Complexes in polymers IV. FTIR microscopic characterization of thin organic polymer films containing embedded transition-metal carbonyl complexes

Thin films of polystyrene (PS), poly(methyl methacrylate) (PMMA) and polystyrene-polyacrylonitrile copolymer (PS-AN), containing various embedded transition-metal complexes, have been studied by FTIR microscopy. The spatial distributions of the transition-metal carbonyl complexes throughout the thin organic polymer films have been determined by a two-dimensional IR mapping procedure. The spectral variations observed in the distribution of the metal carbonyls throughout the different polymer films are discussed. The IR data show that the technique used to prepare the organometallic-embedded thin films (viz. freeze-drying of solutions followed by hot mechanical pressing of the residues) does in general lead to homogeneous films which may eventually find industrial application, e.g. as membrane sensors for small molecules.     

广义复合隐迭代格式逼近非扩张映像公共不动点

提出并使用如下广义复合隐迭代格式逼近非扩张映像族{Ti}Ni=1公共不动点:{xn=αnxn-1 (1-αn)Tnyn,yn=rnxn snxn-1 tnTnxn wnTnxn-1,rn sn tn wn=1,{αn},{rn},{sn},{tn},{wn}∈[0,1],这里Tn=TnmodN.该文提出的广义复合隐迭代格式包含了目前多种迭代格式,因此,所得强弱收敛定理推广及发展了Mann,Ishikawa,XuandOri,等许多作者的结果.     

The James constant, the Jordan-von Neumann constant, weak orthogonality, and fixed points for multivalued mappings

We give some sufficient conditions for the Domínguez-Lorenzo condition in terms of the James constant, the Jordan-von Neumann constant, and the coefficient of weak orthogonality. As a consequence, we obtain fixed point theorems for multivalued nonexpansive mappings.     

Mappings of Domains in Rn and Their Metric Tensors

We consider quasi-isometric mappings of domains in multidimensional Euclidean spaces. We establish that a mapping depends continuously in the sense of the topology of Sobolev classes on its metric tensor to within isometry of the space. In the space of metric tensors we take the topology determined by means of almost everywhere convergence. We show that if the metric tensor of a mapping is continuous then the length of the image of a rectifiable curve is determined by the same formula as in the case of mappings with continuous derivatives. (Continuity of the metric tensor of a mapping does not imply continuity of its derivatives.)     

On the isomorphism problem in the class of extensions of a free group by an infinite cyclic group

In the automorphism group of a rank 3 free group we find two nonconjugate automorphisms whose mapping tori are isomorphic groups.     

The fixed point property for multivalued nonexpansive mappings

We show some properties concerning geometrical constants of Banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties.     

Generalized KKM Type Theorems in FC-Spaces with Applications (I)

The class KKM(X,Y) (resp., s-KKM(X,Y,Z)) of set-valued mappings with KKM (resp., s-KKM) property is introduced in FC-spaces without any convexity structure. Some generalized KKM (resp., s-KKM) type theorems are proved in FC-spaces under much weak assumptions. As applications, some new section theorems and coincidence theorems are established in FC-spaces. These theorems generalize many known results in literature. The further applications of these results will be given in a follow-up paper.     

向量变分不等式的严格可行性问题

本篇文章首先定义了向量变分不等式的严格可行点概念,其次在假设了映射是强(D)-伪单调的情况下,证明了向量变分不等式解集非空有界与其严格可行点存在的等价性问题,推广了在数量变分不等式上得到的相应结果．     

Extension of Isometries Between the Unit Spheres of Normed Space E and C（Ω）

In this paper, we study the extension of isometries between the unit spheres of normed space E and C（Ω）. We obtain that any surjective isometry between the unit spheres of normed space E and C（Ω） can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley＇s problem （where Ω be a compact metric space）.     

Automatic continuity and representation of group homomorphisms defined between groups of continuous functions

Let C(X,G) be the group of continuous functions from a topological space X into a topological group G with pointwise multiplication as the composition law, endowed with the uniform convergence topology. To what extent does the group structure of C(X,G) determine the topology of X? More generally, when does the existence of a group homomorphism H between the groups C(X,G) and C(Y,G) implies that there is a continuous map h of Y into X such that H is canonically represented by h? We prove that, for any topological group G and compact spaces X and Y, every non-vanishing C-isomorphism (defined below) H of C(X,G) into C(Y,G) is automatically continuous and can be canonically represented by a continuous map h of Y into X. Some applications to specific groups and examples are given in the paper.