Influence of steady background gradients on the accuracy of molecular diffusion anisotropy measurements

Spatial susceptibility variations of body components lead to local gradients of the static magnetic field. Effects of such background gradients on fractional diffusion anisotropy (FA) measurements on whole-body magnetic resonance units operating at 1.5, 3.0 and 7.0 T were analyzed theoretically and experimentally. Analytical expressions were derived for the cases of diffusion occurring in isotropic media and in tissues with cylindrical symmetry (e.g., white matter tracts or skeletal musculature). Typical magnitudes of background gradient strengths were estimated from in vivo and in vitro measurements with B0 field mapping sequences. Additionally, numerical simulations of magnetic field distributions and resulting field gradients were performed considering tissue-air interfaces in simplified geometrical arrangements. For media with isotropic diffusion, both measurements and analytical calculations showed increasing FA inaccuracy with stronger coupling between diffusion-encoding and background gradients. For cylindrical symmetry, FA values were estimated for a standard diffusion tensor imaging protocol in a realistic scenario. At 1 mm distance from a water-air interface, susceptibility-related background gradients amount to approximately 9 mT/m at 7 T and lead to a relative error of the measured FA of up to 48%. The error in the anisotropy assessment rises considerably with increasing field strength and must be taken into account especially for experimental and clinical studies on modern high-field systems.     

Broadband fivefold reduction of vacuum fluctuations probed by dyes in photonic crystals

We observed for the first time a strong angle-independent modification of spontaneous emission spectra from laser dyes in photonic crystals, made of inverse opals in titania. Comparison with spectra from such crystals with much smaller lattice spacing, for which emission is in the long wavelength limit, reveals inhibition of emission up to a factor approximately 5 over a large bandwidth of 13% of the first order Bragg resonance frequency. The center frequency and bandwidth of the inhibition agree with calculated total density of states, while the measured inhibition of vacuum fluctuations is much larger. Because of the specific location of the dye molecules, we likely probe the strongly modulated local photonic density of states.     

Reversibility in Infinite Hamiltonian Systems with Conservative Noise

The set of stationary measures of an infinite Hamiltonian system with noise is investigated. The model consists of particles moving in with bounded velocities and subject to a noise that does not violate the classical laws of conservation, see [OVY]. Following [LO] we assume that the noise has also a finite radius of interaction, and prove that translation invariant stationary states of finite specific entropy are reversible with respect to the stochastic component of the evolution. Therefore the results of [LO] imply that such invariant measures are superpositions of Gibbs states. Received: 26 September 1996 / Accepted: 3 January 1997     

Covering space for monotonic homotopy of trajectories of control systems

This paper considers monotonic (or causal) homotopy between trajectories of control systems. The main result is the construction of an analogue of the simply connected covering space. The constructed covering Γ(Σ,x) has the structure of a manifold and satisfies the property that two trajectories are monotonic homotopic if and only if the end points of their liftings coincide.     

Voltammetry of Organic Microparticles

 Solid microparticles of several different insoluble organic compounds were mechanically immobilized on the surface of graphite electrodes and immersed into a liquid electrolyte in order to study their electrochemical reactions. Cyclic staircase voltammetry and square-wave voltammetry were used. Quinhydrone was found to be a stable intermediate in the reversible redox reaction of solid quinone and hydroquinone on the electrode surface. The reaction occurs on the surface of the solid particle which is in contact with water. Indigo can be reduced to leucoindigo and oxidized to dehydroindigo in two separate reversible redox reactions. In strongly basic medium indigo dissolves in water upon electroreduction. A hydroacridine radical was detected as a stable intermediate in the electrochemically irreversible redox reaction of acridine and dihydroacridine. Famotidine can be electrooxidized and the product of this reaction can be electroreduced in two separate chemically irreversible reactions. Probucol is oxidized to a semiquinone radical which can be re-reduced in an electrochemically irreversible redox reaction. Propyl- thiouracil can be also oxidized to an unknown product which can be re-reduced in a chemically reversible, but slow solid state surface redox reaction. Reductions of solid thionicotinoylanilide and nicotinoylanilide are totally irreversible. Received September 22, 1998. Revision March 19, 1999.     

Bildung siliciumorganischer Verbindungen. 85 [1]. Bildung,Reaktionen und Struktur des 1,1,3,3-Tetramethyl-2,4-bis(trimethylsilyl)-1,3-disilabicyclo[1, 1, 0]butans

me₃Si? CCl₂?Sime₂Cl (me ? CH₃) läßt sich mit n-buLi (bu ? C₄H₉) bei–100°C (Lösungsmittel THF/Äther) in me₃Si? CCl(Li)? Sime₂Cl a überführen. das mit meJ me₃Si? CClme? Sime₂Cl bildet. Wird a in Abwesenheit eines Abfangreagenzes langsam erwärmt, so bildet sich unter Abspaltung von LiCl (Cl aus der SiCl-Gruppe) über eine reaktive Zwischenstufe des Bicyclobutans b . Die Struktur von b ist durch NMR-Untersuchung, Röntgenstrukturanalyse und Abbaureaktionen gesichert. Mit HBr bzw. CH₃OH werden die Si? C-Bindungen der Dreiringe in b gespalten, so daß sich me₃Si? CH₂? C(Sime₂X)₂Sime₃ (X ? Br, OCH₃) bildet. Formation of Organosilicon Compounds. 85. Formation, Reactions, and Structure of 1,1,3,3-Tetramethyl-2,4-bis(trimethylsilyl)-1,3-disilabicyclo[1, 1, 0]butane me₃Si? CCl₂? Sime₂Cl (me ? CH₃) with n-buLi (bu ? C₄H₉) at –100°C (solvent: THF/ether) yields me₃Si? CCl(Li)? Sime₂Cl a , which forms me₃Si? CClme? Sime₂Cl with meI. By warming a slowly in absence of any trapping reagent the bicyclobutane b is obtained via a reactive intermediate under elimination of LiCl (Cl from the SiCl group). The structure of b is established by nmr investigations, X-ray structure determination and chemical derivatisation.     

