一类三点边值问题正解的存在性

在与线性问题第一特征值相关的条件下,通过应用不动点指数理论讨论了三点边值问题u″ 9(t)f(u)=0,t∈(0,1),u′(0)=0,u(1)=αu(η)正解的存在性,这里η∈(0,1),α∈R且0<α<1.本文结果推广和改进了文献[1]的主要结论.     

Schwarz Lemma at the Boundary on the Classical Domain of Type Ⅲ

Let R_Ⅲ(n) be the classical domain of type Ⅲ with n≥2. This article is devoted to a deep study of the Schwarz lemma on R_Ⅲ(n) via not only exploring the smooth boundary points of R_Ⅲ(n) but also proving the Schwarz lemma at the smooth boundary point for holomorphic self-mappings of R_Ⅲ(n).     

齐型空间上$L^1$ 与{\rm BMO}的内插空间

本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于摘要：本文讨论齐型空间上L^1与BMO的内插空间，得到下列结果：对于0〈θ〈1，1≤q≤∞，有（L^1，BMO）θ，q=Lpq，其中θ=1-1/p。     

Estimates of Dirichlet Eigenvalues for One-Dimensional Fractal Drums

Let $\Omega$, with finite Lebesgue measure $|\Omega|$, be a non-empty open subset of $\mathbb{R}$, and $\Omega=\bigcup_{j=1}^\infty\Omega_j$, where the open sets $\Omega_j$ are pairwise disjoint and the boundary $\Gamma=\partial\Omega$ has Minkowski dimension $D\in (0,1)$. In this paper we study the Dirichlet eigenvalues problem on the domain $\Omega$ and give the exact second asymptotic term for the eigenvalues, which is related to the Minkowski dimension $D$. Meanwhile, we give sharp lower bound estimates for Dirichlet eigenvalues for such one-dimensional fractal domains.     

Co-commuting Mappings of Generalized Matrix Algebras

Let G be a generalized matrix algebra over a commutative ring R and Z(G)be the center of G.Suppose that F,T:G→G are two co-commuting R-linear mappings,i.e.,F(x)x=xT(x) for all x∈G.In this note,we study the question of when co-commuting mappings on G are proper.     

局部分数阶拉普拉斯算子的狄利克雷问题弱解的细正则性

In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^αΩ on a bounded open set Ω ■R(N ≥ 2) with C^(1,1) boundary ■Ω. We prove that when f ∈ L^p(Ω), and g ∈ C(Ω), the following problem (-△)^αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.     

Microlocal Analysis of the Doppler Transform on R<Superscript>3</Superscript>

The Doppler transform of a vector field $F = (f_1,f_2,f_3)$ on $\mathbb{R}^3$ is defined by \[\displaystyle\mathcal{D}F(x,\omega) = \sum_j\int_\mathbb{R} \omega_j f_j(x+t\omega)\, dt~,\] where $x\in \mathbb{R}^3$ and $\omega \in S^2$ specifies the direction of a line passing through $x$. In practical applications, $\mathcal{D}F$ is known only for a small subset of lines in $\mathbb{R}^3$. In this article, we deal with the case of $\mathcal{D}F$ restricted to all lines passing through a fixed smooth curve. Using techniques from microlocal analysis, we study the problem of recovering the wavefront set of $\mbox{curl}(F)$ from that of the restricted Doppler transform of $F$.     

缺项广义Dirichlet级数所表示的整函数的增长性

对于有限级广义Dirichlet级数所表示的整函数f(s),引进级ρ_R,型■_R,分别讨论它们与在水平直线上的级ρ_L,型■_L之间的关系．应用于,Taylor级数时,有类似结果．     

One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics

Acta Applicandae Mathematicae - This paper study the type of integrability of differential systems with separable variables $\dot{x}=h\left (x\right )f\left (y\right )$ , $\dot{y}= g\left (y\right...     

