随机变量和、差、积、商的相关分析(待续)

在水文水资源分析计算中，为了求得形式上比较高的相关系数，常将两变量作和、差、积、商的变换，这就造成了具有共同成份的两组随机变量的“假相关”。对此，从基本的数学原理出发，对应统计数学中的原点矩及中心矩，提出相关因数及相关矩数的概念，导出了随机变量和、差、积、商变换后的相关系数计算公式，进一步分析了变量变换后相关系数的特性，认为“假相关”的作法并非均能得到较高的相关系数，有时适得其反，应予引起注意和重视。

正余弦和差化积公式的向量证明

文[1]利用面积相等关系给出了正弦和差化积公式的一种构造证法,本文再给出正余弦和差化积公式的向量证法,供参考.

谈数列拆项求和

数列求和问题是初等数学重要内容之一。数列求和的题目,往往形式比较复杂,不少学生束手无策。数列求和的方法可直接利用等差、等比数列求和公式来求;或通过某些方法(如加、减、拆、错位相减……等方法)把某些不是等差、等比数列的数列“转化”为等差等比数列,来求和;对某些不易转化为等差、等比数列的数列“拆项求和法”是一种最常用的方法。本文仅对中学数学常见的几种类型的拆项求和作一些介绍。

等比数列求和公式在数学竞赛题中的应用

在国际国内数学竞赛题中,一些求值题,证明题以及一些初等数论问题,因式分解问题,可通过初等变换转化为等比数列求和问题来解决。本文谈一下等比数列求和公式在以上几方面的应用。一求值例1 求cos5°+cos77°+cos149°+cos(?)21°+cos293°的值。分析若利用和差化积公式来解决此题,难度太大,不易找到头绪,但可通过复数转化为等比数列求和问题来解决。

两个互为相反数之和为零的应用

两个互为相反数之和为零的应用孙殿华两个互为相反数之和为零，这是初中一年级的学生要掌握的简单知识。它是合并同类项的特殊情况。但对于一些特殊的多项式的化简及三角求和，这却是特殊的技巧。并且，运用互为相反数之和为零，在用初等方法求级数之和、用定义求定积分等...

Climatic Factors for Limiting Northward Distribution of Eight Temperate Tree Species in Eastern North America

Eight temperate deciduous tree species, Acer rubrum L., A. saccharinum L., A. saccharum Marsh., Belluta alleghaniensis Britton., Fraxinus nigra Marsh., Quercus rubra L., Titia americana L., and Ulmus americana L. in eastern North America, were selected to explore relationship between the northward distribution of temperate tree species and climatic factors. For each species, more than 30 sites at their north limits of distribution were obtained from their distribution maps, and 11 climatic indices at the north limits were computed. The standardized standard deviation (SD) method, which compares the magnitude of variance of climatic indices, was used to detect which climatic parameter was the most important for explaining northward distribution of these species. We presume that the climatic parameter that has the smallest variance at the north limit would be assigned as the dominant climatic factor for limiting the distribution of this species. The results derived from the standardized SD method indicated that the SD value of warmth index (WI) and/or annual biotemperature (ABT) were the smallest among the 11 climatic indices. Since both WI and ABT represent growing season temperature, it suggested that growing season temperature was the most important climatic factor for explaining the northward distribution of these temperate tree species. The relationships between several climatic indices, WI, coldness index (CI), annual precipitation (AP), annual range of temperature (ART) and humid/arid index were also analyzed. As a result, at the north limits of all these species, both WI and CI decreased with an increase of AP, and CI increased with an increase of ART. Besides growing season temperature, precipitation and climatic continentality also have influence on the northward distribution of the temperate trees in eastern North America.

