Taylor公式求极限时“阶”的分析

本文在剖析一道题目的错误解答的基础上,归纳出利用Taylor展开求极限的可行方法,为初学者找到突破口.

Taylor公式求极限时“阶”的分析

Taylor公式是一个用函数在某点的信息描述其附近取值的公式,其充分运用“无限接近”这一数学理论,将一些复杂的数学函数转化为简易的多项式函数,是数学函数中最基本的理论.本文阐述Taylor公式,分析并归纳Taylor公式求极限的具体方法,以期为初学者提供理论参考.

Performance improvement in stepped solar still modified by sponge layer

In this paper,the experimental investigation on the performance improvement of conventional stepped solar still is conducted.The steps are covered by the porous material to improve the performance of the conventional device and increase the evaporation rate.All the parameters,including the temperature on the glass surface,the water temperature inside the evaporation zone,and the amount of water produced in both conventional and modified stepped solar stills are measured and compared.The efficiency of two devices and their exergy efficiency have been calculated.Finally,the economic analysis of both devices has been done to check the economic feasibility of the modified device.The amount of freshwater generated during one day was 2244.4 and 3076.2 mL/m^(2),respectively for the conventional and modified stepped solar stills.As a result,the amount of water produced in one day by modified stepped solar still is 35.5% more than the conventional one.Also,the costs for the conventional and modified stepped solar stills have been calculated as 0.0359 and 0.029$/(L·m^(-2)),respectively.

Analysis on flutter performance of flexible photovoltaic support based on full-order method

Taking a three-cable flexible photovoltaic(PV)support structure as the research subject,a finite element model was established.Utilizing a full-order flutter analysis method,the flutter critical wind speed and flutter frequency of the flexible PV support structure at a tilt angle of 0°were calculated.The results showed good agreement with wind tunnel test data.Further analysis examined the pretension effects in the load-bearing and stabilizing cables on the natural frequency and flutter critical wind speed of the flexible PV support structure.The research findings indicate increasing the pretension in the load-bearing cables significantly raises the natural frequencies of the first four modes.Specifically,as the pretension in the load-bearing cables increases from 22 to 102 kN,the flutter critical wind speed rises from 17.1 to 21.6 m/s.By contrast,the pretension in the stabilizing cable has a smaller effect on the natural frequency and flutter critical wind speed of the flexible PV support structure.When the pretension in the stabilizing cable increased from 22 to 102 kN,the flutter critical wind speed increased from 17.1 to 17.7 m/s.For wind-resistant design of flexible PV support structures,it is recommended to prioritize increasing the pretension in the load-bearing cables to enhance the structural flutter performance.

On the Local Convergence and Dynamics of New Iterative Method with Sixth Order Convergence

In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity of the new iterative method,we employ several chemical engineering applications and academic test problems.Numerical results show the good numerical performance of the new iterative method.Moreover,the dynamical study of the new method also supports the theoretical results.

学生德育“阶次教育”模式浅析

学生德育“阶次教育”，是指按照青年学生思想品德形成规律和社会发展的要求，根据德育工作的总体目标，将学生学程划分阶段和层次，将总目标分解所形成的具体目标分别落实到每一阶段的具体层次，使之形成序列，由浅入深，逐步提高，环环相接，最后达到总体目标的要求。

“楼梯”“梯子”“阶梯”的语义与句法功能考察

基于大规模的语料库,本文从语义和句法功能两个方面对"楼梯""梯子""阶梯"这三个词进行了辨析,并尽可能地分析出它们之间的差异。

浅谈工科院校的物理实验学科建设

工科物理实验学科建设与改革的出发点必须从工科物理实验的教学目的出发,重点从内容体系、教学模式改革实行"阶""层"教学模式;科学研究规划实验项目训练重心;重视创新平台搭建和创新教育积淀;把握实验技术人员定位,注重团队建设等方面提出了物理实验课程学科的改革和建设思路。

Fracture identification based on remote detection acoustic reflection logging

Fracture identification is important for the evaluation of carbonate reservoirs. However, conventional logging equipment has small depth of investigation and cannot detect rock fractures more than three meters away from the borehole. Remote acoustic logging uses phase-controlled array-transmitting and long sound probes that increase the depth of investigation. The interpretation of logging data with respect to fractures is typically guided by practical experience rather than theory and is often ambiguous. We use remote acoustic reflection logging data and high-order finite-difference approximations in the forward modeling and prestack reverse-time migration to image fractures. First, we perform forward modeling of the fracture responses as a function of the fracture-borehole wall distance, aperture, and dip angle. Second, we extract the energy intensity within the imaging area to determine whether the fracture can be identified as the formation velocity is varied. Finally, we evaluate the effect of the fracture-borehole distance, fracture aperture, and dip angle on fracture identification.

