Fourier type analysis and the marcenko equation

For certain Fourior type operators P a transform calculus is developed and used to derive a general canonical Marcenko equation connecting P and more general Q via scattering data from Q.     

Rapid and efficient sonochemical formation of gold nanoparticles under ambient conditions using functional alkoxysilane

Gold nanoparticles (NPs) are rapidly and efficiently formed under ambient conditions with a novel and highly-efficient sonochemical promoter. Despite of the presence of free oxygen, 3-glycidoxypropyltrimethoxysilane (GPTMS) showed remarkable efficiency in promoting the reduction rate of Au (III) than that of conventional promoters (primary alcohols). This is likely attributed to the formation of a variety of radical scavengers, which are alcoholic products from sonochemical hydrolysis of the epoxide group and methoxysilane moieties of GPTMS under weakly acidic conditions. Interestingly, the promotion is quenched by amine- or thiol-functionalized alkoxysilane, thereby producing marginal amounts of gold NPs. Furthermore, products of hydrolyzed GPTMS were confirmed to attach on the surface of gold NPs by attenuated total reflectance-Fourier transform infrared spectroscopy. However, according to transmission electron microscopy images, gold NPs that were produced in the presence of GPTMS tend to fuse with each other as condensation of silanols occurs, forming worm- or nugget-like gold nanostructures. The use of long chain surfactants (i.e. polyethylene glycol terminated with hydroxyl or carboxyl) inhibited the fusion, leading to mono-dispersed gold NPs. Additionally, the fact that this approach requires neither an ultrasound source with high frequency nor anaerobic conditions provides a huge advantage. These findings could potentially open an avenue for rapid and large-scale green-synthesis of gold NPs in future work.     

Structure elucidation of cyclohexene (9Z)-octadec-9-enyl ethers isolated from the leaves of Uvaria cherrevensis (Annonaceae)

The phytochemical investigation of the leaf extract of Uvaria cherrevensis (Annonaceae) yielded three new cyclohexene (9Z)-octadec-9-enyl ethers, cherrevenols M-O (1–3), and a known fatty ester derivative (4). The structures of the isolated compounds were elucidated by spectroscopic and computer-aided molecular modelling methods. Ozone Induced Dissociation (OzID) mass spectrometry was employed to determine the C-9 position of the side chain olefinic double bonds, while ¹³C NMR spectroscopy indicated their (Z)-configurations. All isolated compounds were evaluated for their antimalarial and cytotoxic activities; all were inactive.     

Analysis of a rapid supercritical extraction aerogel fabrication process: Prediction of thermodynamic conditions during processing

Aerogels have unusual mechanical and thermal properties that render them useful in a range of applications from thermal insulators to chemical sensors. However, aerogel fabrication can be difficult, typically requiring the use of supercritical extraction of solvent from the sol-gel matrix. We employ a rapid supercritical extraction (RSCE) technique for aerogel fabrication that is faster and simpler than the standard methods. This technique relies on a hydraulic hot press to heat the chemical precursors and provide the required temperature and pressure increase needed to reach a supercritical state within a contained mold. Experimental results show that the pressure-temperature curve is characterized by a ‘take-off point’ and a ‘leak point’. The take-off point occurs at the start of a rapid increase in pressure and the leak point occurs where the pressure increase subsides. This paper presents an analytical model that predicts the pressure-temperature relationship of the aerogel precursors during the RSCE fabrication process and shows that the model can be extended to other RSCE systems. Using pure methanol, water and aerogel precursors in separate tests, the effects of initial liquid volume and press force on the pressure and temperature during processing were studied. We find that the take-off point can be estimated using a maximum specific volume model, which is a function of the initial percent volume fill of liquid used in the test. We are also able to predict the rapid pressure increase region observed during the process using a constant volume model. Leaking is determined to be a function of the mechanical forces acting on the system and occurs when the pressure in the contained mold nears the value of the pressure imparted onto the gasket by the hot press. The leak point pressure is found to be independent of the initial percent volume of liquid used in the test; however the leak point temperature decreases with increasing initial percent volume fill.     

