Phosphaniminato‐Cluster von Eisen. Die Kristallstrukturen von [FeCl(NPEt3)]4, [Fe(C=C–SiMe3)(NPEt3)]4 und [Fe3Cl4{NP(NMe2)3}3]

Phosphoraneiminato Cluster of Iron. The Crystal Structures of [FeCl(NPEt₃)]₄, [Fe(C=C–SiMe₃)(NPEt₃)]₄, and [Fe₃Cl₄{NP(NMe₂)₃}₃] The reaction of iron dichloride with the silylated phosphaneimine Me₃SiNPEt₃ in the presence of potassium fluoride at 165 ?C leads to the phosphoraneiminato complex [FeCl(NPEt₃)]₄ ( 1 ). Compound 1 forms black, moisture and oxygen sensitive crystals. According to the crystal structure analysis 1 has a heterocubane structure, in which the iron and the nitrogen atoms of the NPEt₃^– groups occupy the corners of a distorted cube and form Fe–N–Fe bond angles of 83.1? and N–Fe–N angles of 96.5?. This results in significantly short Fe…Fe contacts of 272.9 pm. The results of magnetic susceptibility measurements in the range of temperatures from 1.8 to 293 K and the ⁵⁷Fe‐Mössbauer spectra in the range of temperatures from 2 to 300 K are reported. Compound 1 reacts with the lithiated acetylenes LiC=C–CMe₃ and LiC=C–SiMe₃ in n‐hexane to form the iron‐organic derivatives [Fe(C=C–R)(NPEt₃)]₄ [R = CMe₃ ( 2 a ), R = SiMe₃ ( 2 b )] keeping the heterocubane structure. Compounds 2 a and 2 b form crystals which are very reactive and also black. According to the crystal structure analysis 2 b has a Fe₄N₄ heterocubane structure which is less distorted than that in 1 with bond angles Fe–N–Fe of 85.5? and N–Fe–N of 94.2?. This leads to the longer Fe…Fe contacts of 281.4 pm. With the dimethylamido derivative Me₃SiNP(NMe₂)₃ iron dichloride reacts under conditions similar to those in the synthesis of 1 to form the dark green mixed‐valenced Fe^II/Fe^III cluster [Fe₃Cl₄{NP(NMe₂)₃}₃] ( 3 ). According to the crystal structure analysis the three iron atoms in 3 are connected via one μ₃‐N atom of a NP(NMe₂)₃^– ligand, via two μ‐N atoms of the two remaining phosphoraneiminato ligands, and via one μ‐Cl atom to form an incomplete heterocubane skeleton.     

Configurational Isomerism in Polyoxovanadates

A water‐soluble derivative of the polyoxovanadate {V₁₅E₆O₄₂} (E=semimetal) archetype enables the study of cluster shell rearrangements driven by supramolecular interactions. A reaction unique to E=Sb, induced exclusively by ligand metathesis in peripheral [Ni(ethylenediamine)₃]²⁺ counterions, results in the formation of the metastable α₁* configurational isomer of the {V₁₄Sb₈O₄₂} cluster type. Contrary to all other polyoxovanadate shell architectures, this isomer comprises an inward‐oriented vanadyl group and is ca. 50 and 12 kJ mol^?1 higher in energy than the previously isolated α and β isomers, respectively. We discuss this unexpected reaction in light of supramolecular Sb?O???V and Sb?O???Sb contacts manifested in {V₁₄Sb₈O₄₂}₂ dimers detected in the solid state. ESI MS experiments confirm the stability of these dimers also in solution and in the gas phase. DFT calculations indicate that other, as of yet elusive isomers of {V₁₄Sb₈}, might be accessible as well.     

