共查询到20条相似文献,搜索用时 93 毫秒
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本文旨在运用方程思想解决三角中的一类求取值范围的问题,从中可见数学思想在解题中的运用.1构造方程组,利用函数的有界性解题要点:通过构造关于shu、c。s。,等的方程组,并根据卜un4<l,DcosyS<1,使问题获解.例1已知sin。+Zcosy—2,求ZSlll十COSy的取值范围.解设Zslnx上cosy—a,与sin:r+Zcosy—2联立解得故Zsi。+cosy的取值范围是[,:].N2已知sl。cosy—a(一1<a<1),求COSSSiny的取值范围.解设cosxslny=b,即由①,②解得于是,当a>0时,a—l<b车一a+l;当a<0时,一a—l<b<a+l.综上,可知cosxsin… 相似文献
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关于条件最值问题的几个结论简超武汉铁路成人中专430012给定及有定理1设,且,且,则函数当r>1或r<0时具有最小值Fmin(当0<r<1时具有最大值Fmax.且证由加权益平均不等式[1]可知:当r>1或r<0时,对任意有等号仅当.;一.。—…一.... 相似文献
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奇摄动非线性系统Robin边值问题 总被引:3,自引:0,他引:3
本文研究了非线性系统奇摄动问题:ε2y"-(x,y,y)=0,0<x<1,0<ε≤1,y(0)-py'(0)=A,p>0,y(1)=B,其中y,f,A,B为n维向量.在相应的假设下,利用代数型边界层函数,证明了该问题存在一个解y(x,ε),并利用微分不等式方法得到了其解的渐近估计. 相似文献
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一维抛物型方程如下定解问题狌狋+狌狓=狌狓狓, 0≤狓< ∞,0≤狋< ∞,狌(1,狋)=犵(狋), 0≤狋< ∞,狌(狓,0)=0, 狓≥0烅烄烆.是一个不适定问题.数据犵的微小变化可以引起解的巨大误差.该文通过构造一个在频域具紧支集的小波并在尺度空间上展开数据和解,滤除了高频分量,并结和Galerkin方法,建立了一种逼近准确解的正则化方法,恢复了解对数据的连续依赖性,并建立了误差估计. 相似文献
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一个反应扩散过程的门槛结果 总被引:3,自引:0,他引:3
本文讨论反应扩散方程Cauchy问题(ut-△u=u^p-u^p-u,X∈R^n,t∈(0,T),u(x,0)=u0(x)≥0,X∈R^n,解的整体存在性,渐近性质和Blow-up问题,其中1<q<p<n+2/n-2,n≥3或者1<q<p+∞,n=2.得到门槛结果。 相似文献
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设环境q={q(n)}∞0是取值于[0,1]上一列独立同分布的随机变量列,且Eq(0)=p;{Sn}∞0是随机环境q中取整数值随机游动,S0=0,且满足:对任意的整数xi(i≥0),x,y,P(Sn+1=y|S1=x1,…,Sn-1=xn-1,Sn=x,q)={q(n),y=x+1,1-q(n),y=x-1,0,其他.我们证明了:p>1/2时,Sn→+∞,a.e.,n→∞;p<1/2时,Sn→-∞,a.e.,n→∞;p=1/2时,-∞=(lim infSn)/(n→+∞)<(lim supSn)/(n→+∞)=+∞,a.e.,n→∞. 相似文献
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In the Banach space of functions analytic in a Jordan domain
, we establish order estimates for the Kolmogorov widths of certain classes of functions that can be represented in by Cauchy-type integrals along the rectifiable curve = and can be analytically continued to or to
. 相似文献
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G. Arag��n-Gonz��lez J. L. Arag��n M. A. Rodr��guez-Andrade 《Advances in Applied Clifford Algebras》2011,21(2):259-272
In this work, the equivalence class representatives of integer solutions of the Diophantine equation of the type ${{a_1x_1^2+ .\,.\,. + a_px_p^2 = a_{p+1}x^2_{p+1} + .\,.\,. +a_{p+q}x^2_{p+q} +a_1x^2_{n+1} (a_i > 0,i=1, .\,.\,.\,,p+q,x_{n+1}\neq0)}}${{a_1x_1^2+ .\,.\,. + a_px_p^2 = a_{p+1}x^2_{p+1} + .\,.\,. +a_{p+q}x^2_{p+q} +a_1x^2_{n+1} (a_i > 0,i=1, .\,.\,.\,,p+q,x_{n+1}\neq0)}} are found using simple reflections of orthogonal vectors, manipulated using the Clifford algebra over orthogonal spaces R
p,q
. These solutions are obtained from the application of a useful Lemma: given two different non-zero vectors of the same norm,
we can map one onto the other, or its negative, by means of a simple reflection. With this Lemma, we extend and improve a
previous work [1] concerning generalized Pythagorean numbers, which now can be obtained as a Corollary. We also show that
our technique is promising for solving others Diophantine equations. 相似文献
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This paper determines the –correspondence for the dual pairs (O(p, q), Sp(2n, R)) when p+q=2n+1. As a consequence, there is a natural bijection between genuine irreducible representations of the metaplectic group Mp(2n, R) and irreducible representations of SO(p, q) with p+q=2n+1. 相似文献
