Estimating Averages of Order Statistics of Bivariate Functions

We prove uniform estimates for the expected value of averages of order statistics of bivariate functions in terms of their largest values by a direct analysis. As an application, uniform estimates for the expected value of averages of order statistics of sequences of independent random variables in terms of Orlicz norms are obtained. In the case where the bivariate functions are matrices, we provide a “minimal” probability space which allows us to C-embed certain Orlicz spaces \(\ell _M^n\) into \(\ell _1^{cn^3}\), with \(c,C>0\) being absolute constants.     

Three‐Axis Anisotropic Exchange Coupling in the Single‐Molecule Magnets NEt4[MnIII2(5‐Brsalen)2(MeOH)2MIII(CN)6] (M=Ru,Os)

We have investigated the single‐molecule magnets [Mn^III₂(5‐Brsalen)₂(MeOH)₂M^III(CN)₆]NEt₄ (M=Os ( 1 ) and Ru ( 2 ); 5‐Brsalen=N,N′‐ethylenebis(5‐bromosalicylidene)iminate) by frequency‐domain Fourier‐transform terahertz electron paramagnetic resonance (THz‐EPR), inelastic neutron scattering, and superconducting quantum interference device (SQUID) magnetometry. The combination of all three techniques allows for the unambiguous experimental determination of the three‐axis anisotropic magnetic exchange coupling between Mn^III and Ru^III or Os^III ions, respectively. Analysis by means of a spin‐Hamiltonian parameterization yields excellent agreement with all experimental data. Furthermore, analytical calculations show that the observed exchange anisotropy is due to the bent geometry encountered in both 1 and 2 , whereas a linear geometry would lead to an Ising‐type exchange coupling.     

PAS-cal: a Generic Recombinant Peptide Calibration Standard for Mass Spectrometry

We describe the design, preparation, and mass-spectrometric characterization of a new recombinant peptide calibration standard with uniform biophysical and ionization characteristics for mass spectrometry. “PAS-cal” is an artificial polypeptide concatamer of peptide cassettes with varying lengths, each composed of the three small, chemically stable amino acids Pro, Ala, and Ser, which are interspersed by Arg residues to allow site-specific cleavage with trypsin. PAS-cal is expressed at high yields in Escherichia coli as a Small Ubiquitin-like MOdifier (SUMO) fusion protein, which is easily purified and allows isolation of the PAS-cal moiety after SUMO protease cleavage. Upon subsequent in situ treatment with trypsin, the PAS-cal polypeptide yields a set of four defined homogeneous peptides in the range from 2 to 8 kDa with equal mass spacing. ESI-MS analysis revealed a conveniently interpretable raw spectrum, which after deconvolution resulted in a very simple pattern of four peaks with similar ionization signals. MALDI-MS analysis of a PAS-cal peptide mixture comprising both the intact polypeptide and its tryptic fragments revealed not only the four standard peptides but also the singly and doubly charged states of the intact concatamer as well as di- and trimeric adduct ion species between the peptides, thus augmenting the observable m/z range. The advantageous properties of PAS-cal are most likely a result of the strongly hydrophilic and conformationally disordered PEG-like properties of the PAS sequences. Therefore, PAS-cal offers an inexpensive and versatile recombinant peptide calibration standard for mass spectrometry in protein/peptide bioanalytics and proteomics research, the composition of which may be further adapted to fit individual needs.

Modelling the Magnetic Behaviour of Square‐Pyramidal CoII5 Aggregates: Tuning SMM Behaviour through Variations in the Ligand Shell

Three new μ₄‐bridged Co^II₅ clusters with similar core motifs have been synthesised with the use of N‐tert‐butyldiethanolamine (tbdeaH₂) and pivalic acid (piv): [Co^II₅(μ₄‐N₃)(tbdea)₂(μ‐piv)₄(piv)(CH₃CN)₂]?CH₃CN ( 1 ), [Co^II₅(μ₄‐Cl)(Cl)(tbdea)₂(μ‐piv)₄(pivH)₂] ( 2 ) and [Co^II₅(μ₄‐N₃)(Cl)(tbdea)₂(μ‐piv)₄(pivH)₂] ( 3 ). Magnetic measurements were performed for all three compounds. It was found that while the chloride‐bridged cluster 2 does not show an out‐of‐phase signal, which excludes single‐molecule magnet (SMM) behaviour, the azide‐bridged compounds 1 and 3 show out‐of‐phase signals as well as frequency dependence of the ac susceptibility, as expected for SMMs. We confirmed that 1 is a SMM with zero‐field quantum tunnelling of the magnetisation at 1.8 K. Compound 3 is likely a SMM with a blocking temperature well below 1.8 K. We established a physical model to fit the χT versus T and M versus B curves of the three compounds to reproduce the observed SMM trend. The analysis showed that small changes in the ligand shell modify not only the magnitude of exchange constants, but also affect the J and g matrices in a non‐trivial way.     

A Trigonal Prismatic Cobalt(II) Complex as a Single Molecule Magnet with a Reduced Contribution from Quantum Tunneling

Herein, we report a new trigonal prismatic cobalt(II) complex that behaves as a single molecule magnet. The obtained zero-field splitting, which is also directly accessed by THz-EPR spectroscopy (−102.5 cm⁻¹), results in a large magnetization reversal barrier U of 205 cm⁻¹. Its effective value, however, is much lower (101 cm⁻¹), even though there is practically no contribution from quantum tunneling to magnetization relaxation.