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1.
对于不定方程x3+y3+z3+w3=n,证明了:当n=18k±1或n=18k±7或n=18k±8或n=6k±3时,它有无穷多组整数解,这里k为任意整数.  相似文献   

2.
陈立强 《数学教学》2005,(12):35-37
文[1]给出1^3+2^3+3^3+…+n^3公式的四种求法,文[2]就文[1]的面积法再介绍三种构造方法.笔者深受启发,现再给出几种证明方法.  相似文献   

3.
谭雄姿 《数学教学》2005,(5):33-33,10
《数学教学》2004年第6期《导出公式1^3 2^3 3^3 … n^3的四种方法》一文.笔者有感于其中的第四种方法一面积法,现再介绍另外几种直观、简洁的方法.  相似文献   

4.
在教学公式1^3 2^3 3^3 … n^3=[1/2 n(n 1)]^2时,我们要求学生首先用数学归纳法证明,导出这个公式(为方便书写,我们记Sn^(k)=1^k 2^k 3^k … n^k)。  相似文献   

5.
文[1]的例14中,给出不定方程x3+y3+z3=x+y+z=3仅有4组整数解(x,y,z-)=(1,1,1),(-5,4,4),  相似文献   

6.
9+3     
《贵州教育》2013,(7):F0002-F0002
4月10日,为贯彻刘延东副总理3月30日-4月1日视察贵州时的讲话精神,省政府专门召开了“全省推进教育‘9+3’计划电视电话会议”,对我省教育“9+3”计划实施情况进行总结并安排部署下一步工作。  相似文献   

7.
对Fe3+和Fe2+氧化—还原能力的讨论通渭县一中李俊文杨晓东铁及其化合物的性质是中学化学教学中的重、难点之一。Fe3+和Fe2+的氧化—还原性也是历年高考的热点内容之一。由于学生对Fe3+、Fe2+、Fe的氧化—还原能力没有较为准确的认识,故常常判...  相似文献   

8.
一、问题的提出 一次性的师资培训体制已不能适应时代的发展需要。美、英、法、德、日、俄等国家正在系统地组合教师职前培养和在职进修,在提高新任教师学历层次的同时,努力完善在职教师的继续教育体制。联合国教科文组织《1999年世界教育报告—教师和变革世界中的教学工作》指出,“大多数国家的师范教育虽然仍把重点放在教师的前期培养上,教师的在职培训或进修在最近30年显得日益重要,某些国还有使用‘继续教育’一词。人们逐渐认识到,教学同其他职业一样,是一种‘学习的职业’,  相似文献   

9.
1+3+10=?     
当了十多年的班主任,我遇到不少脾气急躁的学生。这不,刚开学才几天,张钊与赵辉就小摩擦不断。早晨,我刚到办公室,就有学生来报告:“张钊与赵辉吵起来了。”我赶紧来到教室,看到他们俩正仇恨地瞪视着对方。我问怎么回事,张钊说:“赵辉在前面老是向后挤我的桌子。”赵辉急着辩解说:“不是我挤他的桌子,是他不停地踢我的凳子。”  相似文献   

10.
李娜 《中等数学》2012,(10):16-16
文[1]给出不定方程 x^3+y^3+z^3=x+y+z=3仅有4组整数解  相似文献   

11.
1 Introduction Inrecentyears ,high powerlaserdiodeshavebeenemployedaspumpingsourceswithaviewtodevelopcompactup conversionvisible lasersystems .Thefre quencyconversionofinfraredlighttovisiblelighthasbeenextensivelyinvestigatedforrare earthdopedcrystalsandg…  相似文献   

12.
Fluorescence properties of Eu^3 :Y2SiO5 have been investigated.Transitions between ^5D and ^7Fwere were studied with transmission spectra,fluorescence spectra,photoluminescence excitation(or absorption) spectra and site selective fluorescence spectra.The X-ray powder diffraction pattern of Eu^3 :Y2SiO5 shows that the crystal belong to monoclinic,and lattice‘s constants a,b,c and β arc obtaned by a simulation with the measured diffraction angles.  相似文献   

13.
This work investigated the microwave dielectric properties of A-site substitution by rare earth La3+in(Pb0.5Ca0.5)(Fe0.5Ta0.5)O3(PCFT) system.A single perovskite phase was obtained only when the doping content was 2%.Suitable La3+ doping improved microwave dielectric performances.Excessive La3+doping caused the formation of secondary phase,which resulted in the decreasing of permittivity εrand quality factor Qfvalues.Especially,when the doping content is 2%-5%,permittivity εrwas above 75 and Qfvalues were 6...  相似文献   