Fundamentals of synchronization in chaotic systems,concepts, and applications

The field of chaotic synchronization has grown considerably since its advent in 1990. Several subdisciplines and "cottage industries" have emerged that have taken on bona fide lives of their own. Our purpose in this paper is to collect results from these various areas in a review article format with a tutorial emphasis. Fundamentals of chaotic synchronization are reviewed first with emphases on the geometry of synchronization and stability criteria. Several widely used coupling configurations are examined and, when available, experimental demonstrations of their success (generally with chaotic circuit systems) are described. Particular focus is given to the recent notion of synchronous substitution-a method to synchronize chaotic systems using a larger class of scalar chaotic coupling signals than previously thought possible. Connections between this technique and well-known control theory results are also outlined. Extensions of the technique are presented that allow so-called hyperchaotic systems (systems with more than one positive Lyapunov exponent) to be synchronized. Several proposals for "secure" communication schemes have been advanced; major ones are reviewed and their strengths and weaknesses are touched upon. Arrays of coupled chaotic systems have received a great deal of attention lately and have spawned a host of interesting and, in some cases, counterintuitive phenomena including bursting above synchronization thresholds, destabilizing transitions as coupling increases (short-wavelength bifurcations), and riddled basins. In addition, a general mathematical framework for analyzing the stability of arrays with arbitrary coupling configurations is outlined. Finally, the topic of generalized synchronization is discussed, along with data analysis techniques that can be used to decide whether two systems satisfy the mathematical requirements of generalized synchronization. (c) 1997 American Institute of Physics.     

Molecular Structure of 1-Substituted Bicyclo[2.2.0]hexanes: A Combined X-Ray Structural and Ab Initio Study

The synthesis and X-ray crystal structure of the p-bromoanilide derivative of bicyclo[2.2.0]hexane-l-carboxylic acid (1), N-(4-bromophenyl)-bicyclo[2.2.0]hexane-l-carboxamide (2), is reported. N-(4-Bromophenyl)-bicyclo[2.2.0]hexane-l-carboxamide is synthesized in good yield via the DCC coupling of bicyclo[2.2.0]hexane-l-carboxylic acid (1) with p-bromoaniline. Low-temperature X-ray analysis of 2 reveals that the bonds of the bicyclo[2.2.0]hexane skeleton vicinal to the amide group show a slight lengthening due to conjugative interaction with the -accepting amide group. Ab initio calculations at the 6-31G* level of theory on bicyclo[2.2.0]hexane-l-carboxamide, a model for 2, and for other 1-substituted bicyclo[2.2.0]hexanes are also reported.     

K4Nb6O17-derived photocatalysts for hydrogen evolution from water: Nanoscrolls versus nanosheets

The layered hexaniobate K₄Nb₆O₁₇ is known as a photocatalyst for methanol dehydrogenation and hydrogen evolution from water under ultraviolet (UV) light. Here we show that the activity is retained in propylammonium- (PA) or tetrabutylammonium- (TBA) stabilized H₂K₂Nb₆O₁₇ nanosheets and TBA-stabilized H₄Nb₆O₁₇ nanoscrolls that can be obtained by exfoliation of K₄Nb₆O₁₇ followed by cation exchange. The catalytic activity of the exfoliated systems is comparable to K₄Nb₆O₁₇, with scrolls being most active in water, and PA sheets giving enhanced H₂ rates due to sacrificial electron donor action of PA. Femtosecond absorption spectra for TBA scrolls and PA sheets exhibit broad features between 450 and 700 nm due to trapped holes and electrons. Electron–hole recombination follows approximately second-order kinetics, with rates of decay similar for sheets and scrolls. In addition, catalysts were characterized with UV/vis and fluorescence spectroscopy and transmission electron microscopy.     

