Stone代数的Cayley表示定理

首先通过集代数得到了Stone代数的表示定理,然后证明了每一个Stone代数均嵌入到某个集合X上的一个Stone映射类S中.     

The interaction of dibutyltin dilaureate with tetraethyl orthosilicate in sol-gel systems

Sols composed of dibutyltin dilaureate (DTL) and tetraethyl orthosilicate (TEOS) were prepared using a mixture of methyl ethyl ketone (MEK) and acetone as the solvent in order to study the interaction between the oligomeric Sn and Si species. The hydrolysis molar ratio r (r=nH₂O/nM (M: Si, Sn or Si+Sn) was 2. The use of an acid or basic catalyst was avoided, as the sols are intended to be used in the formulation of potential stone consolidants. The sols were studied by several spectroscopic techniques including Small Angle X-ray Scattering (SAXS), ²⁹Si and ¹¹⁹Sn NMR, Fourier Transform Infrared (FTIR) spectroscopy and X-ray diffraction (XRD). According to the spectroscopic results the lauric acid produced by the hydrolysis of DTL modifies the condensation path of the Si species, leading to the formation of two types of oligomeric chains: linear swollen and multiparticle diffusion-limited aggregates, depending on the molar ratio Sn/Si. The ²⁹Si NMR results indicated that the hydrolysis of DTL catalizes the condensation of the Si species, giving as a result higher condensation extents of the Si species in the Sn-Si sols compared to a pure Si sol. Based on the Radial Distribution functions (RDF) and the FTIR results, heterocondensation occurred.     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

Molecular dynamics simulation of gas adsorption on defected graphene

Gas sensing is one of the most promising applications for graphene. Using molecular dynamics simulation method, adsorption isotherm of xenon (Xe) gas on defected and perfect graphene is studied in order to investigate sensing properties of graphene for Xe gas. In this method, first generation of Brenner many-body potential is used to simulate the interaction of carbon–carbon (C) atoms in graphene, and Lennard–Jones two-body potential is used to simulate interaction of Xe–Xe and Xe–C atoms. In the simulated systems, adsorption coverage, radial distribution function, heat of adsorption, binding energy and specific heat capacity at constant volume are calculated for several temperatures between 90 K and 130 K, and various pressures. It was found that both of the defected and perfect graphene could be introduced as very good candidates for adsorption of Xe gas.     

Maeda-type Decomposition of CJ-generated Algebraic Lattices

We prove necessary and sufficient conditions for the decomposition of an arbitrary CJ-generated algebraic lattice into a direct product of subdirectly irreducible lattices. We generalize earlier results due to F. Maeda, T. Katriák and the present author. New structure theorems for two classes of CJ-generated algebraic lattices are also obtained.AMS Subject Classification (1991) 06B05 06B10Research partially supported by Hungarian National foundation for Scientific Research, Grant No. T029525 and T030243 and by János Bolyai Grant of Hungarian Academy of Science.     

The Absolute of a Topological Space and its Application to Abelian l-groups

We give a axiomatic treatment of the absolute in the category of all topological spaces and characterize it as a cover with respect to the full subcategory of extremally disconnected spaces. As an application, we obtain the strongly projectable hull of an abelian l-group as a unique lifting of the absolute of its spectrum. Dedicated to B. V. M.     

A note on isometries of Lipschitz spaces

The main purpose of this article is to generalize a recent result about isometries of Lipschitz spaces. Botelho, Fleming and Jamison [2] described surjective linear isometries between vector-valued Lipschitz spaces under certain conditions. In this article, we extend the main result of [2] by removing the quasi-sub-reflexivity condition from Banach spaces.     

On the Pointwise Limit of Vector Charges with the Saks Property

The well-known theorem about the density of the space of probability charges with the Saks property in the space of all probability charges in the pointwise topology is proved in the vector case. New features are the uniform Saks property for the family of charges and sufficient conditions for the pointwise limit of a sequence of charges to have the Saks property.     

Non-homeomorphic density topologies

In [ANISZCZYK, B.-FRANKIEWICZ, R.: Non homeomorphic density topologies, Bull. Polish Acad. Sci. Math. 34 (1986), 211–213] the authors constructed 2^c non-homeomorphic density topologies tied to the concept of measure. In [WROŃSKI, S.: The number of non-homeomorphic I-density topologies. Institute of Mathematics of Polish Academy of Sciences. Preprint 482, December 1990, XXXIV Semester in Banach Center, Theory of Real Functions] an analogous construction has been given for topologies tied to the concept of category. Here we present a generalization containing both the results mentioned above. This generalization based only on the topological ideas is independent of the concept of measure or category. Communicated by L’ubica Holá     

深圳某电厂H型钢桩沉桩与效果测试

在上部为花岗岩块石填土、下部为相对软弱的粘性土 ,地下水与海水相通的地区进行大型工程建设 ,主要建 (构 )筑物采用桩基础是安全可靠的措施 ,但采用何种桩型、沉桩时怎样才能顺利穿过花岗岩块石填土是一个值得研究的课题。采用潜孔锤引孔穿过花岗岩块石填土 ,往孔内回填碎石 ,然后打H型钢桩 ,在深圳某电厂地基处理中获得了较好的效果