine data are discussed in view of a possible distinction between these species by EPR/ENDOR methods. In addition, ¹⁴N nuclear quadrupole coupling constants (nqcs) computed for BChl a, b, g, and also for Chl a in their charge neutral, radical cation and radical anion states are presented. These nqcs are compared with experimental values obtained by ESEEM spectroscopy on several different radical ions.     

Metal Complexes of Biologically Important Ligands,CLXXVII. Dichlorido Platinum(II) and Palladium(II) Complexes with Long Chain Amino Acids and Amino Acid Amides

The synthesis of Cl₂Pt[NH₂(CH₂)_nCOOH]₂ (n = 5, 10) and the reactions of their carboxylic groups with H₂N(CH₂)₁₇CH₃, d ‐glucosamine, and (R,R)‐1,2‐diaminocyclohexane to give complexes with amino acid amides as ligands, are reported. Cl₂Pd(histidine) is coupled with amino alcohols to give Cl₂Pd(histidineamide) complexes.     

A C2 Fragment as Four‐Electron σ Donor

The formation and X‐ray structure analysis of the Pt^IV complex [(CH₂C{PPh₂C₆H₄}₂)PtI₂] is reported. The molecule possesses the orthometalated ligand (PPh₃)₂C→CH₂, which serves via its C₂ fragment as an unprecedented four‐electron σ donor.     

Evaluation of the evolution of relationships between topics over time

Topics that attract public attention can originate from current events or developments, might be influenced by situations in the past, and often continue to be of interest in the future. When respective information is made available textually, one possibility of detecting such topics of public importance consists in scrutinizing, e.g., appropriate press articles using—given the continual growth of information—text processing techniques enriched by computer routines which examine present-day textual material, check historical publications, find newly emerging topics, and are able to track topic trends over time. Information clustering based on content-(dis)similarity of the underlying textual material and graph-theoretical considerations to deal with the network of relationships between content-similar topics are described and combined in a new approach. Explanatory examples of topic detection and tracking in online news articles illustrate the usefulness of the approach in different situations.     

Minimal tiled orders of finite global dimension

In this paper, we consider the sequence of balancing and Lucas balancing numbers. The balancing numbers \({B_n}\) are given by the recurrence \({B_n = 6 B_{n-1} - B_{n-2}}\) with initial conditions \({B_0 = 0, B_1 = 1}\) and its associated Lucas balancing numbers \({C_n}\) are given by the recurrence \({C_n = 6 C_{n-1} - C_{n-2}}\) with initial conditions \({C_0 = 1, C_1 = 3}\). First we find the perfect powers in the sequence of balancing and Lucas balancing numbers. We also identify those Lucas balancing numbers which are products of a power of 3 and a perfect power. Using this property of Lucas balancing numbers, we solve a conjecture regarding the non-existence of positive integral solution (x, y) for the Diophantine equation \({2x^2 + 1 = 3^b y^m}\) for any even positive integers b and m with \({m > 2}\), given in (Int J Number Theory 11:1259–1274, 2015). Also we prove that the Diophantine equations \({B_n B_{n+d}\ldots B_{n+(k-1)d} = y^m}\) and \({C_n C_{n+d}\ldots C_{n+(k-1)d} = y^m}\) have no solution for any positive integers n, d, k, y, and m with \({m \geq 2, y \geq 2}\) and gcd\({(n,d) = 1}\).     

J. L. Lions’ problem on maximal regularity

This is a survey on recent progress concerning maximal regularity of non-autonomous equations governed by time-dependent forms on a Hilbert space. It also contains two new results showing the limits of the theory.     

