共查询到20条相似文献,搜索用时 968 毫秒
1.
Let $\[(\Omega ,F,\mu )\]$ be a probabilty space with an increasing family $\[{\{ {F_t}\} _{t > 0}}\]$ of sub-fields satisfying the usual conditions. The following results are obtained: for $\[f \in BMO\]$, we have $\[f = g - h\]$ with $\[g,h \in BLO\]$; if in addition, f satisfies
then for $\[s > 0\]$ arbitrary, g,h can be chosen such that $\[g,h \in BLO\]$, and
$$\[E({\varepsilon ^{(a - \varepsilon )(g - {g_t})}}|{F_t}) \le {C_{a,\beta ,\varepsilon }},E({\varepsilon ^{(\beta - \varepsilon )(h - {h_t})}}|{F_t}) \le {C_{a,\beta ,\varepsilon }}\]$$
and for weights z, we have
$\[z \in {A_p} \cap S \Leftrightarrow z = {z_1}z_2^{1 - p}\]$ with $\[{z_i} \in {A_i} \cap S,i = 1,2\]$,
where $\[S = \{ \begin{array}{*{20}{c}}
{weight}&{z:C{z_{{T^ - }}} \le {z_T} \le C{z_{{T^ - }}}}
\end{array}\} \]$, $\[\forall \]$ stopping times T, outside a null set }. 相似文献
2.
Huang Yuanshi 《数学年刊B辑(英文版)》1985,6(1):15-26
First the author considers the system (1)$\frac{dx}{dt}=f(t,x,y,\varepsilon),\varepsilon\frac{dy}{dt}=g(t,x,y,\varepsilon)$ and its degenerate system (2)$\frac{dx}{dt}=f(t,x, y, 0), g(f, x, y, 0) =0$. In both noncritical and critical cases, sufficient conditions are established for the existence of almost periodic solutions of system (1) near the given solutions of system (2). The main method of proof is that, by performing suitable transformation, the author establishes exponential dichotomies, and then applies the theory of integral manifolds. Secondly, for the autonomous system (3)
$\frac{dx}{dt}=f(x,y,\varepsilon),\varepsilon\frac{dy}{dt}=g(x,y,\varepsilon)$, analogous results are obtained by performing the generalized normal coordinate transformation. 相似文献
3.
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
4.
Let P(G,λ) be the chromatic polynomial of a simple graph G. A graph G is chromatically unique if for any simple graph H, P(H,λ) = P(G,λ) implies that H is isomorphic to G. Many sufficient conditions guaranteeing that some certain complete tripartite graphs are chromatically unique were obtained by many scholars. Especially, in 2003, Zou Hui-wen showed that if n 31m2 + 31k2 + 31mk+ 31m? 31k+ 32√m2 + k2 + mk, where n,k and m are non-negative integers, then the complete tripartite graph K(n - m,n,n + k) is chromatically unique (or simply χ-unique). In this paper, we prove that for any non-negative integers n,m and k, where m ≥ 2 and k ≥ 0, if n ≥ 31m2 + 31k2 + 31mk + 31m - 31k + 43, then the complete tripartite graph K(n - m,n,n + k) is χ-unique, which is an improvement on Zou Hui-wen's result in the case m ≥ 2 and k ≥ 0. Furthermore, we present a related conjecture. 相似文献
5.
H. W. GOULD 《数学研究及应用》2019,39(6):603-606
The Catalan numbers $1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862,\ldots$ are given by $C(n)=\frac{1}{n+1}\binom{2n}{n}$ for $n\geq 0$. They are named for Eugene Catalan who studied them as early as 1838. They were also found by Leonhard Euler (1758), Nicholas von Fuss (1795), and Andreas von Segner (1758). The Catalan numbers have the binomial generating function $$\mathbf{C}(z) = \sum_{n=0}^{\infty}C(n)z^n = \frac{1 - \sqrt{1-4z}}{2z}$$ It is known that powers of the generating function $\mathbf{C}(z)$ are given by $$\mathbf{C}^a(z) = \sum_{n=0}^{\infty}\frac{a}{a+2n}\binom{a+2n}{n}z^n.$$ The above formula is not as widely known as it should be. We observe that it is an immediate, simple consequence of expansions first studied by J. L. Lagrange. Such series were used later by Heinrich August Rothe in 1793 to find remarkable generalizations of the Vandermonde convolution. For the equation $x^3 - 3x + 1 =0$, the numbers $\frac{1}{2k+1}\binom{3k}{k}$ analogous to Catalan numbers occur of course. Here we discuss the history of these expansions. and formulas due to L. C. Hsu and the author. 相似文献
6.
