Topological,affine and isometric actions on flat riemannian manifolds II

Explicit examples of finite subgroups of the group of homotopy classes of self-homotopy equivalences of some flat Riemannian manifolds which cannot be lifted to effective actions are given. It is also shown that no finite subgroups of the kernel of π₀(Homeo(M))→Out π₁(M) can be lifted back to Homeo(M), for a large class of flat manifolds M. Some results of an earlier paper by the authors are refined and related to recent work of R. Schoen and S.T. Yau.     

构造正交小波基的基本方法之一

本文不仅给出一种构造局部性好的正交小波基的方法,并且给出了构造各种优良性质的正交小波基的一般思想方法。其特点:使构造的小波母函数有具体的表达式,既有较好的光滑性,又有很好的局部性,并且其收敛速度与│t│~（-（3k 1））同阶,其中k为任意自然数。这种方法不需要每次重新构造函数,只要改变k的值,就能满足不同实际问题的需要。     

Isometric multipliers ofL p (G, X)

Let G be a locally compact group with a fixed right Haar measure andX a separable Banach space. LetL ^p (G, X) be the space of X-valued measurable functions whose norm-functions are in the usualL ^p . A left multiplier ofL ^p (G, X) is a bounded linear operator onB ^p (G, X) which commutes with all left translations. We use the characterization of isometries ofL ^p (G, X) onto itself to characterize the isometric, invertible, left multipliers ofL ^p (G, X) for 1 ≤p ∞,p ≠ 2, under the assumption thatX is not thel ^p -direct sum of two non-zero subspaces. In fact we prove that ifT is an isometric left multiplier ofL ^p (G, X) onto itself then there existsa y ∃ G and an isometryU ofX onto itself such thatTf(x) = U (R _y f)(x). As an application, we determine the isometric left multipliers of L¹ ∩L ^p (G, X) and L¹ ∩C ₀ (G, X) whereG is non-compact andX is not the l^p-direct sum of two non-zero subspaces. If G is a locally compact abelian group andH is a separable Hubert space, we define where г is the dual group of G. We characterize the isometric, invertible, left multipliers ofA ^p (G, H), provided G is non-compact. Finally, we use the characterization of isometries ofC(G, X) for G compact to determine the isometric left multipliers ofC(G, X) providedX ^* is strictly convex.     

Adsorption-energetic and IR spectroscopic studies of NH4 natrolite

The ammonium form of natural zeolite, natrolite, obtained by vapor phase ion exchange is similar to calcium-containing zeolites of the natrolite group in its de- and rehydration characteristics and the heats of immersion in water. The adsorption capacity and the heat of immersion in water are maximum after evacuation of the zeolite at 200 °C. The irreversible sintering of NH₄ natrolite occurs above 200 °C (up to 45% at 500 °C), accompanied by the formation of hydroxyl groups. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 359–361, February, 1998.     

Möbius Homogeneous Hypersurfaces with One Simple Principal Curvature in Sn+1

Let Möb(Sⁿ⁺¹) denote the Möbius transformation group of Sⁿ⁺¹. A hypersurface f:Mⁿ → Sⁿ⁺¹ is called a Möbius homogeneous hypersurface, if there exists a subgroup G ? Möb(Sⁿ⁺¹) such that the orbit G(p)={φ(p)|φ ∈ G}=f(Mⁿ), p ∈ f(Mⁿ). In this paper, we classify the Möbius homogeneous hypersurfaces in Sⁿ⁺¹ with at most one simple principal curvature up to a Möbius transformation.     

Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties

Let be a surjective mapping from a uniform algebra on a compact Hausdorff space onto a uniform algebra on a compact Hausdorff space . Suppose that holds for every . Then we have that is an almost isometric isomorphism, which is a generalization of results of Molnár (2002) and Rao and Roy (2005).

     

Totally geodesic immersions of Kähler manifolds and Kähler Frenet curves

In a given Kähler manifold (M,J) we introduce the notion of Kähler Frenet curves, which is closely related to the complex structure J of M. Using the notion of such curves, we characterize totally geodesic Kähler immersions of M into an ambient Kähler manifold and totally geodesic immersions of M into an ambient real space form of constant sectional curvature .     

Electrochemical behaviors of the magnesium alloy substrates in various pretreatment solutions

Interface reactions and film features of AZ91D magnesium alloy in pickling, activation and zinc immersion solutions have been investigated. The surface morphologies of the specimens were observed with scanning electron microscope (SEM). Electrochemical behaviors of AZ91D magnesium alloy in the baths of pickling, activation and zinc immersion were analyzed based on the open circuit potential (OCP) - time curves in various solutions. The results show that the corrosive rate in HNO₃ + CrO₃ or HNO₃ + H₃PO₄ pickling solution was more rapid than in KMnO₄ pickling-activation solution. Both α phase and β phase of the substrates were uniformly corroded in HNO₃ + CrO₃ or HNO₃ + H₃PO₄ pickling solution, the coarse surface can augment the mechanical occlusive force between the subsequent coatings and the substrates, so coatings with good adhesion can be obtained. In HF activation solution, the chromic compound formed via HNO₃ + CrO₃ pickling was removed and a compact MgF₂ film was formed on the substrate surface. In K₄P₂O₇ activation solution, the corrosion products formed via HNO₃ + H₃PO₄ pickling were removed, a new thin film of oxides and hydroxides was formed on the substrate surface. In KMnO₄ pickling-activation solution, a film of manganic oxides and phosphates was adhered on the substrate surface. Zinc film was symmetrically produced via K₄P₂O₇ activation or KMnO₄ pickling-activation, so it was good interlayer for Ni or Cu electroplating. Asymmetrical zinc film was produced because the MgF₂ film obtained in the HF activation solution had strong adhesive attraction and it was not suitable for interlayer for electroplating. However, the substrate containing compact MgF₂ film without zinc immersion was fit for direct electroless Ni-P plating.     

On Asymptotically Isometric Copies of lβ (0 《β《1)

We get the characterizations of the family of all nonnegative,subadditive,β-absolutely homogeneous and continuous functionals defined on X,when the β-normed space X contains an asymptotically isometric copy of lβ.Moreover,it is proved that if a closed bounded β-convex subset K of a β-normed space contains an asymptotically isometric lβ-basis,then K contains a closed β-convex subset C which fails the fixed point property.     

On Linearly Isometric Extensions for 1-Lipschitz Mappings Between Unit Spheres of ALP-spaces （p 〉 2）

In this paper, we show that if Vo is a 1-Lipschitz mapping between unit spheres of two ALP-spaces with p 〉 2 and -Vo（S1（LP）） C Vo（S1（LP））, then V0 can be extended to a linear isometry defined on the whole space. If 1 〈 p 〈 2 and Vo is an ＂anti-l-Lipschitz＂ mapping, then Vo can also be linearly and isometrically extended.