共查询到20条相似文献,搜索用时 281 毫秒
1.
确定了一类中心循环的有限p-群G的自同构群.设G=X_3(p~m)~(*n)*Z_(p~(m+r)),其中m≥1,n≥1和r≥0,并且X_3(p~m)=x,y|x~(p~m)=y~(p~m)=1,[x,y]~(p~m)=1,[x,[x,y]]=[y,[x,y]]=1.Aut_nG表示Aut G中平凡地作用在N上的元素形成的正规子群,其中G'≤N≤ζG,|N|=p~(m+s),0≤s≤r,则(i)如果p是一个奇素数,那么AutG/Aut_nG≌Z_(p~((m+s-1)(p-1))),Aut_nG/InnG≌Sp(2n,Z_(p~m))×Z_(p~(r-s)).(ii)如果p=2,那么AutG/Aut_nG≌H,其中H=1(当m+s=1时)或者Z_(2~(m+s-2))×Z_2(当m+s≥2时).进一步地,Aut_nG/InnG≌K×L,其中K=Sp(2n,Z_(2~m))(当r0时)或者O(2n,Z_(2~m))(当r=0时),L=Z_(2~(r-1))×Z_2(当m=1,s=0,r≥1时)或者Z_(2~(r-s)). 相似文献
2.
M. I. Graev 《Acta Appl Math》2005,86(1-2):3-19
One considers Gelfand’s hypergeometric functions on the space of p×q matrices and their generalizations to the case of multi-dimensional matrices of arbitrary order k 1×???×k p. It is shown that these functions form bases of some $\frak g$ -modules, where $\frak g=\frak{gl}(p,\mathbb{C})\times\frak{gl}(q,\mathbb{C})$ or $\frak g=\frak{gl}(k_{1},\mathbb{C})\times\cdots\times\frak{gl}(k_{p},\mathbb{C})$ , respectively. 相似文献
3.
Xiaoping YUAN 《数学年刊B辑(英文版)》2017,38(5):1037-1046
It is shown that all solutions are bounded for Duffing equation x+ x~(2n+1)+2∑i=nPj(t)x~j= 0, provided that for each n + 1 ≤ j ≤ 2 n, P_j ∈ C~y(T~1) with γ 1-1/n and for each j with 0 ≤ j ≤ n, Pj ∈ L(T~1) where T~1= R/Z. 相似文献
4.
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
5.
Classification of Solutions to a Critically Nonlinear System of Elliptic Equations on Euclidean Half-Space 下载免费PDF全文
Mathew R. Gluck & Lei Zhang 《偏微分方程(英文版)》2015,28(1):74-94
For $N\geq 3$ and non-negative real numbers $a_{ij}$ and $b_{ij}$ ($i,j= 1, \cdots, m$), the semi-linear elliptic system\begin{equation*}
\begin{cases}\Delta u_i+\prod\limits_{j=1}^m u_j^{a_{ij}}=0,\text{in}\mathbb{R}_+^N,\\dfrac{\partial u_i}{\partial y_N}=c_i\prod\limits_{j=1}^m u_j^{b_{ij}},\text{on} \partial\mathbb{R}_+^N,\end{cases}\qquad
i=1,\cdots,m,\end{equation*}
%
is considered, where $\mathbb{R}_+^N$ is the upper half of $N$-dimensional Euclidean space. Under suitable assumptions on the exponents $a_{ij}$ and $b_{ij}$, a classification theorem for the positive $C^2(\mathbb{R}_+^N)\cap C^1(\overline{R_+^N})$-solutions of this system is proven. 相似文献
6.
Qingyu Zheng & Zunwei Fu 《数学研究通讯:英文版》2009,25(3):241-245
In this paper, it is proved that the commutator$\mathcal{H}_{β,b}$ which is generated by the $n$-dimensional fractional Hardy operator $\mathcal{H}_β$ and $b\in \dot{Λ}_α(\mathbb{R}^n)$ is bounded from $L^P(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$, where $0<α<1,1
相似文献
7.
Hu Shuan 《数学年刊B辑(英文版)》1987,8(4):428-433
V is an n-dim unitary space.(?)~kV is the k-th tensor product space with the customaryinduced inner product.(?)∈L((?)~kV),W~⊥(?)={((?)x~(?),x(?)|x~(?)=x_1(?)…(?)x_k,x_1,…,x_k o.n}is called the numerical range of (?).Wang Boying proved in[11]that if (?)=A_1(?)…(?)A_k,A_i∈L(V),i=1,…,k,k相似文献
8.