Yu Jianshe 《数学年刊B辑(英文版)》1997,18(4):449-456
ASYMPTOTICSTABILITYFORACLASSOFNONAUTONOMOUSNEUTRALDIFFERENTIALEQUATIONS**YUJIANSHE*ManuscriptreceivedJuly4,1995.RevisedMarch2... 相似文献
7.
Dvid Kunszenti-Kovcs 《Archiv der Mathematik》2019,112(2):205-212
Extending a result by Chilin and Litvinov, we show by construction that given any
$$\sigma $$
-finite infinite measure space
$$(\Omega ,\mathcal {A}, \mu )$$
and a function
$$f\in L^1(\Omega )+L^\infty (\Omega )$$
with
$$\mu (\{|f|>\varepsilon \})=\infty $$
for some
$$\varepsilon >0$$
, there exists a Dunford–Schwartz operator T over
$$(\Omega ,\mathcal {A}, \mu )$$
such that
$$\frac{1}{N}\sum _{n=1}^N (T^nf)(x)$$
fails to converge for almost every
$$x\in \Omega $$
. In addition, for each operator we construct, the set of functions for which pointwise convergence fails almost everywhere is residual in
$$L^1(\Omega )+L^\infty (\Omega )$$
. 相似文献
8.
Deng Guantie 《数学年刊B辑(英文版)》1986,7(3):330-338
In the present paper, we show that there exist a bounded, holomorphic function $\[f(z) \ne 0\]$ in the domain $\[\{ z = x + iy:\left| y \right| < \alpha \} \]$ such that $\[f(z)\]$ has a Dirichlet expansion $\[\sum\limits_{n = 0}^{ + \infty } {{d_n}{e^{ - {u_n}}}} \]$ in the halfplane $\[x > {x_f}\]$ if and only if $\[\frac{a}{\pi }\log r - \sum\limits_{{u_n} < r} {\frac{2}{{{u_n}}}} \]$ has a finite upperbound on $\[[1, + \infty )\]$, where $\[\alpha \]$ is a positive constant,$\[{x_f}( < + \infty )\]$ is the abscissa of convergence of $\[\sum\limits_{n = 0}^{ + \infty } {{d_n}{e^{ - {u_n}}}} \]$ and the infinite sequence $\[\{ {u_n}\} \]$ satisfies $\[\mathop {\lim }\limits_{n \to + \infty } ({u_{n + 1}} - {u_n}) > 0\]$. We also point out some necessary conditions and sufficient ones Such that a bounded holomorphic function in an angular(or half-band) domain is identically zero if an infinite sequence of its derivatives and itself vanish at some point of the domain. Here some result are generalizations of those in [4]. 相似文献
9.
Gao Ruxi 《数学年刊B辑(英文版)》1983,4(3):293-298
This paper deals with the following mixed problem for Quasilinear hyperbolic equationsThe M order uniformly valid asymptotic solutions are obtained and there errors areestimated. 相似文献
10.
S. H. Rasouli & H. Norouzi 《偏微分方程(英文版)》2015,28(1):1-8
We prove the existence of positive solutions for the system$$\begin{align*}\begin{cases}-\Delta_{p} u =\lambda a(x){f(v)}{u^{-\alpha}},\qquad x\in \Omega,\\-\Delta_{q} v = \lambda b(x){g(u)}{v^{-\beta}},\qquad x\in \Omega,\\u = v =0, \qquad x\in\partial \Omega,\end{cases}\end{align*}$$where $\Delta_{r}z={\rm div}(|\nabla z|^{r-2}\nabla z)$, for $r>1$ denotes the r-Laplacian operator and $\lambda$ is a positive parameter, $\Omega$ is a bounded domain in $\mathbb{R}^{n}$, $n\geq1$ with sufficiently smooth boundary and $\alpha, \beta \in (0,1).$ Here $ a(x)$ and $ b(x)$ are $C^{1}$ sign-changingfunctions that maybe negative near the boundary and $f,g $ are $C^{1}$ nondecreasing functions, such that $f, g :\ [0,\infty)\to [0,\infty);$ $f(s)>0,$ $g(s)>0$ for $s> 0$, $\lim_{s\to\infty}g(s)=\infty$ and$$\lim_{s\to\infty}\frac{f(Mg(s)^{\frac{1}{q-1}})}{s^{p-1+\alpha}}=0,\qquad \forall M>0.$$We discuss the existence of positive weak solutions when $f$, $g$, $a(x)$ and $b(x)$ satisfy certain additional conditions. We employ the method of sub-supersolution to obtain our results. 相似文献
11.
