Operator preconditioning with efficient applications for nonlinear elliptic problems

This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.     

Magnetic resonance studies of laryngeal tumors implanted in nude mice: effect of treatment with bleomycin and electroporation

Recently, a new type of cancer treatment has been introduced that combines pulsed electric fields (PEF) with anticancer drugs. The proposed mode of action is that PEF create transient pores in the membranes which allow entry of drugs into the cells. This method increases cytotoxicity of some anticancer drugs like bleomycin (BLM) by 2-3 orders of magnitude, which, in turn, reduces systemic drug dosage without decreasing efficacy. In the present study, magnetic resonance imaging (MRI) was used to determine changes in apparent water self-diffusion coefficients (ADC) and spin-lattice (T(1)) and spin-spin (T(2)) relaxation times that occur in an animal laryngeal tumor (HEp-2 cells) model with BLM delivered by PEF. A Bruker 14 Tesla (600 MHz) wide-bore spectrometer with micro-imaging capability was used to generate all the data. Mice carrying approximately 8 mm tumors were treated with several combinations of drug and PEF. All measurements were made on tumor samples excised from mice 24 and 48 hours after treatment with (i) saline, intratumor injection (i.t.), (ii) BLM, i.t., (iii) saline with PEF, and (iv) BLM, i.t., followed by PEF. Although T(1) does not differ between the controls (i, ii, and iii) and full treatment (iv) 6.72 +/- 0.20 s vs. 6.31 +/- 1.7 s, T(2) for (iv) at 24 hours is significantly different from the controls 52.4 +/- 0.91 ms vs. 46.5 +/- 1.54 ms. T(2) differences between treatment and controls disappear at 48 hours. ADC increases significantly from 24 to 48 hours (7.31 +/- 0.16 x 10(-6) to 8.28 +/- 0.28 x 10(-6) cm(2)/sec, p = 0.05). Longer T(2) values may reflect early apoptosis and tumor death when the tumor is structurally less dense. Higher ADC's, associated with the periphery of the tumors and the central region, may indicate loose structural organization and necrosis resulting from the combination treatment.     

Synthesis of bilin-1,19-diones and biladiene-ac-1,19-diones with c(10) adamantyl and tert-butyl groups

Bilirubin and biliverdin analogs bearing bulky adamantyl and tert-butyl groups at the central C(10) position were synthesized and their structures were analyzed by nmr and ultraviolet-visible spectroscopy and by molecular mechanics calculations, all of which collectively indicated a preference for helical conformations.     

Comparison of Ab Initio MP2/6-311+G(d,p) Predicted Carbon–Hydrogen Bond Distances with Experimentally Determined r 0 (C–H) Distances

Fifty different carbon–hydrogen distances have been predicted from ab initio MP2/6-311+G(d,p) calculations, which range from a short value of 1.0611 Å for HCNO to a long value of 1.1044 Å for H₂CO. The values include those predicted for a series of methyl (CH₃) moieties where the two different C–H distances vary by as much as 0.005 Å. These predicted values are compared to r ₀(C–H) distances obtained from the isolated carbon–hydrogen stretching frequencies, as well as to r ₀ or r _s parameters obtained from microwave data. Except for the very short C–H bonds, the ab initio values from the MP2/6–311+G(d,p) calculations can be used for the carbon–hydrogen distances with error limits of ± 0.003 Å. By utilizing the spectral data from CD₃CClO, it is shown that combination bands in the C–H stretching region could cause problems in the identification of the isolated C–H stretching frequency from the CD₂HCClO isotopomer. The value of the ab initio predicted C–H distances for checking unusually long or short r _s (C–H) or r ₀ values is demonstrated.     

Bending of Light and Gravitational Signals in Certain On-Brane and Bulk Geometries

In this article, we first investigate the bending of light rays in 4D line elements representing spherically symmetric, static on–brane geometries. The amount of bending in these four dimensional, strong and weak field solutions is derived. Signatures, which appear in the bending formulae, due to the presence of extra dimensions are discussed. Subsequently, as a separate exercise, we calculate the bending of null geodesic trajectories in a bulk five dimensional spacetime with a Schwarzschild line element on the 3-brane section. We interpret the deviation of null trajectories as that of gravitational signals or five dimensional photons, which are, unlike light rays confined to four dimensions, allowed to propagate along the fifth (extra) dimension. Features of the presence of extra dimensions in the effective potentials and the bending formula are analysed in this context.     