完整地确定了换位子群是不可分Abel群的有限秩可除幂零群的结构,证明了下面的定理.设G是有限秩的可除幂零群,则G的换位子群是不可分Abel群当且仅当G'=Q或Q_p/Z且G可以分解为G=S×D,其中当G'=Q时,■当G'=Q_p/Z时,S有中心积分解S=S_1*S_2*…*S_r,并且可以将S形式化地写成■其中■,式中s,t都是非负整数,Q是有理数加群,π_κ(k=1,2,…,t)是某些素数的集合,满足π_1■Cπ_2■…■π_t,Q_π_k={m/n|(m,n)=1,m∈Z,n为正的π_k-数}.进一步地,当G'=Q时,(r;s;π_1,π_2,…,π_t)是群G的同构不变量;当G'=Q_p/Z时,(p,r;s;π_1,π_2,…,πt)是群G的同构不变量.即若群H也是有限秩的可除幂零群,它的换位子群是不可分Abel群,那么G同构于H的充分必要条件是它们有相同的不变量. 相似文献
9.
洪勇 《数学年刊A辑(中文版)》2011,32(5):599-606
设核函数K(u,v)具有对称性和齐次性,对如下定义的奇异重积分算子T:(Tf)(y)=∫R_+~n K(‖x‖α,‖y‖α)f(x)dx,y∈R_+~n,其中‖x‖α=(x_1~α+…+x_n~α)~1/α(α>0),研究了T的范数及其应用. 相似文献
10.
Abderrahmane Nitaj 《计算数学(英文版)》2002,20(4):337-348
AbstractAn elliptic curve is a pair (E,O), where ?is a smooth projective curve of genus 1 and O is a point of E, called the point at infinity. Every elliptic curve can be given by a Weierstrass equationE:y2 a1xy a3y = x3 a2x2 a4x a6.Let Q be the set of rationals. E is said to be dinned over Q if the coefficients ai, i = 1,2,3,4,6 are rationals and O is defined over Q.Let E/Q be an elliptic curve and let E(Q)tors be the torsion group of points of E denned over Q. The theorem of Mazur asserts that E(Q)tors is one of the following 15 groupsE(Q)tors Z/mZ, m = 1,2,..., 10,12,Z/2Z × Z/2mZ, m = 1,2,3,4.We say that an elliptic curve E'/Q is isogenous to the elliptic curve E if there is an isogeny, i.e. a morphism : E E' such that (O) = O, where O is the point at infinity.We give an explicit model of all elliptic curves for which E(Q)tors is in the form Z/mZ where m= 9,10,12 or Z/2Z × Z/2mZ where m = 4, according to Mazur's theorem. Morever, for every family of such elliptic curves, we give an explicit m 相似文献
11.
Let K be an algebraically closed field of characteristic zero, $\frak {g}$ be a countably dimensional locally finite Lie algebra over K, and $\frak {h} \subset \frak {g}$ be a (a priori non-abelian) locally
nilpotent subalgebra of $\frak {g}$ which coincides with its zero Fitting component. We classify all such pairs $(\frak {g}, \frak {h})$ under the assumptions that the locally solvable radical of $\frak {g}$ equals zero and that $\frak {g}$
admits a root decomposition with respect to $\frak {h}$. More precisely, we prove that $\frak {g}$ is the union of
reductive subalgebras $\frak {g}_n$ such that the intersections $\frak {g}_n \cap \frak {h}$ are nested Cartan subalgebras of $\frak {g}_n$
with compatible root decompositions. This implies that $\frak {g}$ is root-reductive and that $\frak {h}$ is abelian.
Root-reductive locally finite Lie algebras are classified in [6]. The result of the present note is
a more general version of the main classification theorem in [9] and is at the same time a new
criterion for a locally finite Lie algebra to be root-reductive. Finally we give an explicit example
of an abelian selfnormalizing subalgebra $\frak {h}$ of $\frak {g} = \frak {sl}(\infty)$ with respect to which $\frak {g}$ does not admit a
root decomposition.Work Supported in Part by the University of Hamburg and the Max Planck Institute for Mathematics, Bonn 相似文献
12.
Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y + εh_l~1(x) + ε~2h_l~2(x),y=-x- ε(f_n~1(x)y~(2p+1) + g_m~1(x)) + ∈~2(f_n~2(x)y~(2p+1) + g_m~2(x)),which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials h_l~1 and h_l~2 have degree l;f_n~1and f_n~2 have degree n;and g_m~1,g_m~2 have degree m.p ∈ N and[·]denotes the integer part function. 相似文献
13.
Order - We show that the poset of copies $\mathbb {P} (\mathbb {Q}_{n} )=\langle \{ f[X]: f\in \text {Emb} (\mathbb {Q}_{n} ) \},\subset \rangle $ of the countable homogeneous universal n-labeled... 相似文献
14.
15.
A monomial basis and a filtration of subalgebras for the universal enveloping algebra U(gl) of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V (λ) as a U(gl)-module into a direct sum of Weyl modules V (μ)’s as U(gl-1)modules is described. In particular, a new multiplicity formula for the Weyl module V (λ) is obtained in this note. 相似文献
16.
王建飞 《数学年刊A辑(中文版)》2013,34(2):223-234
在有界星形圆形域上定义了一个新的星形映射子族, 它包含了$\alpha$阶星形映射族和$\alpha$阶强星形映射族作为两个特殊子类.
