Robust flows over time: models and complexity results

Mathematical Programming - The problem of finding a zero of the sum of two maximally monotone operators is of central importance in optimization. One successful method to find such a zero is the...     

Universal Deformation Rings for the Symmetric Group <Emphasis Type="Italic">S</Emphasis><Subscript>4</Subscript>

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Let S ₄ denote the symmetric group on 4 letters. We determine the universal deformation ring R(S ₄,V) for every kS ₄-module V which has stable endomorphism ring k and show that R(S ₄,V) is isomorphic to either k, or W[t]/(t ²,2t), or the group ring W[ℤ/2]. This gives a positive answer in this case to a question raised by the first author and Chinburg whether the universal deformation ring of a representation of a finite group with stable endomorphism ring k is always isomorphic to a subquotient ring of the group ring over W of a defect group of the modular block associated to the representation.     

Universal deformation rings and generalized quaternion defect groups

We determine the universal deformation rings R(G,V) of certain mod 2 representations V of a finite group G which belong to a 2-modular block of G whose defect groups are isomorphic to a generalized quaternion group D. We show that for these V, a question raised by the author and Chinburg concerning the relation of R(G,V) to D has an affirmative answer. We also show that R(G,V) is a complete intersection even though R(G/N,V) need not be for certain normal subgroups N of G which act trivially on V.     

Oxidative addition of asparagusic acid based disulfides to Pt

[Pt(PPh₃)₄] reacts smoothly and swiftly at room temperature with asparagusic acid and with selected amide and ester derivatives of this cyclic disulfide to afford Pt^II dithiolate chelates of the type cis-[Pt{CRR′(CH₂S)₂}(PPh₃)₂]. The crystal structures of three such products are reported.     

Chiral close-packing of achiral star-shaped molecules on solid surfaces

From the interplay of scanning tunneling microscopy and theoretical calculations, we study the chiral self-assembly of achiral HtB-HBC molecules upon adsorption on the Cu(110) surface. We find that chirality is expressed at two different levels: a +/-5 degrees rotation of the molecular axis with respect to the close-packed direction of the Cu(110) substrate and a chiral close-packed arrangement expected for star-shaped molecules in 2D. Out of the four possible chiral expressions, only two are found to exist due the effect of van der Waals (vdW) interactions forcing the molecules to simultaneously adjust to the atomic template of the substrate geometry and self-assemble in a close-packed geometry.     

How IAF and ILAC manage the recognition of Regional Accreditation Groups: the peer evaluation system of IAF and ILAC for Regional Accreditation Groups

The peer evaluation of single accreditation bodies in order to sign an Arrangement for Recognition of the international accreditation organizations International Accreditation Forum, Inc. (IAF) and International Laboratory Accreditation Cooperation (ILAC), whether performed by Regional Accreditation Groups or directly by IAF and/or ILAC, is standard practice. The fundamental requirements for such evaluations are well specified in documents. However, the careful evaluation of all their Arrangement members poses an enormous logistic task for IAF and ILAC, and the signatories can be evaluated more thoroughly within their Regional Groups. Hence, IAF and ILAC typically evaluate only the Regional Accreditation Groups and accept all signatories of a Regional Accreditation Group once successfully evaluated by their respective Regional Group. However, the requirements for the evaluation of a Regional Group are extensive, and the evaluation procedure is highly complicated and must be conducted very carefully in order to assure that the results of accreditation can be trusted. This article describes the evaluation procedure used by IAF and/or ILAC for Regional Groups wishing to sign the IAF/ILAC Arrangement. We wish to inform and to aid these Regional Groups setting out for evaluation, and also to build confidence in the IAF/ILAC Arrangements.     

Sr[C2(COO)2]: the first anhydrous salt of acetylenedicarboxylic acid

Single crystals of Sr[C(2)(COO)(2)] were formed at the phase boundary of an aqueous silica gel that contained acetylenedicarboxylic acid and an aqueous solution of SrCl(2). The crystal structure (I4(1)/amd, Z=4) shows a diamond-like topology, with the strontium ions in an eightfold co-ordination by the oxygen atoms of six carboxylate ligands with two of them co-ordinating in a chelating-type bidentate mode. As each oxygen atom of the carboxylate groups is involved in both a chelating-type bidentate and unidentate co-ordination and, therefore, bridging two strontium atoms, a three-dimensional framework results. Sr[C(2)(COO)(2)] exhibits a surprising thermal stability. In air decomposition starts at about 720 K and in an argon atmosphere around 750 K. This decomposition is accompanied by a mass loss of approximately 12 %, which is probably due to the loss of one CO molecule. The resulting residue is amorphous to X-rays. A small negative thermal expansion is found between 30 and 280 K, whereas between room temperature and 573 K almost no thermal expansion is observed. Single-crystal investigations at different temperatures show a strong "guitar string" vibration of the oxygen atom perpendicular to the contacts to the strontium atoms; this could be responsible for the thermal expansion behaviour.     

A simple radiochemical determination of90Sr in environmental samples

A simple procedure for the determination of⁹⁰Sr in environmental samples is described. The method uses the different solubilities of the oxalates of calcium and strontium in presence of a large excess of calcium. For this reason the method is especially suited for Ca-rich samples, as e.g., bones or soils. However, after addition of supplementary calcium it works equally well for other types of samples. The method was tested by analyzing the IAEA Certified Reference Materials soil, animal bone and algae.     

Ternäre Halogenide vom Typ A3MX6. VI [1]. Ternäre Chloride der Selten-Erd-Elemente mit Lithium,Li3MCl6 (M  Tb?Lu,Y, Sc): Synthese,Kristallstrukturen und Ionenbewegung

Ternary Halides of the A₃MX₆ Type. VI. Ternary Chlorides of the Rare-Earth Elements with Lithium, Li₃MCl₆ (M ? Tb? Lu, Y, Sc): Synthesis, Crystal Structures, and Ionic Motion Single crystal X-ray studies on the ternary chlorides Li₃ErCl₆, Li₃YbCl₆ and Li₃ScCl₆ show that they crystallize in three different structure types. Li₃ErCl₆ (trigonal, P3 ml, Z = 3, a = 1117.7(2); c = 603.6(2) pm; the chlorides with M ? Tb? Tm, Y are isotypic) and Li₃YbCl₆ (orthorhombic, Pnma, Z = 4, a = 1286.6(1); b = 1113.2(1); c = 602.95(8) pm; Li₃LuCl₆ is isotypic) have very similar structures that may be derived from hexagonal closest packings of chloride ions with the cations occupying octahedral holes in part statistically. Li₃ScCl₆ (monoclinic, C2/m, Z = 2, a = 639.8(1); b = 1104.0(2); c = 639,1(1) pm; β = 109.89(1)°) crystallizes isotypic with Na₃GdI₆ and Li₃ErBr₆, structures that may be derived from a cubic closes packings of anions. The ionic movement in Li₃YCl₆ and Li₃YbCl₆ has been investigated by impedance and ⁷Li-NMR spectroscopy.