Principal part of resolvent and factorization of an increasing nonanalytic operator-function

Let a selfadjoint operator-valued functionL() be given on the interval [a,b] such thatL(a)0,L(b)0,L()0 (ab), andL() has a certain smoothness (for instance, it satisfies Hölder's condition). It turns out that the spectral theory of the operator-valued functionL() can be reduced to the spectral theory of one operatorZ, the spectrum of which lies on (a, b) and which is similar to a selfadjoint operator. In particular, the factorization takes place:L()=M()(I–Z), where the operator-valued functionM() is invertible on [a, b]. Earlier similar results were known only for analytic operator-valued functions. The authors had to use new methods for the proof of the described theorem. The key moment is the decomposition ofL ^–1() into the sume of its principal and regular parts.     

Methanofullerene Molecular Scaffolding: Towards C60-substituted poly(triacetylenes) and expanded radialenes,preparation of a C60–C70 hybrid derivative,and a novel macrocyclization reaction

The synthesis of (E)-hex-3-ene-l, 5-diynes and 3-methylidenepenta-1, 4-diynes with pendant methano[60]-fullerene moieties as precursors to C₆₀-substituted poly(triacetylenes) (PTAs, Fig. 1) and expanded radialenes (Fig. 2) is described. The Bingel reaction of diethyl (E)-2, 3-dialkynylbut-2-ene-1, 4-diyl bis(2-bromopropane-dioates) 5 and 6 with two C₆₀ molecules (Scheme 2) afforded the monomeric, silyl-protected PTA precursors 9 and 10 which, however, could not be effectively desilylated (Scheme 4). Also formed during the synthesis of 9 and 10 , as well as during the reaction of C₆₀ with thedesilylated analogue 16 (Scheme 5 ), were the macrocyclic products 11, 12 , and 17 , respectively, resulting from double Bingel addition to one C-sphere. Rigorous analysis revealed that this novel macrocyclization reaction proceeds with complete regio- and diastereoselectivity. The second approach to a suitable PTA monomer attempted N, N′-dicyclohexylcarbodiimide(DCC)-mediated esterification of (E)-2, 3-diethynylbut-2-ene-l, 4-diol ( 18 , Scheme 6) with mono-esterified methanofullerene-dicarboxylic acid 23 ; however, this synthesis yielded only the corresponding decarboxylated methanofullerene-carboxylic ester 27 (Scheme 7). To prevent decarboxylation, a spacer was inserted between the reacting carboxylic-acid moiety and the methane C-atom in carboxymethyl ethyl 1, 2-methano[60]fullerene-61, 61-dicarboxylate ( 28 , Scheme 8), and DCC-mediated esterification with diol 18 afforded PTA monomer 32 in good yield. The formation of a suitable monomeric precursor 38 to C₆₀-substituted expanded radialenes was achieved in 5 steps starting from dihydroxyacetone (Schemes 9 and 10), with the final step consisting of the DCC-mediated esterification of 28 with 2-[1-ethynyl(prop-2-ynylidene)]propane-1, 3-diol ( 33 ). The first mixed C₆₀-C₇₀ fullerene derivative 49 , consisting of two methano[60]fullerenes attached to a methano[70]fullerene, was also prepared and fully characterized (Scheme 13). The C_s-symmetrical hybrid compound was obtained by DCC-mediated esterification of bis[2-(2-hydroxy-ethoxy)ethyl] 1, 2-methano[70]fullerene-71, 71-dicarboxylate ( 46 ) with an excess of the C₆₀-carboxylic acid 28 . The presence of two different fullerenes in the same molecule was reflected by its UV/VIS spectrum, which displayed the characteristic absorption bands of both the C₇₀ and C₆₀ mono-adducts, but at the same time indicated no electronic interaction between the different fullerene moieties. Cyclic voltammetry showed two reversible reduction steps for 49 , and comparison with the corresponding C₇₀ and C₆₀ mono-adducts 46 and 30 indicated that the three fullerenes in the composite fullerene compound behave as independent redox centers.     

Fulven-Dimere: Synthese,Strukturbeweis and thermisches Verhalten

Fulvene-Dieters: Synthesis, Structure Elucidation and Thermal Behaviour In contrast to earlier assumptions, thermal reaction of pure fulvene ( 1a ), 6-methylfulvene ( lb ) and 6, 6-dimethylfuivene ( 1c ) at 227deg; gives oligomeric mixtures consisting mainly of the endo-[4 + 2]-eycloaddition products 2a , 2b and 2c . Thermal reactivity of the fulvenes decreases strongly in the series 1a > 1b > 1c . While the dimers 2b and 2c equilibrate very easily in solution above room temperature with 1b and 1c , respectively, 2a equilibrates with the isomer 5a (? 1, 6-Dimethyliden3a α, 3bβ, 6a α, 6bβ-tetrahydro-1-H), 6 H-bi (cyclopentadienylen). This surprising rearrangement envolves a formal 1,3-shift of the 1, 2-dihydrofulvene-unit of 2a (s. Scheme 4).     

