共形平坦黎曼流形中紧致极小子流形的一个刚性定理

首先得到一个推广的Simons积分不等式,然后用它给出共形平坦黎曼流形中紧致极小子流形的一个拼挤定理,推广了Li的定理.     

A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces

In this paper, we study the existence of solutions and approximation of the solutions by using a Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces. The results presented in this paper generalize the corresponding results of J. Li [J. Li, On the existence of solutions of variational inequalities in Banach spaces, J. Math. Anal. Appl. 295 (2004) 115-126].     

Numerical solution of reaction–diffusion equations by compact operators and modified equation methods

A system of reaction–diffusion equations which governs the propagation of an ozone decomposition laminar flame in Lagrangian co-ordinates is analysed by means of compact operators and modified equation methods. It is shown that the use of fourth-order accurate compact operators yields very accurate solutions if sufficient numbers of grid points are located at the flame front, where very steep gradients of temperature and species concentrations exist. Modified equation methods are shown to impose a restriction on the time step under certain conditions. The solutions obtained by means of compact operators and modified equation methods are compared with solutions obtained by other methods; good agreement is obtained.     

On a Problem Proposed by Kartsatos

§１．ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＬｅｔＸｂｅａｒｅａｌｒｅｆｌｅｘｉｖｅＢａｎａｃｈｓｐａｃｅｗｉｔｈｎｏｒｍａｎｄｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇＪ．Ａｓｕｓｕａｌ，ｗｅｓｕｐｐｏｓｅｔｈａｔｔｈｅｓｐ...     

Faithful compact quantum group actions on connected compact metrizable spaces

We construct faithful actions of quantum permutation groups on connected compact metrizable spaces. This disproves a conjecture of Goswami.     

不同权Bloch型空间之间的加权Cesàro 算子

该文讨论了$\a$-Bloch空间$\ba$和对数Bloch空间$\bl$之间的加权Ces\'aro算子$\tg$的有界性和紧性,给出$\tg$是$\ba$到$\bl$的有界算子或紧算子的充要条件和$\tg$是$\bl$到$\ba$的有界算子或紧算子的充要条件.     

Compact operators which factor through subspaces of lp

Let 1 ≤ p ≤ ∞. A subset K of a Banach space X is said to be relatively p ‐compact if there is an 〈x_n 〉 ∈ l^s _p (X) such that for every k ∈ K there is an 〈α_n 〉 ∈ l_{p ′} such that k = σ^∞_n=1 α_n x_n . A linear operator T: X → Y is said to be p ‐compact if T (Ball (X)) is relatively p ‐compact in Y. The set of all p ‐compact operators K_p (X, Y) from X to Y is a Banach space with a suitable factorization norm κ_p and (K_p , κ_p ) is a Banach operator ideal. In this paper we investigate the dual operator ideal (K^d _p , κ^d _p ). It is shown that κ^d _p (T) = π_p (T) for all T ∈ B (X, Y) if either X or Y is finite‐dimensional. As a consequence it is proved that the adjoint ideal of K^d _p is I_{p ′}, the ideal of p ′‐integral operators. Further, a composition/decomposition theorem K^d _p = Π_p K is proved which also yields that (Π^min _p )^inj = K^d _p . Finally, we discuss the density of finite rank operators in K^d _p and give some examples for different values of p in this respect. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Binding of a surfactant counterion to low-charge-density poly(acrylic acid) and poly(methacrylic acid)

The binding of a cationic surfactant, dodecylpyridinium (C12Py) chloride, with a low-charge-density poly (methacrylic acid) (PMA) was investigated in buffer solutions under the condition of constant pH. The binding isotherms with PMA consisted of two and three steps at a pH lower and higher than 3.2, respectively. Bindings in the first step were independent of pH and this step was considered to correspond to the solubilization of the hydrocarbon chains of C12Py into the nonpolar region of the compact form of PMA. This is the indication of the compact form from the binding isotherm. At pH higher than 3.2, the second step was discriminated and it depended on the pH. In the third step, a sharp rise in the degree of binding (β) was observed accompanying the solubilization of the precipitates of the PMA–C12Py complex. The binding with poly(acrylic acid) (PAA) and PMA in conventional unbuffered NaCl solutions was also examined and the pH profile of the solution during the binding process was determined. In the case of unbuffered NaCl solutions, the binding with PAA took place cooperatively at the critical association concentration (cac). The binding isotherm consisted of two steps and the pH decreased with the increase in β. The binding isotherm of PMA, on the other hand, consisted of three steps: the pH decreased slightly in the first step and considerably in the second step with the increase in β but it increased with β in the third step, exhibiting a pH minimum around 3.2. The binding in the first step coincided with that obtained in the buffered solutions. Linear relationships between β and the pH were found for both polymers. In the case of PMA, no cac was observed in both buffered and unbuffered NaCl solutions. Received: 24 January 2001 Accepted: 23 May 2001     

Convergence Results of the ERM Method for Nonlinear Stochastic Variational Inequality Problems

This paper considers the expected residual minimization (ERM) method proposed by Luo and Lin (J. Optim. Theory Appl. 140:103–116, 2009) for a class of stochastic variational inequality problems. Different from the work mentioned above, the function involved is assumed to be nonlinear in this paper. We first consider a quasi-Monte Carlo method for the case where the underlying sample space is compact and show that the ERM method is convergent under very mild conditions. Then, we suggest a compact approximation approach for the case where the sample space is noncompact. This work was supported in part by Project 10771025 supported by NSFC and SRFDP 20070141063 of China.