例谈小偏方在数学教学中的应用

在数学教学中,部分高中学生对高中数学内容感到无趣、枯燥.面对这个现实,文章从教学过程出发,总结和归纳一些教学方法上的“小偏方”以实例呈现的方式,阐述“小偏方”在数学教学中的应用,起到治疗“大病”的效果.

小偏方

果蔬汁治疗老慢支;

小偏方让你不再做特“困”生（下）

8．自习课，一坐到书桌前做作业就犯困？偷偷说，听歌吧。一定要听节奏较快、歌词又昂扬向上的。千万别听低吟浅唱的小情歌，它们让你不是思绪万千就是哈欠连天。

小偏方让你不再做特“困”生（上）

有道是“春困秋乏夏打盹，睡不醒的冬三月”。夏日炎炎，知了在树梢不停地叫，仿佛在奏一首催眠曲。慵懒的阳光倾洒下来，微风轻抚，不知不觉间带来了一丝丝倦意。很多同学都在这个季节成为了特“困”生。小编特意为同学们总结了各种偏方，希望同学们从此摆脱特“困”生的称号。

Correlation Analysis between Quality Characteristics and Fruit Mineral Element Contents in 'Fuji' Apples

[Objective] The aims were to explore the relationship between the contents of fruit mineral elements and quality features of the ＇Fuji＇ apple, screen major mineral elements of the fruit affecting fruit quality features, and set up optimum proposals of fruit mineral elements for good fruit qualities, so as to provide a theoretical basis for the reasonable orchard soil and foliar fertilizer applications to increase fruit quality and reduce the physiological diseases related to the ＇Fuji＇ apple. [Methods] The fruit mineral elements and quality indicators of ＇Fuji＂ apples were in- vestigated and analyzed, which were collected from the 153 commercial apple or- chards of ＂Fuji＇ apple located in 51 counties. The variable importance for projection （VlP） of partial least squares regression （PLS） method was used to analyze the model effect and weight analysis impact of the fruit mineral element contents to fruit quality, screen out major factors of fruit mineral elements influencing the different fruit qualities, and set up the regression equation of the fruit qualities and major fruit mineral elements. Linear programming was used to obtain optimum proposals of the fruit mineral elements to achieve good ＇Fuji＇ apple qualities. [Results] The mineral elements content and quality characteristics in ＂Fuji＇ apple fruit had great differences in the different produce regions in which the maximum content of nitro- gen, iron, zinc and boron in the ＇Fuji＇ fruit were12.06, 6.17, 7.7, and 10.08 times greater than the minimum respectively, and the differences for titratable acid and the SSC/TA ratio were 2.33 and 2.16 times respectively. The correlation analysis between the fruit mineral element contents and qualities showed that the nitrogen content of fruit had a significantly negative correlation with the soluble solid content, SSC/TA ratio and red color area, while the calcium and iron contents in the fruit were in significantly positive correlation with the soluble solid content and SSC/TA ratio. The model effect and weight analysis showed that the content of nitrogen and iron in the fruit had a greater influence on the integral fruit quality, followed by phosphorus, potassium and calcium. The variable importance for projection （VlP） technology of PLS found that the mean fruit weight was primarily affected by nitro- gen, phosphorus and potassium, and the soluble solid was primarily affected by ni- trogen, calcium and iron, while the red color area was primarily affected by nitro- gen, potassium, calcium, iron and zinc. The regression equation between fruit quality and mineral element contents showed that the mean fruit weight had a greater pos- itive effect coefficient with the content of phosphorus and potassium, and a greater negative effect coefficient with the content of nitrogen in the fruit. Moreover, the sol- uble solid had the largest negative effect coefficient with nitrogen and largest posi- tive effect coefficient with calcium and iron in the fruit. [Conclusion] The maximum content of soluble solid and titratable acid were 1.5 times more than the minimum, and nitrogen, iron, zinc and boron were 6 times more than in the ＇Fuji＇ apple fruit in the different produce regions. Therefore, it is a key technological measure to improve the overall qualities of the ＂Fuji＇ apple by decreasing the content of nitrogen, and increasing the contents of iron, phosphorus, potassium and calcium in the fruit.

Quality prediction and control of tube hollow

The quality prediction of tube hollow model based on the variance staged multiway partial least square (MPLS) method was proposed.The key aspects of staged decomposition of the productive data,calculation of the variance value,modeling,and on-lined prediction in the variance-staged MPLS method were introduced.Based on the model,iterative optimal control method was used for quality control of tube hollow.The experimental results show that the obvious benefits of this method are low maintenance cost,good real time function,high reliability precision,and practical application to on-line prediction and optimization on the quality of tube hollow.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance Under the General Linear Model

Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.

