Asymptotic factorization of evolution equations which involve linear operators

Operator splitting for evolution equations which involve linear operators is investigated. A systematic method for identifying multifactor fractional-step operator splittings is proposed. The classical second-order accurate splittings of Strang readily emerge, as well as various third-order splittings of nonstandard type. Factorizations possessing mixed positive-negative fractional steps are discovered, as well as bizarre splittings whose factors include complex fractional steps. It is found that no higher-order accurate splitting which employs all positive fractional steps and which possesses less than nine operator factors can exist. For the linear case this implies second-order accurate splittings are optimal, as a further increase of one power in accuracy essentially requires a three-fold increase in work. This estimate slightly improves, for cases where the nonstandard splittings can be employed. Some numerical experiments which illustrate the theory are provided.     

Premature in-bore separation of sabot-jacketed projectiles

The premature separation of saboted projectiles undergoing high-mach-number in-bore acceleration is investigated. Results from a simplified numerical model for the problem are presented. Measured short-term velocity history for a typical projectile is used to describe the motion of a nonuniformly accelerating piston. Two numerical algorithms for calculating the shocked flow in tront of the accelerating piston are presented. Mach number and pressure time histories for the flow afford corrective input to the sabot design process. © 1993 John Wiley & Sons, Inc.     

Determination of Cryptotanshinone, a Major Active Component in Salvia miltiorrhiza, in Caco-2 Monolayers by HPLC with UV Detection

Cryptotanshinone is the major active component from the root of Salvia miltiorrhiza which has been widely used for the management of coronary heart disease. The aims of this study were to develop and validate an HPLC method for the determination of cryptotanshinone in the human intestinal cell line Caco-2 monolayers, and to investigate the transport kinetics of cryptotanshinone. The developed HPLC method was sensitive and reliable, with acceptable accuracy (90–110% of true values) and precision (intra- and inter-assay CV < 10%). The total running time was within 10 min, with acceptable separation of the compounds of interest. The limit of quantitation (LOQ) for cryptotanshinone was 10 ng mL⁻¹. A simple liquid–liquid extraction procedures resulted in an extraction efficiency of 90.8 ± 8.9 and 93.5 ± 6.2% for cryptotanshinone at 0.1 and 3 μg mL⁻¹. The calibration curve was linear over the concentration range of 0.05–3.0 μg mL⁻¹ with the mean correlation coefficients >0.999. The validated HPLC method was applied to examine the epithelial transport of cryptotanshinone by Caco-2 monolayers. The transport across the monolayers from the apical (B) to basolateral (A) side was significantly higher than that from A to B side. The structural analog of cryptotanshinone and a known substrate of P-glycoprotein, tanshinone II_A, dramatically inhibited the B to A transport of cryptotanshinone in the monolayers. These results indicate that the developed HPLC method was suitable for the study of transport of cryptotanshinone by Caco-2 monolayers and cryptotanshinone is a substrate of P-glycoprotein.     

Synthesis and characterization of a fluorinated polyanhydride

A fluorinated aromatic polyanhydride ( B ) was synthesized from the melt condensation of mixed anhydrides of 4,4′‐(hexafluoroisopropylidene)bis benzoic acid. Although the mixed anhydride from acetic anhydride yielded only a mixture of oligomers (weight‐average molecular weight < 2000), higher weight‐average molecular weight materials in the range of 15,000–18,000 were obtained with trifluoroacetic anhydride. Polymer B was soluble in chloroform and tetrahydrofuran, had a relatively high glass‐transition temperature of 176 °C with no melting point detected to 310 °C, and showed excellent thermal stability (5% weight loss observed at 380 °C by thermogravimetric analysis). The hydrolytic degradation of the fluorinated polyanhydride in a 0.1 M phosphate buffer of pH 7.4 at 37 °C was initially zero‐order, with 35% degradation occurring in 10 days. Loss of film integrity following that led to accelerated degradation, and almost complete dissolution was observed by the 16th day. The stability of the fluorinated polyanhydride in the solid state and in the solvent tetrahydrofuran was also evaluated. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3027–3036, 2002     

