共查询到20条相似文献,搜索用时 31 毫秒
1.
Yuhai Zhang 《计算数学(英文版)》2004,22(4):567-580
A number of new results on sufficient conditions for the solvability and numerical algorithms of the following general algebraic inverse eigenvalue problem are obtained: Given $n+1$ real $n\times n$ matrices $A=(a_{ij}),A_k=(a_{ij}^{(k)})(k=1,2,\cdots,n)$ and $n$ distinct real numbers $\lambda_1,\lambda_2,\cdots,\lambda_n,$ find $n$ real number $c_1,c_2,\cdots,c_n$ such that the matrix $A(c)=A+\sum\limits_{k=1}^{n}c_k A_k$ has eigenvalues $\lambda_1,\lambda_2,\cdots,\lambda_n.$ 相似文献
2.
Let G(V, E) be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V(Cm). The G - E(Cm) are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui : i = 1, 2 , m}. Let κ = ec+1. Forj = 1,2,...,k- 1, let δij = max{dv : dist(v, ui) = j,v ∈ Ti}, δj = max{δij : i = 1, 2,..., m}, δ0 = max{dui : ui ∈ V(Cm)}. Then λ1(G)≤max{max 2≤j≤k-2 (√δj-1-1+√δj-1),2+√δ0-2,√δ0-2+√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 (G) is the largest eigenvalue of the adjacency matrix of G. 相似文献
3.
设k和r是满足k≥3及r≥Ψ(k)+1的正整数,这里当3≤k≤4时,Ψ(k)=2~(k-1);而当k≥5时,Ψ(k)=1/2k(k+1).假定δ和ε是给定的足够小的正数,λ_1,λ_2,…,λ_(r+1)是不全同号且两两之比不全为有理数的非零实数.对于任意实数η与0σ2~(1-2k)/r-1,证明了:存在一个正数序列X→+∞,使得不等式|λ_1p_1~k+λ_2p_2~k+···+λ_rp_r~k+λ_(r+1)p_(r+1)+η|(max(1≤j≤r+1)p_j)~(-σ)有》■X~(■-(2~(1-2k))/(r-1)+ε组素数解(p_1,p_2,…,p_(r+1)),这里(δX)~(1/k)≤p_j≤X~(1/k)(1≤j≤r)及δX≤p_(r+1)≤X.这改进了之前的结果. 相似文献
4.
假定Γ是一个有限的、单的、无向的且无孤立点的图,G是Aut(Γ)的一个子群.如果G在Γ的边集合上传递,则称Γ是G-边传递图.我们完全分类了当G为一个有循环的极大子群的素数幂阶群时的G-边传递图.结果为:设图Γ含有一个阶为pn(p是素数,n≥2)的自同构群,且G有一个极大子群循环,则Γ是G-边传递的,当且仅当Γ同构于下列图之一1)pmK1,pn-1-m,0≤m≤n-1;2)pmK1,pn-m,0≤m≤n;3)pmKp,pn-m-1,0≤m≤n-2;4)pn-mCpm,pm≥3,m<n;5)2n-2K1,1;6)pn-1-mCpm,pm≥3,m≤n-1;7)2pn-mCpm,pm≥3,m≤n-1;8)2pn-mK1,pm,0≤m≤n;9)pn-mK1,2pm,0≤m≤n;10)pn-mK2,pm,0<m≤n;11)C(2pn-m,1,pm);12)pkC(2pm-k,1,pn-m),0<k<m,0<m≤n;13)(t-s,2m)C(2m 1/(t-s,2m),1,2n-1-m),其中0≤m≤n-1,2n-2(s-1)≡0(mod 2m),t≡1(mod 2),s(≠)t(mod 2m),1≤s≤2m,1≤t≤2n-1;14)∪p i=1 Ci p n-1,其中Ci p n-1=Ca1a1 [1 (i-1)pn-2]a 1 2[1 (i--1)p n-2]…a 1 (pn-1-1)[1 (i-1)p n-2]≌Cp n-1,i=1,2,…,p;15)∪2 i=1 Ci 2n-1,其中Ci 2n-1=Ca1a 1 [1 (i-1)(2n-2-1)]a1 2[1 (i-1)(2n-2-1)]…a1 (2n-1-1)[1 (i-1)(2n-2-1)]≌C2n-1,i=1,2. 相似文献
5.
