共查询到19条相似文献，搜索用时 203 毫秒
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2010青少年数学国际城市邀请赛 总被引：1，自引：1，他引：0
个人赛
一、填空题(每小题5分,共60分)
1.已知实数p、q、r满足
p+q+r=26,1/p+1/q+1/r=31.
则p/q+q/r+r/p+p/r+r/q+q/p=______. 相似文献
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Congruences for finite triple harmonic sums 总被引：1，自引：0，他引：1
FU Xu-dan ZHOU Xia CAI Tian-xin 《浙江大学学报(A卷英文版)》2007,8(6):946-948
Zhao (2003a) first established a congruence for any odd prime p>3, S(1,1,1;p)≡-2Bp-3 (mod p), which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S(α,β,γ;p) (mod p) is considered for all positive integers α,β,γ. We refer to w=α β γ as the weight of the sum, and show that if w is even, S(α,β,γ;p)≡0 (mod p) for p≥w 3; if w is odd, S(α,β,γ;p)≡rBp≥w (mod p) for p≥w, here r is an explicit rational number independent of p. A congruence of Catalan number is obtained as a special case. 相似文献
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设n是奇完全数,p是r的Euler因子.此时n=P4r+1m2,其中m,r是适合m≠0 (mod p)的正整数.本文证明了:τ(m2)≥15p4r+1,其中σ(m2)是m2的不同约数之和. 相似文献
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第一试 一、选择题(每小题7分,共42分) 1.已知p、q、r都是实数,且r q=6-4p 3p~2,r-q=5-4p p~2。则p、q、r之间的大小关系是( )。 相似文献
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文 [1 ]将命题 :对任何自然数n ,存在自然数m ,使得(2 - 1 ) n=m +1 -m作如下推广 :1 .对任何自然数p、n ,存在自然数m ,使得(p +1 -p) n=m +1 -m .2 .对任何自然数n、p、r,存在自然数m ,使得(p +r -p) n=m +rn-m .笔者将此命题再作如下推广 :1 .对于任何自然数n ,存在自然数m ,使得(2 - 1 ) -n=m +1 +m .2 .对于任何自然数p、n ,存在自然数m ,使得(p +1 -p) -n=m +1 +m .3 .对于任何自然数n、p、r,存在自然数m ,使得(p +r -p) -n=m +rn+mrn .下面证明推广 3 .证明 :因为 (p +r -p) n(p +r -p) -n=1 ,而由文 [1 ]知(p +r -p) n=m +rn-m .所… 相似文献
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《福建中学数学》2004年第5期《垂足三角形的几个有趣性质及其猜想》一文证明了下述命题:设△ABC为锐角三角形,△DEF是它的垂足三角形(AD,BE,CF是它的三条高线),记BC=a,CA=b,AB=c,EF=a0,FD=b0,DE=c0.△ABC,△DEF,△AEF,△BDF,△CDE的外接圆半径分别记作R,R0,R1,R2,R3;内切圆半径分别记作r,r0,r1,r2,r3;半周长分别记作p,p0,p1,p2,p3;面积分别记作?,?0,?1,?2,?3.则有r1+r2+r3≤3r/2,①②R1+R2+R3≤3R/2,p1+p2+p3≤3p/2,③?1+?2+?3≤3?/2,④⑤a/r1+b/r2+c/r3≥123,a/R1+b/R2+c/R3≥63,⑥⑦R1/r1+R2/r2+R3/r3≥6,a0/a+b0/… 相似文献
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设r是大于1的奇数,m是偶数,U_r和V_r是适合的整数,证明了:当r=3(mod4),m=2(mod4),m>r/Ⅱ且c是素数方幂时,方程口。a~x+b~y=c~x仅有正整数解(x,y,z)一(2,2,r). 相似文献
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设ｆ为超越亚纯函数，Ｒ（ｚ）为有理函数，Ｆ．Ｇｒｏｓｓ和Ｃ．ＣＹａｎｇ在［１］中猜测：当Ｒ（ｚ）分子，分母最高次数≥３时，Ｒ（ｆ）有无穷个不动点，并指出附加上条件Ｎ（ｒ，ｆ）＝Ｓ（ｒ，ｆ）时结论是成立的．Ｃ．Ｃ，Ｙａｎｇ在［２］中附加条件Ｎ（ｒ，ｆ）＝Ｓ（ｒ，ｆ）后证明了这一结论的正确性，本文减弱了这一附加条件。本文还改进了Ｃ．Ｃ．Ｙａｎｇ的另些结果和Ｇ．Ｐ．Ｂａｒｋｅｒ，Ａ．Ｐ．Ｓｉｎｇｈ关于微分方程亚纯解的两个结果． 相似文献
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陆法林 《洛阳师范学院学报》2003,22(5)
将中心势场中Schrdinger方程的径向波函数写成多项式函数与指数函数乘积的形式,即作变换u(r)=f(r)e~(p(r)),通过该变换可方便地得到多项式函数f(r)所满足的方程.以氢原子和谐振子为例加以讨论. 相似文献
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Daniel T. Barney 《The International Journal of Art & Design Education》2019,38(3):618-626
A/r/tography is often considered to be an arts and education practice‐based research methodology, but this author explores a/r/tography as a pedagogical strategy that has informed the author's artistic practice and pedagogical experiments. The author tracks his own journey of entering into an a/r/trographic world and where that entering has positioned him as an artist and educator and then moves on to speculate a possible arts education as his a/r/tography contorts into conceptual doings. Walking is used as a concept, as a process or method to generate more concepts, and as an art form with pedagogical potential within several undergraduate and one graduate course at the author's university. The author also investigates alongside or in concert with the courses he gives. The author equates artistic concepts, like walking, with theoretical and philosophical arguments, assertions and propositions. Artistic processes are equated with methods and methodological concerns, even though these systems of inquiry and knowing may be idiosyncratic in artistic inquiry. And finally, an art form can be understood in research terms as a type of research product or creation, that can be an event, performance, or a continuation of these as write ups or presentations, that are shared with the general or a particular public. 相似文献
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腾文 《常熟理工学院学报》2014,(2):28-31
设 Xn={1,2,…,n}（n＞3）并赋予自然序。 POIn为 Xn上的保序部分一一变换半群,引入一类新的POIn的子半群POIn,r ,讨论了半群POIn,r的生成秩,所得结果推广了有关文献中相应的结论。 相似文献
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给定非负整数r,s和t,简单图G=（V,E）的一个[r,s,t]-着色是从集合V∪E到色集{0,1,2…,k-1}的映射c,使得对任意相邻的两点vi,vj有︱c（vi）-c（vj）︱≥r,对任意相邻的两边ei,ej,有︱c（ei）-c（ej）︱≥s,对相关联的任意点vi和边ej,有︱c（vi）-c（ej）︱≥t.图G的[r,s,t]-色数r,s,t（G）定义为使得图G存在[r,s,t]-着色的最小的整数k.本文给出了参数r=0和r=t=1的[r,s,t]着色的几个结果. 相似文献
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We examined the beliefs about science teaching and learning held by elementary preservice teachers in a science methods course, comparing students who had experienced an inquiry-based physics course with those who had not. Students who had taken the physics course prior to the methods semester were better equipped to recognize and learn from inquiry and better able to apply an inquiry approach to their lesson planning. Students who were concurrently enrolled in the physics course began to revise their incoming beliefs about what it means for students to be active learners in science. The students with no experience in the inquiry-based physics course maintained their limited view that science teaching should be fun, with the teacher as teller and fun-maker. 相似文献