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RESEARCH ANNOUNCEMENTS——Dynamical Behavior for the Three-dimensional Generalized Hasegawa-Mima Equations 总被引:1,自引:0,他引:1
We consider the following generalized three-dimensional (3-D) dissipative Hasegawa-Mima equations:
△ut - ut + {u, △u} + knuy - vz + α△(u - △u) + f(x, y, z) = 0, (1)
vt + {u, v} + uz + γv - β△v = g(x, y, z) (2)
with initial datum
v|t=0=u0(x,y,z),v|t=0=v0(x,y,z),(x,y,z)∈Ω∈R^3 (3). 相似文献
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我们知道,实系数一元二次方程ax2+bx+c=0的根的情况,可由根的判别式△=b2-4ac来判定,有如下根的判别式法则:定理1实系数一元二双方程ax2+bx+c=0,其中a、b、c∈R,a≠0,当△>0时,方程有两个不相等的实根;当△=0时,方程有两个相等的实根;当△<0时,方程有两个共轭虚根.定理1的逆命题也成立.现在问:如果一元二次方程ax2+bx+c=0中的系数是一般复数,定理1是否仍成立?容易看出,不能简单地将定理1推广到复数范围.这是困为:当a、b、C中有虚数时,△=b2-4ac可能为虚数,这时△>0,△=0,△<0均不成立;即使△… 相似文献
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进入初三年级,我们学习了二次方程ax^2+bx+c=0根的判别式△=b^2-4ac,学习了二次函数f(x)=ax^2+bx+c与x轴有无交点的判别方法,将二次函数f(x)=ax^2+bx+c化简变形得到f(x)=a[(x+b/2a)^2-△/4a^2],当a〉0,△=b^2-4ac≤0时,有f(x)≥0. 相似文献
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在三角形中,有这样一个用面积表示的向量定理:
设O为△ABC内任意一点,记△BOC,△COA,△AOB的面积分别为SA,SB,SC,则有SAOA→+SBOB→+Sc→OC=0. 相似文献
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2004年全国高中联赛第4题:设O点在△ABC内部,且有OA+2OB+3OC=0,则△ABC的面积和△AOC面积之比( ). 相似文献
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例题 已知P是△ABC所在平面内一点,PB+PC+PA=0,现将一粒黄豆随机撒在△ABC内,则黄豆落在△PBC内的概率是_______。 相似文献
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命题1 已知P是△ABC所在平面内一点,满足PA^→·PB^→+PB^→·PC^→+PC^→·PA^→=0,那么点P为△ABC的垂心. 相似文献
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构造二次函数巧用判别式解一类题 总被引:1,自引:1,他引:0
判别式△=b^2-4ac是二次函数f(x)=ax^2+bx+c(a≠0)的一个重要的特征数字,其一条性质:若f(x)=ax^2+bx+c且a〉0,则f(x)≥0对x∈R恒成立 △≤0,为我们利用二次函数解决一些数学问题提供了突破IZl.本文将利用这一性质,构造适当二次函数,灵活解决一类问题. 相似文献
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With the help of continued fractions, we plan to list all the elements of the set Q△ = {aX2 + bXY + cY2 : a,b, c ∈Z, b2 - 4ac = △ with 0 ≤ b 〈 √△}of quasi-reduced quadratic forms of fundamental discriminant △. As a matter of fact, we show that for each reduced quadratic form f = aX2 + bXY + cY2 = (a, b, c) of discriminant △〉0(and of sign σ(f) equal to the sign of a), the quadratic forms associated with f and defined by {〈a+bu+cu2,b+2cu.c〉},with 1≤σ(f)u≤b/2|c| (whenever they exist), 〈c,-b-2cu,a+bu+cu2〉 with b/2|c|≤σ(f)u≤[w(f)]=[b+√△/2|c|], are all different from one another and build a set I(f) whose cardinality is #I(f)={1+[ω(f)],when(2c)|b,[ω(f)],when (2c)|b. If f and g are two different reduced quadratic forms, we show that I(f) ∩ I(g) = Ф. Our main result is that the set Q△ is given by the disjoint union of all I(f) with f running through the set of reduced quadratic forms of discriminant △〉0. This allows us to deduce a formula for #(Q△) involving sums of partial quotients of certain continued fractions. 相似文献
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文[1]给出了三角形的一个简捷的性质:
已知ΔABC及其内部一点P,若λ1PA+λ2PB+λ3 PC=0,λ1,λ2,λ3都是大于0的实数,则△PBC,△PAC,△PAB的面积之比为λ1:λ2:λ3. 相似文献
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ZHENG Tingting ZHAO Junning 《偏微分方程(英文版)》2009,(3):199-204
In this note we study the nonexistence of nontrivial global solutions on S = R^N × (0,∞) for the following inequalities:|u|t≥△(|u|^m-1u)+|u|^q and |u|t≥div(|△u|^p-2△|u|)+|u|^q.When m,p,q satisfy some given conditions, the nonexistence of nontrivial global solution is proved, without taking their traces on the hyperplans t = 0 into account. 相似文献
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MOUSSAOUI Abdelkrim KHODJA Brahim 《偏微分方程(英文版)》2009,22(2):111-126
In this paper, we study the existence of nontrivial solutions for the problem
{-△u=f(x,u,v)+h1(x)in Ω
-△v=g(x,u,v)+h2(x)inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 (Ω). The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g:
{lim s,|t|→+∞f(x,s,t)/s=lim |s|,t→+∞g(x,s,t)/t=λ+1 uniformly on Ω,
lim -s,|t|→+∞f(x,s,t)/s=lim |s|,-t→+∞g(x,s,t)/t=λ-,uniformly on Ω,
where λ+,λ-∈(0)∪σ(-△),σ(-△)denote the spectrum of -△. The cases (i) where λ+ = λ_ and (ii) where λ+≠λ_ such that the closed interval with endpoints λ+,λ_ contains at most one simple eigenvatue of -△ are considered. 相似文献
{-△u=f(x,u,v)+h1(x)in Ω
-△v=g(x,u,v)+h2(x)inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 (Ω). The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g:
{lim s,|t|→+∞f(x,s,t)/s=lim |s|,t→+∞g(x,s,t)/t=λ+1 uniformly on Ω,
lim -s,|t|→+∞f(x,s,t)/s=lim |s|,-t→+∞g(x,s,t)/t=λ-,uniformly on Ω,
where λ+,λ-∈(0)∪σ(-△),σ(-△)denote the spectrum of -△. The cases (i) where λ+ = λ_ and (ii) where λ+≠λ_ such that the closed interval with endpoints λ+,λ_ contains at most one simple eigenvatue of -△ are considered. 相似文献
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This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping(r(t)φ(x^△(t))^△+p(t)φα(x^△α(t)+q(t)f(xδ(t))=0on a time scale T which is unbounded above. Sign changes are allowed for the coefficient functions r, p and q. Several examples are given to illustrate the main results. 相似文献