投影下的Gronwall不等式

本文对Ｊ．Ｋ．Ｈａｌｅ曾提出的一类广泛的投影下的Ｇｒｏｎｗａｌ不等式问题作了讨论，对满足ｕ（ｔ）≤ａ（ｔ）＋∫_０^tｂ（ｔ－ｓ）ｕ（ｓ）ｄｓ＋∫_０^∞ｃ（ｓ）ｕ（ｔ＋ｓ）ｄｓ，(?)ｔ≥０的函数ｕ（ｔ）∈Ｃ_b⁰（Ｒ₊，Ｒ₊）作了估计．其结果对讨论微分方程的有界解、不变流形及其Ｆｏｌｉａｔｉｏｎ和进一步讨论奇性Ｇｒｏｎｗａｌ不等式都有意义     

关于G-Matlis自反模的换环定理

设Ｒ和Ｔ是Ｎｏｅｔｈｅｒ完备半局部环，Ｒ→Ｔ是环同态．本文证明了，若Ｔ是有限生成或ＡｒｔｉｎＲ－模，Ｍ为Ｇ－Ｍａｔｌｉｓ自反Ｒ－模，则对所有ｎ≥０，Ｅｘｔ^Ｒ_ｎ（Ｔ，Ｍ），Ｅｘｔ^Ｒ_ｎ（Ｍ，Ｔ），Ｔｏｒ^Ｒ_ｎ（Ｔ，Ｍ）以及Ｔｏｒ^Ｒ_ｎ（Ｍ，Ｔ）均是Ｇ－Ｍａｔｌｉｓ自反Ｔ－模．所得结果推广了Ｒ．Ｂｅｌｓｈｏｆ的结果．     

Banach空间上非Lipschitz映射的渐近行为

设Ｃ是具Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间Ｅ的非空凸闭子集，Ｇ是定向集．｛Ｔ_ｔ：ｔ∈Ｇ｝是Ｃ上的渐近非扩张型映照．本文给出了｛Ｔ_ｔ：ｔ∈Ｇ｝的弱收敛定理．     

双曲型时滞偏差分方程解的振动性

本文主要讨论了双曲型时滞偏差分方程(?)的所有解振动的充分必要条件和振动性的判别准则,其中ａ－１≠０,ｐ＋ａ＞０,ｑ_ｉ是实数,ｋ_ｉ,ｌ_ｉ是非负整数,ｕ是一个正整数,ｉ＝１,２,…,ｕ.     

α型β级Bazilevic函数的Fekete-Szeg?问题

设Ｂ（α，β）（α＞０，０≤β＜１）表示在单位圆盘内定义的规范化的α型β级Ｂａｚｉｌｅｖｉｃ函数类．本文对Ｂ（α，β）中函数ｆ（ｚ）＝ｚ＋∑from∞to(ｎ＝２)ａ_ｎｚ^ｎ得到｜ａ３－λａ₂²｜（０≤λ≤１）的准确估计．     

关于一类微分方程周期解的存在性的注记

本文主要探讨下列周期系数微分方程dy/dt=(A₁(t)y+A₂(t)y²+A₃(t)y³)/(a₀(t)+a₁(t)y+a₂(t)y²)(**)的周期解个数问题，利用方程（**）解的差率法得到了方程（**）周期解的个数定理．本文仅在Ａ_i（ｔ），ａ_j（ｔ）（ｉ＝１，２，３，ｊ＝０，１，２）是连续周期函数的条件下得到这一结论，从而减弱了文［２］中相应定理的条件，即Ａ_i（ｔ），ａ_j（ｔ）均是连续可微的周期函数．     

关于迭代函数方程f2(x)=af(x)+bx的通解

设λ的二次三项式λ²－ａλ－ｂ的两个零点为λ₁＝ｒ，λ₂＝ｓ（ａ及ｂ为实数）．对０＜ｒ＜ｓ，ｒ＜０＜ｓ≠－ｒ及ｒ＝ｓ≠０这三种情形，Ｊ．Ｍａｔｋｏｗｓｋｉ与Ｗｅｉｎｉａｎ Ｚｈａｎｇ在“Ｍｅｔｈｏｄ ｏｆ ｃｈａｒａｃｔｅｒｉｓｔｉｃｓ ｆｏｒ ｆｕｎｃｔｉｏｎａｌ ｅｑｕａｔｉｏｎｓ ｉｎ ｐｏｌｙｎｏｍｉａｌ ｆｏｒｍ”一文中给出了迭代函数方程ｆ²（ｘ）＝ａｆ（ｘ）＋ｂｘ，对任ｘ∈Ｒ；ｆ∈Ｃ⁰     