广义Grotzsch环函数的几个精确不等式

对$a\in(0,1/2]$和$r\in(0,1)$, Ramanujan广义模方程中的广义Gr\"otzsch环函数$\mu_a(r)$定义如下:$\mu_a(r)=[\pi\K'_a(r)]/[2\sin(\pi a)\K_a(r)]$. 该文通过研究$\mu_a(r)$和$\mu(r)$的关系,以及$\mu_a(r)$和一些初等函数的组合的单调性和凹凸性,获得了$\mu_a(r)$的几个精确不等式,从而把$\mu(r)$的一些熟知的性质推广到$\mu_a(r)$上.     

On a class of singular p-Laplacian semipositone problems with sign-changing weights

We study existence of positive weak solution for a class of $p$-Laplacian problem $$\left\{\begin{array}{ll}-\Delta_{p}u = \lambda g(x)[f(u)-\frac{1}{u^{\alpha}}], &amp; x\in \Omega,\\u= 0 , &amp; x\in\partial \Omega,\end{array\right.$$ where $\lambda$ is a positive parameter and $\alpha\in(0,1),$ $\Omega $ is a bounded domain in $ R^{N}$ for $(N &gt; 1)$ with smooth boundary, $\Delta_{p}u = div (|\nabla u|^{p-2}\nabla u)$ is the p-Laplacian operator for $( p &gt; 2),$ $g(x)$ is $C^{1}$ sign-changing function such that maybe negative near the boundary and be positive in the interior and $f$ is $C^{1}$ nondecreasing function $\lim_{s\to\infty}\frac{f(s)}{s^{p-1}}=0.$ We discuss the existence of positive weak solution when $f$ and $g$ satisfy certain additional conditions. We use the method of sub-supersolution to establish our result.     

不完全椭球约束下多元线性模型线性估计的可容许性

本文研究了多元线性模型当未知参数受不完全椭球约束$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$时线性估计的可容许性问题.具体而言,我们研究了约束$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$中$N$和非中心点$\Theta_1$对线性估计的可容许性的影响.主要结果表明在两个不同的不完全椭球约束条件$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$与$\mbox{tr}(\Theta-\Theta_2)'N(\Theta-\Theta_2)\leq\sigma^2$ 下,当$\Theta_1$和$\Theta_2$满足一定的关系时,可容许的齐次线性估计类是相同的.     

Regularity Results for a Nonlinear Elliptic-Parabolic System with Oscillating Coefficients

In this paper we study the initial boundary value problem for the system $\mbox{div}(\sigma(u)\nabla\varphi)=0,$ $ u_t-\Delta u=\sigma(u)|\nabla\varphi|^2$. This problem is known as the thermistor problem which models the electrical heating of conductors. Our assumptions on $\sigma(u)$ leave open the possibility that $\liminf_{u\rightarrow\infty}\sigma(u)=0$, while $\limsup_{u\rightarrow\infty}\sigma(u)$ is large. This means that $\sigma(u)$ can oscillate wildly between $0$ and a large positive number as $u\rightarrow \infty$. Thus our degeneracy is fundamentally different from the one that is present in porous medium type of equations. We obtain a weak solution $(u, \varphi)$ with $|\nabla \varphi|, |\nabla u|\in L^\infty$ by first establishing a uniform upper bound for $e^{\varepsilon u}$ for some small $\varepsilon$. This leads to an inequality in $\nabla\varphi$, from which the regularity result follows. This approach enables us to avoid first proving the Hölder continuity of $\varphi$ in the space variables, which would have required that the elliptic coefficient $\sigma(u)$ be an $A_2$ weight. As it is known, the latter implies that $\ln\sigma(u)$ is "nearly bounded''.     

Marcinkiewicz积分算子交换子在Hardy空间及Herz型Hardy空间上的有界性

该文主要讨论一类Marcinkiewicz积分算子$\mu_{\Omega}$与函数$b\in $LipMarcinkiewicz积分;Hardy空间;Herz型Hardy空间;Lipschitz空间;原子;交换子国家自然科学基金 , 安徽省自然科学基金 , 安徽师范大学校科研和教改项目2005年2月21日2008年4月30日该文主要讨论一类Marcinkiewicz积分算子$\mu_{\Omega}$与函数$b\in $LipMarcinkiewicz积分;Hardy空间;Herz型Hardy空间;Lipschitz空间;原子;交换子国家自然科学基金 , 安徽省自然科学基金 , 安徽师范大学校科研和教改项目2005年2月21日2008年4月30日该文主要讨论一类Marcinkiewicz积分算子μΩ函数b ∈Lipβ所生成的交换子μΩ,b在Hardy空间及Herz型Hardy空间上的有界性.     

