共查询到20条相似文献,搜索用时 281 毫秒
1.
Let $A \subset {{\Bbb Z}_N}$, and ${f_A}(s) = \left\{ {\begin{array}{*{20}{l}}{1 - \frac{{|A|}}{N},}&{{\rm{for}}\;s \in A,}\\{ - \frac{{|A|}}{N},}&{{\rm{for}}\;s \notin A.}\end{array}} \right.$ We define the pseudorandom measure of order k of the subset A as follows, Pk(A, N) = $\begin{array}{*{20}{c}}{\max }\\D\end{array}$|$\mathop \Sigma \limits_{n \in {\mathbb{Z}_N}}$fA(n + c1)fA(n + c2) … fA(n + ck)|, where the maximum is taken over all D = (c1, c2, . . . , ck) ∈ ${\mathbb{Z}^k}$ with 0 ≤ c1 < c2 < … < ck ≤ N - 1. The subset A ⊂ ${{\mathbb{Z}_N}}$ is considered as a pseudorandom subset of degree k if Pk(A, N) is “small” in terms of N. We establish a link between the Gowers norm and our pseudorandom measure, and show that “good” pseudorandom subsets must have “small” Gowers norm. We give an example to suggest that subsets with “small” Gowers norm may have large pseudorandom measure. Finally, we prove that the pseudorandom subset of degree L(k) contains an arithmetic progression of length k, where L(k) = 2·lcm(2, 4, . . . , 2|$\frac{k}{2}$|), for k ≥ 4, and lcm(a1, a2, . . . , al) denotes the least common multiple of a1, a2, . . . , al. 相似文献
2.
Liang Zhaojun 《数学年刊B辑(英文版)》1984,5(1):37-42
In this paper, we consider the relative position of limit cycles for the system
$$\[\begin{array}{*{20}{c}}
{\frac{{dx}}{{dt}} = \delta x - y + mxy - {y^2}}\{\frac{{dy}}{{dt}} = x + a{x^2}}
\end{array}\]$$
under the condition
$$\[a < 0,0 < \delta \le m,m \le \frac{1}{a} - a\]$$
The main result is as follows:
(i)Under Condition (2), if $\[\delta = \frac{m}{2} + \frac{{{m^2}}}{{4a}} \equiv {\delta _0}\]$, then system $\[{(1)_{{\delta _0}}}\] $ has no limit cycles and
on singular closed trajectory through a saddle point in the whole plane,
(ii)Under condition (2), the foci 0 and R'' cannot be surrounded by the limit cycles of system (1) simultaneously. 相似文献
3.
Ai Hua Fan 《Monatshefte für Mathematik》1994,118(1-2):83-89
Consider the Riesz product $\mu _a = \mathop \prod \limits_{n = 1}^\infty (1 + r\cos (q^n t + \varphi _n ))$ . We prove the following approximative formula for the dimension ofμ a. $$\dim \mu _a = 1 - \frac{1}{{\log q}}\int_0^{2\pi } {(1 + r\cos x)\log (1 + r\cos x)\frac{{dx}}{{2\pi }} + 0\left( {\frac{r}{{q^2 \log q}}} \right).}$$ 相似文献
4.
In this paper we generalize the method used to prove the Prime Number Theorem to deal with finite fields, and prove the following
theorem:
$
\pi (x) = \frac{q}
{{q - 1}}\frac{x}
{{\log _q x}} + \frac{q}
{{(q - 1)^2 }}\frac{x}
{{\log _q^2 x}} + O\left( {\frac{x}
{{\log _q^3 x}}} \right),x = q^n \to \infty
$
\pi (x) = \frac{q}
{{q - 1}}\frac{x}
{{\log _q x}} + \frac{q}
{{(q - 1)^2 }}\frac{x}
{{\log _q^2 x}} + O\left( {\frac{x}
{{\log _q^3 x}}} \right),x = q^n \to \infty
相似文献
5.
V. Tkachenko 《Functional Analysis and Its Applications》2007,41(1):54-72
We prove an explicit formula for spectral expansions in L 2(?) generated by self-adjoint differential operators 相似文献
$( - 1)^n \frac{{d^{2n} }}{{dx^{2n} }} + \sum\limits_{j = 0}^{n - 1} {\frac{{d^j }}{{dx^j }}p_j (x)\frac{{d^j }}{{dx^j }}} ,p_j (x + \pi ) = p_j (x),x \in \mathbb{R}.$ 6.
Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces
![]() In this paper, we study the subcritical dissipative quasi-geostrophic equation. By using the Littlewood Paley theory, Fourier analysis and standard techniques we prove that there exists $v$ a unique global-in-time solution for small initial data belonging to the critical Fourier-Besov-Morrey spaces $ \mathcal{F} {\mathcal{N}}_{p, \lambda, q}^{3-2 \alpha+\frac{\lambda-2}{p}}$. Moreover, we show the asymptotic behavior of the global solution $v$. i.e., $\|v(t)\|_{ \mathcal{F} {\mathcal{N}}_{p, \lambda, q}^{3-2 \alpha+\frac{\lambda-2}{p}}}$ decays to zero as time goes to infinity. 相似文献
7.
A. L. Shydlich 《Ukrainian Mathematical Journal》2009,61(10):1649-1671
We study the behavior of functionals of the form
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