三角域上分片二次函数Bernstein多项式的退化性

设Ｓ_２（Ｔ）为三角域Ｔ的二阶剖分，本文给出在Ｓ_２（Ｔ）下分片二次函数f(P)∈Ｃ¹（Ｔ）的Ｂｅｒｎｓｔｃｉｎ多项式的退化性及递推公式。这里的条件Ｓ_２（Ｔ）及Ｃ¹（Ｔ）类都是重要的。我们举例说明更一般情况下分片二次函数Ｂｅｒｎｓｔｃｉｎ多项式的复杂性。     

若干广义Ramsey数

本文讨论了关于树对完全图删去一些相交的三阶路的广义Ｒａｍｓｅｙ数Ｒ（Ｔ_ｍ，Ｋ_n－ｔＰ₃）和关路对完全图删去一些不相交的三阶完全图的广义Ｒａｍｓｅｙ数Ｒ（Ｐ_ｍ，Ｋ_n－ｔＫ₃），获得如下结果：1．如果m≥3,n≥3，那么Ｒ（Ｔ_ｍ，Ｋ_n－ｔＰ₃）=(m-1)(n-t-1)+1,0≤t≤[n/3].２．若m≥4,n,T≥1，则Ｒ（P_ｍ，Ｋ_n－ｔK₃）=(m-1)(n+2t-1)+1.从而，这两个结果部分地回答了１９８３年Ｒ．Ｊ．Ｇｏｕｌｄ和Ｍ．Ｓ．Ｊａｃｏｂｓｏｎ在［１］中提出的未解决问题．     

简单对角BL时间序列模型的参数的矩估计及其渐近分布

本文研究简单对角ＢＬ模型ｘ_ｔ＝ｅ_ｔ＋ｂｘ_ｔ－１ｅ_ｔ-1参数ｂ和σ_t^２的估计问题，其中｛ｅ_ｔ｝是白噪声，Ｅ（ｅ_ｔ）＝０，ｅ（ｅ_ｔ）＜＋∞证明了矩估计b和σ_t^２的渐近正态性．     

On Initial-boundary-value Problems for a Class of Systems of Quasi-linear Evolution Equations

In this paper the initial-boundary-value problems for pseudo-hyperbolic system of quasi-linear equations: {(-1)^Mu_{tt} + A(x, t, U, V)u_x^{2M}_{tt} = B(x, t, U, V)u_x^{2M}_{t} + C(x, t, U, V)u_x^{2M} + f(x, t, U, V) u_x^k(0,t) = ψ_{0k}(t), \quad u_x^k(l,t) = ψ_{lk}(t), \quad k = 0,1,…,M - 1 -u(x,0) = φ_0(x), \quad u_t(x,0) = φ_1(x) is studied, where U = (u_1, u_x,…,u_x^{2M - 1}) V = (u_t, u_{xt},…,u_x^{2M - 1_t}), A, B, C are m × m matrices, u, f, ψ_{0k}, ψ_{1k}, ψ_0, ψ_1 are m-dimensional vector functions. The existence and uniqueness of the generalized solution (in H² (0, T; H^{2M} (0, 1))) of the problems are proved.     

On Global Solvability of Nonlinear Kirchhoff Model in Infinitely Increasing Moving Domains

The purpose of this article is to study the existence and uniqueness of global solution for the nonlinear hyperbolic-parabolic equation of Kirchhoff-Carrier type: $$ u_{tt} + \mu u_t - M\left (\int _{\Omega _t}|\nabla u|^2dx\right )\Delta u = 0\quad \hbox {in}\ \Omega _t\quad \hbox {and}\quad u|_{\Gamma _t} = \dot \gamma $$ where $ \Omega _t = \{x\in {\shadR}^2 | \ x = y\gamma (t), \ y\in \Omega \} $ with boundary o t , w is a positive constant and n ( t ) is a positive function such that lim t M X n ( t ) = + X . The real function M is such that $ M(r) \geq m_0 \gt 0 \forall r\in [0,\infty [ $ .     