森田六元组的几乎分裂序列

令ΛA_1,Λ_2为两个环,M是(A_2-Λ_1)-双模,且N是(Λ_1-Λ_2)-双模.六元组Γ=(Λ_1,Λ_2,N,M,ψ,φ)是一个森田六元组.对于Γ的表示,确定其几乎分裂序列(也称AR-序列)是非常重要的.通过modΛ_1和modΛ_2的右(左)几乎分裂同态、既约同态构造Γ上的相应同态,并进一步确定它的几乎分裂序列.     

对带混合非线性项的基尔霍夫方程规范解问题的补充

在本文中,我们研究了带有质量约束条件的基尔霍夫方程规范解的存在性问题, $$-\Big(a+b \int_{\mathbb{R}^{3}}|\nabla u|^{2} \text{d} x\Big)\Delta u=\lambda u+\mu|u|^{q-2} u+|u|^{p-2} u,~~x\in \mathbb{R}^{3},$$ 其中质量约束条件为$$S_{c}:=\Big\{u \in H^{1}(\mathbb{R}^{3}):\int_{\mathbb{R}^{3}}|u|^{2} \text{d} x=c\Big\},$$ 这里$a$, $b$, $c>0$, $\mu\in \mathbb{R}$, $20$, 当$(p, q)$ 属于$\mathbb{R}^{2}$中的某个域时. 我们通过使用约束最小化、集中紧性原理和Minimax方法证明了规范解的存在性.我们部分地扩展了已经被研究的结果.     

Complete Hyper-elliptic Integrals of the First Kind and the Chebyshev Property

This paper is devoted to study the following complete hyper-elliptic integral of the first kind $$J(h)=\oint\limits_{\Gamma_h}\frac{\alpha_0+\alpha_1x+\alpha_2x^2+\alpha_3x^3}{y}dx,$$ where $\alpha_i\in\mathbb{R}$, $\Gamma_h$ is an oval contained in the level set $\{H(x,y)=h, h\in(-\frac{5}{36},0)\}$ and $H(x,y)=\frac{1}{2}y^2-\frac{1}{4}x^4+\frac{1}{9}x^9$. We show that the 3-dimensional real vector spaces of these integrals are Chebyshev for $\alpha_0=0$ and Chebyshev with accuracy one for $\alpha_i=0\ (i=1,2,3)$.     

On Hermite-Hadamard-type characterizations of higher-order differential inequalities

Let $I$ be an open interval of $\mathbb{R}$ and $f: I\to \mathbb{R}$. It is well-known that $f$ is convex in $I$ if and only if, for all $x,y\in I$ with $x相似文献   

一般$\delta$\,-冲击模型中无失效数据的Bayes统计推断

在这篇文章中, 我们针对一般冲击模型, 研究Bayes方法处理无失效数据的问题. 所谓一般$\delta$\,-冲击模型是指系统受到强度为$\lambda$的Poisson冲击, 当两个连续冲击之间时间间隔的长度不属于某个固定的区间[$\delta_1,\delta_2$]时, 系统将失效. 我们分别选择均匀分布和Beta分布作为先验分布, 用Bayes方法和多层Bayes方法得到了参数$\delta_1$和$\delta_2$的估计.     

两类具有标量旗曲率的弱Berwald度量

In this paper, we study the （α,β）-metrics of scalar flag curvature in the form of F = α ＋ εβ ＋ κβ^2/α （ε and k ≠ 0 are constants） and F = α^2/α-β. We prove that these two kinds of metrics are weak Berwaldian if and only if they are Berwaldian and their flag curvatures vanish. In this case, the metrics are locally Minkowskian.