共查询到18条相似文献,搜索用时 203 毫秒
1.
该文讨论了增长曲线模型$Y=X_{1}BX_{2}+\epsilon$在约束条件$X_{2}'B'X_{1}'NX_{1}BX_{2}\leq\Sigma$下回归系数线性估计$DYF$的泛可容许性问题,在损失函数$(d(Y)-KBL)'(d(Y)-KBL)$下,给出了回归系数的线性估计是泛可容许性的充要条件,其结果推广了文献中已有的结论. 相似文献
2.
本文证明了存在一个一一对应$\varphi: {\cal J}\cup{\cal J}'\longrightarrow\delta\cup\delta'$,它满足: \ \ (1) $\varphi|{\cal J}: ({\cal J},\subset)\longrightarrow(\delta,\leq)$是frame同构. \ \ (2) $\varphi|{\cal J}': ({\cal J}',\subset)\longrightarrow(\delta',\leq)$是coframe同构. 相似文献
3.
令\{$X$, $X_n$, $n\ge 1$\}是期望为${\mathbb{E}}X=(0,\ldots,0)_{m\times 1}$和协方差阵为${\rm Cov}(X,X)=\sigma^2I_m$的独立同分布的随机向量列, 记$S_n=\sum_{i=1}^{n}X_i$, $n\ge 1$. 对任意$d>0$和$a_n=o((\log\log n)^{-d})$, 本文研究了${{\mathbb{P}}(|S_n|\ge (\varepsilon+a_n)\sigma \sqrt{n}(\log\log n)^d)$的一类加权无穷级数的重对数广义律的精确速率. 相似文献
4.
李云霞 《数学物理学报(A辑)》2006,26(5):675-687
该文主要讨论的是滑线性过程 $X_k=\sum\limits_{i=-\infty}^\infty a_{i+k}\varepsilon_i$,其中 $\{\varepsilon_i; -\infty$\varphi$ -混合或负相伴随机变量序列,$\{a_i;-\inftyp$, 若 $E|\varepsilon_1|^r<\infty$$\lim_{\epsilon\searrow 0}\epsilon^{2(r-p)/(2-p)}\sum\limits_{n=1}^\infty n^{r/p-2}P\{|S_n|\geq \epsilonn^{1/p}\}=\frac{p}{r-p}E|Z|^{2(r-p)/(2-p)},$ 其中 $Z$ 是服从均值为零,方差为 $\tau^2=\sigma^2\cdot(\sum\limits_{i=-\infty}^\infty a_i)^2$的正态分布. 相似文献
5.
在$\C^n$中的有界完全Reinhardt域$\Omega$上推广的Roper-Suffridge算子$\Phi(f)$定义为 \begin{eqnarray*} \Phi^r_{n,\beta_2, \gamma_2,\ldots, \beta_n, \gamma_n}(f)(z)\!=\!\Big(rf\Big(\frac{z_1}{r}\Big), \Big(\frac{rf(\frac{z_1}{r})}{z_1}\Big)^{\beta_2}\Big(f’\Big(\frac{z_1}{r}\Big)\Big)^{\gamma_2}z_2,\ldots, \Big(\frac{rf(\frac{z_1}{r})}{z_1}\Big)^{\beta_n}\Big(f’\Big(\frac{z_1}{r}\Big)\Big)^{\gamma_n}z_n \Big), \end{eqnarray*} 其中 $n\geq2$, $(z_1, z_2,\ldots, z_n)\in \Omega$, $r=r(\Omega)=\sup\{|z_1|: (z_1, z_2,\ldots, z_n)\in \Omega\}, 0\leq \gamma_j\leq 1-\beta_j, 0\leq \beta_j\leq 1$, 这里选取幂函数的单值解析分支, 使得 $(\frac{f(z_1)}{z_1})^{\beta_j}|_{z_1=0}= 1$ 和 $(f’(z_1))^{\gamma_j}|_{z_1=0}=1, j=2,\ldots, n$. 