Translations and Associated Dirichlet Polyhedra in Complex Hyperbolic Space

We study a nonidentity transvection (i.e. (strictly) hyperbolic isometry) or nonidentity Heisenberg translation f of complex hyperbolic space H ⁿ and a Dirichlet polyhedron P of the cyclic group f. We have four main results: (a) If z & in H ⁿ and the axis of a nonidentity transvection are not complex collinear, then, roughly speaking, any two distinct 'naturally arising' geodesics passing through z are not complex collinear. (b) If g is also a transvection or Heisenberg translation of H ⁿ and z & in H ⁿ such that f(z)=g(z) and f ^–1(z)=g ^–1(z), then f=g. (c) We classify all this kind of polyhedra up to congruence in H ⁿ. (d) We obtain an equivalent condition for P to be cospinal (which means that the complex spines of the two sides of P coincide) in terms of the distance of the spines of the two sides of P.     

Femtosecond time-resolved absorption processes in lithium niobate crystals

Femtosecond pump pulses are strongly attenuated in lithium niobate owing to two-photon absorption; the relevant nonlinear coefficient beta(p) ranges from approximately 3.5 cm/GW for lambda(p) = 388 nm to approximately 0.1 cm/GW for 514 nm. In collinear pump-probe experiments the probe transmission at the double pump wavelength 2lambda(p) = 776 nm is controlled by two different processes: A direct absorption process involving pump and probe photons (beta (r) = 0.9 cm/GW) leads to a pronounced short-duration transmission dip, whereas the probe absorption by pump-excited charge carriers results in a long-duration plateau. Coherent pump-probe interactions are of no importance. Hot-carrier relaxation occurs on the time scale of < or approximately equal to 0.1 ps.     

Femtosecond holography in lithium niobate crystals

Spatial gratings are recorded holographically by two femtosecond pump pulses at 388 nm in lithium niobate (LiNbO3) crystals and read out by a Bragg-matched, temporally delayed probe pulse at 776 nm. We claim, to our knowledge, the first holographic pump-probe experiments with subpicosecond temporal resolution for LiNbO3. An instantaneous grating that is due mostly to the Kerr effect as well as a long-lasting grating that results mainly from the absorption caused by photoexcited carriers was observed. The Kerr coefficient of LiNbO3 for our experimental conditions, i.e., pumped and probed at different wavelengths, was approximately 1.0 x 10(-5) cm2/GW.     

A New β-Ionone from Liriodendron tulipifera

Chemistry of Natural Compounds - A new β-ionone, litulipiferic acid (12), was isolated from the leaves of Liriodendron tulipifera (Magnoliaceae). The structure of the new β-ionone was...     

Structural variations in novel silver(I) complexes with bitopic pyrazole/n-heterocyclic carbene ligands

The synthesis and structural characterization of several new silver complexes of L (L = a bidendate ligand of pyrazole and N-heterocyclic carbene) are described. The result shows that the choice of counterions, N-substitutions of L, and reaction conditions are crucial which lead to a variety of structural motifs, including novel metallomacrocycles [Ag2(mu-L)2]2+ with or without Ag...Ag close contact, a mononuclear [AgL2]+ complex, and a [LAg(NO3)]n coordination polymer. In particular, the nonbonding Ag...Ag distance and the overall geometry of the metallomacrocycles are controllable with different N-substitutions and counterions. All these complexes have been determined by X-ray diffraction. The solid-state aggregates are retained in solution as supported by the electrospray mass spectroscopic studies.     

