A simple proof of P. Carter's theorem

We give a simple proof of the following result of P. Carter: Given a twist homeomorphism of an annulus with at most one fixed point in the interior of the annulus, then there exists an essential simple closed curve inside this annulus meeting its image in at most the (possible) interior fixed point.

     

Reconstruction of infinite locally finite connected graphs

Let G be an infinite locally finite connected graph. We study the reconstructibility of G in relation to the structure of its end set . We prove that an infinite locally finite connected graph G is reconstructible if there exists a finite family (Ω_i)_0i (n2) of pairwise finitely separable subsets of such that, for all x,y,x′,y′V(G) and every isomorphism f of G−{x,y} onto G−{x′,y′} there is a permutation π of {0,…,n−1} such that for 0i<n. From this theorem we deduce, as particular consequences, that G is reconstructible if it satisfies one of the following properties: (i) G contains no end-respecting subdivision of the dyadic tree and has at least two ends of maximal order; (ii) the set of thick ends or the one of thin ends of G is finite and of cardinality greater than one. We also prove that if almost all vertices of G are cutvertices, then G is reconstructible if it contains a free end or if it has at least a vertex which is not a cutvertex.     

Multiplicative Loops of 2-Dimensional Topological Quasifields

We determine the algebraic structure of the multiplicative loops for locally compact 2-dimensional topological connected quasifields. In particular, our attention turns to multiplicative loops which have either a normal subloop of positive dimension or which contain a 1-dimensional compact subgroup. In the last section, we determine explicitly the quasifields which coordinatize locally compact translation planes of dimension 4 admitting an at least 7-dimensional Lie group as collineation group.     

Subspaces with Equal Closure

We take a new and unifying approach toward polynomial and trigonometric approximation in topological vector spaces used in analysis on R ⁿ . The idea is to show in considerable generality that in such a space a module, which is generated over the polynomials or trigonometric functions by some set, necessarily has the same closure as the module which is generated by this same set, but now over the compactly supported smooth functions. The particular properties of the ambient space or generating set are, to a large degree, irrelevant for these subspaces to have equal closure. This translation—which goes in fact beyond modules—allows us, by what is now essentially a straightforward check of a few properties, to replace many classical results in various spaces by more general statements of a hitherto unknown type. Even in the case of modules with one generator the resulting theorems on, e.g., completeness of polynomials are then significantly stronger than the classical statements. This extra precision stems from the use of quasi-analytic methods (in several variables) rather than holomorphic methods, combined with the classification of quasi-analytic weights. In one dimension this classification, which then involves the logarithmic integral, states that two well-known families of weights are essentially equal. As a side result we also obtain an integral criterion for the determinacy of multidimensional measures which is less stringent than the classical version. The approach can be formulated for Lie groups and this interpretation then shows that many classical approximation theorems are actually theorems on the unitary dual of R ⁿ , thus inviting to a change of paradigm. In this interpretation polynomials correspond to the universal enveloping algebra of R ⁿ and trigonometric functions correspond to the group algebra. It should be emphasized that the point of view, combined with the use of quasi-analytic methods, yields a rather general and precise ready-to-use tool, which can very easily be applied in new situations of interest which are not covered by this paper.     

Azido‐Functionalized 5′ Cap Analogues for the Preparation of Translationally Active mRNAs Suitable for Fluorescent Labeling in Living Cells

The 7‐methylguanosine (m⁷G) cap structure is a unique feature present at the 5′ ends of messenger RNAs (mRNAs), and it can be subjected to extensive modifications, resulting in alterations to mRNA properties (e.g. translatability, susceptibility to degradation). It also can provide molecular tools to study mRNA metabolism. We developed new mRNA 5′ cap analogues that enable the site‐specific labeling of RNA at the 5′ end using strain‐promoted azide–alkyne cycloaddition (SPAAC) without disrupting the basic function of mRNA in protein biosynthesis. Some of these azide‐functionalized compounds are equipped with additional modifications to augment mRNA properties. The application of these tools was demonstrated by labeling translationally active mRNAs in living cells.     

粗交流结果最优传递序列的模拟退火算法

粗交流中,确定概念在多个agents间传递时,由于各个agent有不同的语言,相互之间不能提供准确的信息交流,从而导致概念在传递过程中会丢失部分信息,最后得到粗糙的结果。在不同的粗交流传递序列中,信息的丢失量往往是不同的。利用模拟退火算法,得到使参与粗交流的最后一个agent获得信息量最大的粗交流传递序列。算法的分析和仿真验证了该方法的有效性。