Duality Principles in Frame Theory

Duality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article we present a general approach to derive duality principles in abstract frame theory. For each sequence in a separable Hilbert space we define a corresponding sequence dependent only on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract frame setting. In the last part we apply our results to Gabor systems.     

Durch Bromierung ausgelöste Umlagerung tertiärer Allylalkohole: Der Einfluss eines Fluor-Substituenten auf Reaktionsgeschwindigkeit und Reaktionsverlauf

Rearrangement of Tertiary Allyl Alcohols Induced by Bromination: The Effect of a Fluorine Substituent on the Rate and the Outcome of the Reaction The allyl alcohol bearing a methyl and a t-butyl group at the hydroxylated position was found to undergo a rearrangement when treated with bromine (or N-bromosuccinimide) in an aqueous medium and to afford a product mixture containing two regioisomeric ketones and one oxirane. Introduction of an additional methyl group or a fluorine atom at the non-terminal olefinic center led to a more selective discrimination between potential migratory groups. As the result of an exclusive t-butyl shift only one product, a ketone, was formed in both cases. Whereas the reaction rate was only slightly affected by the additional methyl group, it was substantially decreased by the fluorine atom.     

The (CF3S)2N. radical : preparation,dimerization, ESR-studies

The Bis (trifluormethylmercapto) amino radical (CF₃S)₂N· has been prepared by oxidation of Bis (trifluormethylmercapto) amine, (CF₃S)₂NH with activated lead diooxide in CCl₃F solution at room temperature. The 10^?5 – 10^?6 molar solution of the radical shows in the ESR- spectrum a triplett of septetts with a isotropic nitrogen hyperfine splitting constant a(¹⁴N) = 13,2 G, a(¹⁹F) = 1.95 G, indicating that the radical is a planar sp² species where the unpaired electron is located predominantly in the nitrogen 2p orbital. It is suggested that in solution an thermal equilibrium exists between the (CF₃S)₂ N radical and its dimer Tetrakis (trifluormethylmercapto)-hydrazine:

Aspects of preparation as well as thermodynamic and kinetic details of the hydrazine (NN bond strength 7 kcal/mol^?1) and the equilibrium, which can be followed by ESR-spectroscopy will be given.     

Five-membered ring formation in unimolecular reactions of peptides: a key structural element controlling low-energy collision-induced dissociation of peptides

Unimolecular fragmentation reactions of peptides in low-energy collision-induced dissociation are reviewed in the mechanistic context of five-membered ring formation. This structure of intermediates or of fragment ions is recognized as a key element that governs unimolecular peptide fragmentation within the structural framework determined by the peptide backbone and its side-chains. A collection of collision-induced dissociation reactions is presented covering (i) b-ion formation, (ii) the fragmentation of N-terminally acylated peptides, (iii) neutral loss of the C-terminal amino acid in alkali or silver cationized peptides, (iv) the fragmentation of isoAsp-containing peptides and (v) the fragmentation of negatively charged Asp- or Glu-containing peptides. It appears that for all possible nucleophile-electrophile interactions leading to a five-membered ring structure an associated unimolecular peptide fragmentation reaction can be observed.     

Trifluoromethoxy substituted anilines: metalation as the key step for structural elaboration

Trifluoromethoxy-substituted anilines undergo hydrogen/lithium permutation ("metalation") with optional site selectivity depending on the N-protective group employed. N-tert-Butoxycarbonyl-2- and -4-(trifluoromethoxy)aniline react with tert-butyllithium at the nitrogen-adjacent 6- and 2-position affording, after electrophilic trapping, products 1-6. In contrast, deprotonation of the para isomer occurs at the oxygen-neighboring 3-position, giving rise to the acid 12, when the amino group is carrying two trimethylsilyl groups. sec-Butyllithium attacks 3-trifluoromethoxy-N-mono(trimethylsilyl)aniline at the 2-position, but 3-trifluoromethoxy-N,N-bis(trimethylsilyl)aniline at the 4-position to provide respectively the acids 10 and 11 after carboxylation. The synthesis of two new benzodiazepines illustrates (19 and 22) the preparative potential of the aniline functionalization mediated by organometallic reagents.     

Synthèses de produits organofluorés VI Solvolyse de chlorofluorocyclopropanes

Fluoro-organic Syntheses VI: The Solvolysis of Chlorofluoro-cyclopropanes 2-Fluoro-allylic carbocations, generated from 1-chloro-1-fluoro-cyclopropanes or 2-fluoro-allyl p-toluene-sulfonates in water or acetic acid, undergo either proton loss or addition of hydroxyl or acetoxyl. In the latter case, an alkyl-substituted 2-fluoro-allyl ion leads predominantly to the more branched product (e.g. 3-fluoro-2-methyl-3-buten-2-ol) which may be converted into the less branched one (e.g. 2-fluoro-3-methyl-2-buten-2-ol) through reversible reactions.     