Integral Formulas for the r-Mean Curvature Linearized Operator of a Hypersurface

For a normal variation of a hypersurface M ⁿ in a space form Q _c ⁿ⁺¹ by a normal vector field fN, R. Reilly proved:

Curvature homogeneous metrics on principal fibre bundles

Summary We consider a principal fibre bundle P=P(M, , G) with one-dimensional fibre G over a curvature homogeneous Riemannian manifold (M,g) and we give a list of sufficient conditions for some distinguished metric on P to be curvature homogeneous. We give examples to illustrate the result.This work was partially supported by MPI 40% and GNSAGA of the CNR.     

On the boundedness and the asymptotic behaviour of the non-negative solutions of Volterra-Hammerstein integral equations

We study the Volterra-Hammerstein integral equation $$U(t,x) = U_O (t,x) + \mathop \smallint \limits_O^t \mathop \smallint \limits_D f(y, U (t - s,y)) h (x,y,s)dsdy,$$ t≥0, x∈D. We derive sufficient conditions for the boundedness of all non-negative solutions U. We show that, for bounded non-negative solutions U, U(t,.) is positive on D for sufficiently large t>0, if we impose appropriate positivity assumptions on f and h. If we additionally assume that, for y∈D, rf(y,r) strictly monotone increases and f(y,r)/r strictly monotone decreases as r>0 increases, the following alternative holds for any bounded non-negative solution U: Either U(t,.) converges toward zero for t→∞, pointwise on D, or U(t,.) converges, for t→∞, toward the unique bounded positive solution of the corresponding Hammerstein integral equation, uniformly on D. We indicate conditions for the occurrence of each of the two cases.     

三角代数上Lie三重导子的刻画

设u=Tri(A,M,B)是三角代数.证明了在一般的假设下,如果线性映射δ:u→u,满足对任意的U,V,W∈u且UV=UW=0(或U·V=U·W=0),有δ([[U,V],W])=[[δ(U),V],W]+[[U,δ(V)],W]+[[U,V],δ(W)],则对任意U∈u,δ(U)=φ(U)+h(U),其中φ:u→u是一个导子,线性映射h:u→Z(u),满足对任意的U,V,W∈u且UV=UW=0(或U·V=U·W=0),有h([[U,V],W])=0.     

非负曲率流形的体积增长估计

本文利用非负曲率流形上的Busemann函数和穷竭函数的性质,得出了在某紧致子集外满足一定非负曲率条件的完备非紧的(复) n维K■hler流形的体积增长至少是n次的．推广了陈兵龙和朱熹平教授新近的一个结果．     

The Heat Kernel on Constant Negative Curvature Space Form

Let M be a n-dimensional simply connected, complete Riemannian manifold with constant negative curvature. The heat kernel on M is denoted by H^M_t(x, y) = H^M_t(r(x, y)), where r(x, y) = dist(x, y). We have the explicit formula of H^M_t(x, y) for n=2, 3, and the induction formula of H^M_t(x, y) for n ≥ 4^{[-1]}. But the explicit formula is very complicated for n ≥ 4. ln this paper we give some simple and useful global estimates of H^M_t(x, y), and apply these estimates to the problem of eigenvalue.     

Optimal Transportation for Generalized Lagrangian

This paper deals with the optimal transportation for generalized Lagrangian L = L(x, u, t), and considers the following cost function: c(x, y) = inf x(0)=x x(1)=y u∈U∫_0~1 L(x(s), u(x(s), s), s)ds, where U is a control set, and x satisfies the ordinary equation x(s) = f(x(s), u(x(s), s)).It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation:V_t(t, x) + sup u∈UV_x(t, x), f(x, u(x(t), t), t)-L(x(t), u(x(t), t), t) = 0,V(0, x) = Φ0(x).     

Integrated semigroups and integrodifferential equations

A class of partial integrodifferential equation from viscoelasticity is formulated as the abstract integrodifferental equations in Banach space :