Dispersion of the local parameters of quasilocalized low-frequency vibrational modes in a low-temperature glass: direct observation via single-molecule spectroscopy

Spectra of single tetra-tert-butylterrylene chromophore molecules embedded in an amorphous polyisobutylene matrix as microprobes were recorded. The individual temperature dependences of the spectral linewidths for the same single molecules (SMs) in a broad temperature interval (1.6 < T < 40 K) have been measured. This enabled us to separate the contributions of tunneling two-level systems and quasilocalized low-frequency vibrational modes (LFMs) to the observed linewidths. The analysis of the T dependences yields the values of LFM frequencies and SM-LFM coupling constants for the LFMs in the local environment of a given chromophore. Pronounced distributions of the observed parameters of LFMs were found. This result can be regarded as the first direct experimental proof of the localized nature of LFMs in glasses.     

Swallowtail porphyrins: synthesis, characterization and incorporation into porphyrin dyads

The incorporation of symmetrically branched tridecyl ("swallowtail") substituents at the meso positions of porphyrins results in highly soluble building blocks. Synthetic routes have been investigated to obtain porphyrin building blocks bearing 1-4 swallowtail groups. Porphyrin dyads have been synthesized in which the zinc or free base (Fb) porphyrins are joined by a 4,4'-diphenylethyne linker and bear swallowtail (or n-pentyl) groups at the nonlinking meso positions. The swallowtail-substituted Zn(2)- and ZnFb-dyads are readily soluble in common organic solvents. Static absorption and fluorescence spectra and electrochemical data show that the presence of the swallowtail groups slightly raises the energy level of the filled a(2u)(pi) HOMO. EPR studies of the pi-cation radicals of the swallowtail porphyrins indicate that the torsional angle between the proton on the alkyl carbon and p-orbital on the meso carbon of the porphyrin is different from that of a porphyrin bearing linear pentyl groups. Regardless, the swallowtail substituents do not significantly affect the photophysical properties of the porphyrins or the electronic interactions between the porphyrins in the dyads. In particular, time-resolved spectroscopic studies indicate that facile excited-state energy transfer occurs in the ZnFb dyad, and EPR studies of the monocation radical of the Zn(2)-dyad show that interporphyrin ground-state hole transfer is rapid.     

The effect of polymers on the phase behavior of balanced microemulsions: diblock-copolymer and comb-polymers

The effect of some amphipilic diblock-copolymers and comb-polymers on a balanced Winsor III microemulsion system is investigated with the quaternary system n-octyl-β-d-glucoside/1-octanol/n-octane/D₂O as basis system. The diblock-copolymers are polyethyleneoxide-co-polydodecenoxide (PEO _x PEDODO _y ) and polyethyleneoxide-co-polybutyleneoxide (PEO _x PEBU _y ), constituted of a straight chain hydrophilic part and a bulky hydrophobic part. Addition of the diblock-copolymer leads to an enhancement of the swelling of the middle phase by uptake of water and oil; a maximum boosting factor of 6 was obtained for PEO₁₁₁PEDODO₂₅. Nuclear magnetic resonance diffusometry yields the self-diffusion coefficients of all the components in the system. The diffusion experiments provide information on how the microstructure of the bicontinuous microemulsion changes upon addition of the polymers. The reduced self-diffusion coefficients of water and oil are sensitive to the type of polymer that is incorporated in the film. For the diblock-copolymers, as mainly used here, the reduced self-diffusion coefficient of oil and water will respond to how the polymer bends the film. When the film bends away from water, the reduced self-diffusion of the water will increase, whereas the oil diffusion will decrease due to the film acting as a barrier, hindering free diffusion. The self-diffusion coefficient of the polymer and surfactant are similar in magnitude and both decrease slightly with increasing polymer concentration.     

Synthese und Charakterisierung neuer intramolekular stickstoffstabilisierter Organoaluminium‐ und Organogalliumalkoxide