Investigation of the NMR enhancement factor in CuMn spin glasses

The NMR enhancement factor of a frozenCuMn spin glass has been measured at a temperatureT?T _g /5. The measurements were performed as function of static magnetic fields of different directions. A two component model of a spin glass has been outlined. One component being a “system of single spins” and the other one being a “subsystem of clusters”. Both components were attributed to different kinds of interaction being RKKY and dipole interaction respectively. The effective anisotropy field of the single spin system consists of two unidirectional contributionsH _a ^s andH _a ^c , which have been measured for different conditions. A second anisotropy fieldH _d binds the cluster system to the system of single spins. All anisotropy fields depend on the annealing temperature of the alloys.     

Prescriptions and Ingredients for Controlled CC Bond Formation with Organometallic Reagents. New synthetic methods (5)

Merits and drawbacks of known carbon-carbon linking procedures are outlined. Two novel methods are discussed in some detail: the copper-catalyzed alkylation of Grignard reagents and reactions with allylpotassium compounds. Both methods provide a very efficient access to saturated, unsaturated, as well as functionally substituted hydrocarbons and moreover permit an astonishing degree of regio- and stereoselective control of olefin synthesis.     

Glycosylation site analysis of human alpha-1-acid glycoprotein (AGP) by capillary liquid chromatography-electrospray mass spectrometry

A new anionic surfactant (RapiGest SF) was successfully used for site-specific analysis of glycosylation in human alpha-1-acid glycoprotein (AGP). By means of this analytical approach combined with capillary HPLC-mass spectrometry (and tandem mass spectrometry), the N-linked glycosylation pattern of AGP was explored. On the basis of mass matching and MS/MS experiments ca 80 different AGP-derived glycopeptides were identified. Glycosylation shows a markedly different pattern for the various glycosylation sites. At sites I and II, triantennary complex-type oligosaccharides predominate and at sites III, IV and V, tetra-antennary complex-type oligosaccharides predominate. Sites IV and V show the presence of additional N-acetyl lactosamine (Gal-GlcNAc) units (even higher degree of branching and/or longer antennae are also present).     

Silacyclohexadienylanionen bis- und tris-trimethylsilyl)-silacyclohexadiene

1,1-Dialkyl(1,1-diaryl)-4-R-1-silacyclohexadienyl anions (1) are available by ether cleavage of the corresponding, 1,1-dialkyl(1,1-diaryl)-4-methoxy-4-R-1-silacyclohexa-2,5-dienes (4), or by deprotonation of the 1,1-dialkyl(1,1-diaryl)-4-R-1-silacyclohexa-2,4-dienes (3) - which are available from 4 - with n-BuLi or LDA resp.The anions 1 are regioselectively silylated by trimethylchlorosilane to give the 6-trimethylsilyl-1-silacyclohexa-2,4-dienes (7,8), their alkylation or acylation occurs exclusively in 4-position to 16 or 17 resp.Deprotonation of 7, 8 with n-BuLi gives the 2-trimethylsilyl-1-silacyclohexadienyl (9), with trimethylchlorosilane they react regioselectively to give the 2,6-bis(trimethylsilyl)-1-silacyclohexa-2,4-dienes (10, 11), with alkyl halides and ketones the anion 9 reacts only in the 4-position.The 1-silacyclohexa-2,5-dienes 22, 25, 28 substituted at the silicon atom by functional groups (O-i-Prop) or by hydrogen can be transformed into 2,6-bis(trimethylsilyl)-1-silacyclohexa-2,4-dienes 24, 27, 33 resp., if LDA is used as base.The easily formed 4-R-2,6-bis(trimethylsilyl)-1-silacyclohexa-2,4-dienyl anions (by deprotonation of 10, 11, 24, 27, 33 with LDA) react with trimethylchlorosilane regioselectively to give the 4-R-2,4,6-tris(trimethylsilyl)-1-silacyclohexa-2,5-dienes 37. Accessing 37 succeeds very simply by manifold-silylation of the 1-sila-2,4-cyclohexadienes 38 with excess trimethylchlorosilane in the presence of 3 mol LDA.Owing to trimethylsilyl substitution in the 2,6-position of the 1-silacyclohexa-2,4-dienes, the ring-silicon atom is strongly sterically shielded, therefore reactions of functional groups at the silicon atom are restricted.