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In this paper, the structure of the solution space of y n +3 + ry n +2 + qy n +1 + py n =0, n S 0, is studied, keeping oscillatory/nonoscillatory behaviour of solutions of the equation in view, where p , q and r are constants. Some of these results are generalized partially to hold for y n +3 + r n y n +2 + q n y n +1 + p n y n =0, n S 0, where { p n }, { q n } and { r n } are sequences of real numbers. 相似文献
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J. C. Lagarias 《Monatshefte für Mathematik》1993,115(4):299-328
Given a vector of real numbers=(1,...
d
)
d
, the Jacobi-Perron algorithm and related algorithms, such as Brun's algorithm and Selmer's algorithm, produce a sequence of (d+1)×(d+1) convergent matrices {C(n)():n1} whose rows provide Diophantine approximations to . Such algorithms are specified by two mapsT:[0, 1]
d
[0, 1]
d
and A:[0,1]
d
GL(d+1,), which compute convergent matrices C(n)())...A(T())A(). The quality of the Diophantine approximations these algorithms find can be measured in two ways. The best approximation exponent is the upper bound of those values of for which there is some row of the convergent matrices such that for infinitely many values ofn that row of C(n)() has
. The uniform approximation exponent is the upper bound of those values of such that for all sufficiently large values ofn and all rows of C(n)() one has
. The paper applies Oseledec's multiplicative ergodic theorem to show that for a large class of such algorithms and take constant values and on a set of Lebesgue measure one. It establishes the formula where are the two largest Lyapunov exponents attached by Oseledec's multiplicative ergodic theorem to the skew-product (T, A,d), whered is aT-invariant measure, absolutely continuous with respect to Lebesgue measure. We conjecture that holds for a large class of such algorithms. These results apply to thed-dimensional Jacobi-Perron algorithm and Selmer's algorithm. We show that; experimental evidence of Baldwin (1992) indicates (nonrigorously) that. We conjecture that holds for alld2. 相似文献
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高红亚 《中国科学A辑(英文版)》2003,46(4)
In this paper, we first give the definition of weakly (K1, K2)-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Holder inequality, we obtain their regularity property: For any ql that satisfies 0 < K1n(n+4)/22n+1 × 100n2[23n/2(25n + 1)](n - q1) < 1, there exists p1 = p1(n, q1, K1, K2) > n, such that any (K1, K2)-quasiregular mapping f ∈W(loc)(1,q1)(Ω,Rn) is in fact in W(loc)(1,p1)(Ω,Rn). That is, f is (K1, K2)-quasiregular in the usual sense. 相似文献
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Let G be a finite group,
a normal subgroup, p a prime,
a finite splitting field of characteristic p for
G and
We prove that
is a splitting field for N, using the action
of the Galois group of the field extension
on the irreducible representations of N.
As
is a splitting field for the symmetric group
Sn
we get as a corollary that
is a splitting field for the alternating group
An.
Received: 31 July 2003 相似文献
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Let M() be the Mahler measure of an algebraic number and let G() be the modulus of the product of logarithms of absolute values of its conjugates. We prove that if is a nonreciprocal algebraic number of degree d 2 then M()2
G()1/d
1/2d. This estimate is sharp up to a constant. As a main tool for the proof we develop an idea of Cassels on an estimate for the resultant of and 1/. We give a number of immediate corollaries, e.g., some versions of Smyth's inequality for the Mahler measure of a nonreciprocal algebraic integer from below. 相似文献