Pseudocompact Algebras and Highest Weight Categories

We develop a new approach to highest weight categories $\cal{C}$ with good (and cogood) posets of weights via pseudocompact algebras by introducing ascending (and descending) quasi-hereditary pseudocompact algebras. For $\cal{C}$ admitting a Chevalley duality, we define and investigate tilting modules and Ringel duals of the corresponding pseudocompact algebras. Finally, we illustrate all these concepts on an explicit example of the general linear supergroup GL(1|1).     

2,6-Diacylnaphthalene-1,8:4,5-bis(dicarboximides): synthesis, reduction potentials, and core extension

2,6-Diacyl derivatives of naphthalene-1,8:4,5-bis(dicarboximide)s have been synthesized via Stille coupling reactions of the corresponding 2,6-distannyl derivative with acyl halides. Reaction of these diketones with hydrazine gave phthalazino[6,7,8,1-lmna]pyridazino[5,4,3-gh][3,8]phenanthroline-5,11(4H,10H)-dione fused-ring derivatives. The products were characterized by UV-vis absorption spectroscopy and electrochemistry, modeled using density functional theory calculations, and, in some cases, studied and compared using single-crystal X-ray diffraction.     

Minimum supports of eigenfunctions of Johnson graphs

We study the weights of eigenvectors of the Johnson graphs $J(n,w)$. For any $i\in \{1,\dots ,w\}$ and sufficiently large $n,n\ge n(i,w)$ we show that an eigenvector of $J(n,w)$ with the eigenvalue ${\lambda }_i=(n?w?i)(w?i)?i$ has at least $2^i\left(\genfrac{}{}{0ex}{}{n?2i}{w?i}\right)$ nonzeros and obtain a characterization of eigenvectors that attain the bound.     

Mechanistic aspects of reactions of triphenylphosphine with electron‐deficient alkenes in acetic acid solution

Kinetic data provide evidence that proton transfer to the carbanion centre of a phosphonium zwitterion is the rate‐determining step in quarternization reactions of triphenylphosphine with electron‐deficient alkenes in acetic acid solution. This conclusion is based on the third‐order rate equation, the reactivity of the alkenes, and solvent isotope effects in deuteroacetic acid. Copyright © 2013 John Wiley & Sons, Ltd.     

Algebra of Screening Operators for the Deformed W n Algebra

We construct a family of intertwining operators (screening operators) between various Fock space modules over the deformed W _n algebra. They are given as integrals involving a product of screening currents and elliptic theta functions. We derive a set of quadratic relations among the screening operators, and use them to construct a Felder-type complex in the case of the deformed W ₃ algebra. Received: 3 March 1997 / Accepted: 20 May 1997     

Structures of cabergoline anhydrate form II and novel cabergoline solvates

Crystal forms of N-[3-(dimethylamino)propyl]-N-(ethylcarbamoyl)-6-allyl-ergoline-8β-carboxamide (cabergoline) originating from various solvents have been examined by X-ray diffraction at 298 or 150 K. Crystal structures of cabergoline anhydrate, (form II, P2₁2₁2₁) and solvates (all P2₁2₁2₁) with tert-butyl methyl ether (form VIII), cyclohexane (form XV), toluene (form IX), p-xylene (form XVI), and 1,2,4-trimethylbenzene (form XVII) are described. Conformation of cabergoline in these forms was compared with crystal structures of forms I and VII of cabergoline (P2₁) described in the literature. Despite a high degree of molecular conformational freedom, cabergoline possesses similar conformation in forms I, II, VIII, IX, XV, XVI, and XVII. Molecular conformations, crystal packing and the effect of the solvent on the former two properties are examined.     

Steroid 19,B‐dinor‐8,10‐iso‐analogues

The Birch reduction of 3‐methoxy‐B‐nor‐8‐isoestra‐1,3,5(10)‐trienes followed by acid hydro­lysis produces steroid androgen 19,B‐dinor‐8,10‐iso‐analogues. By means of X‐ray analysis and correlation NMR spectroscopy of 16,16‐di­methyl‐D‐homo‐19,B‐dinor‐8‐isotestosterone, C₂₀H₃₀O₂, it is demonstrated that the main conformations in the crystal and in solution for two 19,B‐dinor‐8,10‐iso‐analogues are, in general, the same.     

Profiling of cyclic hexadepsipeptides roseotoxins synthesized in vitro and in vivo: a combined tandem mass spectrometry and quantum chemical study

High-performance liquid chromatography and tandem mass spectrometry (HPLC/MS/MS) was used for the detection of cyclic hexadepsipeptides roseotoxins produced by Trichothecium roseum. Roseotoxins were found in both submerged standard cultivation on CzapekDox medium and in vivo cultivation extract obtained from an apple. Roseotoxin chromatographic profiles from these two experiments were compared. Product-ion collision-induced dissociation (CID) spectra obtained on an ion trap (electrospray ionisation, ESI) were used for the identification of natural roseotoxins A, B, C and of minor destruxins A and B. The dissociation behavior of roseotoxins is discussed in terms of a fragmentation scheme proposed for describing the dissociation pathways of cyclic peptides. This scheme involves opening of the cyclopeptide ring via formation of oxazolone derivatives and fragmentation of the resulting linear species, which have a free N-terminus and an oxazolone ring at the C-terminus. Some aspects of this fragmentation scheme are underlined by modeling the dissociation channels of roseotoxin A using quantum chemical calculations. The structures of roseotoxin A and destruxin B were verified by nuclear magnetic resonance (NMR) spectroscopy. Structures of three new minor natural roseotoxins [Val(4)]RosA, [MeLxx(4)]RosA and [MeLxx(4)]RosB were deduced by ion cyclotron resonance Fourier transform mass spectrometry (ICR-FT-MS) and ion trap tandem mass spectrometry by examining the pre-separated roseotoxin fraction.     

Molecular motions and the structure ofβ-cyclodextrin inclusion complexes with ferrocene, [3]-ferrocenophane-1,3-dione and ruthenocene

Spin-lattice relaxation time measurements in laboratory and rotating frames as well as proton second moment analysis have been used to investigate molecular motions in -cyclodextrin (CD) and its solid inclusion complexes with the title organometallic compounds. Different dynamical processes have been identified in the host lattice along with high mobility of the ferrocene and ruthenocene guest molecules. The Arrhenius parameters of all motions were obtained. The assumption based on the second moment measurements was made about the axial structure of the ferrocene complex and the equatorial one of the ruthenocene complex at low temperatures. The bridged ferrocenophane molecule was shown to be rigid on the NMR time scale. The ternary inclusion complex of -CD with ruthenocene and iodine was also studied and no evidence of redox reactions was observed.     

Coordination of Bimuth(III) to Cucurbit[8]uril. Preparation and X‐ray Structure of [{Bi(NO3)(H2O)5}2(Q8)][Bi(NO3)3(H2O)4]2[Bi(NO3)5]2·Q8·19H2O

Bi(NO₃)₃ reacts with cucurbit[8]uril, (Q8), in 3M HNO₃ to give the title complex whose structure includes three discrete Bi complexes: [{Bi(NO₃)(H₂O)₅}₂(Q8)]⁴⁺ (CN of Bi = 9, both NO₃^— and cucurbit[8]uril are bidentate), [Bi(NO₃)₅]^2— (CN of Bi = 10, all NO₃^— are bidentate), and [Bi(NO₃)₃(H₂O)₄] (CN of Bi = 10, all NO₃^— are bidentate).