Influence of process parameters on deep drawing of AA6111 aluminum alloy at elevated temperatures

To gain a deep insight into the hot drawing process of aluminum alloy sheet, simulations of cylindrical cup drawing at elevated temperatures were carried out with experimental validation. The influence of four important process parameters, namely,punch velocity, blank holder force(BHF), friction coefficient and initial forming temperature of blank on drawing characteristics(i.e.minimum thickness and thickness deviation) was investigated with the help of design of experiments(DOE), analysis of variance(ANOVA) and analysis of mean(ANOM). Based on the results of ANOVA, it is shown that the blank holder force has the greatest influence on minimum thickness. The importance of punch velocity for thickness deviation is 44.35% followed by BHF of 24.88%,friction coefficient of 15.77% and initial forming temperature of blank of 14.995%. After determining the significance of each factor on forming characteristics, how the individual parameter affects characteristics was further analyzed by ANOM.

Optimizing process of preparing artificial-similar material for rocky slope with uniform formula design

The determination of material formula needs try-and-error experiment,and consumes large amount of time and fund.In order to solve the problem,a comprehensive method is established,via the experiment of artificial-similar material formula of a mine slope.We controlled the samples by the compactness,and arranged the formula of the test group with the method of the uniform formula experiment.The physical and mechanical parameters of these samples were analyzed using the method of the partial least-squares regression(PLS).And a mathematical model of the indexes of physical and mechanics parameters relating to the factors of formulation constituents was established eventually.We used the model to analyze the effect of each formulation constituent on physical and mechanics parameters of samples.The experiment results and analysis illustrates that1)in the formulation of similar material,the effect of raw materials on the internal friction angleφand cohesion C is opposite;2)The method can highly facilitate the process of the of preparing artificial-similar materials,more economic and effective.

A Novel Two-step Frequency Offset Estimator for OFDM

Based on an orthogonal frequency division multiplexing(OFDM) training symbol with L identical parts, a novel carrier frequency offset (CFO) estimator is proposed for OFDM systems. The CFO is estimated in two steps, fine estimate and coarse estimate. In the first step, the fine estimation is performed based on the principle of minimum variance. However, the fine estimation has ambiguity since its estimate range is limited. In the second step, the coarse estimation is obtained, which results in a larger estimate range but less precision. Using the coarse estimation, the ambiguity of fine estimation is resolved. To fully use the correlation among L identical parts, the fine estimation resolved the ambiguity and the coarse estimation are optimally combined to obtain the final estimation. Furthermore, the estimation variance of the proposed method is derived. Simulation results demonstrate that the novel two-step estimator outperforms the conventional two-step estimator in terms of estimate performance and computational complexity.

Research on Determination of Nitrogen Content in Petroleum Using Mid-infrared Spectroscopy

Nitrogen content is an important parameter for petroleum refining processes. The combined use of mid-infrared attenuated total reflection spectroscopy and multivariate calibration allows accurate determination of nitrogen content in petroleum and its products. The calibration models of nitrogen content in crude oils have been established by partial least squares (PLS) method. The results predicted by this method were very close to those determined by standard methods. Compared with standard methods, this method is provided with advantages such as high-speed, simplicity and good-repeat- ability without any needs for pretreatment.

Determination of Vitamins B2,B3,B6 and B7 in Corn Steep Liquor by NIR and PLSR

Corn steep liquor(CSL) is an important raw material that has high nutritional value and serves as a nitrogen source.Biotin in CSL is especially of great importance to fermentation.In order to develop a fast,versatile,cheap,and environmentally safe analytical method for quantifying vitamins B2(VB2),B3(VB3),B6(VB6) and B7(VB7) in CSL,the near-infrared spectroscopy(NIR) measurements of 66 samples(22 batches) of CSL were analyzed by partial least-square regression(PLSR).Multivariate models developed in the NIR regions showed good predictive abilities for VB2,VB3,VB6 and VB7.Results confirmed the probability of the multivariate spectroscopic approach as a replacement for expensive and time-consuming conventional chemical methods.

