Geometric Algebra for Multidimension-Unified Geographical Information System

Traditional Euclidean geometry-based Geographical Information System (GIS) is not multidimensional unification with weak ability to object expression and analysis of high dimensions. Geometric algebra (GA) can connect different geometric and algebra systems, and provide rigorous and elegant foundation for expression, modeling and analysis in GIS. This paper proposes the implementation methods for system construction and key components of multidimension-unified GIS. Based on such properties as multidimension-unified and coordinate-free of GA, data models, data indexes, and data analysis algorithms for multidimensional vector data, raster and vector field data are developed. This study indicates that GA provides a new mathematical tool for the development of GIS characterized as multidimension-unified expression and computation. For the development of geographical analysis methods, it can represent multidimensional spatio-temporal changes conveniently.     

The spectrum of semi-Cayley graphs over abelian groups

In this paper, a formula of the spectrum of semi-Cayley graphs over finite abelian groups will be given. In particular, the spectrum of Cayley graphs over dihedral groups and dicyclic groups will be given, respectively.     

Determination of cimetidine in human plasma by use of coupled-flow injection, solid-phase extraction, and capillary zone electrophoresis

Summary An on-line flow injection-solid-phase extraction-capillary zone electrophoresis (FI-SPE-CZE) method has been developed for determination of cimetidine in human plasma. Sodium dodecylsulfate (SDS) was used as dynamic chemical modifier for elimination of capillary contamination by biological macromolecules. FI on-line preconcentration and cleaning of the analyte by means of a C₁₈ microcolumn was performed automatically and CZE separation was performed consecutively without interruption of the applied voltage and between-run-washing of the capillary. A detection limit of 8 μgL⁻¹ (3×σ) was achieved at a sample throughput of 12h⁻¹. The approach was successfully used for a pharmacokinetic study of cimetidine.     

Mean square stability analysis of impulsive stochastic differential equations with delays

In this article, based on Lyapunov–Krasovskii functional method and stochastic analysis theory, we obtain some new criteria ensuring mean square stability of trivial solution of a class of impulsive stochastic differential equations with delays. As an application, a class of stochastic impulsive neural network with delays has been discussed. One illustrative example has been provided to show the effectiveness of our results.     

Broadening-independent demodulation for wavelength modulation spectroscopy based on even-order harmonics

The line broadening of gas absorption spectrum is a significant but unknown factor in traditional demodulation of wavelength modulation spectroscopy, which is a kind of tunable diode laser absorption spectroscopy in weak absorption cases. In this paper, another signal demodulation method based on some simple algebraic operations with the amplitudes of the zero-, second-, and fourth-order harmonics was proposed. With this method the effect of spectrum broadening could be selfeliminated. That makes the amplitude of the demodulated signal is irrelevant to the broadening, and enables the direct and fast measurement without complex simulations and curve fittings in traditional method.     

对用稳定图识别真假模态的一点改进

利用单位样值响应矩阵和自由响应的特征值分解形式中的特征值前的系数矩阵的范数作稳定判据，结合稳定图识别真假模态，计算表明，本方法具有较好的分解能力。     

Ethylene glycol reflux synthesis of carbon nanotube/ceria core-shell nanowires

Carbon nanotube (CNT)/ceria core-shell nanowires were prepared facilely on a large scale under the boiling reflux of ethylene glycol. The composites are characterized by transmission electron microscopy, X-ray diffraction as well as Fourier transformed infrared spectra. It is found that the entire outer surface of CNTs is fully sheathed with a dense layer of uniform nanosized CeO₂, and that the thickness of the coating sheath can be readily manipulated by tuning the molar ratio of ceria to CNTs. Finally, a possible formation mechanism has been suggested as follows: with the high reaction temperature, ethylene glycol is partially converted to oxalic acid, and the surface hydroxyl groups of CeO₂ tiny particles react with oxalic acid to form the polymer-like inorganic-organic compounds. Subsequently, in view of the low-energy point, the polymer-like inorganic-organic compounds are coated on the surface of CNTs, and thus CNTs/ceria core-shell composites are obtained.     

Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps

A strong solutions approximation approach for mild solutions of stochastic functional differential equations with Markovian switching driven by Lévy martingales in Hilbert spaces is considered. The Razumikhin–Lyapunov type function methods and comparison principles are studied in pursuit of sufficient conditions for the moment exponential stability and almost sure exponential stability of equations in which we are interested. The results of [A.V. Svishchuk, Yu.I. Kazmerchuk, Stability of stochastic delay equations of Itô form with jumps and Markovian switchings, and their applications in finance, Theor. Probab. Math. Statist. 64 (2002) 167–178] are generalized and improved as a special case of our theory.     

Determination of Trace Lithium in Uranium Compounds by Adsorption on Activated Alumina Using a Micro-column Method

A novel method using a micro-column packed with active alumina as solid phase was proposed for separation of trace lithium from uranium compounds prior to determination. The method is based on a preliminary chromatographic separation of the total amount of uranium. This separation involves passing the solution containing sodium carbonate through active alumina and then eluting the trace lithium retained by the solid phase with a solution of sulfuric acid. Two modes, off-line and on-line micro-column preconcentration, were performed. In conjunction with atomic absorption spectrometry, this on-line preconcentration technique allows a determination of lithium at 10(-9) level. Both off-line and on-line mode operation conditions were investigated in separation and determination of trace lithium by micro-column method (length of column bed, flow rate, etc.). The adsorption capacity of activated alumina was found to be 343 microg g(-1) for lithium. Under the optimal operation condition, the detection limit (DL) of on-line preconcentration corresponding to three times the standard deviation of the blank (S/N = 3) was found to be 1.3 ng mL(-1) and the RSD of this method is 3.32% (n = 5). The on-line calibration graph was linear over the range 20 - 200 ng mL(-1). A good preconcentration factor 820 was achieved by experiment under the on-line mode. The developed method was applied to the analysis of trace lithium in nuclear grade uranium compounds.