Theories of rings with divisibility

We consider several different theories of commutative rings with a new predicate symbol | together with the additional axiom a|b ? ?c (a . c = b) and show that none of these has a model companion.     

Protein Mimicry: A New Dimension for Peptides as Lead Compounds?

A short peptide as mimic for the hemopoietic growth factor erythropoietin (containing 165 amino acids) could be identified with the aid of peptide libraries on phage surfaces (phage display). The crystal structure of a peptide dimer complexed with two erythropoietin receptors (shown on the right) provides an insight into the molecular basis of this protein mimicry.     

Canonical basis linearity regions arising from quiver representations

In this paper we show that there is a link between the combinatorics of the canonical basis of a quantized enveloping algebra and the monomial bases of the second author [Math. Z. 237 (2001) 639] arising from representations of quivers. We prove that some reparametrization functions of the canonical basis, arising from the link between Lusztig's approach to the canonical basis and the string parametrization of the canonical basis, are given on a large cone by linear functions arising from these monomial bases for a quantized enveloping algebra.     

Assembly of metal-organic frameworks from large organic and inorganic secondary building units: new examples and simplifying principles for complex structures

The secondary building unit (SBU) has been identified as a useful tool in the analysis of complex metal-organic frameworks (MOFs). We illustrate its applicability to rationalizing MOF crystal structures by analysis of nine new MOFs which have been characterized by single-crystal X-ray diffraction. Tetrahedral SBUs in Zn(ADC)(2).(HTEA)(2) (MOF-31), Cd(ATC).[Cd(H(2)O)(6)](H2O)(5) (MOF-32), and Zn(2)(ATB)(H2O).(H2O)(3)(DMF)(3) (MOF-33) are linked into diamond networks, while those of Ni(2)(ATC)(H(2)O)(4).(H2O)(4) (MOF-34) have the structure of the Al network in SrAl(2). Frameworks constructed from less symmetric tetrahedral SBUs have the Ga network of CaGa(2)O(4) as illustrated by Zn(2)(ATC).(C(2)H(5)OH)(2)(H2O)(2) (MOF-35) structure. Squares and tetrahedral SBUs in Zn(2)(MTB)(H2O)(2).(DMF)(6)(H2O)(5) (MOF-36) are linked into the PtS network, which is the simplest structure type known for the assembly of these shapes. The octahedral SBUs found in Zn(2)(NDC)(3).[(HTEA)(DEF)(ClBz)](2) (MOF-37) form the most common structure for linking octahedral shapes, namely, the boron network in CaB(6). New structure types for linking triangular and trigonal prismatic SBUs are found in Zn(3)O(BTC)(2).(HTEA)(2) (MOF-38) and Zn(3)O(HBTB)(2)(H2O).(DMF)(0.5)(H2O)(3) (MOF-39). The synthesis, crystal structure, and structure analysis using the SBU approach are presented for each MOF.     

X-ray structure determination of new monomers to establish their polymerizability: Copolymerization of two tetrasubstituted electrophilic olefins with electron-rich styrenes giving polymers with an average 1.25 functional groups per chain carbon atom

X-Ray crystal structure determination for two tetrasubstituted electrophilic olefins, tetramethyl ethylenetetracarboxylate TMET and dimethyl dicyanofumarate DDCF, revealed two fundamentally different molecular structures. TMET is a nonplanar molecule that possesses two opposite ester groups planar and the others above and below the molecular plane. In contrast, DDCF is a molecule for which both ester groups lie in the plane of the double bond and nitrile groups. DDCF underwent thermal spontaneous copolymerization with electron-rich styrenes to give 1:1 alternating copolymers in moderate yields and molecular weights. These copolymers, which result from the first copolymerizations of a tetrasubstituted olefin, possess an average functionality of 1.25 per chain carbon atom. Polymerization is made possible by low steric hindrance and the high delocalization in the propagating radical. The yields were limited by competing cycloaddition reaction. The corresponding diethyl ester also copolymerized, but not so well. Neither electrophilic olefin homopolymerized under γ-irradiation. TMET did not copolymerize at all when treated under identical conditions.     

cis-Dihydrodiols microbially produced from halo- and methylbenzoic acids

The preparation of thirteen halo- and methyl-substituted 3,5-cyclohexadiene-1, 2-diol-1'carboxylic acids from microbial oxidation of the corresponding benzoic acids is reported. The properties, including CD-, UV-, MS-spectra are compared. The cis-configuration of the glycol group is determined by acetonide formation with 2,2-dimethoxypropane and from spectroscopic data.     

Abelian Quiver Invariants and Marginal Wall-Crossing

We prove the equivalence of (a slightly modified version of) the wall-crossing formula of Manschot, Pioline and Sen and the wall-crossing formula of Kontsevich and Soibelman. The former involves abelian analogues of the motivic Donaldson–Thomas type invariants of quivers with stability introduced by Kontsevich and Soibelman, for which we derive positivity and geometricity properties.     

Cones from quantum groups to tropical flag varieties

Journal of Algebraic Combinatorics - We relate quantum degree cones, parametrizing PBW degenerations of quantized enveloping algebras, to (negative tight monomial) cones introduced by Lusztig in...