Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.     

The innovation research of financial early-warning index measurement

The period economic fluctuation is vital for an enterprise to exist and further develop,it directly affect the enterprise financial health.So,it is significant to build up financial early-warning index and measure the warning condition that the enterprise faces and take the effective measures to eliminate. We criticize Altman's Z calculating model and build up some new indexes for enterprise financial early-warning condition measuring and making sound decision.     

Synthesis of new thermosetting poly(2,6‐dimethyl‐1,4‐phenylene oxide)s containing epoxide pendant groups

A new class of thermosetting poly(2,6‐dimethyl‐1,4‐phenylene oxide)s containing pendant epoxide groups were synthesized and characterized. These new epoxy polymers were prepared through the bromination of poly(2,6‐dimethyl‐1,4‐phenylene oxide) in halogenated aromatic hydrocarbons followed by a Wittig reaction to yield vinyl‐substituted polymer derivatives. The treatment of the vinyl‐substituted polymers with m‐chloroperbenzoic acid led to the formation of epoxidized poly(2,6‐dimethyl‐1,4‐phenylene oxide) with variable pendant ratios, and the structures and properties were studied with nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy, differential scanning calorimetry, thermogravimetric analysis, and gel permeation chromatography. The ratios of pendant functional groups were tailored for the polymer properties, and the results showed that the glass‐transition temperatures increased as the benzylic protons were replaced by bromo‐, vinyl‐, or epoxide‐functional groups, whereas the thermal stability decreased in comparison with the original polymer. Within a molar fraction of 20–50%, the degree of functionalization had little effect on the glass‐transition temperature; however, it correlated inversely with the thermal stability of each functionalized polymer. The thermal curing behavior of the epoxide‐functionalized polymer was enhanced by the increment of the pendant functionality, which resulted in a significant increase in the glass‐transition temperature as well as the thermal stability after the curing reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5875–5886, 2006     

Crystal structure and morphology of phenyl‐capped tetraaniline in the leucoemeraldine oxidation state

A series of crystals of phenyl‐capped tetraaniline in the leucoemeraldine oxidation state were obtained at different isothermal temperatures and were observed directly under transmission electron microscope. The crystals obtained at higher temperatures exhibit more perfect structures than those obtained at lower temperatures. Both the lamella thickness and the crystal size increase with crystallization temperature. The tetraaniline is apt to form larger scale crystals under lower degree of supercooling. However, their crystal structures keep steady with the crystallization temperature. The tetramer was found to adopt a monoclinic lattice with unit cell parameter of a = 13.93 Å, b = 8.82 Å, c = 23.20 Å, and β = 95.03°, as determined using electron diffraction tilting method combined with wide‐angle X‐ray diffraction experiment. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 764–769, 2006     

Adsorption, desorption and activities of acid phosphatase on various colloidal particles from an Ultisol

Adsorption, desorption and activity of acid phosphatase on various soil colloidal particles and pure clay minerals were studied. Higher adsorption amounts and low percentage of desorption of acid phosphatase were found on fine soil clays (<0.2 μm). Electrostatic force and ligand exchange are the major driving forces that are involved in the adsorption of enzymes on soil clays. More enzyme molecules were adsorbed on soil clays in the presence of organic components. However, enzymes on organic clays were more easily released. One-third of the enzyme on goethite was adsorbed via ligand exchange process. Some other interactions, such as van der Waals force, hydrophobic force and hydrogen bonding may be more important in the adsorption of enzyme on kaolinite and the enzyme in this system cannot be easily removed. Coarse clays (0.2–2 μm) and inorganic soil clays had higher affinities for enzyme molecules than fine clays and organic clays, respectively. The activity of enzyme bound on soil clays was inhibited and the thermal stability was increased in the presence of organic matter. Data obtained in this study are helpful for a better understanding of the interactions of enzymes with inorganic and organic constituents in soil and associated environments.     

Coriatone and corianlactone, two novel sesquiterpenes from Coriaria nepalensis

Both coriatone (1). a novel highly oxygenated picrotoxane-type sesquiterpene, and corianlactone (2). with an unprecedented sesquiterpene basic skeleton, named coriane, were isolated from Coriaria nepalensis Wall. The structures of 1 and 2 were determined by analysis of their two-dimensional NMR data, and the structure of 2 was confirmed by X-ray analysis. Compounds 1 and 2 showed no remarkable inhibitory activity toward K(562) cells. They are cytotoxic with IC(50) > 50 microg/mL (cis-platinim: IC(50) = 0.49 microg/mL).     

Separation of dideoxyribonucleosides in trace amounts by automated liquid chromatography and capillary electrophoresis.

No satisfactory high-performance liquid chromatographic (HPLC) method is currently available for the separation of the major dideoxyribonucleosides (ddNs) and their derivatives. A method involving HPLC has been developed for the separation of five major ddNs [ddA, ddC, ddI, azT and 2',3'-dideoxy-2',3'-didehydrothymidine (d4T)]. Elution of the common and modified components of DNA was also examined under the selected separation conditions of HPLC. The elution characteristics of these compounds were studied using serum plasma samples spiked with ddN derivatives. In addition, capillary electrophoresis (CE) was investigated for the separation of ddNs and their derivatives. Picomolar amounts of the five major ddNs and the metabolic product of azT [5'-O-glucuronide-3'-azido-3'-deoxythymidine (Glo-azT)] were satisfactorily resolved in 10 min by using a modification of CE. The spectral properties of the ddNs were characterized under different pH conditions and compared with those of their parent deoxyribonucleosides (dNs) because these compounds are commonly measured in HPLC by their spectral properties. The spectra of ddC and ddT derivatives resemble very closely those of dC and dT, but those of ddA and ddI differ to some extent from their parent dNs. The HPLC method was extensively examined for satisfactory resolutions of these compounds. For example, an isocratic elution method, although simple, failed to resolve these compounds and ion-pair chromatography did not offer any advantage. Gradient elution involving buffered solutions and increasing amounts of an organic modifier yielded satisfactory results. Methanol appeared to be the organic modifier of choice. A reversed-phase matrix with smaller than octadecyl alkyl chains did not produce the necessary interactions. Uniform spherical beads of smaller diameter produced superior resolutions. The separation of these compounds on three commercially available columns is discussed. The separation of human plasma samples spiked with dideoxynucleoside derivatives by HPLC was accomplished in ca. 16 min. The presence of the dNs did not interfere in their separations.     

Differential operator Lie algebras on the ring of Laurent polynomials

A class of differential operator Lie algebras on the unit circle is introduced and discussed. They are the natural generalizations of the Witt algebra and the Virasoro algebra. Among them are the higher-spin algebrasW ₁₊ andW which occur in the physics literature.