Qualitative analysis of a modified Leslie–Gower and Holling-type II predator–prey model with state dependent impulsive effects

In this paper, we present a two-dimensional autonomous dynamical system modeling a predator–prey food chain which is based on a modified version of the Leslie–Gower scheme and on the Holling-type II scheme with state dependent impulsive effects. By using the Poincaré map, some conditions for the existence and stability of semi-trivial solution and positive periodic solution are obtained. Numerical results are carried out to illustrate the feasibility of our main results.     

Dynamic analysis of multi-directional functionally graded annular plates

Dynamic analysis of multi-directional functionally graded annular plates is achieved in this paper using a semi-analytical numerical method entitled the state space-based differential quadrature method. Based on the three-dimensional elastic theory and assuming the material properties having an exponent-law variation along the thickness, radial direction or both directions, the frequency equations of free vibration of multi-directional functionally graded annular plates are derived under various boundary conditions. Numerical examples are presented to validate the approach and the superiority of this method is also demonstrated. Then free vibration of functionally graded annular plates is studied for different variations of material properties along the thickness, radial direction and both directions, respectively. And the influences of the material property graded variations on the dynamic behavior are also investigated. The multi-directional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material.     

A new super-extension of the KdV hierarchy

A new super-extension of the KdV hierarchy is proposed, which is associated with a 3×3 matrix spectral problem. Using super-trace identity, generalized bi-Hamiltonian structures of this hierarchy are established. Moreover, infinite conservation laws of the new super-KdV equation are derived.     

Using Gaussian model to improve biological sequence comparison

One of the major tasks in biological sequence analysis is to compare biological sequences, which could serve as evidence of structural and functional conservation, as well as of evolutionary relations among the sequences. Numerous efficient methods have been developed for sequence comparison, but challenges remain. In this article, we proposed a novel method to compare biological sequences based on Gaussian model. Instead of comparing the frequencies of k‐words in biological sequences directly, we considered the k‐word frequency distribution under Gaussian model which gives the different expression levels of k‐words. The proposed method was tested by similarity search, evaluation on functionally related genes, and phylogenetic analysis. The performance of our method was further compared with alignment‐based and alignment‐free methods. The results demonstrate that Gaussian model provides more information about k‐word frequencies and improves the efficiency of sequence comparison. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Combining the least correlation design, wavelet packet transform and correlation coefficient test to reduce the size of calibration set for NIR quantitative analysis in multi-component systems

The paper focuses on solving a common and important problem of NIR quantitative analysis in multi-component systems: how to significantly reduce the size of the calibration set while not impairing the predictive precision. To cope with the problem orthogonal discrete wavelet packet transform (WPT), the least correlation design and correlation coefficient test (r-test) have been combined together. As three examples, a two-component carbon tetrachloride system with 21 calibration samples, a two-component aqueous system with 21 calibration samples, and a two-component aqueous system with 41 calibration samples have been treated with the proposed strategy, respectively. In comparison with some previous methods based on much more calibration samples, the results out of the strategy showed that the predictive ability was not obviously decreased for the first system while being clearly strengthened for the second one, and the predictive precision out of the third one was even satisfactory enough for most cases of quantitative analysis. In addition, all important factors and parameters related to our strategy are discussed in detail.     

Inductance-based sensing technique for wireless, remote-query measurement in liquid media

A novel inductance-based sensing technique is presented for remote query measurement in different liquid media including organic solvents and inorganic solutions. The inorganic solutions tested included salt solutions of different concentrations, and the organic solvents detected included 1,4-dioxane and tetrahydrofuran. To extend the application of the sensor, bacterial culture media were also detected, and the growth of Escherichia coli (E. coli) was controlled. The influential factors which may affect the inductance responses were studied in detail. It was found that quantitative relationships exist between the sensor’s inductance response and the physico-chemical parameters of the liquid media. The sensor’s inductance response (L) decreases with the increase of salt concentration (C) and its ionic valence (e) according to a semi-logarithmic equation LgL = ?aeC + b, where a and b are constants, which is in accordance with the theoretically deduced equation. The inductance variation rate (ΔK) increases directly with the temperature (T): ΔK = a′ T + b′. As for organic solutions, the sensor’s inductance was found to increase with the increasing permittivity of the organic solution. The wireless sensor we designed is simple and easy to manipulate. It has the potential for remote determination of not only chemical substances but also microbiological species such as bacteria. Using the newly developed inductance-based sensor, the pathogenic E. coli was monitored with a limit of detection of 10 cells/mL and a linear semi-logarithmic range of 1.0 × 10¹ to 2.5 × 10⁹ cells/mL.     

Dy~(3+)掺杂Ge-Ga-Se-KBr硫卤玻璃近红外和中红外发光特性研究

用熔融淬冷法制备了系列掺杂浓度的Dy3+∶Ge-Ga-Se-KBr硫卤玻璃样品,测试了样品的折射率、吸收光谱、近红外及中红外荧光谱。应用Judd-Ofelt理论计算了Dy3+离子的强度参数(Ωi,i=2,4,6)、自发辐射跃迁几率(A)、荧光分支比(β)和辐射寿命(τrad)等光谱参数。研究了810 nm激光泵浦下样品中红外荧光特性与掺杂浓度之间的关系,利用McCumber(MC)和Futchbauer-Ladenburg(FL)理论分别计算了常温Dy3+:6F5/2→6H9/2(2.17μm),6F11/2(6H9/2)→6H13/2(2.47)和6H13/2→6H15/2(2.86μm)中红外荧光的受激发射截面。