Nakao Hayashi Elena I. Kaikina Pavel I. Naumkin 《Transactions of the American Mathematical Society》2006,358(3):1165-1185
We study large time asymptotics of small solutions to the Cauchy problem for nonlinear damped wave equations with a critical nonlinearity
where 0,$"> and space dimensions . Assume that the initial data
where \frac{n}{2},$"> weighted Sobolev spaces are
Also we suppose that
where
Then we prove that there exists a positive such that the Cauchy problem above has a unique global solution satisfying the time decay property
for all 0,$"> where
where 0,$"> and space dimensions . Assume that the initial data
where \frac{n}{2},$"> weighted Sobolev spaces are
Also we suppose that
0,\int u_{0}\left( x\right) dx>0, \end{displaymath}">
where
Then we prove that there exists a positive such that the Cauchy problem above has a unique global solution satisfying the time decay property
for all 0,$"> where
12.
On ground state of fractional $p$-Kirchhoff equation involving subcritical and critical exponential growth 下载免费PDF全文
In this paper, we concern the existence of nontrivial ground state solutions of
fractional $p$-Kirchhoff equation
$$\left\{\begin{array}{ll}
m\left(\|u\|^p\right) [(-\Delta)_p^su+V(x)|u|^{p-2}u]
=f(x,u) \quad\text{in}\, \mathbb{R}^N, \vspace{0.2
cm}\\ \|u\|=\left(\int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy +\int_{\mathbb{R}^N}V(x)|u|^pdx\right)^{\frac{1}{p}},
\end{array}\right.$$
where $m:[0,+\infty)\rightarrow [0,+\infty)$ is a continuous function, $(-\Delta)_p^s$ is the fractional $p$-Laplacian operator with $0相似文献
13.
朱立 《数学年刊A辑(中文版)》2019,40(4):365-376
令■设λ_1,λ_2,λ_3是不全同号的非零实数,且满足λ_1/λ_2为无理数,则对于任意实数η和ε 0,不等式■有无穷多组素数解p_1,p_2,p_3.该结果改进了Gambini,Languasco和Zaccagnini的结果. 相似文献
14.
设$K$是自反的并且具有一致Gateaux可微范数的Banach空间$E$的非空有界闭凸子集.设$T:K\rightarrow K$是一致连续的伪压缩映象.假设$K$的每一非空有界闭凸子集对非扩张映象具有不动点性质.设$\{\lambda_n\}$是$(0,\frac{1}{2}]$中序列满足: (i) $\lim_{n\rightarrow \infty}\lambda_n=0$; (ii) $\sum_{n=0}^{\infty}\lambda_n=\infty$.任给$x_1\in K$,定义迭代序列$\{x_n\}$为:$x_{n+1}=(1-\lambda_n)x_n+\lambda_nTx_n-\lambda_n(x_n-x_1),n\geq 1.$若$\lim_{n\rightarrow \infty}\|x_n-Tx_n\|=0$, 则上述迭代产生的$\{x_n\}$强收敛到$T$的不动点. 相似文献
15.
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
16.
Dong Guangchang 《数学年刊B辑(英文版)》1986,7(3):277-302
In this paper, the author proves the existence and uniqueness of nonnegative solution for the first boundary value problem of uniform degenerated parabolic equation
$$\[\left\{ {\begin{array}{*{20}{c}}
{\frac{{\partial u}}{{\partial t}} = \sum {\frac{\partial }{{\partial {x_i}}}\left( {v(u){A_{ij}}(x,t,u)\frac{{\partial u}}{{\partial {x_j}}}} \right) + \sum {{B_i}(x,t,u)} \frac{{\partial u}}{{\partial {x_i}}}} + C(x,t,u)u\begin{array}{*{20}{c}}
{}&{(x,t) \in [0,T]}
\end{array},}\{u{|_{t = 0}} = {u_0}(x),x \in \Omega ,}\{u{|_{x \in \partial \Omega }} = \psi (s,t),0 \le t \le T}
\end{array}} \right.\]$$
$$\[\left( {\frac{1}{\Lambda }{{\left| \alpha \right|}^2} \le \sum {{A_{ij}}{\alpha _i}{\alpha _j}} \le \Lambda {{\left| \alpha \right|}^2},\forall a \in {R^n},0 < \Lambda < \infty ,v(u) > 0\begin{array}{*{20}{c}}
{and}&{v(u) \to 0\begin{array}{*{20}{c}}
{as}&{u \to 0}
\end{array}}
\end{array}} \right)\]$$
under some very weak restrictions, i.e. $\[{A_{ij}}(x,t,r),{B_i}(x,t,r),C(x,t,r),\sum {\frac{{\partial {A_{ij}}}}{{\partial {x_j}}}} ,\sum {\frac{{\partial {B_i}}}{{\partial {x_i}}} \in \overline \Omega } \times [0,T] \times R,\left| {{B_i}} \right| \le \Lambda ,\left| C \right| \le \Lambda ,\],\[\left| {\sum {\frac{{\partial {B_i}}}{{\partial {x_i}}}} } \right| \le \Lambda ,\partial \Omega \in {C^2},v(r) \in C[0,\infty ).v(0) = 0,1 \le \frac{{rv(r)}}{{\int_0^r {v(s)ds} }} \le m,{u_0}(x) \in {C^2}(\overline \Omega ),\psi (s,t) \in {C^\beta }(\partial \Omega \times [0,T]),0 < \beta < 1\],\[{u_0}(s) = \psi (s,0).\]$ 相似文献
17.
