Tosylation and acylation of cellulose in 1-allyl-3-methylimidazolium chloride

Tosylation and acylation of cellulose were performed under mild reaction conditions using imidazolium based ionic liquids (ILs) as solvents. The non-degradative nature, lower viscosity, as well as higher solubility of cellulose in [amim]Cl encouraged us to carry out the reactions in this media. The reactions described here were optimised for this particular solvent in order to obtain different cellulose derivatives with high yields, homogeneity and degree of substitution (DS). Two reagents employed for the in situ activation of carboxylic acids were N,N′-carbonyldiimidazole (CDI) and 1-ethyl-3-(3′-dimethylaminopropyl)carbodiimide hydrochloride (EDCI). Final products were characterised by solution and solid-state NMR techniques. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Efficient numerical methods for pricing American options under stochastic volatility

Five numerical methods for pricing American put options under Heston's stochastic volatility model are described and compared. The option prices are obtained as the solution of a two‐dimensional parabolic partial differential inequality. A finite difference discretization on nonuniform grids leading to linear complementarity problems with M‐matrices is proposed. The projected SOR, a projected multigrid method, an operator splitting method, a penalty method, and a componentwise splitting method are considered. The last one is a direct method while all other methods are iterative. The resulting systems of linear equations in the operator splitting method and in the penalty method are solved using a multigrid method. The projected multigrid method and the componentwise splitting method lead to a sequence of linear complementarity problems with one‐dimensional differential operators that are solved using the Brennan and Schwartz algorithm. The numerical experiments compare the accuracy and speed of the considered methods. The accuracies of all methods appear to be similar. Thus, the additional approximations made in the operator splitting method, in the penalty method, and in the componentwise splitting method do not increase the error essentially. The componentwise splitting method is the fastest one. All multigrid‐based methods have similar rapid grid independent convergence rates. They are about two or three times slower that the componentwise splitting method. On the coarsest grid the speed of the projected SOR is comparable with the multigrid methods while on finer grids it is several times slower. ©John Wiley & Sons, Inc. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Slip flow over structured surfaces with entrapped microbubbles

On hydrophobic surfaces, roughness may lead to a transition to a superhydrophobic state, where gas bubbles at the surface can have a strong impact on a detected slip. We present two-phase lattice Boltzmann simulations of a Couette flow over structured surfaces with attached gas bubbles. Even though the bubbles add slippery surfaces to the channel, they can cause negative slip to appear due to the increased roughness. The simulation method used allows the bubbles to deform due to viscous stresses. We find a decrease of the detected slip with increasing shear rate which is in contrast to some recent experimental results implicating that bubble deformation cannot account for these experiments. Possible applications of bubble surfaces in microfluidic devices are discussed.     

High-efficiency broadband diffractive elements based on polarization gratings

A method is introduced for designing paraxial-domain diffractive elements working over a broad frequency range. The method is based on space-variant manipulation of the state of polarization by form-birefringent binary diffractive structures. It is shown that any scalar phase transmission function can be realized by use of such polarization-modulating structures and that at least in some cases it is even possible to exceed the scalar paraxial-domain upper bounds of diffraction efficiency over a broad frequency band.     

Tunneling between two-dimensional electron systems in a strong magnetic field

We calculate the tunnel current between two parallel two-dimensional electron systems in a strong perpendicular magnetic field. We model the strongly correlated electron systems by Wigner crystals, and describe their low-energy dynamics in terms of magnetophonons. The effects of the magnetophonons on the tunneling processes can be described by an exactly solvable independent-boson model. A tunneling electron shakes up magnetophonons, which results in a conductance peak that is displaced away from zero voltage and broadened compared with the case of no magnetic field. At low temperatures and low enough voltages the tunneling conductance is strongly suppressed, and the I–V characteristics exhibit a power-law behavior. The zero-voltage conductance is thermally activated with an activation temperature 10 K. The results are in very good agreement with experiment.     

Spectral and network methods in the analysis of correlation matrices of stock returns

Correlation matrices inferred from stock return time series contain information on the behaviour of the market, especially on clusters of highly correlating stocks. Here we study a subset of New York Stock Exchange (NYSE) traded stocks and compare three different methods of analysis: (i) spectral analysis, i.e. investigation of the eigenvalue-eigenvector pairs of the correlation matrix, (ii) asset trees, obtained by constructing the maximal spanning tree of the correlation matrix, and (iii) asset graphs, which are networks in which the strongest correlations are depicted as edges. We illustrate and discuss the localisation of the most significant modes of fluctuation, i.e. eigenvectors corresponding to the largest eigenvalues, on the asset trees and graphs.     

Predicting the drug concentration in starch acetate matrix tablets from ATR-FTIR spectra using multi-way methods

The amounts of drug and excipient were predicted from ATR-FTIR spectra using two multi-way modelling techniques, parallel factor analysis (PARAFAC) and multi-linear partial least squares (N-PLS). Data matrices consisted of dissolved and undissolved parallel samples having different drug content and spectra, which were collected at axially cut surface of the flat-faced matrix tablets. Spectra were recorded comprehensively at different points on the axially cut surface of the tablet. The sample drug concentrations varied between 2 and 16% v/v. The multi-way methods together with ATR-FTIR spectra seemed to represent an applicable method for the determination of drug and excipient distribution in a tablet during the release process. The N-PLS calibration method was more robust for accurate quantification of the amount of components in the sample whereas the PARAFAC model provided approximate relative amounts of components.     

An iterative method for pricing American options under jump-diffusion models

We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou?s and Merton?s jump-diffusion models show that the resulting iteration converges rapidly.     

1-Oxo-1,3-dithiolanes--synthesis and stereochemistry

1-Oxo-1,3-dithiolane (4) and its cis- and trans-2-methyl (5,6), -4-methyl (7,8) and -5-methyl (9,10) derivatives were prepared by oxidizing the corresponding 1,3-dithiolanes (1-3) with NaIO(4) in water. The oxides were purified and their isomers separated using thin layer chromatography. The structural characterization was carried out with (1)H and (13)C NMR spectroscopy and molecular modelling. The sulfoxides 4-6 and 8-10 attain two S(1) type envelopes (sometimes slightly distorted) the S=O(ax) envelope greatly dominating. Cis-4-methyl-1-oxo-1,3-dithiolane is a special case exhibiting both two closely related S=O(ax) (30 and 27%) as well as S=O(eq) (21 and 22%) forms [S(1) and C(4) envelopes, respectively]. The relative energies of these conformations, the values of (1)H-(1)H coupling constants and (1)H and (13)C chemical shifts were estimated by computational methods and they support well the conclusions based on the experimental data.     

Image reconstruction in diffuse optical tomography using the coupled radiative transport-diffusion model

The coupled radiative transport-diffusion model can be used as light transport model in situations in which the diffusion equation is not a valid approximation everywhere in the domain. In the coupled model, light propagation is modelled with the radiative transport equation in sub-domains in which the approximations of the diffusion equation are not valid, such as within low-scattering regions, and the diffusion approximation is used elsewhere in the domain. In this paper, an image reconstruction method for diffuse optical tomography based on using the coupled radiative transport-diffusion model is developed. In the approach, absorption and scattering distributions are estimated by minimising a regularised least-squares error between the measured data and solution of the coupled model. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the coupled radiative transport-diffusion model can be utilised in image reconstruction problem of diffuse optical tomography and that it produces as good quality reconstructions as the full radiative transport equation also in the presence of low-scattering regions.