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1.
设d(x)表示实数x的十分位数,I为正奇数,n,k为正整数,f(n,k,I)=√n2+nl+k.本文证明了,当n≥c(k)=5k-(5t2+6t+1)时,d(f(n,k,I))=5. 相似文献
2.
考虑定义在整点格网Ld上的参数为p的上临界Bernoulli渗流,研究无穷大开簇上构型的发生情况.用Λn表示一个给定的构型P在限制于框B(n)=[-n,n]d中的无穷大开簇上发生的次数,得到了关于Λn的强大数律和中心极限定理. 相似文献
3.
毕达哥拉斯定理又称勾股定理或商高定理,该定理称若x和y为一直角三角的两直角,z为其斜边,则x2 y2=z2三条边长均为正整数的直角三角形我们称为毕达哥拉斯三角形,对毕达哥拉斯三角形(以下简称三角形)的探讨就等同于求方程x2 y2=z2(A)的所有正整数解,下面我们就分步讨论:一、三角形的基本解首先,我们不妨假设x与y互,如若它们不互素,即(x,y)=d,则因x2 y2=z2得d z,故有并且我们还知道=1,这就说明,欲求方程(A)的任意解,只要先找出使它左端两项互素的一组解,然后再乘上一个适当的因子即可,于是,只要求出x2 y2=z2的满足(x.y)=的所有解,就能求出x2 y… 相似文献
4.
目前教科书中针对1∞型未定式极限普遍采用的是两种求法:(1)化为重要极限limlx→∞(1+1/x)x=e的形式来求;(2)化为0/0型未定式再根据罗必达法则来求.但这两种方法不但要求学员有非常扎实的基础知识,而且还要掌握一些比较高超的运算技巧才易于学会.本论文给出一种新颖求法,此方法既简单又容易掌握,同时对我们的经济工作(譬如连续复利的计算问题)也带来了方便. 相似文献
5.
沈忠民 《中国科学院研究生院学报》1986,(1)
本文研究了高次多项式系统的极限环数目。如果记 P_n 表示次数不大于 n 的实系数多项式全体,我们定义多项式系统(dx)/(dt)=f(x,y)(dy)/(dt)=g(x,y)(1)的 Hilbert 数 H(n)如下H(n){系统(1)的极限环数目}则有定理:如果 p,q 为任意正整数,它们满足 p|q,则(H(q-1))/q~2≥(H(p-1))/p~2 相似文献
6.
定义:函数f(x)如果对其定义域中任意的x1、x2都有如下不等式成立,即f(x1+x2/2)≤f(x1)+f(x2)/2则称f(x)为下凸函数,等号当且仅当x1=x2时成立.如果总有f(x1+x2/2)≥f(x1)+f(x2)/2则称f(x)为上凸函数,等号当且仅当x1=x2时成立.…… 相似文献
7.
刘树军 《内蒙古科技与经济》2001,(3):119-119
最值问题在各级各类数学竞赛中经常出现 ,有些最值问题用常规方法处理有一定的难度 ,而采用构造法 s既巧妙、又简捷 ,能启发人的思维。本文通过实例浅谈一下具体应用。1 构造方程例 1 ,设两个实数 XY的平方和为 7,立方和为1 0 ,求 x+y的最大值。 (1 983年美国数学竞赛题 )解 :依题意 :x2 +y2 =7x3+y3=1 0令 :x+y=s,xy=t,即可构造如下方程s3- 2 1 s+2 0 =0 即 (s- 1 ) (s- 4) (s+5) =0因此 maxs=max(x+y) =4。2 构造图形例 2 ,求函数 f(x) =x4 - 5x2 +4x+1 3+x4 - 9x2 - 6x+34的最小值。解 :先将 f(x)变形为 :f(x) =(x- 2 ) 2 +(x2 - 3)… 相似文献
8.
在度量空间中,研究了φ压缩型集值映射列的公共不动点定理,给出了如下结果:设集值映射序列Ai:X→Pf(x)满足:任意i2j=1,2,…,x,y∈X及μ∈Ax,存在υ∈Aiy,使得d(μ,υ)≤φ(d(x,y),d(x,Ax),d(y,ajy),d(y,a,x)):则{Ai}有公共不动点. 相似文献
9.
窦井波 《中国科学院研究生院学报》2010,27(3):306-313
借助环绕定理和非线性分析技巧,研究如下一类带Hardy-Sobolev临界指数和权函数的半线性椭圆方程 - Δ u-μ u |x|2 =λu+K(x) |u|2*(s)-2u |x|s , x∈Ω; u=0, x∈Ω, 解的存在性,其中Ω是 R N具有光滑边界的有界开区域,0∈Ω,N≥5,0≤s≤2, 0≤μ≤ N-2 2 2, λ>０,K(x)是 上有界正函数. 相似文献
10.
