Properly discontinuous actions of subgroups in amenable algebraic groups and its application to affine motions

This note will concern properly discontinuous actions of subgroups in real algebraic groups on contractible manifolds. Let (π,X,ρ) be such an action, where ρ:π→ Diff(X) is a homomorphism. We assume that ? extends to a smooth action of a real algebraic group G containing π. If such π has a nontrivial radical (i.e., unique maximal normal solvable subgroup), then we can apply the method of Seifert construction [14],[17] to yield that the quotient π\X supports the structure of an injective Seifert fibering with typical (resp. exceptional) fiber diffeomorphic to a solv (resp. infrasolv)-manifold (when π acts freely). When G is an amenable algebraic group, we can say about a uniqueness property for such actions. Namely, let (π_i, X_i, ρ_i) be actions as above (i= 1,2). Then, given an isomorphism f of π₁ onto ?₂, there is a diffeomorphism h: X₁→X₂ such that h(ρ₁(r)x)=ρ₂(f(r)h(x).As an application, we try to decide the structure of affine motions of some euclidean space $\text{R}$ⁿ. First we verify the conjecture of [17, 4 5], i.e., a compact complete affinely flat manifold admits a maximal toral action if its fundamental group has a nontrivial center. Second, a compact complete affinity flat manifold whose fundamental group is virtually polycyclic supports the structure of an infrasolvmanifold. This structure varies depending on its solvable kernel (if it is abelian or nilpotent, it must be a euclidean space form or an infranilmanifold respectively). If a group of the affine group A(n) acts properly discontinuously and with compact quotient of $\text{R}$ⁿ, then it is called an affine crystallographic group. Finally, we can say so far as to a uniqueness property that two virtually polycyclic affine crystallographic groups are conjugate inside Diff($\text{R}$ⁿ) if they are isomorphic (cf.[8]).     

Investigation of proton diffusion in Nafion®117 membrane by electrical conductivity and NMR

The proton dynamics in Nafion ^®117 is investigated by comparison of the diffusion coefficient D_NMR estimated from PFG-NMR with that of D_σ estimated from electrical conductivity. At high water content region, D_σ is about two times higher than D_NMR as a result of Grotthuss mechanism. At low water content region, D_σ and D_NMR are in good agreement with each other. Both of the diffusion coefficients decrease steeply at low water content region. It can be explained as a result of the percolation transition due to the isolation of ion clusters, which is suggested by the recent small angle X-ray scattering data.     

Holomorphic Torus Actions on Compact Locally Conformal Kähler Manifolds

Given a torus action (T ², M) on a smooth manifold, the orbit map ev _x(t)=t·xfor each xMinduces a homomorphism ev _*: ²H ₁(M;). The action is said to be Rank-kif the image of ev _*has rank k(2) for each point of M. In particular, if ev _*is a monomorphism, then the action is called homologically injective. It is known that a holomorphic complex torus action on a compact Kähler manifold is homologically injective. We study holomorphic complex torus actions on compact non-Kähler Hermitian manifolds. A Hermitian manifold is said to be a locally conformal Kähler if a lift of the metric to the universal covering space is conformal to a Kähler metric. We shall prove that a holomorphic conformal complex torus action on a compact locally conformal Kähler manifold Mis Rank-1 provided that Mhas no Kähler structure.     

Improvement of initial permeability for Z-type ferrite by Ti and Zn substitution

We have found that the initial permeability μ^′${\mu }^{\prime }$ of _Co2Z${\mathrm{Co}}_2\mathrm{Z}$ ferrite is improved by the substitution of Ti⁴⁺${\mathrm{Ti}}^{4+}$ and Zn²⁺${\mathrm{Zn}}^{2+}$ ions for Fe³⁺${\mathrm{Fe}}^{3+}$ ions. The substituted sample of _{Ba3Co2TixZnxFe24-2xO41}${\mathrm{Ba}}_3{\mathrm{Co}}_2{\mathrm{Ti}}_x{\mathrm{Zn}}_x{\mathrm{Fe}}_{24-2x}{\mathrm{O}}_{41}$ with x=0.85$x=0.85$ has a maximum μ^′${\mu }^{\prime }$ of 24, which is twice as large as that of the non-substituted sample with x=0$x=0$. The particle size and shape are changed by the substitution. This is influential in the densification and the preferential orientation of a toroidal-shape sample, which results in the improvement of μ^′${\mu }^{\prime }$.     

Lorentzian similarity manifolds

An (m+2)-dimensional Lorentzian similarity manifold M is an affine flat manifold locally modeled on (G,ℝ ^m+2), where G = ℝ ^m+2 ⋊ (O(m+1, 1)×ℝ⁺). M is also a conformally flat Lorentzian manifold because G is isomorphic to the stabilizer of the Lorentzian group PO(m+2, 2) of the Lorentz model S ^m+1,1. We discuss the properties of compact Lorentzian similarity manifolds using developing maps and holonomy representations.     

On the holomorphic torus-Bott tower of aspherical manifolds

We introduce a notion of holomorphic torus-Bott tower which is an iterated holomorphic Seifert fiber space with fiber a complex torus. This is thought of as a holomorphic version of a real Bott tower. The top space of the holomorphic torus-Bott tower is called a holomorphic torus-Bott manifold. We discuss the structure of holomorphic torus-Bott manifolds and particularly the holomorphic rigidity of holomorphic torus-Bott manifolds.     

Correlation effects among thermal displacements of atoms in VSe by diffuse neutron scattering measurement

Neutron diffraction measurements have been performed on powder VSe at 294 K. The diffuse scattering theory including correlation effects among thermal displacements of atoms is applied to background function in the Rietveld analysis. The oscillatory scheme of the diffuse scattering intensity from hexagonal VSe is explained by the correlation effects among far-neighboring Se–Se atoms. The values of the correlation effects depend on the inter-atomic distance and not on the crystal structure. The relation between correlation effects and force constants is discussed.     

Calculation of stacking geometries by a modified MM2 method

The MM2 method has been modified using a three‐center charge model aimed at determining stacking geometries. The stacking interactions for the benzene dimer, porphine dimer, and bis(4,5‐diazafluoren‐9‐one thiosemicarbazonato)palladium(II) have been assessed with both the three‐center charge model and the conventional single‐center charge model using the MM2 method. The modified MM2 method always gave better results than the conventional method, and the obtained structures by the former method are in good agreement with the proposed structures from those theoretical and experimental results. The possible advantages of using the three‐center charge model for complex systems are also discussed. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 835–845, 2001