“作和比较法”与“作积比较法”

比较法是证明不等式的基本方法，但学生往往局限于“作差比较法”与“作商比较法”．另辟蹊径，可把比较法拓广到“作和比较法”及“作积比较法”，展现数学和谐之关、奇异之关．

一种积件系统的设计与实现

积件是针对课件的局限性而发展起来的新技术和新方法。文章提出了一个切实可行的积件CAI的系统模型和数据运行模式，并对系统的模型结构，教学资源和CAI教学软件的组织，应用以及教学平台软件的组成和功能进行了重点阐述。

关于12的神奇特征(续八)

本文给出数字12的神奇特征。

关于3的整数倍的神奇特征(续3)

上文续[2]给出了以3、6、9打头和结尾的数的神奇特征。本文将这一结果推广到3的整数倍。

关于数字3的另外神奇特征(续5)

本文继文[1],再给出数字3的另外神奇特征。

关于数字3.6.9的神奇特征(续2)

本文继文<1>.<2>.<3>,再给出3.6.9的新的特征。

关于6的整数倍的第三个神奇特征(续十)

本文给出6的整数倍更广的神奇特征。

关于12与18的整数倍的另一神奇特征(续十一)

本文继文[1],给出12的整数倍的另一神奇特征,又给出了18的整数倍的一个神奇特征。

关于自然数的两个神奇特征(续4)

本文给出自然数的两个特征,特别是继文[3]给出的以3的整数倍打头和结尾的数特征之后,又给出了以3的整数倍居中的数的同样特征。

关于6的整数倍的另一神奇特征(续九)

本文继文[4]给出的6的整数倍的另一种神奇特征。

关于自然数的另一种神奇特征(续十四)

本文继文[1],再给出自然数的另一神奇特征。

Investigation on the Accumulation of Heavy Metals from Organic Fertilizer in Soil and Plant

ObjectiveThis study aimed to investigate the accumulation of heavy metals from organic fertilizer in soil and plant. MethodThree plots were chosen in Shanghai suburb to measure the heavy metal accumulation by monitoring their concentrations in soil and plant after organic fertilizer was applied. We also analyzed the correlations of the heavy metals in soil and plants. Single-factor pollution index and Nemerow’s synthetical pollution index were adopted to evaluate the heavy metal contamination in soils. Moreover, how many years before the heavy metal accumulation will exceed the environmental capability if 45 t/hm 2 organic fertilizer is applied every year was also estimated in the present study. ResultThe rules of heavy metals’ accumulation in soil changed with the various soil characters and pH. The average concentrations of Pb, Cd and As in the tested plants exceeded the limits. The average concentration of Cu in the tested soil shared positive correlation with that in the tested plants. The average concentration of Pb in the tested soil was negatively correlated with that in the tested plant while the other heavy metals didn’t show the rule like that. Organic fertilizer application caused no obvious pollution to the soils. Cu would exceed the standard environmental capacity within 15 years if 45 t/hm 2 organic fertilizer is applied every year, while for Hg, it will be 2 000 years. ConclusionWhen the excessive organic fertilizer is put into the land, the heavy metals from organic fertilizer would accumulate in soil and plant. With continued excessive fertilization, the heavy metals especially Cu would exceed the stan- dard environmental capacity. More attention should be paid to the inputting amount of the organic fertilizer.

Application of molecular interaction volume model in separation of Pb-Sn-Sb ternary alloy by vacuum distillation

Based on the molecular interaction volume model （MIVM）, the activities of components of Pb Sn Sb ternary alloy were predicted. The vapo^liquid phase equilibrium of Pb-Sn-Sb alloy system was calculated using the activity coefficients of Pb Sn-Sb alloy system in the process of vacuum distillation. The calculated results show that the content of Sn in vapor phase increases with the increasing distillation temperature and content of Sn in liquid phase. However, the content of Sn in vapor phase is only 0.45% （mass fraction） while 97% in liquid phase at 1100 ℃, which shows that the separating effect is very well. Experimental investigations on the separation of Pb-Sn-Sb ternary alloy were carried out in the distillation temperature range of 1100-1300 ℃ under vacuum condition. It is found that the Sn content in vapor phase is 0.54% while 97% in liquid phase at 1100 ℃. Finally, the predicted data were compared with the experimental results showing good agreement with each other.

