共查询到20条相似文献,搜索用时 140 毫秒
1.
Upper bounds for the associated number of zeros of Abelian integrals for two classes of quadratic reversible centers of genus one 下载免费PDF全文
Xiaochun Hong Junliang Lu Yanjie Wang 《Journal of Applied Analysis & Computation》2018,8(6):1959-1970
In this paper, by using the method of Picard-Fuchs equation and Riccati equation, we study the upper bounds for the associated number of zeros of Abelian integrals for two classes of quadratic reversible centers of genus one under any polynomial perturbations of degree $n$, and obtain that their upper bounds are $3n-3$ ($n\geq 2$) and $18\left[\frac{n}{2}\right]+3\left[\frac{n-1}{2}\right]$ ($n\geq 4$) respectively, both of the two upper bounds linearly depend on $n$. 相似文献
2.
Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One 下载免费PDF全文
Qiuli Yu Houmei He Yuangen Zhan Xiaochun Hong 《Journal of Nonlinear Modeling and Analysis》2024,6(1):218-227
By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree $n$. We obtain that the upper bound is $7[(n-3)/2]+5$ when $n\ge 5$, $8$ when $n=4$, $5$ when $n=3$, $4$ when $n=2$, and $0$ when $n=1$ or $n=0$, which linearly depends on $n$. 相似文献
3.
P(t,n)和C(t,n)分别表示在阶为n的路和圈中添加t条边后得到的图的最小直径;f(t,k)表示从直径为k的图中删去t条边后得到的连通图的最大直径.这篇文章证明了t≥4且n≥5时,P(t,n)≤(n-8)/(t 1) 3;若t为奇数,则C(t,n)≤(n-8)/(t 1) 3;若t为偶数,则C(t,n)≤(n-7)/(t 2) 3.特别地,「(n-1)/5」≤P(4,n)≤「(n 3)/5」,「n/4」-1≤C(3,n)≤「n/4」.最后,证明了:若k≥3且为奇数,则f(t,k)≥(t 1)k-2t 4.这些改进了某些已知结果. 相似文献
4.
对任意的正整数与集合,令为解的个数.杨全会和陈永高证明了:若整数且,则不存在集合使得对所有充分大的整数成立,其中.对整数和,定义为满足对所有整数成立的集合的个数.杨全会和陈永高证明了是有限的,且.同时,他们问对任意整数,是否存在使得对所有整数成立.在本文中,我们给出了在时的准确公式.从而推出在时成立. 相似文献
5.
6.
Infinitely many low- and high-energy solutions for a class of elliptic equations with variable exponent 下载免费PDF全文
This paper is concerned with the $p(x)$-Laplacian equation of the form
$$
\left\{\begin{array}{ll}
-\Delta_{p(x)} u=Q(x)|u|^{r(x)-2}u, &\mbox{in}\ \Omega,\u=0, &\mbox{on}\ \partial \Omega,
\end{array}\right. \eqno{0.1}
$$
where $\Omega\subset\R^N$ is a smooth bounded domain, $1
p^+$ and $Q: \overline{\Omega}\to\R$ is a nonnegative continuous function. We prove that (0.1) has infinitely many small solutions and infinitely many large solutions by using the Clark''s theorem and the symmetric mountain pass lemma. 相似文献
7.
Kaora Yoneda 《Proceedings of the American Mathematical Society》1996,124(6):1795-1800
8.
If p(z) is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then it is proved[5] that max |z|=1 |p′(z)| ≤ kn1n + kn m|z|=ax1 |p(z)|. In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type p(z) = cnzn + ∑n j=μ cn jzn j, 1 ≤μ≤ n. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros. 相似文献
9.
Chen Xiru 《数学年刊B辑(英文版)》1983,4(2):193-198
In 1979 R. S. Singh(Ann. Statist, 1979, p. 890) made a conjecture concerning the convergence rate of EB estimates of the parameter θ in an one-dimensional continuous exponential distribution family, under the square loss function, the prior distribution family being confined to a bounded interval. The conjecture asserts that the rate cannot reach o(1/n) or even O(1/n). In this article, the weaker part of this conjecture(i. e. the o(1/n) part) is shown to be correct. 相似文献
10.