给出了此类星形映射子族的增长定理和掩盖定理. 另外, 还证明了Reinhardt域$\Omega_{n,p_{2},\cdots,p_{n}}$上此星形映射子族在Roper-Suffridge算子
\begin{align*}
F(z)=\Big(f(z_{1}),\Big(\frac{f(z_{1})}{z_{1}}\Big)^{\beta_{2}}(f'(z_{1}))^{\gamma_{2}}z_{2},\cdots,
\Big(\frac{f(z_{1})}{z_{1}}\Big)^{\beta_{n}}(f'(z_{1}))^{\gamma_{n}}z_{n}\Big)'
\end{align*}
作用下保持不变, 其中
$\Omega_{n,p_{2},\cdots,p_{n}}=\{z\in
{\mathbb{C}}^{n}:|z_1|^2+|z_2|^{p_2}+\cdots + |z_n|^{p_n}<1\}$,
$p_{j}\geq1$, $\beta_{j}\in$ $[0, 1]$, $\gamma_{j}\in[0,
\frac{1}{p_{j}}]$满足$\beta_{j}+\gamma_{j}\leq1$,
所取的单值解析分支使得 $\big({\frac{f(z_{1})}{z_{1}}}\big)^{\beta_{j}}\big|_{z_{1}=0}=1$,
$(f'(z_{1}))^{\gamma_{j}}\mid_{{z_{1}=0}}=1$, $j=2,\cdots,n$. 这些结果不仅包含了许多已有的结果, 而且得到了新的结论. 相似文献
17.
Paul Alton Hagelstein 《Proceedings of the American Mathematical Society》2005,133(8):2327-2334
Let denote a sequence of measurable functions on , and let denote the weak norm. It is shown that
where is a sequence of independent random variables taking on values and with equal probability. Moreover, it is shown that
The paper concludes by providing an example indicating that, if , then the estimate
is the best possible.
where is a sequence of independent random variables taking on values and with equal probability. Moreover, it is shown that
The paper concludes by providing an example indicating that, if , then the estimate
is the best possible.
18.
Let $M^{n}(n\geq4)$ be an oriented compact submanifold with parallel
mean curvature in an $(n+p)$-dimensional complete simply connected
Riemannian manifold $N^{n+p}$. Then there exists a constant
$\delta(n,p)\in(0,1)$ such that if the sectional curvature of $N$
satisfies $\ov{K}_{N}\in[\delta(n,p), 1]$, and if $M$ has a lower
bound for Ricci curvature and an upper bound for scalar curvature,
then $N$ is isometric to $S^{n+p}$. Moreover, $M$ is either a
totally umbilic sphere $S^n\big(\frac{1}{\sqrt{1+H^2}}\big)$, a
Clifford hypersurface
$S^{m}\big(\frac{1}{\sqrt{2(1+H^2)}}\big)\times
S^{m}\big(\frac{1}{\sqrt{2(1+H^2)}}\big)$ in the totally umbilic
sphere $S^{n+1}\big(\frac{1}{\sqrt{1+H^2}}\big)$ with $n=2m$, or
$\mathbb{C}P^{2}\big(\frac{4}{3}(1+H^2)\big)$ in
$S^7\big(\frac{1}{\sqrt{1+H^2}}\big)$. This is a generalization of
Ejiri''s rigidity theorem. 相似文献
19.
证明了拟线性次椭圆方程组-X_α~*(a_(ij)~(αβ)(x,u)X_βu~j)=-X_α~*f_i~α+g_i,i=1,2,…,N,x∈Ω的弱解广义梯度Xu在Morrey空间L_x~(p,λ)(Ω,R~(mN))(p2)上的部分正则性,其中光滑实向量场族X=(X_1,X_2,…,X_m)满足H(o|¨)rmander有限秩条件,X_α~*是X_α的共轭;而且主项系数a_(ij)~(αβ)(x,u)关于x一致VMO(Vanishing Mean Oscillation的缩写,消失平均震荡)间断,且关于u为一致连续. 相似文献
20.
赵俊燕 《数学年刊A辑(中文版)》2017,38(4):405-418
研究了欧氏空间R~2中单位方体Q~2=[0,1]~2上沿曲面(t,s,γ(t,s))的振荡奇异积分算子T_(α,β)f(u,v,x)=∫_(Q~2)f(u-t,v-s,x-γ(t,s))e~(it~(-β_1)s~(-β_2))t~(-1-α_1)s~(-1-α_2)dtds从Sobolev空间L_τ~p(R~(2+n))到L~p(R~(2+n))中的有界性,其中x∈R~n,(u,v)∈R~2,(t,s,γ(t,s))=(t,s,t~(P_1)s~(q_1),t~(p_2)s~(q_2),…,t~(p_n)s~(q_n))为R~(2+n)上一个曲面,且β_1α_1≥0,β_2α_20.这些结果推广和改进了R~3上的某些已知的结果.作为应用,得到了乘积空间上粗糖核奇异积分算子的Sobolev有界性. 相似文献