Mathematical Programming Method as a Means of Calibration of NIR Analyzers

In addition to the conventional methods of the calibration model construction, such as PCR （principal components regression） and PLS （partial least-squares）, a MPM （mathematical programming method） is developed and proposed for practical use in NIR analyses of agricultural and food products. The proposed method involves the mathematical programming techniques to seek the regression coefficients for the calibration model calculation. It is based on the optimization theory used for finding the extremum of the objective function in the given domain of a vector space and employs the method of the complementarity problems solving. The MPM algorithm is described in detail. The MPM was tested on an InfraLUM FT-10 NIR analyzer of Lumex company with samples of dry milk （for fat）, corn （for protein） and rye flour （for moisture）. The obtained results show that the MPM can be used for constructing multivariate calibrations with the qualitative characteristics superior over those of the classical PCR and PLS methods of analysis.

Statistical Methods for Classification of Medicinal Plants

Statistical classification methods are frequently applied to analyze metabolomics data, especially from medicinal plants. Combined with variable selection techniques, we are able to identify marker candidates, which can be used to discriminate the group to which unknown subjects belong. After preprocessing, such as outlier checking, normalization, missing value imputation and transformation, we then mainly utilized four novel classification methods： RF （random forest）, NSC （nearest shrunken centroid）, PLS-DA （partial least square discriminant analysis） and SAM （significant analysis ofmicroarrays）. Each method has its own device to measure the importance of single metabolite, so that, it is probable to choose highly ranked metabolites, which show the best prediction accuracy. Adapting above strategy, we have successfully analyzed several kinds of metabolomics data including Panax ginseng, Lespedeza species, Anemarrhean asphodeloides and Gastrodia elata.

The Influence of Spiritual Values on Work Motivation, Management Control, and Quality of Financial Information on IFIs in Indonesia

This study aims to investigate the influence of spiritual values on work motivation, management control, and the quality of financial information on Islamic financial institutions （IFIs） in Indonesia. Spiritual values are measured using four reflexive indicators, namely, Shiddiq, Fathanah, Amanah, and Tabligh. Work motivation is formed by four formative indicators, namely, compensation, recognition, work experience, and openness. Management control variable is formed by four formative indicators, namely, planning, implementing, evaluating, and monitoring, and finally, the quality of financial information is manifested in four reflexive variables, namely, relevant, comparable, understandable, and consistent. Data are collected through questionnaires with 125 respondents as samples from three types of IFIs, such as Islamic banking, Islamic pawnshop, and Islamic insurance in Indonesia. Methods of data analysis include the use of partial least squares （PLS） to analyze the influence of spiritual values on work motivation, management control, and quality of financial information. The results of this study showed that the manifestation of spiritual values in IFIs is able to influence the quality of financial information through the media as motivation and management control, but directly spiritual values are not able to influence the quality of financial information. While work motivation and management control significantly influence the quality of financial information.

治便秘

炙甘草、柏子仁、郁李仁、玄参各10克，生白芍、生麦芽各15克水煎分2次温服，每日1剂。

Superiority of empirical Bayes estimator of the mean vector in multivariate normal distribution

In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator(MVUE) and a revised James-Stein estimators(RJSE) are investigated respectively under mean square error(MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.

Wavelet solutions of Burgers' equation with high Reynolds numbers

A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.

Least-squares reverse-time migration for reflectivity imaging

A least-squares reverse-time migration scheme is presented for reflectivity imaging. Based on an accurate reflection modeling formula, this scheme produces amplitude-preserved stacked reflectivity images with zero phase. Spatial preconditioning, weighting and the Barzilai-Borwein method are applied to speed up the convergence of the least-squares inversion. In addition, this scheme compensates the effect of ghost waves to broaden the bandwidth of the reflectivity images. Furthermore, roughness penalty constraint is used to regularize the inversion, which in turn stabilizes inversion and removes high-wavenumber artifacts and mitigates spatial aliasing. The examples of synthetic and field datasets demonstrate the scheme can generate zerophase reflectivity images with broader bandwidth, higher resolution, fewer artifacts and more reliable amplitudes than conventional reverse-time migration.

Applications of differential algebra for computing Lie algebras of infinitesimal CR-automorphisms

We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C9by employing differential algebra computer tools—mostly within the Maple package DifferentialAlgebra—in order to automate the handling of the arising highly complex linear systems of PDE’s.Before treating these new examples which prolong previous works of Beloshapka,of Shananina and of Mamai,we provide general formulas for the explicitation of the concerned PDE systems that are valid in arbitrary codimension k 1 and in any CR dimension n 1.Also,we show how Ritt’s reduction algorithm can be adapted to the case under interest,where the concerned PDE systems admit so-called complex conjugations.