Multiple solutions for a nonhomogeneous Schrodinger-Poisson system with concave and convex nonlinearities 下载免费PDF全文
In this paper, we consider the following nonhomogeneous Schrodinger-Poisson equation
$$
\left\{
- \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\\ \Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3,
\right.
$$
where $1
相似文献
11.
A. L. Shydlich 《Ukrainian Mathematical Journal》2009,61(10):1649-1671
We study the behavior of functionals of the form
$ \mathop {\sup }\limits_{l > n} \left( {l - n} \right){\left( {\sum\limits_{k = 1}^l {\frac{1}{{{\psi^r}(k)}}} } \right)^{{{ - 1} \mathord{\left/{\vphantom {{ - 1} r}} \right.} r}}}, $ \mathop {\sup }\limits_{l > n} \left( {l - n} \right){\left( {\sum\limits_{k = 1}^l {\frac{1}{{{\psi^r}(k)}}} } \right)^{{{ - 1} \mathord{\left/{\vphantom {{ - 1} r}} \right.} r}}}, 相似文献
12.
Sun Xiehua 《数学年刊B辑(英文版)》1987,8(4):468-470
To answer the rest part of the problem of Boas R. P. on derivative of polynomial, it is shown that if $\[p(z)\]$ is a polynomial of degree n such that $\[\mathop {\max }\limits_{\left| z \right| \le 1} \left| {p(z)} \right| \le 1\]$ and $\[{p(z) \ne 0}\]$ in $\[\left| z \right| \le k,0 < k \le 1\]$, then $\[\left| {{p^''}(z)} \right| \le n/(1 + {k^n})\]$ for $\[\left| z \right| \le 1\]$. The above estimate is sharp and the equation holds for $\[p(z) = ({z^n} + {k^n})/(1 + {k^n})\]$. 相似文献
13.
In 1992, P. Polácik showed that one could linearly imbed any vector field into a scalar semi-linear parabolic equation on with Neumann boundary condition provided that there exists a smooth vector field on such that
14.
Let n = p1p2 ··· pk, where pi(1 ≤ i ≤ k) are primes in the descending order and are not all equal. Let Ωk(n) = P(p1 + p2)P(p2 + p3) ··· P(pk-1+ pk)P(pk+ p1), where P(n) is the largest prime factor of n. Define w0(n) = n and wi(n) = w(wi-1(n)) for all integers i ≥ 1. The smallest integer s for which there exists a positive integer t such thatΩs k(n) = Ωs+t k(n) is called the index of periodicity of n. The authors investigate the index of periodicity of n. 相似文献
15.
Astrid Baumann 《Aequationes Mathematicae》2003,65(3):201-235
Summary. Let $\widehat{\widehat T}_n$ and $\overline U_n$ denote the modified Chebyshev polynomials defined by $\widehat{\widehat T}_n (x) = {T_{2n + 1} \left(\sqrt{x + 3 \over 4} \right) \over \sqrt{x + 3 \over 4}}, \quad \overline U_{n}(x) = U_{n} \left({x + 1 \over 2}\right) \qquad (n \in \mathbb{N}_{0},\ x \in \mathbb{R}).$ For all $n \in \mathbb{N}_{0}$ define $\widehat{\widehat T}_{-(n + 1)} = \widehat{\widehat T}_n$ and $\overline U_{-(n + 2)} = - \overline U_n$, furthermore $\overline U_{-1} = 0$. In this paper, summation formulae for sums of type $\sum\limits^{+\infty}_{k = -\infty} \mathbf a_{\mathbf k}(\nu; x)$ are given, where
$\bigl(\mathbf a_{\mathbf k}(\nu; x)\bigr)^{-1} = (-1)^k \cdot \Bigl( x \cdot \widehat{\widehat T}_{\left[k + 1 \over 2\right] - 1} (\nu) +\widehat{\widehat T}_{\left[k + 1 \over 2\right]}(\nu)\Bigr) \cdot \Bigl(x \cdot \overline U_{\left[k \over 2\right] - 1} (\nu) + \overline U_{\left[k \over 2\right]} (\nu)\Bigr)$ with real constants $ x, \nu $. The above sums will turn out to be telescope sums. They appear in connection with projective geometry. The directed euclidean measures of the line segments of a projective scale form a sequence of type $(\mathbf a_{\mathbf k} (\nu;x))_{k \in \mathbb{Z}}$ where $ \nu $ is the cross-ratio of the scale, and x is the ratio of two consecutive line segments once chosen. In case of hyperbolic $(\nu \in \mathbb{R} \setminus] - 3,1[)$ and parabolic $\nu = -3$ scales, the formula $\sum\limits^{+\infty}_{k = -\infty} \mathbf a_{\mathbf k} (\nu; x) = {\frac{1}{x - q_{{+}\atop(-)}}} - {\frac{1}{x - q_{{-}\atop(+)}}} \eqno (1)$ holds for $\nu > 1$ (resp. $\nu \leq - 3$), unless the scale is geometric, that is unless $x = q_+$ or
$x = q_-$. By $q_{\pm} = {-(\nu + 1) \pm \sqrt{(\nu - 1)(\nu + 3)} \over 2}$ we denote the quotient of the associated geometric sequence.