证明了 $\Omega$上的算子 $\Phi^r_{n,\beta_2, \gamma_2,\ldots, \beta_n, \gamma_n}(f)$ 是将 $S^*_\alpha(U)$ 的子集映入$S^*_\alpha\,(\Omega)\,(0\leq \alpha<1)$, 且对于一些合适的常数 $\beta_j, \gamma_j, p_j$, $D_p$上的这个算子 $\Phi^r_{n,\beta_2, \gamma_2,\ldots, \beta_n, \gamma_n}(f)$ 保持$\alpha$阶星形性或保持$\beta$ 型螺形性, 其中 $ D_p=\bigg\{(z_1, z_2,\ldots, z_n)\in \C^n: \he{j=1}{n}|z_j|^{p_j}<1\bigg\},\quad p_j>0, j=1, 2,\ldots, n, $ $U$是复平面$\C$上的单位圆, $S^*_\alpha(\Omega)$ 是 $\Omega$ 上所有正规化$\alpha$阶星形映射所成的类. 也得到: 对于某些合适的常数 $\beta_j, \gamma_j, p_j$ 和 在$\C^n$中的有界完全Reinhardt域$\Omega$上推广的Roper-Suffridge算子$\Phi(f)$定义为 \begin{eqnarray*} \Phi^r_{n,\beta_2, \gamma_2,\ldots, \beta_n, \gamma_n}(f)(z)\!=\!\Big(rf\Big(\frac{z_1}{r}\Big), \Big(\frac{rf(\frac{z_1}{r})}{z_1}\Big)^{\beta_2}\Big(f’\Big(\frac{z_1}{r}\Big)\Big)^{\gamma_2}z_2,\ldots, \Big(\frac{rf(\frac{z_1}{r})}{z_1}\Big)^{\beta_n}\Big(f’\Big(\frac{z_1}{r}\Big)\Big)^{\gamma_n}z_n \Big), \end{eqnarray*} 其中 $n\geq2$, $(z_1, z_2,\ldots, z_n)\in \Omega$, $r=r(\Omega)=\sup\{|z_1|: (z_1, z_2,\ldots, z_n)\in \Omega\}, 0\leq \gamma_j\leq 1-\beta_j, 0\leq \beta_j\leq 1$, 这里选取幂函数的单值解析分支, 使得 $(\frac{f(z_1)}{z_1})^{\beta_j}|_{z_1=0}= 1$ 和 $(f’(z_1))^{\gamma_j}|_{z_1=0}=1, j=2,\ldots, n$. 证明了 $\Omega$上的算子 $\Phi^r_{n,\beta_2, \gamma_2,\ldots, \beta_n, \gamma_n}(f)$ 是将 $S^*_\alpha(U)$ 的子集映入$S^*_\alpha\,(\Omega)\,(0\leq \alpha<1)$, 且对于一些合适的常数 $\beta_j, \gamma_j, p_j$, $D_p$上的这个算子 $\Phi^r_{n,\beta_2, \gamma_2,\ldots, \beta_n, \gamma_n}(f)$ 保持$\alpha$阶星形性或保持$\beta$ 型螺形性, 其中 $ D_p=\bigg\{(z_1, z_2,\ldots, z_n)\in \C^n: \he{j=1}{n}|z_j|^{p_j}<1\bigg\},\quad p_j>0, j=1, 2,\ldots, n, $ $U$是复平面$\C$上的单位圆, $S^*_\alpha(\Omega)$ 是 $\Omega$ 上所有正规化$\alpha$阶星形映射所成的类. 也得到: 对于某些合适的常数 $\beta_j, \gamma_j, p_j$ 和 在C~n中的有界完全Reinhardt域Ω上推广的Roper-Suffridge算子Φ(f)定义为Φ_(n,β_2,γ_2,…,β_n,γ_n)~r(f)(z)=(rf(z_1/r),((rf(z_1/r))/z_1)~(β_2)(f′(z_1/r))~γ_2_(z_2,…,)((rf(z_1/r))/z_1)~(β_n)(f′(z_1/r))~(γ_n)_(z_n),其中n≥2,(z_1,z_2,…,z_n)∈Ω,r=r(Ω)=sup{|z_1|:(z_1,z_2,…,z_n)∈Ω},0≤γ_j≤1-β_j,0≤β_j≤1,这里选取幂函数的单值解析分支,使得((f(z_1))/z_1)~(β_j)|_(z_1=0)=1和(f′(z_1))~(γ_j)|_(z_1=0)=1,j= 2,…,n.证明了Ω上的算子Φ_(n,β_2,γ_2,…,β_n,γ_n)~r(f)是将S_α~*(U)的子集映入S_α~*(Ω)(0≤α<1),且对于一些合适的常数β_j,γ_j,p_j,D_p上的这个算子Φ_(n,β_2,γ_2,…,β_n,γ_n)~r(f)保持α阶星形性或保持β型螺形性,其中(?) U是复平面C上的单位圆,S_α~*(Ω)是Ω上所有正规化α阶星形映射所成的类.也得到:对于某些合适的常数β_j,γ_j,p_j和0≤α<1,Φ_(n,β_2,γ_2,…,β_n,γ_n)~r(f)∈S_α~*(D_p)当且仅当f∈S_α~*(U). 相似文献
6.
