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1.
本文研究捕食者种群具有线性密度制约的一类稀疏效应下捕食-被捕食者系统x=x(ax-cx-by),y=y(-α+βx-γy).(*)得到:(1)当A<A,A2<A2,A3>A3时,系统(*)在第一象限内存在极限环;(2)当A2<A2,A3>A3时,系统(*)在第一  相似文献   

2.
一、单项选择题(每小题5分,共50分)1.已知点(3,-4),那么它到x轴的距离为( )(A)3 (B)4 (C)-3 (D)52.如果k>b>0,那么直线y=kx+b的图象必不经过( )(A)第一象限 (B)第二象限(C)第三象限 (D)第四象限3.函数y=kx的图象经过点(-2,2),那么直线y=kx-k的图象经过( )(A)第二、三、四象限 (B)第一、二、三象限(C)第一、二、四象限 (D)第一、三、四象限4.满足b<0,c<0的二次函数y=x2+bx+c的图象大致是( )  5.两圆圆…  相似文献   

3.
本文利用旋转向量场理论得到了系统x=-y+δx+lx2+mxy+ny2,y=x(1+y),{(-1<n<0,0<l<1)存在极限环的充要条件.  相似文献   

4.
一类Kolmogorov捕食系统的极限环   总被引:6,自引:0,他引:6  
本文研究Kolmogrov的捕食系统x=x(a0+a1x-a2x^2-ψ(y)) y=y(bx^2-d),得到了极限环存在唯一的充要条件,从而推广了前人相关的结果,其中ψ(0)=0,ψ(y)>δ>0,y>0。  相似文献   

5.
文[1]将Popoviciu不等式修正为:“设xi,yi≥0(i=1,2,…,n),且xp1-∑ni=2xpi>0和yp1-∑ni=2ypi>0,其中0<p≤2,则(xp1-∑ni=2xpi)(yp1-∑ni=2ypi)≤(x1y1-∑ni=2xiyi)p①当且仅当p=2且x1y1=x2y2=…=xnyn时,①式取等号”.这里,应加上“当0<p≤2,x2=x3=…=xn=y2=y3=…=yn=0时,①也取等号”才完整.本文我们将不等式①进一步推广为:定理 设xij>0(i=1,2,…,m,j=1…  相似文献   

6.
乐茂华 《数学进展》1996,25(4):328-333
本文证明了:方程x2+2m=yn,x,y,m,n∈N,gcd(x,y)=1,n>2仅有有限多组解(x,y,m,n),而且当(x,y,m,n)≠(5,3,1,3),(11,5,2,3),(7,3,5,4)时,n是适合n≡7(mod8)以及23≤n<8.5·106的奇素数,max(x,y,m)<C1;方程x2-2m=yn,x,y,m,n∈N,gcd(x,y)=1,y>1;n>2仅有有限多组解(x,y,m,n),而且这些解都满足n<2·109炉以及max(x,y,m)<C2,这里C1,C2是可有效计算的绝对常数.  相似文献   

7.
§1.Forthesystemx=-y+δx+lx2+ny2=P(x,y),y=x(1+ax-y)=Q(x,y),{(1.1)wecanfindin[1]thefolowing:ConjectureI.Assume1a<0,n>1,n+l>0,na2...  相似文献   

8.
设A是布尔矩阵,而矩阵G满足AGA=A.(1)如果对所有Ax=y的向量x,y.有ω(Gy)≤ω(x)(*)称G是A的一个极小权g-逆,表示为A-ω.(2)如果对所有向量x,y,有d(AGy,y)≤d(Ax,y)(**)称G是A的最小距离g-逆,表示为A-d.(3)如果(*)和(**)都成立,就称G是极小权最小距离g-逆,表示为A-ωd.本文研究这三类广义逆矩阵的最大逆的存在性及表示式.主要结果如下:假定对于矩阵A.A-ω,A-d,A-ωd分别存在,那么.(1)存在最大A-ω,当且仅当A中设有两个相同的非零列,且最大A-ω为Aω=[ICAT]C.(2)最大A-d存在,且为Ad=[ATACAT+AT(JAT)C]C.(3)存在最大A-ωd,当且仅当A的所有非零列向量线性独立,且最大A-ωd为Aωd=[ATAcAT+AT(JAT)c+(ATJ)cAT]C.其中J为全1矩阵  相似文献   

9.
若直线l1:A1x+B1y+C1=0,l2:A2x+B2y+C2=0相交于点A,则方程(A1x+B1y+C1)+λ(A2x+B2y+C2)=0(λ为任意实数)是通过l1和l2的交点的直线系方程(除去l2本身).在解析几何问题中,有一类问题,如果用直线系过定点来解,则可使问题轻松地得以解决.例1 求证:无论a为何值,直线(a-2)y=(3a-1)x-1都过第一象限.分析 此题从表面看,觉得很难下手,但若将a看作参数,则该直线即为直线系,若该直线系过的定点就在第一象限,那么问题就迎刃而解了.证明 将…  相似文献   

10.
y=±x特别是y=x由于其方程与图象简单且特殊,与许多重要知识结构相关联,因此有不少奇特的妙用.图11.y=x是幂函数y=xα,α>0的图象的分界线,有助于这种幂函数性质的讨论.如图1,在第一象限内,首先,它们都交汇于点(0,0)、(1,1).当α>1时,x∈(0,1),y=xα在y=x的下方;x∈(1,+∞)则转为上方.当α<1时,x∈(0,1),y=xα在y=x的上方;x∈(1,+∞)则转为下方.2.对于等轴双曲线的标准形式,y=±x恰是渐近线;对于反比例函数y=kx(k≠0),即xy=k,…  相似文献   

11.
12.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

13.
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.  相似文献   

14.
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).  相似文献   

15.
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

16.
In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p(R^n) into the Lebesgue space L^p with p 〈 1.  相似文献   

17.
In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.  相似文献   

18.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

19.
正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in  相似文献   

20.
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