相似文献
16.
Hu Ke 《数学年刊B辑(英文版)》1983,4(2):187-190
AIn this paper, the author obtains the following results:(1) If Taylor coeffiients of a function satisfy the conditions:(i),(ii),(iii)A_k=O(1/k) the for any h>0 the function φ(z)=exp{w(z)} satisfies the asymptotic equality the case h>1/2 was proved by Milin.(2) If f(z)=z α_2z~2 …∈S~* and,then for λ>1/2 相似文献
17.
Suppose that $${g\left( n \right)}$$ is an additive real-valued function, W(N) = 4+ $$\mathop {\min }\limits_\lambda $$ ( λ2 + $$\sum\limits_{p < N} {\frac{1}{2}} $$ min (1, ( g(p) - λlog p)2), E(N) = 4+1 $$\sum\limits_{\mathop {p < N,}\limits_{g(p) \ne 0} } {\frac{1}{p}.} $$ In this paper, we prove the existence of constants C1, C2 such that the following inequalities hold: $\mathop {\sup }\limits_a \geqslant \left| {\left\{ {n, m, k: m, k \in \mathbb{Z},n \in \mathbb{N},n + m^2 + k^2 } \right.} \right. = \left. {\left. {N,{\text{ }}g(n) \in [a,a + 1)} \right\}} \right| \leqslant \frac{{C_1 N}}{{\sqrt {W\left( N \right)} }},$ $\mathop {\sup }\limits_a \geqslant \left| {\left\{ {n, m, k: m, k \in \mathbb{Z},n \in \mathbb{N},n + m^2 + k^2 } \right.} \right. = \left. {\left. {N,{\text{ }}g(n) = a} \right\}} \right| \leqslant \frac{{C_2 N}}{{\sqrt {E\left( N \right)} }},$ . The obtained estimates are order-sharp. 相似文献
18.
Based on [3] and [4],the authors study strong convergence rate of the k_n-NNdensity estimate f_n(x)of the population density f(x),proposed in [1].f(x)>0 and fsatisfies λ-condition at x(0<λ≤2),then for properly chosen k_nlim sup(n/(logn)~(λ/(1 2λ))丨_n(x)-f(x)丨C a.s.If f satisfies λ-condition,then for propeoly chosen k_nlim sup(n/(logn)~(λ/(1 3λ)丨_n(x)-f(x)丨C a.s.,where C is a constant.An order to which the convergence rate of 丨_n(x)-f(x)丨andsup 丨_n(x)-f(x)丨 cannot reach is also proposed. 相似文献
19.
Fernando Bernal-Vílchis Nakao Hayashi Pavel I. Naumkin 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(3):329-355
We study the global in time existence of small classical solutions to the nonlinear Schrödinger equation with quadratic interactions of derivative type in two space dimensions $\left\{\begin{array}{l@{\quad}l}i \partial _{t} u+\frac{1}{2}\Delta u=\mathcal{N}\left( \nabla u,\nabla u\right),&;t >0 ,\;x\in {\bf R}^{2},\\ u\left( 0,x\right) =u_{0} \left( x\right),&;x\in {\bf R}^{2}, \end{array}\right.\quad\quad\quad\quad\quad\quad (0.1)$ where the quadratic nonlinearity has the form ${\mathcal{N}( \nabla u,\nabla v) =\sum_{k,l=1,2}\lambda _{kl} (\partial _{k}u) ( \partial _{l}v) }
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