Crystallographic and microstructural aspects of the superconductor YBa2Cu3O7-y —an overview

Crystal structures and structural inhomogeneities observed in YBa₂Cu₃O_7-y are reviewed. It is brought out that a proper understanding of the nature of the structural inhomogeneities is essential for exploiting the technological potential of this material. The need for an adequate characterization of specimens used for experiments is emphasized. Practical implications of the ferroelastic nature of the material are discussed.     

A weak approach to finite elasticity

On the ground of four axioms we define thekinematics of perfectly elastic bodies and in particular the notion ofweak deformations of a perfectly elastic body. Weak deformations turn out to agree withweak diffeomorphisms introduced in [10], a class of rectifiable currents which enjoys good closure and compactness properties. Defining thedynamics of perfectly elastic bodies in terms of twoconstitutive conditions on the stored energy function, we can therefore prove existence of stable equilibrium weak deformations for mixed boundary value problems, which moreover satisfy equilibrium and conservation equations.This work has been partially supported by the Ministero dell'Universitá e della Ricerca Scientifica, by C.N.R. contract n. 91.01343.CT01, by the European Research Project GADGET, and by Grant n.11957 of the zech Acad. of Sciences.This article was processed by the author using the LaT_EX style filepljour1 from Springer-Verlag.     

Deciding Frattini is NP-complete

We show that it is a NP-complete problem to decide whether a finite poset arises as the (Birkhoff) dual of the Frattini sublattice of some finite distributive lattice.This work was supported in part by Swiss NSF grant 20-32644.91.     

New lower semicontinuity results for polyconvex integrals

Summary We study integral functionals of the formF(u, )= f(u)dx, defined foru C¹(;R ^k), R ⁿ . The functionf is assumed to be polyconvex and to satisfy the inequalityf(A) c₀¦(A)¦ for a suitable constant c₀ > 0, where (A) is then-vector whose components are the determinants of all minors of thek×n matrixA. We prove thatF is lower semicontinuous onC ¹(;R ^k) with respect to the strong topology ofL ¹(;R ^k). Then we consider the relaxed functional , defined as the greatest lower semicontinuous functional onL ¹(;R ^k ) which is less than or equal toF on C¹(;R ^k). For everyu BV(;R ^k) we prove that (u,) f(u)dx+c₀¦D^su¦(), whereDu=u dx+D^su is the Lebesgue decomposition of the Radon measureDu. Moreover, under suitable growth conditions onf, we show that (u,)= f(u)dx for everyu W^1,p(;R ^k), withp min{n,k}. We prove also that the functional (u, ) can not be represented by an inte- gral for an arbitrary functionu BV_loc(R ⁿ;R ^k). In fact, two examples show that, in general, the set function (u, ) is not subadditive whenu BV_loc(R ⁿ;R ^k), even ifu W _loc ^1,p (R ⁿ;R ^k) for everyp < min{n,k}. Finally, we examine in detail the properties of the functionsu BV(;R ^k) such that (u, )= f(u)dx, particularly in the model casef(A)=¦(A)¦.     

A note on the reflection principle for the biharmonic equation and the Stokes system

In this note, we discuss the reflection principle of the Stokes system in a half space for the threedimensional case, and of the biharmonic equation. Admitting different boundary conditions, we use the reflection principle to prove uniqueness of solutions of the Stokes system or the biharmonic equation in weightedLq-spaces     

Fractal dimension,attractors, and the boussinesq approximation in three dimensions

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.     

On the two-gap elliptic potentials

The-parametrized family of two-gap elliptic potentials is constructed so that (i) 0<<1, (ii) for rational values of such potentials are elliptic (i.e., double-periodic), (iii) within the limit0 this family degenerates to the soliton potential, (iv) within the limit1 this family degenerates to the one-gap Lamé potential.Dedicated to the memory of J.-L. Verdier     

On Cesari's property (Q)

In the present paper, we generalize, within the family of convex-valued multifunctions, a selection theorem of Cole (Ref. 1). This then leads us to prove some new results concerning Cesari's property (Q) and to the introduction of the Cesari limit of sets, which is then compared to the Kuratowski-Mosco limit.This work was done while the author was a visiting professor at the University of Pavia, Pavia, Italy. Financial support was provided by CNR and by NSF Grant No. 84-03135.     

稀土焦绿石化合物R2Fe4/3W2/3O7的高温高压稳定性研究和X射线相分析

 本文利用X射线粉末衍射和位敏探测技术，研究了R₂Fe_4/3W_2/3O₇（R=Er、Yb、Dy）化合物经高温高压处理后的变化情况。在3.7 GPa，1 200 ℃条件下，六方相R₂Fe_4/3W_2/3O₇化合物按两种方式分解，而直接由R₂O₃，Fe₂O₃和WO₃原料出发，经上述同样的高温高压条件合成所得的产物与六方相高温高压分解产物相同，均为R₂WO₆、RFeO₃、WO₃和Fe₂O₃的多相聚合物。同时给出了R₂Fe_4/3W_2/3O₇六方相高温高压下的稳定区范围。     

Hyperfine structure in Iodine at the 612-nm and 640-nm helium-neon laser wavelengths

The hyperfine structure of iodine-127 at 612 nm and 640 nm is observed by saturated absorption in a gas cell placed within a He-Ne laser cavity modified to operate at these wavelengths. At 612 nm, all the 21 components of the strong R 47 9-2 line lie within the laser gain profile, and the resulting saturated absorption peaks have a contrast of 10% at a gas pressure of 3 Pa.