秦九韶、时曰醇、黄宗宪的求定数方法

中国古代数学没有素数和把一个整数分解成素因数的概念。在《九章算术》(公元一世纪)中,为了把一个分数约简,采取"可半者半之;不可半者,副置分母子之数,以少减多,更相减损,求其等数,以等数约之。"这里的"等数"就是最大公约数。若"等数"为1(即两数互素),则置之不论.《孙子算经》(公元四世纪)提出一个一次同余式组解法的实例,其模数为3、5、7,恰是两两互素。秦九韶为了把一次同余式组解法一般化,除提出"大衍求一术"解决k_i(M/A_i)(?)1(modA_i),i=1,2,…,n的k_i外。

宽范围高精度转速测量算法

基于ATMEL89C52单片机硬件 ,研究了一种新的软件算法———“限时定数法”。解决了常规转速测量仪表无法在较宽范围内取得较高测量精度的问题。利用本文所提出的软硬件方案 ,在2～ 60 0 0r/min的转速范围内 ,测量精度可达 0 .0 2 %。

提取合并同位积数法

第一章 基础知识 第一节 什么是提取合并同位积数法一、什么是同位积数在乘法中,同一个数位上的若干个积数,是同位积数。例如:74 ×7=?

对一个多方竞赛取胜问题的分析

多方竞赛取胜受着很多因素的制约 ,大多数无规律可言。文章对实际中抽象出的一个多方竞赛问题 ,进行了分析 ,得出了一些规律 ,具有开创性。

Determination of Stability Constants of Cadmium-Glycine Complexes by a Unified Treatment for Potentiometric and Polarographic Data

The cadmium（Ⅱ）-glycine system was studied by the two experimental techniques, ion sensitive electrode （ISE） and differential pulse polarography （DPP）, and the experimental data obtained were used by a unified mathematical treatment to calculate the complex stability constants. The combination of the two techniques is of many advantages as ISE can be performed at low [LT]：[MT] ratios and significantly higher [MT], whereas DPP could be used well at large [LT]：[MT] ratios and much smaller [MT]. This makes it possible to study a metal-ligand system in a relatively broader range of experimental conditions that, in turn, provides more information about the metakligand system of interest. Applying the unified mathematical treatment to the cadmium-glycine system, two new complexes MHL and ML2（OH） as well as three complexes ML, ML2 and ML3, reported in literatures, could be modeled and all their stability constants have been refined.

一种定数／概率综合法用于储量计算

本文目的是提出石油工业内烃类储量分类、分类系统统一的必要性及评价方法的讨论。文中还介绍了Ｍｏｂｉｌ石油公司储量评价和分类的方法，并给出简单的实例，我们不想对所有过去和现在的方法进行总结。

Stability analysis for nonlinear multi-variable delay perturbation problems

This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), and εy′(t)=g(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), where 0<ε1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.

Determination of Precise Instantaneous Height at Multibeam Transducer

To overcome the shortcomings of the traditional multibeam survey and data processing, a new method is presented for the precise determination of the instantaneous height at the multibeam transducer by the blend of GPS height and heave signals. Before signal blend, GPS height and heave signals need to be corrected first to the transducer center by attitude correction. Second, the GPS height needs to be checked and modified by heave check and modification itself. Butterworth and FFT （fast Fourier transformation） were used in the signal blend. Finally, FFT is thought to be appropriate in signal processing. The new method efficiently overcomes the shortcomings of the traditional method, and this is proven well by the MBS （multibeam bathymetric system） experiment.

New self-calibration approach to space robots based on hand-eye vision

To overcome the influence of on-orbit extreme temperature environment on the tool pose(position and orientation) accuracy of a space robot,a new self-calibration method based on a measurement camera(hand-eye vision) attached to its end-effector was presented.Using the relative pose errors between the two adjacent calibration positions of the space robot,the cost function of the calibration was built,which was different from the conventional calibration method.The particle swarm optimization algorithm(PSO) was used to optimize the function to realize the geometrical parameter identification of the space robot.The above calibration method was carried out through self-calibration simulation of a six-DOF space robot whose end-effector was equipped with hand-eye vision.The results showed that after calibration there was a significant improvement of tool pose accuracy in a set of independent reference positions,which verified the feasibility of the method.At the same time,because it was unnecessary for this method to know the transformation matrix from the robot base to the calibration plate,it reduced the complexity of calibration model and shortened the error propagation chain,which benefited to improve the calibration accuracy.

Features and correct application of coal vitrinite reflectance index

The law of mathematical statistics, which the coal vitrinite reflectance index obeys, the existing vitrinite representing deviations, and the advantages of judging coalification and the shortage of judging coal type were analyzed. The advantages and disadvantages of various determination methods and the expression index and different methods of identifying vitrinite on the determination results were compared. The vitality of coal vitrinite reflectance depends on its full play the unique function of reflectance histogram and the systematic errors between different determination methods do not affect the application based on reflectance histogram are considered.

IMC-PID tuning method based on sensitivity specification for process with time-delay

To overcome the deficiencies addressed in the conventional PID control and improve the dynamic performance and robustness of the system, a simple design and parameters tuning approach of internal model control-PID （IMC-PID） controller was proposed for the first order plus time-delay （FOPTD） process and the second order plus time-delay （SOPTD） process. By approximating the time-delay term of the process model with the first-order Taylor series, the expressions for IMC-PID controller parameters were derived, and they had only one adjustable parameter 2 which was directly related to the dynamic performance and robustness of the system. Moreover, an analytical approach of selecting 2 was given based on the maximum sensitivity Ms. Then, the robust tuning of the system could be achieved according to the value of Ms. In addition, the proposed method could be extended to the integrator plus time-delay （IPTD） process and the first order delay integrating （FODI） process. Simulation studies were carried out on various processes with time-delay, and the results show that the proposed method could provide a better dynamic performance of both the set-point tracking and disturbance rejection and robustness against parameters perturbation.