Overexpression of Proline Transporter Gene Isolated from Halophyte Confers Salt Tolerance in Arabidopsis

Proline is one of the most important and widespread osmolyte which functions in adaptation to adverse environmental stresses in many organisms. Also it is an important carbon and nitrogen resource in higher plants. Metabolism of proline has been elucidated in many plant species. However, transport of proline was poorly characterized although transport system plays an important role in proline distribution in different tissues. We isolated one full_length cDNA encoding proline transporter from the typical halophyte: Atriplex hortensis L. through cDNA library screening and 5′_RACE. The deduced amino acid sequence had eleven transmembrane domains, showed 60%-69% similarities to other ProTs and the gene was designated AhProT1. In the phylogenetic tree, higher plants' ProTs, e.g. AhProT1, showed more similar to ProP from microorganisms than ProT from mammalians. AhProT1 gene was transformed into Arabidopsis thaliana under 35S promoter. In MS medium containing [U_ 14 C] proline, AhProT1 + plants were able to accumulate much more radiolabeled proline in the roots than control plants. In MS medium containing different concentrations of NaCl, AhProT1 + plants could endure 200 mmol/L NaCl and keep development and biomass increase with proline supply, whereas control plants died back at 150 mmol/L NaCl.

Lecturers’Efforts in Building Rapport in the English-Medium Instruction(EMI)Context:Focus on the Use of Communication Strategies

Past studies reveal the prevalence of anxiety,coupled with low motivation and disengagement among students in English-medium instruction(EMI)programs.Given the detrimental impact these negative emotions can have on learning outcomes,it is imperative that teachers establish positive emotional rapport with their students.This study explores how experienced and highly rated EMI lecturers at a Chinese university’s overseas campus use communication strategies to build rapport with their students during interactive academic activities.It identifies the strategies used by these lecturers and examines how the strategies facilitate the teaching-learning process.The data,consisting of 10 hours of tutorials and 10 hours of supervisor-student supervision meetings,is analyzed using an adapted Conversation Analysis(CA)approach.The analysis reveals three types of communication strategies(CSs)frequently used by lecturers:back-channeling,codeswitching,and co-creation of messages.By employing these strategies,the lecturers established a strong rapport with the students,which created an encouraging and supportive learning environment.Consequently,this positive atmosphere facilitated students’learning of content knowledge through English.The findings of this study have implications for the training of lecturers who encounter difficulties in establishing rapport with multilingual students in the EMI setting.

Equivalence of crossed product of linear categories and generalized Maschke theorem

Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#＇_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.

Effects of Intercropping Patterns on Dry Matter Accumulation and Transportation of Maize(Zea mays L.) and Soybean[Glycine max(L.) Merrill]

[Objective] The aim was to discuss the group dry matter accumulation and economic benefits under the patterns of intercropping maize （Zea mays L.） with soy-bean [Glycine max （L.） Merril ]. [Methods] Zhengdan-958 and Luhuang-1 were used as the testing breeds to study the effects of intercropping patterns on dry matter accumulation and transportation of maize and soybean in Huang-huai-hai. [Results] For maize, the dry matter accumulation amounts per hectare of intercropping was significant higher than that of the monoculture patterns, especial y after silking, when it reached extremely level; while for soybean, the dry matter accumulation amounts before flowering and after flowering of monocropping were al significantly higher than that of the intercropping patterns. For both maize and soybean, the transfer amounts of monocropping were al significantly or extremely significantly higher than that of intercropping; and the transfer ratio of maize intercropping was 0.59% higher than that of maize monocropping, while for soybean, it was 4.74% higher. Fitted dry matter accumulation with Logistic equation, it showed that the difference in maximum dry matter accumulation rate between maize monocropping and intercropping reached significant level, while for soybean, the maximum dry matter accumulation rate and its appearance time as wel as duration time between intercropping and monocropping were al reached significant level. The total land equivalent ratio of intercropping was 1.30. From yield and output value, the total yield of intercropping were 10.97 t/hm2, 0.64% and 326.85% higher than monocropping of maize and soy-bean, respectively. The total output value of intercropping was 25 796.23 yuan/hm2, respectively 12.67% and 104.68% higher than of maize and soybean monocropping. [Conclusion] The study lays a basis for improving grain yield and economic benefits.