设有该文第1节所描述的广义线性回归模型,以$\underline{\lambda}_n$和$\overline{\lambda}_n$分别记$\sum\limits_{i=1}^{n}Z_iZ_i^{\prime}$的最小和最大特征根,$\hat{\beta}_n$记$\beta_0$的极大似然估计.在文献[1]中,当\{$Z_i,i\ge1$\}有界时得到$\hat{\beta}_n$强相合的充分条件,在自然联系和非自然联系下分别为$\underline{\lambda}_n\rightarrow\infty$, $(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$(对某$\delta>0$)以及$\underline{\lambda}_n\rightarrow\infty$, $\overline{\lambda}_n=O(\underline{\lambda}_n)$.作者将后一结果改进为只要求$(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$,从而与自然联系情况下的条件达到一致. 相似文献
7.
该文证明带有粗糙核的分数次积分算子的多线性算子\[T_{\Omega,\alpha}^{A}(f)(x)={\rm {\rm p.v.}}\int_{R^{n}}P_{m}(A;x,y)\frac{\Omega(x-y)}{|x-y|^{n-\alpha+m-1}}f(y){\rm d}y\]的$(H^{1}(\rr^{n}),L^{\frac{n}{n-\alpha},\infty}(\rr^{n}))$有界性. 相似文献
8.
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
9.
该文研究一类推广的${\bf R}^{d}$中具有有限记忆的随机递归模型,引入了一个与该结构有关的函数$\Psi(\beta),\beta\geq 0$,构造了一个随机测度$\mu_\omega$,证明了由该结构产生的随机集 $K(\omega)$的Hausdorff维数是$\alpha:=\inf\{\beta:\Psi(\beta)\leq1\}$. 相似文献
10.
张良云 《数学物理学报(A辑)》2006,26(4):601-611
该文在弱双代数$H$上给出了扭曲积$(H^\sigma,\cdot_\sigma)$成为弱双代数的充分必要条件.设$[B, H, \tau]$是一个弱斜配对, 并且$\tau$可逆,则在某个条件下弱双交叉积$B\bowtie_\tau H$是一个弱双代数. 如果$(B,H, \sigma)$是弱相关Long双代数, 并且$\sigma$可逆,则弱双交叉积$B^{OP}\bowtie_\sigma H$可以被构造. 它的乘法是:$(x\otimes h)(y\otimes g)=\Sigma\sigma(y_1, h_1)y_2x\otimes h_2g\sigma^{-1}(y_3, h_3),$ 特别地, 如果$(B, H,\sigma)$是相关Long双代数, 则$(B^{OP \bowtie_\sigma H,\beta)$是Long双代数当且仅当对任意$b, d\in B^{OP}; g, \ell\in H$,$\Sigma\sigma^{-1}(b, g_2\ell)\sigma(d, g_1)=\Sigma\sigma^{-1}(b,\ell g_1)\sigma(d, g_2),$ 其中$B$为$H$的子Hopf代数,$\beta$定义为$\beta(b\bowtie_\sigma h\otimes c\bowtie_\sigma g)=\varepsilon_H(h)\varepsilon_{B^{OP}}(c)\sigma^{-1}(b, g).$ 对于Sweedler 4维Hopf代数$H$, 作者给出一个例子说明:此弱双交叉积$(B^{OP}\bowtie_\sigma H, \beta)$不仅是一个Long双代数,而且是一个非可换和非余可换的8维Hopf代数. 最后, 设$B,H$都是弱双代数, $\sigma: B\otimes H\rightarrow k$是一个线性映射, 作者给出了$(B,\sigma,\leftharpoonup, \Delta_B)$是弱相关右$(H, B)$ -重模代数的充分必要条件. 相似文献
11.
多尺度分析生成元的刻画 总被引:1,自引:0,他引:1
本文将给出多尺度分析生成元的一种完全刻画.将证明:函数φ∈L~2(R)是二进多尺度分析生成元的充要条件是(1)存在{a_k}∈l~2,φ(x)=∑_(k∈Z)a_kφ(2x-k);(2)存在正数A相似文献
12.
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
13.
Benboubker Mohamed Badr Hjiaj Hassan OUARO Stanislas 《Journal of Applied Analysis & Computation》2014,4(3):245-270
In this work, we give an existence result of entropy solutions for nonlinear anisotropic elliptic equation of the type $$- \mbox{div} \big( a(x,u,\nabla u)\big)+ g(x,u,\nabla u) + |u|^{p_{0}(x)-2}u = f-\mbox{div} \phi(u),\quad \mbox{ in } \Omega,$$ where $-\mbox{div}\big(a(x,u,\nabla u)\big)$ is a Leray-Lions operator, $\phi \in C^{0}(I\!\!R,I\!\!R^{N})$. The function $g(x,u,\nabla u)$ is a nonlinear lower order term with natural growth with respect to $|\nabla u|$, satisfying the sign condition and the datum $f$ belongs to $L^1(\Omega)$. 相似文献
14.
