An Example of a Positive Semidefinite Double Sequence Which is Not a Moment Sequence

The first explicit example of a positive semidefinite double sequence which is not a moment sequence was given by Friedrich. We present an example with a simpler definition and more moderate growth as (m, n) .     

Mass spectra of porphyrin alkyl esters and their copper complexes. Studies on products from humans and animals with porphyria

Mass spectra of methyl and higher aliphatic esters of biologically important porphyrins—prepared from human and bovine excreta—were recorded. Variation in the number of esterified carboxyl groups (4 to 8) or in the size of the ester groups causes no change in the fragmentation modes; only the abundances of the fragment ions vary. The conversion of a porphyrin ester to its copper-complex (chelate) has been achieved in a simple way. The mass spectra of the copper chelates are compared with those of the free porphyrin esters and minor differences are observed.     

Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half‐Plane

Let S be a positivity‐preserving symmetric linear operator acting on bounded functions. The nonlinear equation with a parameter z in the complex upper half‐plane ? has a unique solution m with values in ?. We show that the z‐dependence of this solution can be represented as the Stieltjes transforms of a family of probability measures v on ?. Under suitable conditions on S , we show that v has a real analytic density apart from finitely many algebraic singularities of degree at most 3. Our motivation comes from large random matrices. The solution m determines the density of eigenvalues of two prominent matrix ensembles: (i) matrices with centered independent entries whose variances are given by S and (ii) matrices with correlated entries with a translation‐invariant correlation structure. Our analysis shows that the limiting eigenvalue density has only square root singularities or cubic root cusps; no other singularities occur.© 2016 Wiley Periodicals, Inc.     

bSTAB: an open-source software for computing the basin stability of multi-stable dynamical systems

The pervasiveness of multi-stability in nonlinear dynamical systems calls for novel concepts of stability and a consistent quantification of long-term behavior. The basin stability is a global stability metric that builds on estimating the basin of attraction volumes by Monte Carlo sampling. The computation involves extensive numerical time integrations, attractor characterization, and clustering of trajectories. We introduce bSTAB, an open-source software project that aims at enabling researchers to efficiently compute the basin stability of their dynamical systems with minimal efforts and in a highly automated manner. The source code, available at https://github.com/TUHH-DYN/bSTAB/, is available for the programming language Matlab featuring parallelization for distributed computing, automated sensitivity and bifurcation analysis as well as plotting functionalities. We illustrate the versatility and robustness of bSTAB for four canonical dynamical systems from several fields of nonlinear dynamics featuring periodic and chaotic dynamics, complicated multi-stability, non-smooth dynamics, and fractal basins of attraction. The bSTAB projects aims at fostering interdisciplinary scientific collaborations in the field of nonlinear dynamics and is driven by the interaction and contribution of the community to the software package.

     

Iodination of stanna-closo-dodecaborate

The dianionic stannaborate [SnB11H11]2- oxidatively adds iodine at the tin vertex to give the iodinated cluster [I2SnB11H11]2- which maintains a closo structure, albeit having a nido electron count. The iodo-stannaborate [I2SnB11H11]2- is unstable at room temperature, but its structure was elucidated via single-crystal X-ray diffraction at low temperatures. The low-temperature 11B NMR spectrum exhibits a 5:1:5 signal pattern, and the 119Sn NMR shows a resonance at -1039 ppm. Iodination of the zwitterionic stannaborate iron complex Fe(SnB11H11)(triphos) leads to the formation of the corresponding iodo-stannaborate iron complex Fe(I2SnB11H11)(triphos) which features an iodinated stannaborate moiety that has a structure analogous to that of [I2SnB11H11]2-. The zwitterionic iodo-stannaborate complex is stable at room temperature, and the crystal structure and the 1H, 11B, 31P, and 119Sn NMR parameters were determined. 119Sn M?ssbauer spectroscopy supports the assignment of a tin oxidation state of +II for Fe(SnB11H11)(triphos) (delta = 2.71 mm s-1) and +IV for Fe(I2SnB11H11)(triphos) (delta = 1.22 mm s-1). Additional 57Fe M?ssbauer spectra confirm the iron oxidation state +II for both compounds.     

Natural product-derived modulators of cell cycle progression and viral entry by enantioselective oxa Diels-Alder reactions on the solid phase

The underlying frameworks of natural product classes with multiple biological activities can be regarded as biologically selected and prevalidated starting points in vast chemical structure space in the development of compound collections for chemical biology and medicinal chemistry research. For the synthesis of natural product-derived and -inspired compound collections, the development of enantioselective transformations in a format amenable to library synthesis, e.g., on the solid support, is a major and largely unexplored goal. We report on the enantioselective solid-phase synthesis of a natural product-inspired alpha,beta-unsaturated delta-lactone collection and its investigation in cell-based screens monitoring cell cycle progression and viral entry into cells. The screens identified modulators of both biological processes at a high hit rate. The screen for inhibition of viral entry opens up avenues of research for the identification of compounds with antiviral activity.     

Electron transfer in some nucleophilic reactions

Using kinetic, steric and thermodynamic results it is argued that the rate-determining step in some aliphatic, nucleophilic substitutions is the transfer of an electron.     

Nickelphosphankomplexe der Mercaptoessigsäure

Nickel Complexes of Mercaptoacetic Acid The reaction of [Cp°₂Zr(OOCCH₂SH‐κ¹O)(OOCCH₂SH‐κ²O, O′)] (Cp° = C₅EtMe₄) with [NiCl₂(PMe₂Ph)₂] or [NiCl₂(dppe)] (dppe = PPh₂CH₂CH₂PPh₂) in the presence of NEt₃ yields the tetranuclear Zr^IV/Ni^II complex [{Cp°₂Zr(κ¹O‐OOCCH₂S‐κ²O′, S)(κ²O, O′‐OOCCH₂S‐κ¹S)Ni(PMe₂Ph)}₂] ( 1 ) and the chelate complexes [Ni(OOCCH₂S‐κ²O, S)L₂] [L = PMe₂Ph ( 2 ), L₂ = dppe ( 3 )]. 2 and 3 are also accessible from [NiCl₂(PMe₂Ph)₂] or [NiCl₂(dppe)] and mercaptoacetic acid in the presence of NEt₃ in quantitative yield. The structure of 2 is dynamic in solution, whereby a complex with three‐coordinate nickel atom is formed. 2 and 3 were characterized spectroscopically (¹H, ¹³C, ³¹P NMR and IR) and by crystal structure determination.