Zn Accumulation and Subcellular Distribution in the Zn Hyperaccumulator Sedurn alfredii Hance

Zn accumulation and subcellular distribution in leaves of the hyperaccumulating ecotype （HE） and non-hyperaccumulating ecotype （NHE） of Sedum alfredii Hance were studied using radiotracer and gradient centrifugation techniques. Leaf Zn accumulation in the HE of S. alfredii was 18.5-26.7 times greater than that in the NHE when the plants were grown at 1-500μmol Zn L-1. Leaf section uptake of 65Zn was highly dependent on external Zn levels. Greater 65Zn uptake in HE was noted only at external Zn levels 〉 100μmol L-1. Zinc subcellular distribution in the leaves of the two ecotypes of S. alfredii was： cell wall 〉 soluble fraction 〉 cell organelle. However, more Zn was distributed to the leaf cell wall and soluble fractions for HE than for NHE. In the leaf of HE, 91%-94% of the Zn was found in the cell walls and the soluble fraction and only 6%-9% Zn was distributed in the cell organelle fraction. For NHE, about 20%-26% Zn was recovered in the cell organelle fraction. In stems, Zn distribution to the ceil wail fraction was approximately two fold greater in the HE than that in the NHE. For the hyperaccumulating ecotype of S. alfredii, the cell wall and the vacuole played a very important role in Zn tolerance and hyperaccumulation.

Heavy Metal Accumulation in Plants on Mn Mine Tailings

The Xiangtan Manganese (Mn) Mine in the middle of Hunan Province, China, has been mined since 1913 with mine tailings including excavated wastes, wastewater, and smelting wastes. A survey was conducted on the Mn mine tailing soils and eight plants on the Mn mine tailings. The concentrations of soil Mn, Pb, and Cd and the metal-enrichment traits of these eight plants were analyzed simultaneously. Exceptionally high concentrations of these three metals were found in the soils, especially on the tailing dam. Each plant investigated in this study accumulated the three heavy metals, but no hyperaccumulator of these metals was found. However, analysis indicated that Poa pratensis Linn., Gnaphalium affine D. Don, Pteris vittata L., Conyza canadensis (L.) Cronq., and Phytolacca acinosa Roxb. possessed specially good metal-enrichment and metal-tolerant traits. P. pratensis, G. affine, and P. vittata were Pb-tolerant plants; and C. canadensis, P. pratensis, and G. affine were Cd-tolerant plants. P. acinosa had a great tolerance to Mn. and it was a valuable plant for on-site phytoremediation. Phragmites communis Trin. was found to have high metal tolerance and economic benefit as a raw material for paper and should be considered for soil remediation. G. affine and C. canadensis had excessive accumulation of Mn and could be useful in phytoremediation. However, although P. pratensis was a good accumulator, it was not a suitable plant for soil remediation because its biomass was too little.

N Accumulation and Translocation in Four Japonica Rice Cultivars at Different N Rates

Developing high-yielding rice(Oryza sativa L.)cultivars depends on having a better understanding of nitrogen(N) accumulation and translocation to the ear during the reproductive stage.Field experiments were carried out to evaluate the genetic variation for N accumulation and translocation in different Japonica rice cultivars at different N rates and to identify any relationship to grain yield in southeast China.Four Japonica cultivars with similar agronomic characteristics were grown at two experimental sites in 2004 with three N rates of 0,60,and 180 kg N ha^(-1).Dry weights and N contents of rice plants were measured at tillering,initiation,anthesis,and maturity.Grain yields exhibited significant differences (P<0.05)among the cultivars and N application rates.Increasing N rates improved N uptake at anthesis and maturity in all four cultivars(P<0.05).N translocation from vegetative organs to the grains increased with enhanced N rates (P<0.05).N translocation to the grains ranged from 9 to 64 kg N ha^(-1)and N-translocation efficiency from 33% to 68%. Grain yield was linear to N uptake at anthesis(r^2=0.78^(**))and N translocation(r^2=0.67^(**)).Thus,cultivars with a high N uptake at anthesis,low residual N in the straw at maturity,and appropriate low N fertilizer supply in southeast China should efficiently increase N-recovery rate while maintaining grain yield and soil fertility.