对于任意正整数n,Fn=22n 1表示第n个Fermat数.本文讨论了关于含有参数α的x的方程:,当α为何值时,此方程有正整数解;当α为何值时,此方程无正整数解,这里α是实数. 相似文献
11.
研究如下的三维Kirchhoff型问题{-(a+b∫Ω| ▽u | 2dx)△u=| u|q-1u+λ |u|p-2u/|x|s, x∈Ω,u=0, x∈(a)Ω,其中,Ω是R3中具有光滑边界的有界区域,0∈Ω,0＜q＜1,0≤s＜1,4＜p＜2*(s)=2(3-s),a,b,λ＞0.运用变分方法,证明当λ＞0足够小时,这一方程至少有2个正解. 相似文献
12.
周赟 《中国科学院研究生院学报》2007,24(6):725-728
设K为代数闭域k的有限生成扩域.C:f(x)=ayn为K上曲线,其中f是k上至少有3个单零点的多项式且n>3是正整数,n不是域k的特征的倍数,再设a■Kn,那么曲线C不能定义在k上,即曲线C:(x)=ayn不会k(a)同构于一条k上的曲线. 相似文献
13.
本文首次报道特产于我国青藏高原披碱草属Elymus的6种植物的染色体数目和核型。6个种的染色体数目为2n＝42，都是6倍体。它们的核型是：黑药鹅观草，2n=6x＝42=32m+10sm;糙毛鹅观草，2n=6x=42=34m+8sm；大颖鹅观草，2n=6x=42=30m+12sm；疏花鹅观，2n=6x=42=32m+10sm；青海鹅观草，2n=6x= 42＝34m十8sm；长颖鹅观草，2n=6x＝42=34m十8sm。它们的核型属1B或2B型，染色体中均未发现随体。 相似文献
14.
1Intr0ducti0nThekineticsofaheter0geneouscatalyticreactionisdeterminednotonlybythedetails0fthechemistryinvolved,butals0bythedetailsofthegeometryofthecatalyticsurfaceonwhichthecatalyticreactiontakesplace'.However,thegeometriesofcatalystsareoftenfrac-turedandirregular.Becauseofthelackofaneffectivemathematicaltoolt0describethedi-versityofthegeometries,the0riesofthecatalytickineticstreatthecatalyticsurfaceasanide-alplane.Asaresult,thereareconsiderablediscrepanciesbetweenthetheoreticalresultsandthee… 相似文献
15.
《Electronic Journal of Biotechnology》2014,17(6):275-279
BackgroundChlorophytum borivilianum is a rare medicinal plant originally distributed throughout the forest of India. The tubers of C. borivilianum are used as an aphrodisiac and impotence supplement. The propagation of C. borivilianum is possible through seeds and tubers, but conventional methods may take several months. Hence in vitro technique of shoot regeneration could be an efficient alternative means of propagating the species. Latest study reported microtuberization of C. borivilianum but there is no sufficient study on a rapid method for shoot multiplication and elongation.ResultsYoung shoot buds of C. borivilianum were cultured on MS medium containing 6-benzylaminopurine (BAP) and Kinetin (Kn), both at 0, 8.88, 17.8 and 26.6 μM, either individually or in combinations. Proliferated shoots were subcultured on fresh medium of the same constituents on week 3 of culture for further shoot multiplication and elongation. BAP alone (8.88–26.6 μM) was significantly effective on shoot multiplication, while Kn alone (8.88–26.6 μM) was significantly effective on shoot elongation compared to the control containing MS basal medium without any plant growth regulator. However, combination of both cytokinins stimulated an interaction producing higher shoot number and shoot length compared to their individual application.ConclusionsThe most suitable combination was 8.88 μM BAP + 8.88 μM Kn, reaching a mean shoot number of 10.83 and shoot length of 6.85 cm. 相似文献
16.
A system of differential equations A(d/dt) x = Bx+f, along with the initial condition x(0) = k, is considered where A and B are m x n matrices. Generalized inverses of the matrix A are used to derive algebraic conditions for the existence and uniqueness of a solution. An example is presented to illustrate application of the results to circuit theory. 相似文献
17.
