High order local linearization methods: An approach for constructing A-stable explicit schemes for stochastic differential equations with additive noise

An approach for the construction of A-stable high order explicit strong schemes for stochastic differential equations (SDEs) with additive noise is proposed. We prove that such schemes also have the dynamical property that we call Random A-stability (RA-stability), which ensures that, for linear equations with stationary solutions, the numerical scheme has a random attractor that converges to the exact one as the step size decreases. Basically, the proposed integrators are obtained by splitting, at each time step, the solution of the original equation into two parts: the solution of a linear ordinary differential equation plus the solution of an auxiliary SDE. The first one is solved by the Local Linearization scheme in such a way that A-stability is guaranteed, while the second one is approximated by any extant scheme, preferably an explicit one that yields high order of convergence with low computational cost. Numerical integrators constructed in this way are called High Order Local Linearization (HOLL) methods. Various efficient HOLL schemes are elaborated in detail, and their performance is illustrated through computer simulations. Furthermore, mean-square convergence of the introduced methods is studied.     

Photochemical electron transfer through [corrected] the interface of hybrid films of titania nano-sheets and mono-dispersed spherical mesoporous silica particles

Photochemical Electron Transfer (ET) between an organic dye, the porphyrin derivative TMPyP, and an electron acceptor, methyl viologen MV2+, have been investigated at the interface of two different inorganic films, i.e., layered titania nano-sheets (TNS) and a monolayer film of spherical and mono-dispersed mesoporous silica (sMPS) particles (ca. 0.5 microm). TMPyP ions were intercalated within the sMPS nano-cavities to form (TMPyP-sMPS) while MV2+ ions were intercalated into the TNS interlayers to form (MV2+-TNS). The (TMPyP-sMPS) and (MV2+-TNS) films were then stacked on a silica substrate in this order to form a (MV2+-TNS)/(TMPyP-sMPS) film and, upon UV light irradiation, ET could be induced. However, when this film was stacked inversely, i.e., for the (TMPyP-sMPS)/(MV2+-TNS) films on a silica substrate, no photoinduced ET were observed. Interestingly, however, even for this photo-inactive inversely stacked film, ET could be generated by inserting a gold vapor-deposited layer between the (MV2+-TNS) and (TMPyP-sMPS) films. The conjugation conditions at the interface of the inversely stacked (TMPyP-sMPS)/(MV2+-TNS) hybrid film were, thus, confirmed to strongly affect the photoinduced electron transfers and their efficiencies.     

Variations in steady-state and time-resolved background luminescence from surface-enhanced resonance Raman scattering-active single Ag nanoaggregates

We observed a background luminescence emission that was associated with surface-enhanced resonance Raman scattering (SERRS) of rhodamine 6G (R6G) molecules adsorbed on single Ag nanoaggregates and investigated the origin of the background luminescence. Thanks to the observation of single nanoaggregates, we clearly identified nanoaggregate-by-nanoaggregate variations in the steady-state and time-resolved background luminescence spectra of each nanoaggregate. From the variations in the steady-state spectra, two kinds of key properties were revealed. First, the background luminescence spectra were divided into four components: one fluorescence band corresponding to the monomers of R6G and three Lorentzian bands whose maxima were red-shifted from the fluorescence maximum of the monomer by several tens of nanometers. On the basis of the red-shifted luminescence maxima, and experimental and theoretical studies of background luminescence, we attributed the three background luminescences to fluorescence from aggregates (dimer and two kinds of higher-order aggregates) of R6G molecules on an Ag surface. Second, a positive correlation was observed between wavelengths of background luminescence maxima and wavelengths of plasmon resonance maxima. This positive correlation invoked the idea that the dipoles of both the background luminescence and the plasmon radiation are coupled with each other. From the key observations in the steady-state background luminescence spectra, we propose that two factors contribute to the variations in the steady-state background luminescence spectra; one is the aggregation (monomer, dimer, and two kinds of higher-order aggregates) of R6G molecules on an Ag surface, and the other is plasmon resonance maxima of single Ag nanoaggregates. Considering these two factors, we propose that the variations in the time-resolved background luminescence spectra are associated with deaggregation of R6G molecules (higher- to lower-order aggregates) and temporal shifts in the plasmon resonance maxima of single Ag nanoaggregates.     

