Almost sure and moment exponential stability of Euler–Maruyama discretizations for hybrid stochastic differential equations

Positive results are derived concerning the long time dynamics of numerical simulations of stochastic differential equation systems with Markovian switching. Euler–Maruyama discretizations are shown to capture almost sure and moment exponential stability for all sufficiently small timesteps under appropriate conditions.     

Zeros of univariate interval polynomials

Polynomials with perturbed coefficients, which can be regarded as interval polynomials, are very common in the area of scientific computing due to floating point operations in a computer environment. In this paper, the zeros of interval polynomials are investigated. We show that, for a degree n interval polynomial, the number of interval zeros is at most n and the number of complex block zeros is exactly n if multiplicities are counted. The boundaries of complex block zeros on a complex plane are analyzed. Numeric algorithms to bound interval zeros and complex block zeros are presented.     

Some blow-up problems for a semilinear parabolic equation with a potential

The blow-up rate estimate for the solution to a semilinear parabolic equation ut=Δu+V(x)|u|^p−1u in Ω×(0,T) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x,0)=Mφ(x) as M goes to infinity, which have been found in [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006], is improved under some reasonable and weaker conditions compared with [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006].     

NMR analysis of multiple samples using parallel coils: improved performance using reference deconvolution and multidimensional methods

Improvements in the Multiplex Sample NMR method are investigated to explore its capabilities of analyzing multiple samples simultaneously. Issues of quantitation and resolution in the multiple-coil probe are examined in one- and two-dimensional experiments. Improvements in quantitation are shown to result from the use of reference deconvolution for one-dimensional experiments, while the use of two-dimensional methods has much improved resolution and shows the potential for significantly increased parallelism. A multiplicative scheme is shown to be an easily implemented, effective method for generating individual sub-spectra from individual samples.     

Cleavage of polystyrene‐b‐poly(ethylene oxide) block copolymers with a trithiocarbonate linkage in solutions

In this work, the polystyrene‐b‐poly(ethylene oxide) (PS‐b‐PEO) block copolymers with a trithiocarbonate group between the blocks were prepared by polymerization of styrene in the presence of a trithiocarbonate reversible addition fragmentation chain transfer (RAFT) agent connected with PEO. Decomposition of the trithiocarbonate group by UV irradiation was investigated in three different types of solvent: tetrahydrofuran (THF, common solvent for both blocks), cyclohexane/dioxane mixture (selective solvent for the PS block) and N,N‐dimethylformamide (DMF)/ethanol mixture (selective solvent for the PEO block). It is found that cleavage of the block copolymers can take place in all these three solvents and the cleavage ratio ranges from 76 to 86%. The micellar morphologies in selective solvents before and after cleavage were examined. It is observed that the size of the micelles is reduced after cleavage and sometimes aggregation of the micelles occurs due to removal of the corona of micelles. It shows that this work provides a facile and general method for synthesis of cleavable block copolymers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3834–3840, 2010     

A Novel Way to Prepareγ-A1_2O_3 Supported SO_4~(2-)/ZrO_2 Solid Superacid Catalysts for n-Butane Isomerization

The isomerization of n-butane to isobutane, which is a valuable precursor for theproduction of MTBE and alkylated gasoline, on strong acid catalysts is an importantprocess in refining industry. Solid superacid, especially sulfated zirconia, has highcatalytic activity in n-butane isomerization at comparatively low temperatures andtherefore has attracted more attention of researchers in the past twenty years.' However,from the view point of practice, the activity of SZ needs to be improved fur…     

Facile synthesis of 4‐mercaptophenylboronic acid functionalized gold nanoparticles for selective enrichment of glycopeptides

In the work, 4‐mercaptophenylboronic acid (4‐MPBA)‐functionalized gold nanoparticles were synthesized via a facile approach. At first, gold nanoparticles (about 50 nm) were prepared by a simple and convenient hydrothermal method based on a polyol process. Then, gold nanoparticles were modified with 4‐MPBA by the well‐known reaction of Au with the thiol groups. The MPBA‐functionalized gold nanoparticles were characterized by Fourier transform infrared spectra and UV/Vis adsorption spectra. Due to the fact that the boronic acid group on the surface of 4‐MPBA‐modified gold particles can form tight yet reversible covalent bonds with glycopeptides containing cis‐1,2‐diols groups, the MPBA‐modified gold nanoparticles were successfully applied to selective enrichment of glycopeptides. Isolation and enrichment of glycopeptides in a standard protein (asialofetuin and horseradish peroxidase) digestion and a complex sample were performed using MPBA‐modified gold nanoparticles, followed by matrix‐assisted laser desorption/ionization quadruple ion trap time‐of‐flight (MALDI‐QIT‐TOF) mass spectrometric analysis. The experimental results demonstrated that MPBA‐modified gold nanoparticles synthesized by the facile approach have the powerful potential for selective enrichment of glyciopeptides, and can be an alternative tool in glycoproteomics. Copyright © 2009 John Wiley & Sons, Ltd.     

Identification of metabolites of Danggui Buxue Tang in rat urine by liquid chromatography coupled with electrospray ionization time‐of‐flight mass spectrometry

A method coupling liquid chromatography with electrospray ionization time‐of‐flight mass spectrometry (LC/ESI‐TOF/MS) has been developed for rapid and sensitive analysis of rat urinary metabolite profile of Danggui Buxue Tang (DBT), a well‐known Chinese herbal formula. After oral administration of DBT, urine samples were collected during 0–24 h, and then pretreated by solid‐phase extraction. A total of 68 compounds including 13 parent compounds and 55 metabolites were detected in the drug‐containing urines compared with blank urines. The total analytical time was less than 20 min. Metabolites of DBT were identified using dynamic adjustment of the fragmentor voltage to produce structure‐relevant fragment ions. By using this approach, the mass accuracy of precursor and fragment ions was typically within ±5 ppm of the theoretical values, and enabled the identification of 43 metabolites including 27 isoflavanoid and 16 phthalide metabolites. Our results indicated that glucuronidation and sulfation were the major metabolic pathways of isoflavonoids, while glutathione conjugation, glucuronidation and sulfation were the main metabolic pathways of phthalides. No saponin‐related metabolites were detected. The results of the present study provided important structural information relating to the metabolism of DBT. Furthermore, this work demonstrated the potential of the LC/ESI‐TOF/MS approach for identification of metabolites from Chinese herbal medicines in urine. Copyright © 2009 John Wiley & Sons, Ltd.