Insight into Signal Response of Protein Ions in Native ESI-MS from the Analysis of Model Mixtures of Covalently Linked Protein Oligomers

Native ESI-MS is increasingly used for quantitative analysis of biomolecular interactions. In such analyses, peak intensity ratios measured in mass spectra are treated as abundance ratios of the respective molecules in solution. While signal intensities of similar-size analytes, such as a protein and its complex with a small molecule, can be directly compared, significant distortions of the peak ratio due to unequal signal response of analytes impede the application of this approach for large oligomeric biomolecular complexes. We use a model system based on concatenated maltose binding protein units (MBPn, n = 1, 2, 3) to systematically study the behavior of protein mixtures in ESI-MS. The MBP concatamers differ from each other only by their mass while the chemical composition and other properties remain identical. We used native ESI-MS to analyze model mixtures of MBP oligomers, including equimolar mixtures of two proteins, as well as binary mixtures containing different fractions of the individual components. Pronounced deviation from a linear dependence of the signal intensity with concentration was observed for all binary mixtures investigated. While equimolar mixtures showed linear signal dependence at low concentrations, distinct ion suppression was observed above 20 μM. We systematically studied factors that are most often used in the literature to explain the origin of suppression effects. Implications of this effect for quantifying protein–protein binding affinity by native ESI-MS are discussed in general and demonstrated for an example of an anti-MBP antibody with its ligand, MBP.

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Bonus or flat wage? An experiment into the principal-agent problem

We conduct a simple principal-agent experiment in order to find the effects of information asymmetry on compensation. Our aim is the analysis of the appropriate compensation and its impact on employee’s effort. Furthermore we want to compare the offered compensation and the supplied effort in the version without communication and we want to know whether the experimental observations are consistent with the theoretical considerations.The experimenters found out that compensations observed during the experiment were different from those suggested by the theory and although they were theoretically not enough to induce high effort, we could observe high performance supplied by the agents.     

Dynamic programming based metaheuristics for the dial-a-ride problem

The organization of a specialized transportation system to perform transports for elderly and handicapped people is usually modeled as dial-a-ride problem. Users place transportation requests with specified pickup and delivery locations and times. The requests have to be completed under user inconvenience considerations by a specified fleet of vehicles. In the dial-a-ride problem, the aim is to minimize the total travel times respecting the given time windows, the maximum user ride times, and the vehicle restrictions. This paper introduces a dynamic programming algorithm for the dial-a-ride problem and demonstrates its effective application in (hybrid) metaheuristic approaches. Compared to most of the works presented in literature, this approach does not make use of any (commercial) solver. We present an exact dynamic programming algorithm and a dynamic programming based metaheuristic, which restricts the considered solution space. Then, we propose a hybrid metaheuristic algorithm which integrates the dynamic programming based algorithms into a large neighborhood framework. The algorithms are tested on a given set of benchmark instances from the literature and compared to a state-of-the-art hybrid large neighborhood search approach.     

Optimal dynamic control of predator–prey models

Central European Journal of Operations Research - This paper combines work to use a decision support tool for sustainable economic development, while acknowledging interdependent dynamics of...     

Computational homogenization and parameter-identification for heterogeneous inelastic materials

The aim of this paper is to describe a method for identifying micro material parameters using only macroscopic experimental data. The FE² method is used to model the behavior of the complex materials with heterogeneous micro-structure. The resulting least squares problem is minimized using gradient-based optimization algorithms, where the gradient information is derived analytically within the discretized scheme. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Class numbers of definite binary quadratic lattices over algebraic function fields

Let k be an algebraic function field of one variable X having a finite field GF(q) of constants with q elements, q odd. Confined to imaginary quadratic extensions $\text{K}\text{k}$, class number formulas are developed for both the maximal and nonmaximal binary quadratic lattices L on (K, N), where N denotes the norm from K to k. The class numbers of L grow either with the genus g(k) of k (assuming the fields under consideration have bounded degree) or with the relative genus $\text{g(}\text{K}\text{k}\text{)}$ (assuming the lattices under consideration have bounded scale). In contrast to analogous theorems concerning positive definite binary quadratic lattices over totally real number fields, k is not necessarily totally real.