Two optimized novel potential formulas and numerical algorithms for [Formula: see text] cobweb and fan resistor networks.

The research of resistive network will become the basis of many fields. At present, many exact potential formulas of some complex resistor networks have been obtained. Computer numerical simulation is the trend of computing, but written calculation will limit the time and scale. In this paper, the potential formulas of a [Formula: see text] scale cobweb resistor network and fan resistor network are optimized. Chebyshev polynomial of the second class and the absolute value function are used to express the novel potential formulas of the resistor network, and described in detail the derivation process of the explicit formula. Considering the influence of parameters on the potential formulas, several idiosyncratic potential formulas are proposed, and the corresponding three-dimensional dynamic images are drawn. Two numerical algorithms of the computing potential are presented by using the mathematical model and DST-VI. Finally, the efficiency of calculating potential by different methods are compared. The advantages of new potential formulas and numerical algorithms by the calculation efficiency of the three methods are shown. The optimized potential formulas and the presented numerical algorithms provide a powerful tool for the field of science and engineering.

Analytical potential formulae and fast algorithm for a horn torus resistor network.

In this paper, a (u+1)×v horn torus resistor network with a special boundary is researched. According to Kirchhoff's law and the recursion-transform method, a model of the resistor network is established by the voltage V and a perturbed tridiagonal Toeplitz matrix. We obtain the exact potential formula of a horn torus resistor network. First, the orthogonal matrix transformation is constructed to obtain the eigenvalues and eigenvectors of this perturbed tridiagonal Toeplitz matrix; second, the solution of the node voltage is given by using the famous fifth kind of discrete sine transform (DST-V). We introduce Chebyshev polynomials to represent the exact potential formula. In addition, the equivalent resistance formulae in special cases are given and displayed by a three-dimensional dynamic view. Finally, a fast algorithm of computing potential is proposed by using the mathematical model, famous DST-V, and fast matrix-vector multiplication. The exact potential formula and the proposed fast algorithm realize large-scale fast and efficient operation for a (u+1)×v horn torus resistor network, respectively.

Fast algorithm and new potential formula represented by Chebyshev polynomials for an [Formula: see text] globe network.

Resistor network is widely used. Many potential formulae of resistor networks have been solved accurately, but the scale of data is limited by manual calculation, and numerical simulation has become the trend of large-scale operation. This paper improves the general solution of potential formula for an [Formula: see text] globe network. Chebyshev polynomials are introduced to represent new potential formula of a globe network. Compared with the original potential formula, it saves time to calculate the potential. In addition, an algorithm for computing potential by the famous second type of discrete cosine transform (DCT-II) is also proposed. It is the first time to be used for machine calculation. Moreover, it greatly increases the efficiency of computing potential. In the application of this new potential formula, the equivalent resistance formulae in special cases are given and displayed by three-dimensional dynamic view. The new potential formulae and the proposed fast algorithm realize large-scale operation for resistor networks.

Synthesis and Application of Novel Molecularly Imprinted Solid Phase Extraction Materials Based on Carbon Nanotubes for Determination of Carbofuran in Human Serum by High Performance Liquid Chromatography.

Novel molecularly imprinted polymers (MIPs) based on multiwalled carbon nanotubes (MWNTs) were synthesized using carbofuran as template, methacrylic acid as functional monomer, and trimethylolpropane trimethacrylate as cross-liking agent, respectively. Characterization results showed that the carbofuran MIPs have been successfully grafted onto the surface of MWNTs as a thin layer with high stability. The results of adsorption dynamics indicated that the synthesized MWNT-MIPs displayed a biphase adsorption profile and good selective recognition to carbofuran with equilibrium adsorption of 106.2 mg/g. The MWNTs-MIPs synthesized were further applied as the adsorbent material of solid-phase extraction (SPE) for the pretreatment of carbofuran in human serum, analyzed using high performance liquid chromatograph (HPLC). The recoveries obtained ranged from 89.0 ± 4.8 to 93.6 ± 3.2, showing that the MWNTs-MIPs-SPE system developed have specific recognition toward carbofuran. Results above indicated that the proposed system filled with synthesized MWNTs-MIPs provided a fast and selective extraction of carbofuran in serum.

On optimal backward perturbation analysis for the linear system with skew circulant coefficient matrix.

We first give the style spectral decomposition of a special skew circulant matrix C and then get the style decomposition of arbitrary skew circulant matrix by making use of the Kronecker products between the elements of first row in skew circulant and the special skew circulant C. Besides that, we obtain the singular value of skew circulant matrix as well. Finally, we deal with the optimal backward perturbation analysis for the linear system with skew circulant coefficient matrix on the base of its style spectral decomposition.

[Determination of three phenoxyalkanoic acid herbicides in blood using gas chromatography coupled with solid-phase extraction and derivatization].

A method for the determination of three phenoxyalkanoic acid herbicides, 2,4-dichlorophenoxyacetic acid (2,4-D), 2-(2,4-dichlorophenoxy)-propanoic acid (2,4-DP), and 4-chloro-2-methylphenoxy-acetic acid (MCPA), in blood was developed. The blood sample was diluted with 0.1 mol/L hydrochloric acid, and extracted by solid-phase extraction using porous resin GDX401 as adsorbent and ethyl ether as eluent. The extract was esterified with dichloropropanol in the presence of sulfuric acid as catalyst. The derivatives were analysed by gas chromatography with electron-capture detection. The detection limits of 2,4-D, 2,4-DP and MCPA were 20, 8 and 40 ng/mL, respectively. In quantitative analysis, 2,4-dichlorophenylacetic acid was used as an internal standard. The linear relationships and recoveries were satisfactory. The derivatization of the three herbicides with methanol, ethanol, n-propanol, n-butanol, and trifluoroethanol were also studied, and the analytical methods of these derivatization were compared with that of dichloropropanol as esterifying agent. The method is sensitive enough for the examination of the poison samples in actual.