东北地区小麦族11种植物的核型报道 总被引：1，自引：0，他引：1
本文对中国东北地区小麦族11种植物的核型进行了研究。 结果如下：冰草2n=4x=28=20m
+8sm；偃麦草2n=6x=42=34m(2SAT)+8sm；短芒大麦草2n=4x=28=20m+8sm(4SAT)；吉林
鹅观草2n=4x=28=20m+8sm(4SAT)；大芒鹅观草2n=4x=28=20m(2SAT)+8sm(2SAT)；老芒
麦2n=4x=28=20m+8sm(4SAT)； 披碱草2n=6x=42=32m+10sm(6SAT)； 肥披碱草
2n=6x=42=32m+10sm(6SAT)；羊草2n=4x=28=20m(4SAT)+8sm；纤毛鹅观草2n=4x=28= 22m(2SAT)+6sm(2SAT)；鹅观草2n=6x=42=30m+12sm(4SAT)；其中前5种的核型为首次报道。 相似文献
18.
本文对金缕梅科Hamamelidaceae双花木属Disanthus Maxim．的长柄双花木D．cercidifolius subsp．longipes和单种属壳菜果属Mytilaria Lec.首次进行了染色体计数和核型分析。结果表明：长柄双花木与产自日本的双花木D. cercidifolius subsp．cercidifolius的体细胞染色体数目一致，均为2n＝16，前者无“st”或“t”染色体，表明该亚种可能比较原始；壳菜果Mytilaria laosensis Lec．的染色体数目为2n＝26，x=13。前人报道的金缕梅科染色体基数为x＝8和x＝12，因此x＝13可能是金缕梅科的一个新染色体基数。联系该属的形态特征及其与马蹄荷属Exbucklandia R．W．Brown的关系，作者支持将壳菜果属处理为独立的亚科，即壳菜果亚科Mytilarioideae。 相似文献
19.
20.
四川宝兴地区几种豆科植物的染色体 总被引：1，自引：0，他引：1
洪德元 《中国科学院研究生院学报》1984,22(4):301-305
Meiosis and/or mitosis of six species of Fabaceae (Leguminosae) from
Baoxing County, Sichuan, China, were investigated. The voucher specimens are con-
served in PE. Eight pairs (n=8) and 10 chiasmata in meiosis of pollen mother cells
have been observed in Medicago lupulina L. (Pl. 1, A-C). Meiotic observation on
pollen mother cells in Lotus tenuis W. et K. shows 6 bivalents (n=6) in MI and 9 chias-
mata in diakinesis (Pl. 1, D-E). In this species 12 somatic chromosomes (2n=12) in
anther wall cells have also been observed. The chromosomal formula may be expressed
as 2n=12=8m+2sm+2smSAT (Pl. 1, F-G). In pollen mother cells of Vicia tetrasperma
(L.) Schreb., 7 bivalents in MI and 7 chromosomes in A II have been observed (Pl. 2,
A-B). From A II (Pl. 2, B, the inset on the right) the chromosomal formula, n=7=
2m+2sm+lstSAT+2t, may be constructed. Only three chromosomes in this karyotype may
be found to have counterparts in the one reported by Srivastava (1963), which shows
striking differences between these two karyotypes. Meiotic MI shows 7 pairs (n=7)
in Vicia hirsuta (L.) S. F. Gray. Vicia sativa L. is very variable in its chromosomes.
Our observation shows 6 pairs (n=6) in MI and in diakinesis in pollen mother cells.
In Vicia villosa Roth, all the previous chromosome reports are 2n=14 or n=7, but the
result of our work shows that somatic chromosomes are 2n=12 in anther wall cells
(Pl. 3, D, E). The karyotype in our material (Pl. 3, E) is that the longest pair of chro-
mosomes are metacentric, the pairs 2-4 are terminal, 5 are metacentric and last pair
are submetacentric, differing vastly from the idiogram (Pl. 3, F) presented by Yama-
moto (1973). Therefore both the chromosome number and structure in our material
are greatly different from those in all the previous reports.
The evolutionary trends of chromosomes in the genus Vicia is discussed in the
work. Srivastava (1963) holds that the primitive basic number of chromosome in the
genus is 6 and thus both 5 and 7 are derived. The present author would propose ano-
ther possibility that 7 is the original basic number and the other numbers are derived
ones. First, as shown in Table 1, x=7 occurs in 47 per cent of species in the genus,
but 6 only in 28 per cent. Secondly, x=7 is predominant in the perennial and primitive
section Cracca. Thirdly, in genera related to the genus under consideration, such as
Lens, Pisum and Lathyrus, x=7 is also the predominant basic number. Fourthly, ac-
cording to Raven (1975) 7 is the primitive basic number in the angiosperms and x=
7, 8 and 9 are the predominant in the angiosperms. 相似文献