Directional fluorescence spectra of laser dye in opal and inverse opal photonic crystals

We have investigated the fluorescence from R6G dye molecules embedded in fcc photonic crystals with a large range of lattice parameters. Both polystyrene opals and alumina inverse opals are studied, allowing us to compare direct and inverted structures. We observe clear stop bands in the fluorescence spectra, whose center positions, widths, and depths are analyzed and compared to stop bands from reflectivity measurements. In the frequency range of first-order stop gaps, the measured stop band centers and widths agree well with theoretical predictions. The depths are interpreted in terms of the mean free path (disorder) and the Bragg attenuation length (order). We observe intriguing enhanced emission at the blue side of the stop bands, which is attributed to the escape of diffuse light from the photonic crystal (related to both order and disorder). We perform the first experiments in the range of second-order stop gaps, which is the regime where the photonic band gap is anticipated. We observe complex multiple-Bragg features that correlate favorably with reflectivity peaks.     

Activation and Photoinduced Release of Alkynes on a Biomimetic Tungsten Center: The Photochemical Behavior of the W−S-Phoz System

The synthesis and structural determination of four tungsten alkyne complexes coordinated by the bio-inspired S,N-donor ligand 2-(4′,4′-dimethyloxazoline-2′-yl)thiophenolate (S-Phoz) is presented. A previously established protocol that involved the reaction of the respective alkyne with the bis-carbonyl precursor [W(CO)₂(S-Phoz)₂] was used for the complexes [W(CO)(C₂R₂)(S-Phoz)₂] (R=H, 1 a ; Me, 1 b ; Ph, 1 c ). Oxidation with pyridine-N-oxide gave the corresponding W-oxo species [WO(C₂R₂)(S-Phoz)₂] (R=H, 2 a ; Me, 2 b ; Ph, 2 c ). All W-oxo-alkyne complexes ( 2 a , b , c ) were found to be capable of alkyne release upon light irradiation to afford five-coordinate [WO(S-Phoz)₂] ( 3 ). The photoinduced release of the alkyne ligand was studied in detail by in situ ¹H NMR measurements, which revealed correlation of the photodissociation rate constant ( 2 b>2 a>2 c ) with the elongation of the alkyne C≡C bond in the molecular structures. Oxidation of [WO(S-Phoz)₂] ( 3 ) with pyridine-N-oxide yielded [WO₂(S-Phoz)₂] ( 4 ), which shows highly fluxional behavior in solution. Variable-temperature ¹H NMR spectroscopy revealed three isomeric forms with respect to the ligand arrangement versus each other. Furthermore, compound 4 rearranges to tetranuclear oxo compound [W₄O₄(μ-O)₆(S-Phoz)₄] ( 5 ) and dinuclear [{WO(μ-O)(S-Phoz)}₂] ( 6 ) over time. The latter two were identified by single-crystal X-ray diffraction analyses.     

Versuche mit markierten Atomen über den Mechanismus der Vermehrung von Tabakmosaikvirus in Nicotiana tabacum

Zusammenfassung Tabakmosaikvirus hoher spezifischer Aktivität, das am Phosphor und/oder Kohlenstoff markiert war, wurde biosynthetisch hergestellt. Damit wurde jeweils ein Blatt einer Pflanze von Nicotiana tabacum infiziert und der etwaige Transport von intaktem Virus durch das Leitungssystem der Pflanzen dadurch weitgehend unterbunden, daß die Leitgefäße des behandelten Blattes durchtrennt wurden.Das aus den unbehandelten Blättern der Pflanze nach 17 1/2, 48 und 72 Stdn. isolierte Virus wies im Vergleich zum eingesetzten TMV einen viel geringeren Anteil an Gesamtradiokohlenstoff im Protein auf. Dies deutet darauf hin, daß das Virus der unbehandelten Blätter höchstens zu einem sehr geringen Teil aus intakt transportiertem TMV bestehen könnte.Die nicht im TMV enthaltenen Polynukleotide der unbehandelten Blätter enthalten 7 Stdn. nach der Infektion verhältnismäßig viel³²P, doch tritt derselbe innerhalb 70 Stdn. zum allergrößten Teil in niedermolekulare Verbindungen über.Die in Puffer unlöslichen Polynukleotide der unbehandelten Blätter (Blattnukleinsäure) weisen ein mit der Zeit abnehmendes Verhältnis von³²P/¹⁴C auf. Auch innerhalb der Nukleinsäure (NS) des TMV dieser Blätter nimmt dieses Verhältnis zunächst ab, steigt aber später wieder an.Die angeführten Ergebnisse stehen mit der Vorstellung im Einklang, daß das Virus NS abspaltet und sowohl die systemische Infektion der Pflanze wie auch die Virusvermehrung mindestens zum Teil durch diese freie NS bewirkt wird. Die aus dem Virus stammende freie NS unterliegt zum großen Teil lebhaftem Abbau, wobei ihre Komponenten wahrscheinlich dem Aufbau normaler Blattbestandteile dienen.Mit 3 Abbildungen