Roles of adriamycin and adriamycin dimer in antitumor activity of the polymeric micelle carrier system

Adriamycin (ADR) dimer was prepared and its antitumor activity was evaluated with mouse colon adenocarcinoma 26 (C 26). As compared with original ADR, the dimer did not show significant antitumor activity, either in vitro or in vivo. Furthermore, polymeric micelles containing varied ratios of the dimer to the original ADR were prepared. Polymeric micelles with a higher dimer/ADR ratio (9.7) showed significant antitumor activity, but the effective dose shifted higher. Effective doses were found to largely depend on the concentration of the original ADR, rather than that of the dimer at the tumor sites. Therefore, it was presumed that the original ADR played a major role in antitumor activity, and the dimer played a supplementary role to contribute selective delivery of ADR to the tumor sites.     

Multiwave coupling in a high-gain photorefractive polymer

The characteristics of a new high-gain photorefractive polymer composite with a PNP chromophore are investigated. Competition between beam fanning and two-wave coupling (TWC) is predicted and verified experimentally. The intensity dependence of TWC gain is studied. Higher diffraction order and forward phase conjugation in a TWC geometry are observed and explained.     

Highly regioselective ring opening of epoxides with alcohols catalyzed by organotin phosphate condensates

Organotin phosphate condensates proved to catalyze the ring opening reaction of epoxides with alcohols in a highly regioselective manner.     

Synthesis of novel crownophanes containing two phenolic moieties via a tandem claisen rearrangement

A series of crownophanes containing two phenolic moieties within a macrocyclic ring have been successfully synthesized by a one-step thermal reaction from the corresponding macrocyclic polyethers by using a “Tandem Claisen Rearrangement”.     

Two-dimensional fluorescence correlation spectroscopy II: spectral analysis of derivatives of anthracene and pyrene in micellar solutions

Generalized two-dimensional (2D) correlation spectroscopy has been applied to the analysis of fluorescence spectra in two micellar systems: (1) a mixture of pyrene and 1,3,6,8-pyrenetetrasulfonic acid in the cationic micellar solutions of cetyltrimethylammonium chloride (CTAC) and (2) a mixture of pyrene and 9-anthracencepropionic acid in anionic micellar solutions of sodium dodecyl sulfate (SDS). Fluorescence quenching is employed as a perturbation mode for causing intensity changes in fluorescence bands (quenching perturbation). Iodide ion (I-) is used as a quencher in the former system, and cetyl pridinium chloride (CPC) is used in the latter. Vibronic bands in the complicated fluorescence spectra of the mixture of the analytes were successfully resolved. It is shown that asynchronous maps are especially useful for spectral resolution enhancement when the quenching perturbation is employed in 2D fluorescence correlation spectroscopy. Furthermore, the information about the order of response of the bands to quenching is obtained by comparing the signs of synchronous and asynchronous cross-peaks.     

Generalized two-dimensional correlation spectroscopy

Since the theory of generalized two-dimensional (2-D) correlation spectroscopy was proposed, it has been keenly concerned in scientific research and its analytical method has been widely applied in various analytical fields. The mathematical process to construct generalized 2-D correlation spectroscopy and the physical meaning of 2-D correlation spectral map are described, and three examples in the fields of chemical analysis and molecular biology are provided, such as the component analysis of organic solvent, the analysis of biological molecules in the solvent with different pH values and structural analysis of protein. The theory and analytical method of generalized 2-D correlation spectroscopy are also detailedly commented.     

Titanium alkoxide complex of functionalized conjugated dienes. A versatile bis-anionic template for stereoselective construction of carbon frameworks

1,3-Butadiene-2-carboxylates were treated with a titanium(II) alkoxide reagent, Ti(O-i-Pr)4/2i-PrMgCl, to generate diene-titanium alkoxide complexes, the presence of which was verified by hydrolysis and deuteriolysis to give the corresponding monoolefins or their bis-deuterated counterpart. These diene complexes underwent successive addition to an aldehyde (as the first electrophile) and iodine (as the second one) in a highly regio- and stereoselective manner to give the corresponding iodo alcohol. Optically active 1,3-butadiene-2-carboxylates afforded the same adducts of high asymmetric induction. Besides these electron-deficient dienes, electron-rich 2-siloxy-1,3-butadienes also participated in the formation of the titanium complex, which led to the preparation of functionalized enol silyl ethers through regio- and stereoselective coupling with carbonyl compounds and hydrolytic workup.