Synthesis and Characterization of New Intramolecularly Nitrogen‐stabilized Organoaluminium‐ and Organogallium Alkoxides The intramolecularly nitrogen stabilized organoaluminium alkoxides [Me₂Al{μ‐O(CH₂)₃NMe₂}]₂ ( 1a ), Me₂AlOC₆H₂(CH₂NMe₂)₃‐2,4,6 ( 2a ), [(S)‐Me₂Al{μ‐OCH₂CH(i‐Pr)NH‐i‐Pr}]₂ ( 3a ) and [(S)‐Me₂Al{μ‐OCH₂CH(i‐Pr)NHCH₂Ph}]₂ ( 4 ) are formed by reacting equimolar amounts of AlMe₃ and Me₂N(CH₂)₃OH, C₆H₂[(CH₂NMe₂)₃‐2,4,6]OH, (S)‐i‐PrNHCH(i‐Pr)CH₂OH, or (S)‐PhCH₂NHCH(i‐Pr)CH₂OH, respectively. An excess of AlMe₃ reacts with Me₂N(CH₂)₂OH, Me₂N(CH₂)₃OH, C₆H₂[(CH₂NMe₂)₃‐2,4,6]OH, and (S)‐i‐PrNHCH(i‐Pr)CH₂OH producing the “pick‐a‐back” complexes [Me₂AlO(CH₂)₂NMe₂](AlMe₃) ( 5 ), [Me₂AlO(CH₂)₃NMe₂](AlMe₃) ( 1b ), [Me₂AlOC₆H₂(CH₂NMe₂)₃‐2,4,6](AlMe₃)₂ ( 2b ), and [(S)‐Me₂AlOCH₂CH(i‐Pr)NH‐i‐Pr](AlMe₃) ( 3b ), respectively. The mixed alkyl‐ or alkenylchloroaluminium alkoxides [Me(Cl)Al{μ‐O(CH₂)₂NMe₂}]₂ ( 6 ) and [{CH₂=C(CH₃)}(Cl)Al{μ‐O(CH₂)₂NMe₂}]₂ ( 8 ) are to obtain from Me₂AlCl and Me₂N(CH₂)₂OH and from [Cl₂Al{μ‐O(CH₂)₂NMe₂}]₂ ( 7 ) and CH₂=C(CH₃)MgBr, respectively. The analogous dimethylgallium alkoxides [Me₂Ga{μ‐O(CH₂)₃NMe₂}]₂ ( 9 ), [(S)‐Me₂Ga{μ‐OCH₂CH(i‐Pr)NH‐i‐Pr}]_n ( 10 ), [(S)‐Me₂Ga{μ‐OCH₂CH(i‐Pr)NHCH₂Ph}]_n ( 11 ), [(S)‐Me₂Ga{μ‐OCH₂CH(i‐Pr)N(Me)CH₂Ph}]_n ( 12 ) and [(S)‐Me₂Ga{μ‐OCH₂(C₄H₇NHCH₂Ph)}]_n ( 13 ) result from the equimolar reactions of GaMe₃ with the corresponding alcohols. The new compounds were characterized by elemental analyses, ¹H‐, ¹³C‐ and ²⁷Al‐NMR spectroscopy, and mass spectrometry. Additionally, the structures of 1a , 1b , 2a , 2b , 3a , 5 , 6 and 8 were determined by single crystal X‐ray diffraction.     

Temperature-dependent behavior of a symmetric long-chain bolaamphiphile with phosphocholine headgroups in water: from hydrogel to nanoparticles

The temperature-dependent self-assembly of the single-chain bolaamphiphile dotriacontan-1,1'-diyl-bis[2-(trimethylammonio)ethyl phosphate] (PC-C32-PC) was investigated by transmission electron microscopy (TEM), differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FT-IR), X-ray scattering, rheological measurements, and dynamic light scattering (DLS). At room temperature this compound, in which two phosphocholine headgroups are connected by a C(32) alkyl chain, proved to be capable of gelling water very efficiently by forming a dense network of nanofibers (Kohler et al. Angew. Chem., Int. Ed. 2004, 43, 245). A specific feature of this self-assembly process is that it is not driven by hydrogen bonds but solely by hydrophobic interactions of the long alkyl chains. The nanofibers have a thickness of roughly the molecular length and show a helical superstructure. A model for the molecular structure of the fibrils which considers the extreme constitution of the bolaamphiphile is proposed. Upon heating the suspensions three different phase transitions can be detected. Above 49 degrees C, the temperature of the main transition where the alkyl chains become "fluid", a clear low-viscosity solution is obtained due to a breakdown of the fibrils into smaller aggregates. Through mechanical stress the gel structure can be destroyed as well, indicating a low stability of these fibers. The gel formation is reversible, but as a drastic rearrangement of the molecules takes place, metastable states occur.     

P840-Reaction Centers from Chlorobium tepidum–Quinone Analysis and Functional Reconstitution into Lipid Vesicles

Membranes of Chlorobium tepidum contain about 35, 45 and2–10 molecules of menaquinone-7, chlorobium quinone (1′-oxo-menaquinone-7) and of the polar menaquinone (probably 1′-OH-menaquinone-7) per reaction center, respectively. None of these quinones was retained during the isolation of P840-reaction centers beyond the detection limit of about 0.2 quinones per reaction center, neither in the core complex nor in functionally intact reaction center preparations. The latter is shown to catalyze the formation of an electrochemical proton gradient in the presence of ascorbate and phenazinium methosulfate, when it is incorporated into lipid vesicles.