石油期货市场套期保值与风险规避

套期保值是在现货市场和期货市场对同一种类的商品同时进行数量相等但方向相反的买卖活动,它能在一定程度上将商品价格锁定在期货合约的价格水平上,从而可以规避市场价格波动带来的风险。目前利用套期保值已成为国际石油公司规避经营风险通行的做法。但套期保值操作本身也存在经营风险,即基差风险。因此,国内石油公司既要积极认识套期保值业务的作用,逐步开展以套期保值为惟一目的的石油期货贸易,同时还必须加强风险意识和控制,加强对石油期货业务的管理与市场研究,并从体制上、制度上杜绝巨额损失现象的出现。

Relations Between Red Edge Characteristics and Agronomic Parameters of Crops

The hyperspectral reflectance of the canopy and the leaves on the main stemfor six varieties, two each of rice corn, and cotton crops, were measured at different growth stageswith an ASD FieldSpec Pro FR^(TM) to analyze red edge characteristics forleaf area indices (LAI),aboveground biomass, as well as the chlorophyll, carotenoid, and nitrogen content, emphasizingcomparative differences on the red edge parameters. The results showed a 'double peak' phenomenonfor the red edge of the canopy spectra but not for the leaves. There were 'increase' and 'decrease'change rules for the red edge position, lambda_r, the red edge slope, D lambda_r, and the red edgearea, S_r, of the canopy spectra for all 3 crops with a 'blue shift' for lambda_r of the leafspectra for all 3 crops as the development stages progressed. For rice, corn, and cotton the LAI andfresh leaf mass had highly significant correlations (P < 0.01) to the red edge parameters lambda_r,D lambda_r, and S_r of their canopy spectra. Additionally, for all crops the chlorophyll-a,chlorophyll-b, total chlorophyll, and carotenoid content of the leaves all had highly significant (P< 0.01) correlations to their lambda_r. For rice, the nitrogen content of the leaves in g kg^(-1)and phytomassfor a unit area of land in g m^(-2) also had a highly significant (P < 0.01)correlation to lambda_r, D lambda_r lambda_r, and S_r of the canopy spectra.

The Precise Finite Difference Method for Seismic Modeling

D seismic modeling can be used to study the propagation of seismic wave exactly and it is also a tool of 3-D seismic data processing and interpretation. In this paper the arbitrary difference and precise integration are used to solve seismic wave equation, which means difference scheme for space domain and analytic integration for time domain. Both the principle and algorithm of this method are introduced in the paper. Based on the theory, the numerical examples prove that this hybrid method can lead to higher accuracy than the traditional finite difference method and the solution is very close to the exact one. Also the seismic modeling examples show the good performance of this method even in the case of complex surface conditions and complicated structures.

Estimating extreme temperature differences in steel box girder using long-term measurement data

The extreme temperature differences in fiat steel box girder of a cable-stayed bridge were studied.Firstly,by using the long-term measurement data collected by the structural health monitoring system installed on the Runyang Cable-stayed Bridge,the daily variations as well as seasonal ones of measured temperature differences in the box girder cross-section area were summarized.The probability distribution models of temperature differences were further established and the extreme temperature differences were estimated with a return period of 100 years.Finally,the temperature difference models in cross-section area were proposed for bridge thermal design.The results show that horizontal temperature differences in top plate and vertical temperature differences between top plate and bottom plate are considerable.All the positive and negative temperature differences can be described by the weighted sum of two Weibull distributions.The maximum positive and negative horizontal temperature differences in top plate are 10.30 ℃ and -13.80 ℃,respectively.And the maximum positive and negative vertical temperature differences between top plate and bottom plate are 17.30 ℃ and-3.70 ℃,respectively.For bridge thermal design,there are two vertical temperature difference models between top plate and bottom plate,and six horizontal temperature difference models in top plate.

Robust range-parameterized cubature Kalman filter for bearings-only tracking

In order to improve tracking accuracy when initial estimate is inaccurate or outliers exist,a bearings-only tracking approach called the robust range-parameterized cubature Kalman filter(RRPCKF)was proposed.Firstly,the robust extremal rule based on the pollution distribution was introduced to the cubature Kalman filter(CKF)framework.The improved Turkey weight function was subsequently constructed to identify the outliers whose weights were reduced by establishing equivalent innovation covariance matrix in the CKF.Furthermore,the improved range-parameterize(RP)strategy which divides the filter into some weighted robust CKFs each with a different initial estimate was utilized to solve the fuzzy initial estimation problem efficiently.Simulations show that the result of the RRPCKF is more accurate and more robust whether outliers exist or not,whereas that of the conventional algorithms becomes distorted seriously when outliers appear.