14.
Let Bnp={x ∈ Rn‖|x ‖p≤l} be the unit ball ofp norm in the n-dimensional normed space p. The formula for the volume of Bnp was obtained and its asymptotic properties were found out as n→∞and p→∞.  相似文献   

15.
This paper reports results of study on self-Q-switched Cr4+, Nd3+: YAG microchip lasers at 1.064 μm using a quasi-monolithic setup. Pulses with 6 to 60 ns wide (FWHM) and TEM00 mode produced under cw pumping with repetition rates ranging from 1.5 kHz to 23 kHz. Pulsed pumping yielded output pulses with repetition rates from 1Hz to several kHz and excellent pulse stability. A pulsed pumped microchip oscillator and flash lamp pumped amplifiers were used to set up a MOPA (Master Oscillator and Power Amplifier) system generating 225 kW pulses with 8 ns width. Project supported by BMBF, Germany; National Natural Science Foundation of China (NSFC, No. 69378019); the Key Foundation of Education Ministry of China.  相似文献   

16.
To investigate the effects of salt concentration and freeze-thaw (FT) on the first hydration shell of Zn2+ ions in Zn(NO32 aqueous solutions, extended X-ray absorption fine structure (EXAFS) spectroscopy was used to examine Zn K-edge EXAFS spectra of Zn(NO32 aqueous solutions with various concentrations before and after FT treatment. The influences of salt concentration and freeze-thaw on the structural parameters of the first hydration shell of Zn2+ ions, including hydration number, Zn-O distance and thermal disorder, were analyzed. The results show that Zn2+ ions have 3.2―6.8 nearest oxygen neighbors with the Zn-O distance being 0.202―0.207 nm. In highly concen-trated solutions, Zn2+ ions are hydrated with four water molecules in a tetrahedral form. The dilution of Zn(NO32 aqueous solutions increases the number of water molecules in the first hydration shell of Zn2+ ions to six with their octahedral arrangement. Both the hydration number in the first hydration shell of Zn2+ ions and the degree of thermal disorder increase when the FT treatment is operated in Zn(NO32 aqueous solutions.  相似文献   

17.
以木屑为原料,高温热解制备生物炭。以聚乙烯醇为粘结剂,采用混合法将生物炭与果胶复合,并负载磁性,经烘干定型制备果胶包覆的磁性生物炭材料(果胶@生物炭-Fe3O4)。采用扫描电镜(SEM)、X射线衍射(XRD)及N2吸附-脱附(BET)等方法对果胶@生物炭-Fe3O4进行表征,结合吸附实验分析其对Cu2+的吸附特性。结果表明,当生物炭、果胶、Fe3O4质量比为5:1:1,溶液pH值为6,吸附24 h,果胶@生物炭-Fe3O4对Cu2+吸附效果最好;二级动力学方程能较好地描述果胶@生物炭-Fe3O4对Cu2+的吸附过程,Freundlich模型能较好地拟合其吸附行为;SEM结果显示该材料具有不规则的孔隙结构;XRD分析显示纳米Fe3O4是其主要的晶体结构;BET测得其比表面积为25.654 m2·g-1,平均孔径为20.18 nm。  相似文献   

18.
The new intermetallic compound La3Cu3Bi4 was synthesized by arc melting method followed by annealing. The crystal structure refined using the Rietveld method and X-ray powder diffraction data showed to be Y3Au3Sb4 structure type with space group I-^43D (No.220). The unit cell parameters were a = 0.997 797(7) nm and V = 0.993 41(2) nm^3. The structure was characterized by covalent Cu-Bi4 tetrahedron, which formed three-dimensional network by sharing corners and La atoms separated in the space of Cu-Bi4 tetragon. The expansion of La3Cu3Bi4 studied by using low temperature X-ray diffraction showed to be positive expansion and diminished with the temperature rising.  相似文献   

19.
1IntroductionDiferentialequationswithturningpointsexistwidelyinmanyproblemsofmathematicsphysics,sotheseproblemsareveryimporta...  相似文献   

20.
1IntroductionThe synthesis and characterization of nano-struc-tured materials are the subject of intense current re-search.Hyperfineγ-Fe2O3particle with good perfor-mance,such as magnetism,catalysis,gas-sensitivityand so on,are widely applied in various fields[1].It ishighly significant to research and develop the methodsfor synthesis of nanometerγ-Fe2O3.With the development of nano-science and nano-technology,the methods for preparation ofγ-Fe2O3have been greatly progressed,for example,…  相似文献   

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