Alteration of the carbon and nitrogen stable isotope composition of beef by substitution of grass silage with maize silage

This study investigated the effect of substituting grass silage (C3 photosynthetic plant product) with maize silage (C4 photosynthetic plant product) on the natural abundance carbon (delta13C) and nitrogen (delta15N) stable isotope composition of bovine muscle tissue. Forty-five continental crossbred heifers were assigned to one of three diets consisting of 3 kg of a barley-based concentrate plus grass silage, maize silage or an equal mixture (dry matter basis) of grass silage and maize silage, fed ad libitum, for 167 days. Substitution resulted in less negative delta13C values (P<0.001) in lipid-free muscle and in lipid, and also a lower delta15N (P<0.001) in lipid-free muscle. Feeding of maize silage was clearly reflected in the delta13C of muscle, with each 10% difference in the dietary C4 carbon intake resulting in a 0.9 to 1.0 per thousand shift of delta13C in lipid-free muscle and a 1.0 to 1.2 per thousand in lipid. Minimum detectable mean differences (95% confidence, power 0.80, n=15) in this experiment were about 0.5 per thousand and 1.0 per thousand for delta13C of lipid-free muscle and lipid, respectively, and about 0.5 per thousand for delta15N of lipid-free muscle. The power analysis presented here is useful for estimating minimum isotopic differences that can be detected between any two groups of beef samples with a given number of replicates. It is concluded that carbon stable isotope ratio analysis of meat can be used to quantify C3/C4 dietary constituents in beef production.     

Flux growth of vanadyl pyrophosphate, (VO)(2)P(2)O(7), and spin dimer analysis of the spin exchange interactions of (VO)(2)P(2)O(7) and vanadyl hydrogen phosphate,VO(HPO(4)).0.5H(2)O

Large transparent blue crystals of vanadyl pyrophosphate, (VO)(2)P(2)O(7), were grown from a phosphorus pentoxide flux, and the single-crystal X-ray structure of (VO)(2)P(2)O(7) was determined with high precision. On the basis of spin dimer analysis, we examined the spin exchange interactions of (VO)(2)P(2)O(7) and its precursor VO(HPO(4)).0.5H(2)O. Our analysis of (VO)(2)P(2)O(7) using two high-precision crystal structures shows unambiguously that the V3-V4 chain has a larger spin gap than does the V1-V2 chain and that the super-superexchange (V-O...O-V) interaction is stronger than the superexchange (V-O-V) interaction in the V3-V4 chain while the opposite is true in the V1-V2 chain. Our analysis of VO(HPO(4)).0.5H(2)O reveals that the superexchange interaction must dominate over the super-superexchange interaction, in disagreement with the conclusion from a powder neutron scattering study of VO(DPO(4)).0.5D(2)O.     

On two integrable cellular automata

A representation-free approach to theq-analog of the quantum central limit theorem for is presented. It is shown that for certain functionals one can derive a version of a quantum central limit theorem (qclt) with as a scaling parameter, which may be viewed as aq-analog of qclt.     

The implementation of low-cost urban acoustic monitoring devices

The urban sound environment of New York City (NYC) can be, amongst other things: loud, intrusive, exciting and dynamic. As indicated by the large majority of noise complaints registered with the NYC 311 information/complaints line, the urban sound environment has a profound effect on the quality of life of the city’s inhabitants. To monitor and ultimately understand these sonic environments, a process of long-term acoustic measurement and analysis is required. The traditional method of environmental acoustic monitoring utilizes short term measurement periods using expensive equipment, setup and operated by experienced and costly personnel. In this paper a different approach is proposed to this application which implements a smart, low-cost, static, acoustic sensing device based around consumer hardware. These devices can be deployed in numerous and varied urban locations for long periods of time, allowing for the collection of longitudinal urban acoustic data. The varied environmental conditions of urban settings make for a challenge in gathering calibrated sound pressure level data for prospective stakeholders. This paper details the sensors’ design, development and potential future applications, with a focus on the calibration of the devices’ Microelectromechanical systems (MEMS) microphone in order to generate reliable decibel levels at the type/class 2 level.