LOCALIZATION ALGORITHM BASED ON MINIMUM CONDITION NUMBER FOR WIRELESS SENSOR NETWORKS

During range-based self-localization of Wireless Sensor Network (WSN) nodes, the number and placement methods of beacon nodes have a great influence on the accuracy of localization. This paper proves a theorem which describes the relationship between the placement of beacon nodes and whether the node can be located in 3D indoor environment. In fact, as the highest locating accuracy can be acquired when the beacon nodes form one or more equilateral triangles in 2D plane, we generalizes this conclusion to 3D space, and proposes a beacon nodes selection algorithm based on the minimum condition number to get the higher locating accuracy, which can minimize the influence of distance measurement error. Simulation results show that the algorithm is effective and feasible.

Identification of structural entities in NdF_3-LiF melts with cryoscopic method

Nd-F species in NdF3-LiF melts were studied using cryoscopic method.Liquidus temperatures of melts of various compositions were determined by differential thermal analysis(DTA).Based on the different model calculations,NdF4- was identified as the most likely Nd-F entity in the melts in which the mole fraction of NdF3 was lower than 20%,considering only one single Nd species in the melt,and which was formed in accordance with Temkin model or Flood model.Then,activities of different components in the melts were researched.The results show that activity of LiF decreases,and that of NdF3 increases with increasing the mole fraction of NdF3.The value of activity coefficient of NdF3 is higher than 1,and that of LiF is lower than 1.

Heteroclinic Orbit Existence on a Type of Chaotic System with Delays

In this paper, we discuss a type of chaotic system with delays. We study the equilibrium points and the existence of heteroclinic orbit of the system. Heteroclinic orbit existence theorem is proposed and proved by applying the undetermined coefficient method, which shows the complex dynamical properties of this system.

Determination of Scaling Parameter and Dynamical Resonances in Complex-Rotated Hamiltonian Ⅰ:Theory

In this paper we present a theoretical analysis on the determination of the scaling parameter in the complex-rotated Hamiltonian, which has served as a basis for successful applications of the rigged Hilbert space theory for resonances. Based on the complex energy eigenvalue, E（θ） = ER（θ） - iГ（θ）/2, as a function of the scaling parameter θ, we find that for potential barrier scattering, the condition dГ（θI）/dθ = 0 uniquely determines the scaling parameter 8. The condition d ER （θR）/ dθ = 0 is merely a consequence of the Virial theorem and θI =θR is not a necessary condition for a resonance state. We also provide a harmonic approximation formMism for resonances in scattering over a potential barrier.

Study on fast calibration of a ULA's gain and phase error

Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA's gain and phase errors both in far and near fields are proposed. In the far field, using a single sound source without exact orientation, this method horizontally rotates the array exactly once, performs eigen value decomposition for the covariance matrix of received data, then computes the gain and phase error according to the formulas. In the near field, using the same single sound source, it is necessary to rotate the array horizontally at most three times, build equations according to geometric relations, then solve them. Using the formula proposed in this paper, spherical waves are modified into plane waves. Then eigen values decomposition is performed. These two calibration methods were shown to be valid by simulation and are fast, accurate and easy to use. Finally, an analysis of factors influencing estimation precision is given.

Some Remarks for the Relationships between the Generalized Bernoulli and Euler Polynomials

In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and deduce the corresponding special cases.

Tunnel personnel positioning method based on TOA and modified location-fingerprint positioning

To position personnel in mines, the study discussed in this paper built on the tunnel personnel positioning method on the basis of both TOA and location-finger print(LFP) positioning. Given non-line of sight(NLOS) time delay in signal transmission caused by facilities and equipment shielding in tunnels and TOA measurement errors in both LFP database data and real-time data, this paper puts forth a database data de-noising algorithm based on distance threshold limitation and modified mean filtering(MMF), as well as a real-time data suppression algorithm based on speed threshold limitation and MMF.On this basis, a nearest neighboring data matching algorithm based on historical location and the speed threshold limitation is used to estimate personnel location and realize accurate personnel positioning.The results from both simulation and the experiment suggest that: compared with the basic LFP positioning method and the method that only suppresses real-time data error, the tunnel personnel positioning methods based on TOA and modified LFP positioning permits effectively eliminating error in TOA measurement, making the measured data close to the true positional data, and dropping the positioning error:the maximal positioning error in measurements from experiment drops by 9 and 3 m, respectively, and the positioning accuracy of 3 m is achievable in the condition used in the experiment.

Application of uncertainty reasoning based on cloud model in time series prediction

Time series prediction has been successfully used in several application areas, such as meteoro-logical forecasting, market prediction, network traffic forecasting, etc. , and a number of techniques have been developed for modeling and predicting time series. In the traditional exponential smoothing method, a fixed weight is assigned to data history, and the trend changes of time series are ignored. In this paper, an uncertainty reasoning method, based on cloud model, is employed in time series prediction, which uses cloud logic controller to adjust the smoothing coefficient of the simple exponential smoothing method dynamically to fit the current trend of the time series. The validity of this solution was proved by experiments on various data sets.

Option Pricing Method in a Market Involving Interval Number Factors

The method for pricing the option in a market with interval number factors is proposed. The no-arbitrage principle in the interval number valued market and the rule to judge the reasonability of a price interval are given. Using the method, the price interval where the riskless interest and the volatility under B-S setting is given. The price interval from binomial tree model when the key factors u, d, R are all interval numbers is also discussed.