On the mixed problem for the semilinear Darcy‐Forchheimer‐Brinkman PDE system in Besov spaces on creased Lipschitz domains

The purpose of this paper is to study the mixed Dirichlet‐Neumann boundary value problem for the semilinear Darcy‐Forchheimer‐Brinkman system in L _p ‐based Besov spaces on a bounded Lipschitz domain in ${\mathbb{R}}^3$, with p in a neighborhood of 2. This system is obtained by adding the semilinear term | u | u to the linear Brinkman equation. First, we provide some results about equivalence between the Gagliardo and nontangential traces, as well as between the weak canonical conormal derivatives and the nontangential conormal derivatives. Various mapping and invertibility properties of some integral operators of potential theory for the linear Brinkman system, and well‐posedness results for the Dirichlet and Neumann problems in L _p ‐based Besov spaces on bounded Lipschitz domains in ${\mathbb{R}}^n$(n ≥3) are also presented. Then, using integral potential operators, we show the well‐posedness in L ₂‐based Sobolev spaces for the mixed problem of Dirichlet‐Neumann type for the linear Brinkman system on a bounded Lipschitz domain in ${\mathbb{R}}^n$(n ≥3). Further, by using some stability results of Fredholm and invertibility properties and exploring invertibility of the associated Neumann‐to‐Dirichlet operator, we extend the well‐posedness property to some L _p ‐based Sobolev spaces. Next, we use the well‐posedness result in the linear case combined with a fixed point theorem to show the existence and uniqueness for a mixed boundary value problem of Dirichlet and Neumann type for the semilinear Darcy‐Forchheimer‐Brinkman system in L _p ‐based Besov spaces, with p ∈(2?ε ,2+ε ) and some parameter ε >0.     

Pre-averaged kernel estimators for the drift function of a diffusion process in the presence of microstructure noise

We consider estimation of the drift function of a stationary diffusion process when we observe high-frequency data with microstructure noise over a long time interval. We propose to estimate the drift function at a point by a Nadaraya–Watson estimator that uses observations that have been pre-averaged to reduce the noise. We give conditions under which our estimator is consistent and asympotically normal. Its rate and asymptotic bias and variance are the same as those without microstructure noise. To use our method in data analysis, we propose a data-based cross-validation method to determine the bandwidth in the Nadaraya–Watson estimator. Via simulation, we study several methods of bandwidth choices, and compare our estimator to several existing estimators. In terms of mean squared error, our new estimator outperforms existing estimators.     

Leibniz’s Ontological Proof of the Existence of God and the Problem of »Impossible Objects«

The core idea of the ontological proof is to show that the concept of existence is somehow contained in the concept of God, and that therefore God’s existence can be logically derived—without any further assumptions about the external world—from the very idea, or definition, of God. Now, G.W. Leibniz has argued repeatedly that the traditional versions of the ontological proof are not fully conclusive, because they rest on the tacit assumption that the concept of God is possible, i.e. free from contradiction. A complete proof will rather have to consist of two parts. First, a proof of premise

1. (1)
   God is possible.
    

Second, a demonstration of the “remarkable proposition”

1. (2)
   If God is possible, then God exists.
    

The present contribution investigates an interesting paper in which Leibniz tries to prove proposition (2). It will be argued that the underlying idea of God as a necessary being has to be interpreted with the help of a distinguished predicate letter ‘E’ (denoting the concept of existence) as follows:

1. (3)
   \(g=_{\mathrm{df}} \,\upiota x\square E(x)\).
    

Proposition (2) which Leibniz considered as “the best fruit of the entire logic” can then be formalized as follows:

1. (4)
   \(\diamondsuit E(\upiota x\square E(x)) \rightarrow \, E(\upiota x\square E(x))\).
    

At first sight, Leibniz’s proof appears to be formally correct; but a closer examination reveals an ambiguity in his use of the modal notions. According to (4), the possibility of the necessary being has to be understood in the sense of something which possibly exists. However, in other places of his proof, Leibniz interprets the assumption that the necessary being is impossible in the diverging sense of something which involves a contradiction. Furthermore, Leibniz believes that an »impossible thing«, y, is such that contradictory propositions like \(\hbox {F}(y)\) and \(\lnot F(y)\) might both be true of y. It will be argued that the latter assumption is incompatible with Leibniz’s general views about logic and that the crucial proof is better reinterpreted as dealing with the necessity, possibility, and impossibility of concepts rather than of objects. In this case, the counterpart of (2) turns out to be a theorem of Leibniz’s second order logic of concepts; but in order to obtain a full demonstration of the existence of God, the counterpart of (1), i.e. the self-consistency of the concept of a necessary being, remains to be proven.