Identification algorithm for a kind of fractional order system

The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for those fractional order systems. The basic idea of the algorithm is to compute fractional derivatives and the filter simultaneously, i.e., the filtered fractional derivatives can be obtained by computing them in one step, and then system identification can be fulfilled by the least square method. The instrumental variable method is also used in the identification of fractional order systems. In this way, even if there is colored noise in the systems, the unbiased estimation of the parameters can still be obtained. Finally an example of identifying a viscoelastic system is given to show the effectiveness of the aforementioned method.

Reservoir information extraction using a fractional Fourier transform and a smooth pseudo Wigner-Ville distribution

Currently, it is difficult for people to express signal information simultaneously in the time and frequency domains when analyzing acoustic logging signals using a simple-time or frequency-domain method. It is difficult to use a single type of time-frequency analysis method, which affects the feasibility of acoustic logging signal analysis. In order to solve these problems, in this paper, a fractional Fourier transform and smooth pseudo Wigner Ville distribution （SPWD） were combined and used to analyze array acoustic logging signals. The time-frequency distribution of signals with the variation of orders of fractional Fourier transform was obtained, and the characteristics of the time-frequency distribution of different reservoirs under different orders were summarized. Because of the rotational characteristics of the fractional Fourier transform, the rotation speed of the cross terms was faster than those of primary waves, shear waves, Stoneley waves, and pseudo Rayleigh waves. By choosing different orders for different reservoirs according to the actual circumstances, the cross terms were separated from the four kinds of waves. In this manner, we could extract reservoir information by studying the characteristics of partial waves. Actual logging data showed that the method outlined in this paper greatly weakened cross-term interference and enhanced the ability to identify partial wave signals.

ADRC FRACTIONAL ORDER PID CONTROLLER DESIGN OF HYPERSONIC FLIGHT VEHICLE

Active disturbance rejection controller（ADRC）uses tracking-differentiator（TD）to solve the contradiction between the overshoot and the rapid nature.Fractional order proportion integral derivative（PID）controller improves the control quality and expands the stable region of the system parameters.ADRC fractional order（ADRFO）PID controller is designed by combining ADRC with the fractional order PID and applied to reentry attitude control of hypersonic vehicle.Simulation results show that ADRFO PID controller has better control effect and greater stable region for the strong nonlinear model of hypersonic flight vehicle under the influence of external disturbance,and has stronger robustness against the perturbation in system parameters.

新产品开发网络集成模型

本文在描述新产品开发基本流程基础上,依据"阶-门"模型设计思想,设计了一种新产品开发网络集成模型。该模型通过顾客交互、研发流程和数据集合三层体系结构不仅体现了对现代计算机、通信网络及数据库前沿技术的应用,而且是对"以顾客为中心"的现代市场化经营理念和新产品开发各种资源的综合利用。该模型能够进一步改善研发流程,并有效地缩短新产品开发周期。

Numerical simulation of LWD resistivity response of carbonate formation using self-adaptive hp-FEM

Most of the carbonate formation are highly heterogeneous with cavities of different sizes, which makes the prediction of cavity-filled reservoir in carbonate rocks difficult. Large cavities in carbonate formations pose serious threat to drilling operations. Logging-whiledrilling （LWD） is currently used to accurately identify and evaluate cavities in reservoirs during drilling. In this study, we use the self-adaptive hp-FEM algorithm simulate and calculate the LWD resistivity responses of fracture-cavity reservoir cavities. Compared with the traditional h-FEM method, the self-adaptive hp-FEM algorithm has the characteristics of the self-adaptive mesh refinement and the calculations exponentially converge to highly accurate solutions. Using numerical simulations, we investigated the effect of the cavity size, distance between cavity and borehole, and transmitted frequency on the LWD resistivity response. Based on the results, a method for recognizing cavities is proposed. This research can provide the theoretical basis for the accurate identification and quantitative evaluation of various carbonate reservoirs with cavities encountered in practice.

Biomass, litterfall and the nutrient fluxes in Chinese fir stands of different age in subtropical China

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.), a fast-growing, ever-green conifer tree with high yield and excellent quality, is the most important tree species of timber plantations in subtropical China. We investigated the characteristics of biomass, litterfall and nutrient fluxes in the 8, 14 and 24 year-old stands, representing the young, middle-aged and mature stands. The results showed that Chinese fir plantations in central Fujian province had high productivity, and the proportion of stem mass in total biomass was between 50%-70%. Chinese fir was low nutrient-return tree species with litterfall. Nutrient withdrawal from senescing needles was a strong age-dependence for nitrogen, phosphorous and potassium in Chinese fir. With a management system of such short-rotation and continuously pure-crop planting, harvesting timber can lead to great nutrient loss, which may be one of the causes for site degradation.