关于超越亚纯系数微分方程亚纯解的零点 总被引:6,自引:0,他引:6
本文研究了非齐次线性微分方程的复振荡问题,其中,D0,D1,…,D(k-1),是超越亚纯函数.当存在某个Ds(1≤s≤k-1)比其它Dj(j≠s)有较快增长的意义下起支配作用时,得到了微分方程(I)亚纯解的零点收敛指数的精确估计式. 相似文献
6.
Let $s_n(f,z):=\sum_{k=0}^{n}a_kz^k$ be the $n$th partial sum of
$f(z)=\sum_{k=0}^{\infty{}}a_kz^k$. We show that $\RE s_n(f/z,z)>0$ holds for all $z\in\D,\ n\in\N$, and all starlike functions $f$ of order
$\lambda$ iff $\lambda_0\leq\lambda<1$ where
$\lambda_0=0.654222...$ is the unique solution
$\lambda\in(\frac{1}{2},1)$ of the equation
$\int_{0}^{3\pi/2}t^{1-2\lambda}\cos t \,dt=0$. Here $\D$ denotes
the unit disk in the complex plane $\C$. This result is the best
possible with respect to $\lambda_0$. In particular, it
shows that for the Gegenbauer polynomials $C_{n}^{\mu}(x)$ we
have $\sum_{k=0}^n C_{k}^{\mu}(x)\cos k \theta>0$ for all
$n\in\N,\ x\in[-1,1]$, and
$0<\mu\leq\mu_0:=1-\lambda_0=0.345778...$. This result complements
an inequality of Brown, Wang, and Wilson (1993) and extends a
result of Ruscheweyh and Salinas (2000). 相似文献
7.
Xiao Erjian 《数学年刊B辑(英文版)》1993,14(4):497-506
The author defines, using jets, cohomology $H^p(\Lambda _{f,k-})$ for hypersurfaces, which are invariant under contact transformations. For isolated hypersurface singularities, it is proved that
$H^0(\Lambda _{f,k-})=O_{U,0}/f^{k+1}O_{U,0},$
$H^p(\Lambda _{f,k-})=0,1\leq p \leq N-3 or p=N,$
$dimH^{N-2}(\Lambda _{f,k-})-dimH^{N-1}(\Lambda _{f,k-})=\[\left( {\begin{array}{*{20}{c}}
k \ N
\end{array}} \right)\dim {O_{U,0}}/(f,\frac{{\partial f}}{{\partial {x_1}}}, \cdots ,\frac{{\partial f}}{{\partial {x_N}}}){O_{U,0}}\] $
The algorithm of computation for H^{N-2} and H^{N-1} is given, and it is proved that $H^{N-1}=0$ when f is quasi-homogeneous. 相似文献
8.
朱立 《数学年刊A辑(中文版)》2019,40(4):365-376
令■设λ_1,λ_2,λ_3是不全同号的非零实数,且满足λ_1/λ_2为无理数,则对于任意实数η和ε 0,不等式■有无穷多组素数解p_1,p_2,p_3.该结果改进了Gambini,Languasco和Zaccagnini的结果. 相似文献
9.
Let Fq be a finite field with q = pf elements,where p is an odd prime.Let N(a1x12 + ···+anxn2 = bx1 ···xs) denote the number of solutions(x1,...,xn) of the equation a1x12 +···+ anxn2 = bx1 ···xs in Fnq,where n 5,s n,and ai ∈ F*q,b ∈ F*q.In this paper,we solve the problem which the present authors mentioned in an earlier paper,and obtain a reduction formula for the number of solutions of equation a1x21 + ··· + anxn2 = bx1 ···xs,where n 5,3 ≤ s n,under a certain restriction on coefficients.We also obtain an explicit formula for the number of solutions of equation a1x21 + ··· + anxn2 = bx1 ···xn-1 in Fqn under a restriction on n and q. 相似文献
10.
