A simple proof of some generalized principal ideal theorems

Using symmetric algebras we simplify and slightly strengthen the Bruns-Eisenbud-Evans ``generalized principal ideal theorem' on the height of order ideals of nonminimal generators in a module. We also obtain a simple proof and an extension of a result by Kwiecinski, which estimates the height of certain Fitting ideals of modules having an equidimensional symmetric algebra.

     

Synthesis,Characterization and Structure of Bis‐ and Tetrakis‐Aziridine‐Nickel(II) and Copper(II) Complexes

The synthesis and characterization of mononuclear tetrakis‐aziridine nickel(II ) and copper(II ) complexes as well as of a dinuclear bis‐aziridine copper(II ) complex are described. The reactions of anhydrous MCl₂ (M = Ni^II, Cu^II) with aziridine (= az = C₂H₄NH, C₂H₃MeNH, CH₂CMe₂NH) in CH₂Cl₂ at room temperature in a 1:5 and 1:2 molar ratio, respectively, afforded the tetrakis‐aziridine complexes [M(az)₄Cl₂] (M = Ni, Cu) or the dimeric bis‐aziridine complex [Cu(az)₂Cl₂]₂. After purification, all of the complexes were fully characterized. The single crystal structure analysis revealed two different coordination modes. Whereas both nickel(II ) complexes can be classified as showing an elongated octahedral structure, copper(II ) complexes show either an elongated octahedral or a square pyramidal arrangement forming dimers with chlorido bridges in axial positions. Furthermore, the results of magnetic measurements of the nickel(II ) and copper(II ) compounds are presented.     

An isoperimetric inequality related to a Bernoulli problem

Given a bounded domain Ω we look at the minimal parameter Λ(Ω) for which a Bernoulli free boundary value problem for the p-Laplacian has a solution minimising an energy functional. We show that amongst all domains of equal volume Λ(Ω) is minimal for the ball. Moreover, we show that the inequality is sharp with essentially only the ball minimising Λ(Ω). This resolves a problem related to a question asked in Flucher et al. (Reine Angew Math 486:165–204, 1997).     

The Geometry of Gaussoids

Foundations of Computational Mathematics - A gaussoid is a combinatorial structure that encodes independence in probability and statistics, just like matroids encode independence in linear algebra....     

Robustness analysis of generalized Jackson network

Computational Management Science - Queuing networks are a well-established approach to modeling and analysis of complex systems. This paper develops an approach to risk-analysis of queuing network...     

Release of Molecular Cargo from Polymer Systems by Mechanochemistry

The design and manipulation of (multi)functional materials at the nanoscale holds the promise of fuelling tomorrow's major technological advances. In the realm of macromolecular nanosystems, the incorporation of force-responsive groups, so called mechanophores, has resulted in unprecedented access to responsive behaviours and enabled sophisticated functions of the resulting structures and advanced materials. Among the diverse force-activated motifs, the on-demand release or activation of compounds, such as catalysts, drugs, or monomers for self-healing, are sought-after since they enable triggering pristine small molecule function from macromolecular frameworks. Here, we highlight examples of molecular cargo release systems from polymer-based architectures in solution by means of sonochemical activation by ultrasound (ultrasound-induced mechanochemistry). Important design concepts of these advanced materials are discussed, as well as their syntheses and applications.     

Editorial

JPC – Journal of Planar Chromatography – Modern TLC -     

Boranediyl- and Diborane(4)-1,2-diyl-Bridged Platinum A-Frame Complexes

Diplatinum A-frame complexes with a bridging (di)boron unit in the apex position were synthesized in a single step by the double oxidative addition of dihalo(di)borane precursors at a bis(diphosphine)-bridged Pt⁰₂ complex. While structurally analogous to well-known μ-borylene complexes, in which delocalized dative three-center-two-electron M-B-M bonding prevails, theoretical investigations into the nature of Pt−B bonding in these A-frame complexes show them to be rare dimetalla(di)boranes displaying two electron-sharing Pt−B σ-bonds. This is experimentally reflected in the low kinetic stability of these compounds, which are prone to loss of the (di)boron bridgehead unit.