Targeted identification of phosphorylated peptides by off-line HPLC-MALDI-MS/MS using LC retention time prediction

Protein phosphorylation is a type of posttranslational modification which plays an important role in cell regulation and signal transduction. Because of its biological relevance, a considerable amount of interest has been paid to the development of efficient techniques for phosphopeptide analysis. Although advances in MS control have enabled the high-throughput discovery of proteins from limited amounts of sample, automated selection of MS/MS precursor ions based on intensity alone can significantly hamper the detection of low-abundance phosphopeptides. On the basis of the observation that the introduction of a phosphate moiety does not dramatically change peptide retention time in reverse-phase chromatography, phosphopeptide specific MS/MS fragmentation attempts based on LC retention time and m/z were evaluated using a standard protein mixture, then using in vitro phosphorylated myelin basic protein. Results indicated that the majority (98%) of phosphopeptides identified eluted within a +/- 4-min window of the predicted LC elution time. While studies presented here are primarily proof of concept in nature, data suggest that the use of LC retention time prediction could be a valuable constraint for the identification of phosphopeptides within a set of off-line LC deposited sample spots. It is expected that the development of these methods will not only permit the targeted identification of protein phosphorylation sites but also allow the in-depth analysis of the dynamic events linked to the posttranslational modification.     

Availability Analysis of Repairable <Emphasis Type="Italic">N</Emphasis>-Server <Emphasis Type="Italic">n</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>-Replicated Systems

We develop an exact closed-form expression for the steady-state availability of a repairable, N-server system in which the ith server contains n _i identical, reconfigurable, breakdown-prone units. Our approach, which follows from the Markov chain balance equations and the recursive properties of Hessenberg matrix determinants, is simpler than previously proposed matrix geometric approaches, and can readily be adapted to the availability analysis of more complicated structures. We illustrate this by computing the steady-state availability of a mixed parallel-serial gracefully degrading replicated system.     

Self-sustained oscillations between two tandem cylinders at Reynolds number 1,000

This study focuses on the self-sustained oscillatory flow characteristics between two tandem circular cylinders of equal diameter placed in a uniform inflow. The Reynolds number (Re _D ), based on the cylinder diameter, was around 1,000 and all experiments were performed in a recirculating water channel. The streamwise distance between two tandem cylinders ranged within 1.5 ≤ X _c/D ≤ 7.0. Here X _c denotes the center-to-center distance between two tandem cylinders. For all experiments studied herein, quantitative velocity measurements were performed using hot-film anemometer and the LDV system. The laser sheet technique was employed for qualitative flow visualization. The wavelet transform was applied to elucidate the temporal variation and phase difference between two spectral components of the velocity signals detected in the flow field. The remarkable finding was that when two tandem circular cylinders were spaced at a distance within 4.5 ≤ X _c/D ≤ 5.5, two symmetrical unstable shear layers with a certain wavelength were observed to impinge onto the downstream cylinder. The responding frequency (f _u ), measured between these two cylinders, was much higher than the natural shedding frequency behind a single isolated cylinder at the same Re _D . This responding frequency decreased as the distance X _c/D increased. Not until X _c/D ≥ 6.0, did it recover to the natural shedding frequency behind a single isolated cylinder. Between two tandem cylinders, the Strouhal numbers (St _c = f _u X _c/U_c) maintained a nearly constant value of 3, indicating the self-sustained oscillating flow characteristics with a wavelength X _c/3. Here U _c is the convection speed of the unstable shear layers between two tandem cylinders. At Re _D = 1,000, the self-sustained oscillating characteristics between two tandem circular cylinders were proven to exhibit a sustained flow pattern, not just a sporadic phenomenon.     

Synthesis and thermotropic behaviour of liquid crystals containing tolane-based mesogenic units

Tolane-based liquid crystal materials with three different terminal groups: trifluoromethyltolanes, cyanotolanes, and nitrotolanes, and with different chain lengths of alkenyloxy groups, have been synthesized. The phase behaviour of these liquid crystal materials has been characterized by differential scanning calorimetry, optical polarized light microscopy and X-ray diffraction. The mesophase behaviour of the materials was shown to be significantly influenced by the polarity of the terminal groups. The trifluoromethyltolanes exhibit an enantiotropic smectic E mesophase and the cyanotolanes exhibit a monotropic nematic mesophase. The most polar among the three types of liquid crystal material; the nitrotolanes do not display any liquid crystalline phases, except for the homologue with an eleven methylene unit chain.