Xie Tingfan 《数学年刊B辑(英文版)》1980,1(34):429-436
Let \(f(x)\) be a bounded real function on [-1,1],we define the modulus of continuity of f as \[\omega (f,\delta ) = \mathop {\sup }\limits_{x,y \in [ - 1,1],\left| {x - y} \right| \le \delta } \left| {f(x) - f(y)} \right|\] and the modulus of smoothness of f as \[{\omega _2}(f,\delta ) = \mathop {\sup }\limits_{x \pm h \in [ - 1,1],\left| h \right| \le \delta } \left| {f(x + h) + f(x - h) - 2f(x)} \right|\] Functions \(f(x)\), continuous on [-1,1] and \({\omega _2}(f,\delta ) = o(\delta )\) ,are called uniformly smooth functions. It is well known that there is a uniformly smooth functions whose derivative exisits on a null-set only. It would is of interest to discuss what condition should be added on the nonnegative function \(\varphi (\delta )\), \(\left( {0 \le \delta \le \frac{1}{2}} \right)\),in order that every bounded function f satisfying\[{\omega _2}(f,\delta ) = O(\varphi (\delta ))\] possess continous (or finite) derivative. the main result of this paper are the following two theorems.
Theorem 1 let \(\varphi (\delta )\),\(\left( {0 \le \delta \le \frac{1}{2}} \right)\) ,be a nonnegative function, then, in order that every bounded function \(f(x)\) satisfying condition \[{\omega _2}(f,\delta ) = O(\varphi (\delta ))\] possess continous (or finite) derivative \(f'(x)\) on [-1,1],it is necessary and sufficient that the following condition hold \[\int_0^{\frac{1}{2}} {\frac{{\tilde \varphi (t)}}{t}} dt < \infty \]
where \[\tilde \varphi (\delta ) = {\delta ^2}\mathop {\inf }\limits_{0 \le \eta \le \delta } \left\{ {{\eta ^{ - 2}}\mathop {\inf }\limits_{\eta \le \xi \le 1/2} \varphi (\xi )} \right\}\]
Theorm 2 Let \(f(x)\) be a bounded function with \[\int_0^{\frac{1}{2}} {\frac{{{\omega _2}(f,t)}}{{{t^2}}}} dt < \infty \]
then \(f'(x)\) is a continous function and \[{\omega _2}(f',\delta ) = O\left\{ {\int_0^\delta {\frac{{{\omega _2}(f,t)}}{{{t^2}}}} dt} \right\}\]. 相似文献
18.
In this paper,we are interested in the existence of positive solutions for the Kirchhoff type problems{-(a_1 + b_1M_1(∫_?|▽u|~pdx))△_(_pu) = λf(u,v),in ?,-(a_2 + b_2M_2(∫?|▽v|~qdx))△_(_qv) = λg(u,v),in ?,u = v = 0,on ??,where 1 p,q N,M i:R_0~+→ R~+(i = 1,2) are continuous and increasing functions.λ is a parameter,f,g ∈ C~1((0,∞) ×(0,∞)) × C([0,∞) × [0,∞)) are monotone functions such that f_s,f_t,g_s,g_t ≥ 0,and f(0,0) 0,g(0,0) 0(semipositone).Our proof is based on the sub-and super-solutions techniques. 相似文献
19.
二阶线性中立时滞方程非振动解的存在性 总被引:3,自引:0,他引:3
考虑具有正负系数的中立时滞微分方程这里P∈R和τ∈(0,∞),σ1,σ2∈[0,∞)且Q1,Q2∈C([t0,∞),R+).对于上面方程非振动解的存在性,得到一个用,∫sQids <∞,i=1,2,来表达的充分条件。这个结果去掉了M.R.S.Kulenovic和S.Hadziomerspahic文中一个相当强的假设,改进了其中的相关定理. 相似文献
20.
该文结合算子谱论,应用锥不动点定理,建立了四阶边值问题\[\left\{ {\begin{array}{l}u^{(4)} + B(t){u}' - A(t)u = f(t,u),0 < t < 1 ,\\u(0) = u(1) = {u}'(0) = {u}'(1) = 0 \end{array}} \right.\]正解存在性定理,这里$A(t),B(t) \in C[0,1]$,$f(t,u):[0,1]\times[0,\infty ) \to [0,\infty )$连续. 相似文献