Insight into substrate binding in Shibasaki's Li3(THF)n(BINOLate)3Ln complexes and implications in catalysis

Heterobimetallic Lewis acids M 3(THF) n (BINOLate) 3Ln [M = Li, Na, K; Ln = lanthanide(III)] are exceptionally useful asymmetric catalysts that exhibit high levels of enantioselectivity across a wide range of reactions. Despite their prominence, important questions remain regarding the nature of the catalyst-substrate interactions and, therefore, the mechanism of catalyst operation. Reported herein are the isolation and structural characterization of 7- and 8-coordinate heterobimetallic complexes Li 3(THF) 4(BINOLate) 3Ln(THF) [Ln = La, Pr, and Eu], Li 3(py) 5(BINOLate) 3Ln(py) [Ln = Eu and Yb], and Li 3(py) 5(BINOLate) 3La(py) 2 [py = pyridine]. Solution binding studies of cyclohexenone, DMF, and pyridine with Li 3(THF) n (BINOLate) 3Ln [Ln = Eu, Pr, and Yb] and Li 3(DMEDA) 3(BINOLate) 3Ln [Ln = La and Eu; DMEDA = N, N'-dimethylethylene diamine] demonstrate binding of these Lewis basic substrate analogues to the lanthanide center. The paramagnetic europium, ytterbium, and praseodymium complexes Li 3(THF) n (BINOLate) 3Ln induce relatively large lanthanide-induced shifts on substrate analogues that ranged from 0.5 to 4.3 ppm in the (1)H NMR spectrum. X-ray structure analysis and NMR studies of Li 3(DMEDA) 3(BINOLate) 3Ln [Ln = Lu, Eu, La, and the transition metal analogue Y] reveal selective binding of DMEDA to the lithium centers. Upon coordination of DMEDA, six new stereogenic nitrogen centers are formed with perfect diastereoselectivity in the solid state, and only a single diastereomer is observed in solution. The lithium-bound DMEDA ligands are not displaced by cyclohexenone, DMF, or THF on the NMR time scale. Use of the DMEDA adduct Li 3(DMEDA) 3(BINOLate) 3La in three catalytic asymmetric reactions led to enantioselectivities similar to those obtained with Shibasaki's Li 3(THF) n (BINOLate) 3La complex. Also reported is a unique dimeric [Li 6(en) 7(BINOLate) 6Eu 2][mu-eta (1),eta (1)-en] structure [en = ethylenediamine]. On the basis of these studies, it is hypothesized that the lanthanide in Shibasaki's Li 3(THF) n (BINOLate) 3Ln complexes cannot bind bidentate substrates in a chelating fashion. A hypothesis is also presented to explain why the lanthanide catalyst, Li 3(THF) n (BINOLate) 3La, is often the most enantioselective of the Li 3(THF) n (BINOLate) 3Ln derivatives.     

Use of 73Ge NMR spectroscopy for the study of electronic interactions

The lack of understanding of the structural and electronic factors that affect the often difficult to observe germanium resonance has been a major deterrent to studies of bonding interactions at germanium. We utilized the symmetrical system GeR 4 to determine what structural factors inherent in the R group affect the shape and position of the (73)Ge resonance. The (73)Ge resonances of symmetrical tetrakis germanium compounds of the type GeR 4 (R = alkyl, aryl), GeX 4 (X = F, Cl, Br, I), Ge(OR) 4 (R = alkyl, methoxyalkyl, dimethylaminoalkyl), Ge(NR 2) 4 (R = alkyl), and Ge(SR) 4 (R = alkyl, dimethylaminoalkyl) were examined for evidence of intramolecular coordination. Although many of these compounds have sharp resonances due to idealized tetrahedral symmetry with relatively long relaxation times, others have broad or no observable resonances due to fast quadrupolar relaxation. We hypothesize that the perturbation of symmetry by even weak Lewis interactions or conformational changes causes broadening of the resonance before the interaction can become sufficiently strong to cause the significant low-frequency shift generally associated with hypercoordination in most nuclei. Intermolecular coordination to GeCl 4 is believed to be responsible for the low-frequency shifts in (73)Ge resonances and the associated changes in peak widths in mixtures with bases such as tributylphosphine oxide (TBPO) and triethylphosphine oxide (TEPO). Adduct formation with these bases is confirmed by broad (31)P resonances that are resolved into five peaks at -40 degrees C. The exchange-broadened resonances due to the 1:1 and 1:2 TEPO adducts are also observed at -40 degrees C in the (73)Ge spectrum. Thus, relatively strong bonding to the germanium in GeCl 4 results in both low-frequency shifts and broadening of the resonance. The broad (73)Ge resonances that occur in some compounds may be in part due to exchange as well as quadrupolar relaxation.