OptDesign: extending optimizable k-dissimilarity selection to combinatorial library design

Optimizable k-dissimilarity (OptiSim) selection entails drawing a series of subsamples of size k from a population and choosing the "best" candidate from each such subsample for inclusion in the selection set. By varying the size of the subsample, one can control the balance between representativeness and diversity in the selection set obtained. In the original formulation, a uniform random sampling from among valid candidates was used to draw the subsamples from a single target population. Here we describe in detail two key modifications that serve to extend the OptiSim methodology to vector selection for interdependent variables, specifically as applied to the design of combinatorial sublibraries. The first modification involves pivoting between variables: subsamples are drawn from each reagent pool in turn, with the viability of each candidate being evaluated in isolation as well as in terms of the products it will produce from complementary reagents already selected. The filters applied may be static or dynamic in nature, with molecular weight and hydrophobicity being examples of the former and structural diversity with respect to reagents already selected being an example of the latter. The second key modification is adding the ability to bias the selection of candidate reagents for inclusion in the subsamples. Taken together, these modifications support the efficient generation of multiblock and other sparse matrix designs that are both representative and diverse, and for which "backfilling" of designs edited to remove undesirable reagents or products is straightforward. The method is intrinsically fast and efficient, since enumeration of the full combinatorial is not required- only those candidates actually considered for inclusion need be evaluated. Moreover, because the subsample selection step is separate from the diversity-based selection of the "best" candidate, incorporating such bias in favor of a competing criterion such as low price provides a "natural," nonparametric mechanism for generating designs that are likely to be "good" in a double-objective, Pareto sense.     

Direct continuous supercritical fluid extraction as a novel method of wine analysis. Comparison with conventional indirect extraction and implications for wine variety identification

Direct supercritical fluid extraction (SFE) of wines with carbon dioxide was compared to SFE of the sorbent used for solid-phase extraction of the same wine samples (SPE-SFE). Compared to SPE-SFE, the direct SFE results in amore specific and representative gas chromatographic fingerprint of the wine sample. The multivariate statistical processing of the direct SFE-GC data provides a clear-cut and sharp discrimination among the individual wine varieties while the discrimination based on the SPE-SFE-GC data is relatively poor. This finding reflects the adverse effects of additional analyte-sorbent interactions and sorption/desorption steps involved in SPE-SFE.     

Bound states and dipole polarizability of hydrogen molecular ion H2 in weakly coupled hot plasmas

The effects of hot-dense plasmas on the bound states and the dipole polarizability of the ground state of Coulomb three-body molecular ion H⁺₂ have been investigated using highly correlated basis functions and by considering the Debye shielding approach of plasma modeling. The ground S state and the first excited P state energies along with the dipole polarizability for different shielding parameters are reported.     

HPLC method development and validation of cytotoxic agent phenyl‐heptatriyne in Bidens pilosa with ultrasonic‐assisted cloud point extraction and preconcentration

Extraction and pre‐concentration of a bioactive marker compound, phenyl‐1,3,5‐heptatriyne from Bidens pilosa, prior to HPLC has been demonstrated using both organic and ecofriendly solvents. Non‐ionic surfactants, viz. Triton X‐100, Triton X‐114 and Genapol X‐80, were used for extraction. No back‐extraction or liquid chromatographic steps were required to remove the target phytochemical from the surfactant‐rich extractant phase. The optimized cloud point extraction procedure has been shown to be a potentially useful methodology for the preconcentration of the target analyte, with a preconcentration factor of 4–99. Moreover, the method is simple, sensitive, rapid and consumes lesser solvent than traditional methods. An isocratic chromatographic separation and quantitation was accomplished on a C₁₈ column with acetonitrile–acidified aqueous as mobile phase at a flow rate of 1.0 mL/min, UV detection at 254 nm and specificity with photo diode‐array detector (PDA) and MS. Under the optimum experimental conditions recovery was satisfactory (99.18–100.33%) without interference from the surfactant. The method seems to be reliable with intraday precision and interday precision below 2.0%. Good linearity was obtained in the working range from 7.5 to 30 µg/mL with correlation coefficient >0.99. The limits of detection and quantitation were 1.84 and 6.13 µg/mL, respectively. The method was validated following international guidelines and successfully applied for quantitative assays of cytotoxic compound phenyl‐1,3,5‐heptatriyne in Bidens pilosa. Copyright © 2010 John Wiley & Sons, Ltd.     

Development and validation of a HPLC method for quantification of rivastigmine in rat urine and identification of a novel metabolite in urine by LC‐MS/MS

A sensitive, specific and accurate HPLC method for the quantification of rivastigmine (RSM) in rat urine was developed and validated. The method involves the simple liquid–liquid extraction of RSM and pyridostigmine as an internal standard (IS) from rat urine with tertiary methyl butyl ether. The chromatographic separation of RSM and IS was achieved with 20 mm ammonium acetate buffer (pH 6.5) and acetonitrile (65:35, v/v) delivered at flow‐rate of 1 mL/min on a Kromasil KR‐100. The method was in linear range from 50 to 5000 ng/mL. The validation was done as per FDA guidelines and the results met the acceptance criteria. The method was successfully applied for the quantification of RSM in rat urine. Besides method validation, we have identified two metabolites of RSM in urine. Both the metabolites were characterized by HPLC‐PDA and LC‐MS/MS and it was found that one metabolite is novel. Copyright © 2010 John Wiley & Sons, Ltd.