Guoen HU 《数学年刊B辑(英文版)》2017,38(3):795-814
Let T_σ be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ∈Z∥σ_κ∥W~s(R~(2n)) ∞ for some s ∈ (n, 2n]. In this paper, it is proved that the commutator generated by T_σ and CMO(R~n) functions is a compact operator from L~(p1)(R~n, w_1) × L~(p2)(R~n, w_2) to L~p(R~n, ν_w) for appropriate indices p_1, p_2, p ∈ (1, ∞) with1 p=1/ p_1 +1/ p_2 and weights w_1, w_2 such that w = (w_1, w_2) ∈ A_(p/t)(R~(2n)). 相似文献
15.
In this article,we consider the Bagley-Torvik type fractional differential equation ~cD~(ν1) l(t)-a~cD~(ν2) l(t) = g(t, l(t)) and differential inclusion ~cD~(ν1) l(t)-a~cD~(ν2) l(t) ∈ G(t, l(t)),t ∈(0, 1) subjecting to l(0) = l_0,and■ ds where 1 ν_1 ≤ 2, 1 ≤ν_2 ν_1,0 ω≤ 1, χ = ν_1-ν_2 0, a, λ′are given constants. By using Leray-Schauder degree theory and fixed point theorems, we prove the existence of solutions. Our results extend the existence theorems for the classical Bagley-Torvik equation and some related models. 相似文献
16.
Yunying Huang Bing Zheng Guoliang Chen 《Journal of Applied Analysis & Computation》2018,8(5):1555-1574
For the multiple restricted partitioned linear model ${\mathscr{M}}=\{y, X_1$ $\beta_1+\cdots+X_s\beta_s\mid A_1\beta_1=b_1, \cdots, A_s\beta_s=b_s, \Sigma\}$, the relationships between the restricted partitioned linear model ${\mathscr{M}}$ and the corresponding $s$ small restricted linear models ${\mathscr{M}}_i=\{y, X_i\beta_i\mid A_i\beta_i=b_i, \Sigma\},~i=1, \cdots , s$ are studied. The necessary and sufficient conditions for the best linear unbiased estimators $(\mbox{BLUEs})$ under the full restricted model to be the sums of BLUEs under the $s$ small restricted model are derived. Some statistical properties of the \mbox{BLUEs} are also described. 相似文献
17.
Liu Qiao 《Journal of Applied Analysis & Computation》2014,4(4):355-365
We provide two regularity criteria for the weak solutions of the 3D micropolar fluid equations, the first one in terms of one directional derivative of the velocity, i.e., $\partial_{3}u$, while the second one is is in terms of the behavior of the direction of the velocity $\frac{u}{|u|}$. More precisely, we prove that if \begin{equation*} \partial_{3}u \in L^{\beta}(0,T;L^{\alpha}(\mathbb{R}^{3}))\quad\text{ with }\frac{2}{\beta}+\frac{3}{\alpha}\leq 1+\frac{1}{\alpha}, 2< \alpha \leq\infty, 2\leq\beta< \infty; \end{equation*} or \begin{equation*} \operatorname{div}\left(\frac{u}{|u|}\right)\in L^{\frac{4}{1-2r}}(0,T;\dot{X}_{r}(\mathbb{R}^{3}))\quad \text{ with } 0\leq r< \frac{1}{2}, \end{equation*} then the weak solution $(u(x,t),\omega(x,t))$ is regular on $\mathbb{R}^{3}\times [0,T]$. Here $\dot{X}_{r}(\mathbb{R}^{3})$ is the multiplier space. 相似文献
18.
Consider the Kirchhoff type equation \begin{equation}\label{eq0.1}-\left(a+b\int_{\mathbb{R}^{N}}|\nabla u|^{2}\,dx\right) \Delta u=\left(\frac{1}{|x|^\mu}*F(u)\right)f(u)\ \ \mbox{in}\ \mathbb{R}^N, \ \ u\in D^{1,2}(\mathbb{R}^N), ~~~~~~(0.1)\end{equation}where $a>0$, $b\geq0$, $0<\mu<\min\{N, 4\}$ with $N\geq 3$, $f: \mathbb{R}\to\mathbb{R}$ is a continuous function and $F(u)=\int_0^u f(t)\,dt$. Under some general assumptions on $f$, we establish the existence of a nontrivial spherically symmetric solution for problem (0.1). The proof is mainly based on mountain pass approach and a scaling technique introduced by Jeanjean. 相似文献