用13CNMR研究聚甲基丙烯酸锡酯的立构序列分布

本文测定了自由基型溶液聚合的聚甲基丙烯酸三甲基锡酯(PTMTM),聚甲基丙烯酸三乙基锡酯(PTETM)和聚甲基丙烯酸三丁基锡酯(PTBTM)的¹³C-NMR谱,对其C-2谱扩展分峰,计算立构序列,从定量数据表明,聚合物样品的空间立构富于或稍富于间规立构,随取代基的体积增大而趋于无规分布,作者认为受空间位阻效应和分子内或分子间形成配位键的影响。     

Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds

We prove a Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds with specified asymptotic geometry at infinity. The asymptotic geometry at infinity is either a cusp bundle over a compact space (the fibered cusps) or a fiber bundle over a cone with a compact fiber (the fibered boundary). Many noncompact Einstein manifolds come with such a geometry at infinity.     

On the univalence of derivatives of functions which are univalent in angular domains

We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f ^(k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir’yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane.     

局部紧集上的广义向量均衡问题

利用数值化方法和 Browder 不动点定理,得到一类新的广义向量均衡问题解的存在定理,并用于向量变分不等式、向量相补问题和抽象向量优化问题,得到其解的存在定理.     

Self-commutator inequalities in higher dimension

Three natural multi-dimensional substitutes for the self-commutator of a Hilbert space operator are introduced and generalizations of Putnam's inequality to tuples of operators with semidefinite self-commutators are indicated. In addition, a Riesz transform model is developed and investigated.

     

A note about the Gaussian property of the Brownian bridge

The Gaussian property of the Brownian bridge is characterized as an application of Ramachandran's theorem in terms of the independence of the random variables that appear in the Karhunen-Loéve expansion of the process. A reference about the construction of the Brownian bridge by means of functional transformations is also included.     

Variational inequalities for monotone operators in nonreflexive Banach spaces

The purpose of this paper is to study the existence problem of solutions and perturbation problem for some kind of variational inequalities with monotone operators in nonreflexive Banach spaces, and to obtain some results.     

Parabolic Harnack inequality for divergence form second order differential operators

Old and recent results concerning Harnack inequalities for divergence form operators are reviewed. In particular, the characterization of the parabolic Harnack principle by simple geometric properties -Poincaré inequality and doubling property- is discussed at length. It is shown that these two properties suffice to apply Moser's iterative technique.     

具阻尼的非线性耦合方程组的能量衰减估计

应用一个新的积分不等式,得到了具阻尼的非线性耦合方程组的衰减估计,以及精确的估计常数.     

完备流形上带位势的热核估计

在完备非紧流形上获得了关于带位势热方程正解的梯度估计；接着，利用测地线的技巧获得了Harnack不等式；进一步，建立了两个积分不等式，综合Harnack不等式获得了热核的上下界；最后，利用函数的结果来控制p形式的热核。