Derivative of the exponential mapping for infinite dimensional lie groups

It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=d_exp(X)(e) ₀ ¹ Ad_exp(–tX) Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung.     

Cocycle d'Euler etK2

In this paper we construct a canonical 2-cocycle on the groupP SL(2,k) with values in the Witt groupW(k) of the fieldk. This allows us to produce anatural homomorphism :H ₂(SL(2,k); Z)I ²(k), whereI ²(k) is the square of the fundamental ideal. We prove that this homomorphism is in fact a lift of Milnor's symbol.

     

Two-Arc Transitive Graphs and Twisted Wreath Products

The paper addresses a part of the problem of classifying all 2-arc transitive graphs: namely, that of finding all groups acting 2-arc transitively on finite connected graphs such that there exists a minimal normal subgroup that is nonabelian and regular on vertices. A construction is given for such groups, together with the associated graphs, in terms of the following ingredients: a nonabelian simple group T, a permutation group P acting 2-transitively on a set , and a map F : Tsuch that x = x ^–1 for all x F() and such that Tis generated by F(). Conversely we show that all such groups and graphs arise in this way. Necessary and sufficient conditions are found for the construction to yield groups that are permutation equivalent in their action on the vertices of the associated graphs (which are consequently isomorphic). The different types of groups arising are discussed and various examples given.     

Lattice and continuum wavelets and the block renormalization group

We obtain a resolution of the identity operator, for functions on a latticeZ ^d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl ₂(Z^d) and show how the basis is generated from lattice wavelets. The lattice spacing is taken to zero and continuum wavelets are obtained.     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

含1,3-亚丙基冠醚的合成

为了进一步研究亚丙基冠醚的络合行为,合成了三种含1,3-亚丙基冠醚,即2,3-苯并-1,4,7,11-四氧-环十三-2-烯(苯并-13-冠-4)(1)、2,3-苯并-1,4,8,11,14-五氧-环十七-2-烯(苯并-17-冠-5)(2)、2,3-苯并-1,4,7,10,14,17-六氧-环十九-2-烯(苯并-19-冠-6)(3)。通过元素分析、红外光谱、质谱、核磁共振谱和 X-衍射晶体结构分析,确证了它们的结构。     

ω-氟砜基氟烷基格氏试剂的制备及其反应

合成氟烷基酮的通用方法是将全氟烷基金属试剂与羰基类化合物反应。但对于ω位带有官能团的全氟烷基金属试剂的研究,唯一的例子是:     

Isolated square planar metal complexes of carbon

Based on the group theory analysis and quantum chemical calculations within the framework of SW X _α method (in relativistic approximation for core electrons and non-relativistic for valence ones), the existence possibility of square planar complexes [M₄C] and [M₄C]^2? (M = Al, Ga, In, Tl, Sc, and Y) in gas phase has been shown. The extraction of Kt₂[M₄C] square planar complexes of carbon in the crystal state is possible too. A high stability of these complexes, in comparison with usual tetrahedral, is achieved due to the formation of five-and four-center bonds (bonds M-M and M-C).     

Description of the turbidity measurements near the phase transition temperature of poly(N-isopropyl acrylamide) copolymers: the effect of pH, concentration, hydrophilic and hydrophobic content on the turbidity

Absorbance values between 300 and 800 nm of aqueous solutions of poly(N-isopropyl acrylamide-co-itaconic acid-9.80), poly(N-isopropyl acrylamide-co-itaconic acid-52.05) and poly(N-isopropyl acrylamide)s containing Tegomer H-Si 2111 end groups and/or blocks were measured using a Shimadzu 160-A UV-visible spectrometer. Turbidities obtained from these absorbance values were used to interpret the macromolecular phase transition from a hydrophilic to a hydrophobic structure of the polymers. The effects of comonomer type and content, concentration of the solutions, pH and temperature on the coil-globule transition were discussed in terms of turbidity form factor, β related to size and shapes of particles and calculated by using the simplified form of Debye equation.The results presented in this work show that the presence of Tegomer H-Si 2111 (Si containing end groups and/or blocks) or high amount of itaconic acid (IA) in the chains prevent a collapse transition from hydrated extended coils to hydrophobic globules, which aggregate and form a separate phase (β<2). Furthermore, it was observed that in the case of concentrated solutions intermolecular hydrophobic interactions between isopropyl groups overcame the repulsive forces resulting from the ionized carboxylic acid groups of IA or surface active nature of Si containing hydrophobic groups (β>2). This stage of the transition corresponds to macroscopic phase separation after an intramolecular process.     

Base-labile tert-butoxycarbonyl (Boc) group on phenols

Phenols are deprotected with weak bases from their tert-butoxycarbonyl (Boc) derivatives. Boc deprotection with bases can avoid side reactions during the deprotection with acids. We note the lability of the Boc to bases and are able to utilize it as a new cleavage condition for synthetic studies.