本文我们考虑了无关机上的平行分批排序问题.对于批容量无限的平行批排序模型,目标是极小化总完工时间,我们对$p_{ij}\leq p_{ik}$ $(i=1, \cdots, m; 1\leq j\neq k\leq n)$这种一致性的情况设计了多项式的动态规划算法.对于批容量有限的平行批排序模型,我们讨论了$p_{ij}=p_{i}$ $(i=1, \cdots, m; j=1,\cdots, n)$这种情况, 当不考虑工件可被拒绝时,对极小化加权总完工时间的排序,我们给出了其最优算法;当考虑工件可被拒绝时,对极小化被接收工件的加权总完工时间加上被拒绝工件的总拒绝费用的排序,我们设计了一拟多项时间算法. 相似文献
11.
设$X_1,X_2,\cdots,X_n$和$X^*_1,X^*_2,\cdots,X^*_n$分别服从正态分布$N(\mu_i,\sigma^2)$和$N(\mu^*_i,\sigma^2)$,以$X_{(1)}$,$X^*_{(1)}$分别表示$X_1,\cdots,X_n$和$X^*_1,\cdots,X^*_n$的极小次序统计量,以$X_{(n)}$, $X^*_{(n)}$分别表示$X_1,\cdots,X_n$和$X^*_1,\cdots$,$X^*_n$的极大次序统计量. 我们得到了如下结果:(i)\,如果存在严格单调函数$f$使得$(f(\mu_{1}),\cdots,f(\mu_{n}))\succeq_{\text{m}}$ $(f(\mu^{*}_{1}),\cdots,f(\mu^{*}_{n}))$,且$f'(x)f'(x)\!\geq\!0$, 则$X_{(1)}\!\leq_{\text{st}}\!X^*_{(1)}$;(ii)\,如果存在严格单调函数$f$使得$(f(\mu_{1})$,$\cdots,f(\mu_{n}))\succeq_{\text{m}}(f(\mu^{*}_{1}),\cdots,f(\mu^{*}_{n}))$,且$f'(x)f'(x)\leq 0$, 则$X_{(n)}\geq_{\text{st}}X^*_{(n)}$.(iii)\,设$X_{1},X_{2},\cdots,X_{n}$和\, $X^*_{1},X^*_{2},\cdots,X^*_{n}$分别服从正态分布$N(\mu,\sigma_i^2)$和$N(\mu,\sigma_i^{*2})$,若$({1}/{\sigma_{1}},\cdots,{1}/{\sigma_{n}})\succeq_{\text{m}}({1}/{\sigma^{*}_{1}},\cdots,{1}/{\sigma^{*}_{n}})$,则有$X_{(1)}\leq_{\text{st}}X^*_{(1)}$和$X_{(n)}\geq_{\text{st}}X^*_{(n)}$同时成立. 相似文献
12.
本文考虑离散时间风险模型$U_n=(U_{n-1}+Y_n)(1+r_n)-X_n$,$n=1,2,\cdots$, 其中$U_0=x>0$为保险公司的初始准备金,$r_n$为在第$n$个时刻的利率, $Y_n$为到时刻$n$为止的总保费收入,$X_n$为到时刻$n$为止的所支付的全部索赔,$U_n$表示保险公司在时刻$n$的盈余. 当$Y_n$和$r_n$满足某些温和条件时,我们得到了在\, $x\to\infty$时,有限时间破产概率$\psi(x,N)=\pr\big(\min\limits_{0\leq n\leqN}U_n<0|U_0=x\big)$关于$N\geq1$的一致渐近的关系式\,$\psi(x,N)\sim\tsm_{k=1}^{N}\ol{F}_X((1+r_1)\cdots(1+r_n)x)$,其中$\ol{F}_X(x)$是$X_1$的尾分布. 相似文献
13.
Qing-Ming Cheng Hongcang Yang 《Transactions of the American Mathematical Society》2006,358(6):2625-2635
Let be a connected bounded domain in an -dimensional Euclidean space . Assume that are eigenvalues of a clamped plate problem or an eigenvalue problem for the Dirichlet biharmonic operator: Then, we give an upper bound of the -th eigenvalue in terms of the first eigenvalues, which is independent of the domain , that is, we prove the following: Further, a more explicit inequality of eigenvalues is also obtained.
14.
