Complete and orthonormal eigenfunctions of excitations to a one-dimensional dark soliton

We study linear excitations to a one-dimensional dark soliton described by a defocusing nonlinear Schödinger equation. By solving an eigenvalue problem for the excitations we obtain all eigenvalues and eigenfunctions and prove rigorously that these eigenfunctions are orthonormal and form a complete set. We then use the eigenfunctions to obtain the exact form of linear excitations for any given initial condition and to investigate the transverse stability of the dark soliton. The rigorous results reported in the present work can be applied to study the dynamics of dark solitons in various nonlinear optical media and Bose-Einstein condensates.     

Arrangement of a 4Pi microscope for reducing the confocal detection volume with two-photon excitation

The main advantage of two-photon fluorescence confocal microscopy is the low absorption obtained with live tissues at the wavelengths of operation. However, the resolution of two-photon fluorescence confocal microscopes is lower than in the case of one-photon excitation. The 4Pi microscope type C working in two-photon regime, in which the excitation beams are coherently superimposed and, simultaneously, the emitted beams are also coherently added, has shown to be a good solution for increasing the resolution along the optical axis and for reducing the amplitude of the side lobes of the point spread function. However, the resolution in the transverse plane is poorer than in the case of one-photon excitation due to the larger wavelength involved in the two-photon fluorescence process. In this paper we show that a particular arrangement of the 4Pi microscope, referenced as 4Pi′ microscope, is a solution for obtaining a lateral resolution in the two-photon regime similar or even better to that obtained with 4Pi microscopes working in the one-photon excitation regime.     

A New Chemical Method to Desulfenylate Indol-3-yl Sulfides

Abstract

Desulfenylation of indol-3-yl sulfides liberates the most reactive position of the ring for further transformations. The usual procedure, utilizing Raney Nickel (P. G. Gassman, et. al., J. Am. Chem. SOC. 1974,96, 5495) offers a limited scope due to incompatibility of a number of functional groups towards the reducing agent. Based on our recent mechanistic studies of the acid-catalysed rearrangement of indol-3-yl sulfides to indol-2-yl sulfides (P. Hamel, et. al., Chem. Commun. 1989, 63; J. Org. Chem. 1992, 57, 2694), we have developed a novel, non-reductive desulfenylation method which permits easy access to 3-unsubstituted indoles bearing a wide array of substituents. Thus, 3-indolyl sulfides, readily obtained from appropriate phenylhydrazines (via Fischer indolization) or anilines (Gassman method, vide infra) are smoothly desulfenylated in good yields in trifluoroacetic acid in the presence of an appropriate nucleophilic trapping agent. Thiols proved to be very effective trapping agents and thiosalicylic acid (TSA) is a thiol of choice, being non-volatile and easily separable from reaction products.     

Longitudinal Relaxation Enhancement in 1H NMR Spectroscopy of Tissue Metabolites via Spectrally Selective Excitation

Nuclear magnetic resonance spectroscopy is governed by longitudinal (T₁) relaxation. For protein and nucleic acid experiments in solutions, it is well established that apparent T₁ values can be enhanced by selective excitation of targeted resonances. The present study explores such longitudinal relaxation enhancement (LRE) effects for molecules residing in biological tissues. The longitudinal relaxation recovery of tissue resonances positioned both down‐ and upfield of the water peak were measured by spectrally selective excitation/refocusing pulses, and compared with conventional water‐suppressed, broadband‐excited counterparts at 9.4 T. Marked LRE effects with up to threefold reductions in apparent T₁ values were observed as expected for resonances in the 6–9 ppm region; remarkably, statistically significant LRE effects were also found for several non‐exchanging metabolite resonances in the 1–4 ppm region, encompassing 30–50 % decreases in apparent T₁ values. These LRE effects suggest a novel means of increasing the sensitivity of tissue‐oriented experiments, and open new vistas to investigate the nature of interactions among metabolites, water and macromolecules at a molecular level.     

The influence of nitrogen-15 proton-driven spin diffusion on the measurement of nitrogen-15 longitudinal relaxation times

The effect of nitrogen-15 proton-driven spin diffusion on quantitative (15)N T(1) measurements in solid proteins is investigated, and the impact on the measurement of dynamic parameters is assessed. A simple model of exchange between neighboring nitrogens is used to reproduce the evolution of (15)N spin systems whose longitudinal relaxation rates and exchange rates are compatible with experimental measurements. We show that the induced error in the measured T(1) and its effect on the determination of dynamics parameters is likely to be less than the current experimental error. The use of deuterated protein samples is shown to have a small but sometimes visible effect, and may also considerably slow down or even suppress the exchange of magnetization due to spin diffusion.     

High‐Yield Formation of Substituted Tetracyanobutadienes from Reaction of Ynamides with Tetracyanoethylene

A high‐yielding sequence of [2+2] cycloaddition–retroelectrocyclization of ynamides with tetracyanoethylene (TCNE) is described. The reaction provided tetracyanobutadiene (TCBD) species, which were characterized by various techniques. DFT and TD‐DFT calculations were also performed to complement experimental findings.     

Heavy flags undergo spontaneous oscillations in flowing water

By immersing a compliant yet self-supporting sheet into flowing water, we study a heavy, streamlined, and elastic body interacting with a fluid. We find that above a critical flow velocity a sheet aligned with the flow begins to flap with a Strouhal frequency consistent with animal locomotion. This transition is subcritical. Our results agree qualitatively with a simple fluid dynamical model that predicts linear instability at a critical flow speed. Both experiment and theory emphasize the importance of body inertia in overcoming the stabilizing effects of finite rigidity and fluid drag.     

Investigation in thorium phosphate by NMR II-phosphorus dipolar networks

With through space and through bond experiments in two-dimensional NMR we analyze the transformation from the thorium phosphate-hydrogen phosphate hydrate (TPHPH) to the β form of the thorium phosphate diphosphate (β-TPD) in relation with the phosphorus networks. These techniques are complementary: the through space coupling gives an insight on the dipolar phosphorus networks while the through bond coupling is particularly efficient in the detection of the P₂O₇ groups. With these experiments we show that in a first step, by heating the precursor TPHPH above 250 °C, it transforms into an form of TPD. This transformation is due to the complete condensation of hydrogen phosphate groups HPO₄ into P₂O₇ entities. By heating -TPD above 950 °C it transforms into its well-known β form. The form is characterized by a hygroscopic behavior: some water molecules are present near the P₂O₇ groups that makes non-equivalent their phosphorus nuclei. PO₄ dipolar networks are always present in the form. The main effect of these PO₄ and P₂O₇ units is to give the system a channel structure and the water enters in them.