Modified Jarratt method with sixth-order convergence

In this paper, we present a variant of Jarratt method with order of convergence six for solving non-linear equations. Per iteration the method requires two evaluations of the function and two of its first derivatives. The new multistep iteration scheme, based on the new method, is developed and numerical tests verifying the theory are also given.     

我国固定资产投资的ARIMA模型分析与预测

本文综合运用了时间序列预测方法,对我国固定资产投资总额进行了分析,建立了自回归求积移动模型ARIMA（4,1,4）。检验结果表明,该模型提供了较好的顸测结果,可为我国全社会固定资产投资提供可靠的参考数据。     

A new fourth-order iterative method for finding multiple roots of nonlinear equations

In this paper, we present a new fourth-order method for finding multiple roots of nonlinear equations. It requires one evaluation of the function and two of its first derivative per iteration. Finally, some numerical examples are given to show the performance of the presented method compared with some known third-order methods.     

Some second-derivative-free variants of Halley’s method for multiple roots

In this paper, we present two new families of third-order methods for finding multiple roots of nonlinear equations. Each of them is based on a variant of the Halley’s method (for simple roots) free from second derivative. One of the families requires one evaluation of the function and two of its first derivative per iteration, and the other family requires two evaluations of the function and one of its first derivative. Several numerical examples are given to illustrate the performance of the presented methods.     

Evaluation of fractal dimension of soft terrain surface

By using a laser profiler, the roughness of sowed and plowed surfaces was obtained. Through evaluation of the precision of fractal dimensions based on the Weierstrass–Mandelbort (W–M) function, we found the rescaled (R/S) analysis method and the structure spectral method were not suitable for the calculation of the fractal dimension on a soft terrain surface. Therefore, the fractal dimension, non-scale range and correlation coefficient for each kind of terrain were analyzed using the following fractal computational methods – (i) variate-difference method, (ii) power spectral density method, and (iii) root mean square method. The results showed that: fractal dimension of plowed terrain was large with small fluctuations, while its internal structure was complex. The power spectral density method was not robust enough to compute the fractal dimension of a soft terrain surface. The fractal dimension computed using the root mean square method was found to be more accurate for the soft terrain surface. Moreover, the correlation coefficient of linear regression when using the root mean square method was good and the range of non-scale variation was small.     

火焰原子吸收光谱法测定菘蓝不同部位的金属元素

采用火焰原子吸收光谱法测定药用植物菘蓝的根、茎和叶中 Cu、Zn、Fe、Mg、Ca的含量。加标回收率在 97.6 %— 10 4 .9%之间 ,相对标准偏差 (RSD)小于 1.5 %。该法灵敏度高 ,结果准确。为研究金属元素在菘蓝中的分布及其含量与菘蓝的药效关系提供了有用的数据。     

论声压级平均算法

本文阐述了求声压级平均值的几种算法,特别论述了对声压级数据直接进行算术平均的运算方法。     

Uptake of water from soils by plant roots

Uptake of water by plant roots can be considered at two different Darcian scales, referred to as the mesoscopic and macroscopic scales. At the mesoscopic scale, uptake of water is represented by a flux at the soil–root interface, while at the macroscopic scale it is represented by a sink term in the volumetric mass balance. At the mesoscopic scale, uptake of water by individual plant roots can be described by a diffusion equation, describing the flow of water from soil to plant root, and appropriate initial and boundary conditions. The model involves at least two characteristic lengths describing the root–soil geometry and two characteristic times, one describing the capillary flow of water from soil to plant roots and another the ratio of supply of water in the soil and uptake by plant roots. Generally, at a certain critical time, uptake will switch from demand-driven to supply-dependent. In this paper, the solutions of some of the resulting mesoscopic linear and nonlinear problems are reviewed. The resulting expressions for the evolution of the average water content can be used as a basis for upscaling from the mesoscopic to the macroscopic scale. It will be seen that demand-driven and supply-dependent uptake also emerge at the macroscopic scale. Information about root systems needed to operationalize macroscopic models will be reviewed briefly.     

Random access sequence set design in wireless cellular communication networks

In modern wireless cellular communication systems, Zadoff–Chu (ZC) sequences have been chosen as random access sequences due to their perfect autocorrelation and cross-correlation properties. However, the orthogonality between these sequences is no longer true when there is a frequency offset between the access device and access point. Thereby, the overall performance of ZC sequence-based random access signals will be limited. In this paper, we give a comprehensive analysis on the effect of frequency offset. We show how frequency offset affects the orthogonal property between sequences, and hence incurs the “energy attenuation” and “energy leakage” problems. Consequently, the detection probabilities of the transmitted random access sequences and the false alarm probabilities of the unsent sequences are affected. A frequency offset resistant detection metric is proposed in this paper to improve the detection probability. In order to resist the frequency offset effect as well as apply to the proposed detection metric, mathematical properties of the optimized roots and cyclic shift set are exploited. Finally, we illustrate how to construct a practical random access signal set under the given timing and frequency offset uncertainties. This analytical framework provides a useful insight into ZC sequence-based random access signal design and performance analyses in wireless cellular communication systems.     

力场/溶剂水模型对EGFRvⅢ抗原-MR1(scFv)抗体复合物的MM-PBSA计算精度的影响与实验验证

以表皮生长因子Ⅲ型突变体(EGFRvⅢ)抗原多肽与其抗体(MR1)及其人源化突变体的复合物结构为出发点,采用分子动力学中的6种常用力场及3种常用溶剂水模型,分别对上述抗原-抗体复合物进行100ns的分子动力学模拟与分子力学和连续介质模型计算自由能(MM-PBSA),并在实验上利用等温滴定量热(ITC)仪测定了抗原和抗体相互作用的热力学参数.通过在结构变化、能量变化及野生型与突变体比较等几个方面进行综合分析,给出了最佳的计算模型.对不同力场及水模型计算精度等相关问题进行了探讨.