令$k,\ell \geq 2$是正整数.令$A$是无限非负整数的集合.对$n\in \mathbb{N}$, 令$r_{1,k,\ldots,k^{\ell-1}}(A, n)$表示方程$n=a_0+ka_1+\cdots +k^{\ell-1}a_{\ell-1}$, $a_0, \ldots, a_{\ell-1}\in A$解的个数. 在本文中, 我们证明了对所有$n\geq 0$, $r_{1,k,\ldots,k^{\ell-1}}(A, n)=1$当且仅当$A$是$k^\ell$进制展开中数位小于$k$的所有非负整数的集合. 这个结果部分回答了S\''{a}rk\"{o}zy and S\''{o}s关于多维线性型表示的一个问题. 相似文献
15.
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
16.
Ying-Guang Shi 《计算数学(英文版)》1984,2(4):328-330
The problem discussed in this paper is to determine a nonnegative interpolating polynomial which takes the prescribed nonegative values $y_0,y_1,\cdots,y_n$ at given distinct points $x_0,x_1,\cdots,x_n$: $p(x_i)=y_i),i=0,1,\cdots,n$. This paper shows:(1) $2n$ is the least number of $m$ such that there exists a polynomial $p\in P_m^{+}$, the set of all nonnegative polynomials of degree $\leq m$, satisfying the above equations for any choice of $y_i\geq 0$. (2) the above equations have a unique solution in $P_{2n}^{+}$ if and only if at most one of the $y_i's$ is nonzero. 相似文献
17.
A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let and be two Hermitian matrices, and let and be their eigenvalues arranged in ascending order. Then for any unitarily invariant norm . In this paper, we generalize this to the perturbation theory for diagonalizable matrix pencils with real spectra. The much studied case of definite pencils is included in this.
18.
19.
Xiaomeng Li 《偏微分方程(英文版)》2020,33(2):171-192
Let $\Omega\subset \mathbb{R}^4$ be a smooth bounded domain, $W_0^{2,2}(\Omega)$ be the usual Sobolev space. For any positive integer $\ell$, $\lambda_{\ell}(\Omega)$ is the $\ell$-th eigenvalue of the bi-Laplacian operator. Define $E_{\ell}=E_{\lambda_1(\Omega)}\oplus E_{\lambda_2(\Omega)}\oplus\cdots\oplus E_{\lambda_{\ell}(\Omega)}$, where $E_{\lambda_i(\Omega)}$ is eigenfunction space associated with $\lambda_i(\Omega)$. $E^{\bot}_{\ell}$ denotes the orthogonal complement of $E_\ell$ in $W_0^{2,2}(\Omega)$. For $0\leq\alpha<\lambda_{\ell+1}(\Omega)$, we define a norm by $\|u\|_{2,\alpha}^{2}=\|\Delta u\|^2_2-\alpha \|u\|^2_2$ for $u\in E^\bot_{\ell}$. In this paper, using the blow-up analysis, we prove the following Adams inequalities$$\sup_{u\in E_{\ell}^{\bot},\,\| u\|_{2,\alpha}\leq 1}\int_{\Omega}e^{32\pi^2u^2}{\rm d}x<+\infty;$$moreover, the above supremum can be attained by a function $u_0\in E_{\ell}^{\bot}\cap C^4(\overline{\Omega})$ with $\|u_0\|_{2,\alpha}=1$. This result extends that of Yang (J. Differential Equations, 2015), and complements that of Lu and Yang (Adv. Math. 2009) and Nguyen (arXiv: 1701.08249, 2017). 相似文献
20.
A graph $G$ is $k$-triangular if each of its edge is contained in at least $k$ triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph $G$ is a sequence of distinct triangles $T_1 T_2\cdots T_k$ in $G$ such that for $1\leq i\leq k-1, |E(T_i )\cap E(T_{i+1})|=1$ and
$E(T_i)\cap E(T_j)=\emptyset$ if $j>i+1$. Two edges $e,e''\in E(G)$ are triangularly connected if there is a triangle-path $T_1,T_2,\cdots, T_k$ in $G$ such that $e\in E(T_1)$ and $e''\in E(T_k)$. Two edges $e,e''\in E(G)$ are equivalent if they are the same, parallel or triangularly connected. It is easy to see that this is an equivalent relation. Each equivalent class is called a triangularly connected component. In this paper, we prove that every 4-edge-connected triangular graph $G$ is ${\mathbb Z}_3$-connected, unless it has a triangularly connected component which is not ${\mathbb Z}_3$-connected but admits a nowhere-zero 3-flow. 相似文献