共查询到20条相似文献,搜索用时 31 毫秒
1.
Let e_λ(x) be a Neumann eigenfunction with respect to the positive Laplacian A on a compact Riemannian manifold M with boundary such that △e_λ=λ~2e_λ in the interior of M and the normal derivative of e\ vanishes on the boundary of M.Let χλ be the unit band spectral projection operator associated with the Neumann Laplacian and f be a square integrable function on M.The authors show the following gradient estimate for χλf as λ≥1:‖▽χλ f‖∞≤C(λ‖χλ f‖∞+λ~(-1)‖△χλf‖∞),where C is a positive constant depending only on M,As a corollary,the authors obtain the gradient estimate of e_λ:For every λ≥1,it holds that ‖▽e_λ‖∞≤Cλ‖e_λ‖∞. 相似文献
2.
本文.证明了,当n≥2时,Xat(K_n×K′_n)=2n;当p,q≥2时,Xat(C_(2p)×K_(2q))=2q 3,其中K_n×K′_n是两个不同标号完全图的积图,C_(2p)×K_(2q)是偶圈和偶阶完全图的积图. 相似文献
3.
主要讨论局部域上的Gabor紧框架.首先,建立局部域上Gabor系{xm(bx)g(x-u(n)a)}m.n∈p构成L~2(K)上紧框架的特征.其次,给出Gabor系{X_m(bx)g(x-u(n)a)}_(m,n∈p)成为L~2(K)上标准正交基的充要条件. 相似文献
4.
In this paper, we consider the initial-boundary value problem of the two-species chemotaxis Keller-Segel model where the parameters \(\chi_{1}\), \(\chi_{2}\), \(\alpha_{1}\), \(\alpha_{2}\), \(\gamma \) are positive constants, \(\varOmega \subset \mathbb{R}^{2}\) is a bounded domain with smooth boundary. We obtain the results for finite time blow-up and global bounded as follows: (1) For any fixed \(x_{0}\in \varOmega \), if \(\chi_{1}\alpha_{2}= \chi_{2}\alpha_{1}\), \(\int_{\varOmega }(u_{0}+v_{0})|x-x_{0}|^{2}dx\) is sufficiently small, and \(\int_{\varOmega }(u_{0}+v_{0})dx>\frac{8\pi ( \chi_{1}\alpha_{1}+\chi_{2}\alpha_{2})}{\chi_{1}\alpha_{1}\chi_{2} \alpha_{2}}\), then the nonradial solution of the two-species Keller-Segel model blows up in finite time. Moreover, if \(\varOmega \) is a convex domain, we find a lower bound for the blow-up time; (2) If \(\|u_{0}\|_{L^{1}(\varOmega )}\) and \(\|v_{0}\|_{L^{1}( \varOmega )}\) lie below some thresholds, respectively, then the solution exists globally and remains bounded.
相似文献
$$\begin{aligned} \textstyle\begin{cases} u_{t}=\Delta u-\chi_{1}\nabla \cdot (u\nabla w), &x\in \varOmega , \ t>0, \\ v_{t}=\Delta v-\chi_{2}\nabla \cdot (v\nabla w), &x\in \varOmega , \ t>0, \\ 0=\Delta w-\gamma w+\alpha_{1}u+\alpha_{2}v, &x\in \varOmega , \ t>0, \end{cases}\displaystyle \end{aligned}$$
5.
关于图的星色数的一点注记 总被引:1,自引:0,他引:1
A star coloring of an undirected graph G is a proper coloring of G such that no path of length 3 in G is bicolored.The star chromatic number of an undirected graph G,denoted by χs(G),is the smallest integer k for which G admits a star coloring with k colors.In this paper,we show that if G is a graph with maximum degree △,then χs(G) ≤ [7△3/2],which gets better bound than those of Fertin,Raspaud and Reed. 相似文献
6.
设 $G$ 是简单图. 设$f$是一个从$V(G)\cup E(G)$ 到$\{1, 2,\cdots, k\}$的映射. 对每个$v\in V(G)$, 令 $C_f (v)=\{f(v)\}\cup \{f(vw)|w\in V(G), vw\in E(G)\}$. 如果 $f$是$k$-正常全染色, 且对任意$u, v\in V(G), uv\in E(G)$, 有$C_f(u)\ne C_f(v)$, 那么称 $f$ 为图$G$的邻点可区别全染色(简称为$k$-AVDTC).数 $\chi_{at}(G)=\min\{k|G$ 有$k$-AVDTC\}称为图$G$的邻点可区别全色数.本文给出路$P_m$和完全图$K_n$ 的Cartesion积的邻点可区别全色数. 相似文献
7.
设 $G$ 是一个简单图. 设$f$是从$V(G) \cup E(G)$到 $\{1, 2,\ldots, k\}$的一个映射.对任意的 $v\in V(G)$, 设$C_f(v)=\{f(v)\}\cup \{f (vw)|w\in V(G),vw\in E(G)\}$ . 如果 $f$ 是一个 $k$-正常全染色, 且对 $u, v\in V(G),uv\in E(G)$, 有 $C_f(u)\neq C_f(v)$, 那么称 $f$ 为$k$-邻点可区别全染色 (简记为$k$-$AVDTC$). 设 相似文献
8.
In this paper, we consider the obstacle problem for the inhomogeneous p-Laplace equation
$ \text {div}\big(|\nabla u|^{p-2} \nabla u\big)=f\cdot \chi_{ \{u>0\},} 相似文献 9.
Let f(z) be a holomorphic cusp form of weight κ with respect to the full modular group SL2(Z). Let L(s, f) be the automorphic L-function associated with f(z) and χ be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for k =1/n with n ∈ N,and the result also holds for any real number 0 k 1 under the GRH for L(s, f ■χ).The authors also prove that under the GRH for L(s, f ■χ),for any real number k 0 and any large prime q. 相似文献
10.
In this paper we are concerned with singular points of solutions to the unstable free boundary problem
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