Study on Growth and Development of Early Postembryonic Stage of Onychostoma sima

[Objective] The paper was to study the growth and development of Onychostoma sima in postembryonic development stage. [Method] The oosperm was obtained by artificial spawning and artificial insemination method, and hatched under laboratory condition. The indexes such as body weight, body length, length in front of anus and body height were measured to establish larvae growth model. [Result] When the water temperature was （20±1.5） ℃, the body length and body weight of newly hatched larvae were （10.28±0.05） mm and （7.79±0.08） mg, respectively. O. sima larvae begin to feed on the 4 th day after hatching, the initial feeding rate was 48%, the highest feeding rate was 100% on the 6 th d. The-point-of-no-return （PNR） was 13.5 d. In addition, it was also observed that the appearance time of PNR point of O. sima larvae was close to death time of completely starved group, being only 2 d, indicating that once O. sima larvae reached the PNR point, they would face death threats within short time. Therefore, various growth conditions for O. sima larvae should be satisfied to ensure full development of all organs, thereby reducing death and growth stagnation caused by adverse environment in early postembryonic stage. [Conclusion] The study provided theoretical basis for solving the problems in artificial breeding.

FEM modeling of softened base metal in narrow-gap joint by CMT+P MIX welding procedure

A required finite element method（FEM） model applicable for narrow gap CMT and CMT＋P MIX welding was established based on the interactions between arc,base metal and filler metal.A novel method of simplifying wire feeding pulses and heat input pulses was supposed under the conduction of equivalent input.The method together with composed double-ellipse heat sources was included in the model.The model was employed in the investigation of thermal cycling and the identification of the softened zone of AA7A52 base plates.Low-frequency behavior emerged in the form of low-cooling rate sects,which were not expected under experimental conditions.The softened zone including the quenched zone and averaging zone of the base plate was much wider internal the base plate than that close to the surfaces.The reliability of the predictions in thermal cycling was supported by infrared imaging test results of the thermal cycle process.

Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme

To deal with the numerical dispersion problem, by combining the staggeredgrid technology with the compact finite difference scheme, we derive a compact staggered- grid finite difference scheme from the first-order velocity-stress wave equations for the transversely isotropic media. Comparing the principal truncation error terms of the compact staggered-grid finite difference scheme, the staggered-grid finite difference scheme, and the compact finite difference scheme, we analyze the approximation accuracy of these three schemes using Fourier analysis. Finally, seismic wave numerical simulation in transversely isotropic （VTI） media is performed using the three schemes. The results indicate that the compact staggered-grid finite difference scheme has the smallest truncation error, the highest accuracy, and the weakest numerical dispersion among the three schemes. In summary, the numerical modeling shows the validity of the compact staggered-grid finite difference scheme.

Data fitting and modeling of regional geomagnetic field

The selection of the truncation level （TL） and the control of boundary effect （BE） are critical in regional geomagnetic field models that are based on data fitting. We combine Taylor and Legendre polynomials to model geomagnetic data over China's Mainland for years 1960, 1970, 1990, and 2000. To tackle the TL and BE problems, we first determine the range of TL by calculating the root-mean-square error （RMSE） of the models. Next, we determine the optimum TL using the Akaike information criterion （AIC） and the normalized root- mean-square error （NRMSE）. We use the regional anomaly addition （RAA） and the uniform addition （UA） method to add supplementary point outside the national boundary, and find that the intensities of extreme points gradually decrease and stabilize. The UA method better controls BEs over China, whereas the RAA method does a better job at smaller scales. In summary, we rely on a three-step method to determine the optimum TL and propose criteria to determine the optimum number of supplementary points.

Fast global motion estimation and moving object extraction algorithm in image sequences

A novel and effective approach to global motion estimation and moving object extraction is proposed. First, the translational motion model is used because of the fact that complex motion can be decomposed as a sum of translational components. Then in this application, the edge gray horizontal and vertical projections are used as the block matching feature for the motion vectors estimation. The proposed algorithm reduces the motion estimation computations by calculating the onedimensional vectors rather than the two-dimensional ones. Once the global motion is robustly estimated, relatively stationary background can be almost completely eliminated through the inter-frame difference method. To achieve an accurate object extraction result, the higher-order statistics （HOS） algorithm is used to discriminate backgrounds and moving objects. Experimental results validate that the proposed method is an effective way for global motion estimation and object extraction.