分式化时模理论的一些稳定性性质的保持性

本文讨论了将分式环S－1R上的模归约到R上的模时包（hull）、类（class）、界（bound）、秩（rank）的保持性,证明了：1）NR是A在MR中的包当且仅当NS－1R是A在MS－1R中的包;2）还讨论了分式模（S－1M）S－1R与MR之间上述性质存在单向或双向保持性的条件．     

Microwave backscattering by nonspherical ice particles at 5.6 GHz using second-order perturbation series

Scattering of microwaves by an ensemble of nonspherical ice particles is studied using a scattering model based on a second-order perturbation series at 5.6 GHz (C-band). Particle shapes are defined using a Gaussian random sphere geometry. Particle inhomogeneity is taken into account using three different effective-medium approximations: Maxwell–Garnett, Bruggeman, and Coherent Potential mixing rules. By systematically varying particle size, liquid water content, Gaussian shape parameters, and internal structure, it is found that liquid water content is the most important factor for the co-polarized backscattering; the shape is relatively unimportant. For depolarized backscattering, the shape is of fundamental importance, although the other factors are significant too. Surprisingly, the type of nonsphericity is found to be important for depolarization even for scatterers that are in the Rayleigh region: elongated targets depolarize clearly stronger than more irregular shapes. This finding seems not to be strongly size dependent, at least for size parameters from 0.0059 to 0.47, and indicates that the accurate modeling of shape is important for polarization quantities even in the Rayleigh region.     

Single-run ion chromatographic separation of inorganic and low-molecular-mass organic anions under isocratic elution: Application to environmental samples

For the isocratic ion chromatography (IC) separation of low-molecular-mass organic acids and inorganic anions three different anion-exchange columns were studied: IonPac AS14 (9 μm particle size), Allsep A-2 (7 μm particle size), and IC SI-50 4E (5 μm particle size). A complete baseline separation for all analyzed anions (i.e., F⁻, acetate, formate, Cl⁻, NO₂⁻, Br⁻, NO₃⁻, HPO₄²⁻ and SO₄²⁻) in one analytical cycle of shorter than 17 min was achieved on the IC SI-50 4E column, using an eluent mixture of 3.2 mM Na₂CO₃ and 1.0 mM NaHCO₃ with a flow rate of 1.0 mL min⁻¹. On the IonPac AS14 column, it was possible to separate acetate from inorganic anions in one run (i.e., less than 9 min), but not formate, under the following conditions: 3.5 mM Na₂CO₃ plus 1.0 mM NaHCO₃ with a flow rate of 1.2 mL min⁻¹. Therefore, it was necessary to adapt a second run with a 2.0 mM Na₂B₄O₇ solution as an eluent under a flow rate of 0.8 mL min⁻¹ for the separation of organic ions, which considerably enlarged the analysis time. For the Allsep A-2 column, using an eluent mixture of 1.2 mM Na₂CO₃ plus 1.5 mM NaHCO₃ with a flow rate of 1.6 mL min⁻¹, it was possible to separate almost all anions in one run within 25 min, except the fluoride-acetate critical pair. A Certified Multianion Standard Solution PRIMUS for IC was used for the validation of the analytical methods. The lowest RSDs (less than 1%) and the best LODs (0.02, 0.2, 0.16, 0.11, 0.06, 0.05, 0.04, 0.14 and 0.09 mg L⁻¹ for F⁻, Ac⁻, For⁻, Cl⁻, NO₂⁻, Br⁻, NO₃⁻, HPO₄²⁻ and SO₄²⁻, respectively) were achieved using the IC SI-50 4E column. This column was applied for the separation of concerned ions in environmental precipitation samples such as snow, hail and rainwater.     

Development of an efficient numerical model for hail impact simulation based on experimental data obtained from pressure sensitive film

Aircraft are subjects to a number of unpredictable loadings that can seriously affect their performance. In the spirit of ever increasing the safety of passengers, hail impact has been studied. This paper shows the progress that has been made using pressure sensitive film to measure the hail impact event. Moreover, the smooth particle hydrodynamics (SPH) method in LS-DYNA is used to create a numerical model in order to validate the numerical hail model so that it can be used in future advanced simulations of hail impact on components of aircraft. Results show that the SPH method can be effectively used to create a numerical hail model and that pressure sensitive film is a simple and inexpensive tool to capture the experimental data.