A Model for Estimating Total Forest Coverage with Ground-Based Digital Photography

Vegetation fractional coverage (VFC) is one of the key indicators of vegetation distribution. In the work a measurement-based model was developed to derive total forest VFC (TG) as well as the VFC of trees (T) and shrub-grasses (G) separately in a subtropical forest area in Nanjing, China. Both upward and downward photographs were taken with a digital camera in 72 quadrats (10 m × 10 m each). Fifteen models were established and validated. Models jointly using both T and G performed better than those using the T and G separately. The best model, TG = T + G- 1.134 × T × G- 0.025 (R2 = 0.9115, P < 0.01, root mean squared error = 0.0789), is recommended for application. This model provides a good way to obtain total forest VFC values through taking tree and shrub-grass photos on ground below tree canopy rather than above tree canopy.

Estimating van Genuchten Model Parameters of Undisturbed Soils Using an Integral Method

The van Genuchten model is the most widely used soil water retention curve （SWRC） model. Two undisturbed soils （clay and loam） were used to evaluate the accuracy of the integral method to estimate van Genuchten model parameters and to determine SWRCs of undisturbed soils. SWRCs calculated by the integral method were compared with those measured by a high speed centrifuge technique. The accuracy of the calculated results was evaluated graphically, as well as by root mean square error （RMSE）, normalized root mean square error （NRMSE） and Willmott＇s index of agreement （1）. The results obtained from the integral method were quite similar to those by the centrifuge technique. The RMSEs （4.61 ×10^-5 for Eum-Orthic Anthrosol and 2.74 × 10^-4 for Los-Orthic Entisol） and NRMSEs （1.56 × 10^-4 for Eum- Orthic Anthrosol and 1.45 ×10^-3 for Los-Orthic Entisol） were relatively small. The 1 values were 0.973 and 0.943 for Eum-Orthic Anthrosol and Los-Orthic Entisol, respectively, indicating a good agreement between the integral method values and the centrifuge values. Therefore, the integral method could be used to estimate SWRCs of undisturbed clay and loam soils.

GIS-based Numerical Modelling of Debris Flow Motion across Three-dimensional Terrain

The objective of this study is to incorporate a numerical model with GIS to simulate the movement, erosion and deposition of debris flow across the three dimensional complex terrain. In light of the importance of erosion and deposition processes during debris flow movement, no entrainment assumption is unreasonable. The numerical model considering these processes is used for simulating debris flow. Raster grid networks of a digital elevation model in GIS provide a uniform grid system to describe complex topography. As the raster grid can be used as the finite difference mesh, the numerical model is solved numerically using the Leap-frog finite difference method. Finally, the simulation results can be displayed by GIS easily and used to debris flow evaluation. To illustrate this approach, the proposed methodology is applied to the Yohutagawa debris flow that occurred on 2oth October 2010, in Amami- Oshima area, Japan. The simulation results that reproduced the movement, erosion and deposition are in good agreement with the field investigation. The effectiveness of the dam in this real-ease is also verified by this approach. Comparison with the results were simulated by other models, shows that the present coupled model is more rational and effective.

Adaptive Parameter Selection for Total Variation Image Deconvolution

In this paper,we propose a discrepancy rule-based method to automatically choose the regularization parameters for total variation image restoration problems. The regularization parameters are adjusted dynamically in each iteration.Numerical results are shown to illustrate the performance of the proposed method.

Borehole-GPR numerical simulation of full wave field based on convolutional perfect matched layer boundary

The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.

Correlation of Shear Viscosity of Nanofluids Using the Local Composition Theory

In this study,a new method is presented to correlate the shear viscosity of nanofluids by local composition theory.The Eyring theory and nonrandom two-liquid(NRTL)equation are used for this purpose.The effects of temperature and particle volume concentration on the viscosity are investigated.The adjustable parameters of NRTL equation are obtained by fitting with experimental data.The calculated shear viscosities for nanofluids of CuO/water with 29 nm particle size,Al2O3/water with two different particle diameters,36 nm and 47 nm,and CuO/(ethylene glycol,water)are compared with experimental data and the average absolute deviation(AAD)is 1.2%,while the results from some conventional models yield an AAD of 190%.The results of this study are in excellent agreement with experimental data.

Improved Cotes Formula and Error Analysis

The truncation error of improved Cotes formula is presented in this paper. It also displays an analysis on convergence order of improved Cotes formula. Examples of numerical calculation is given in the end.