Topological versus chemical ordering in network glasses at intermediate and extended length scales

Atomic ordering in network glasses on length scales longer than nearest-neighbour length scales has long been a source of controversy(1-6). Detailed experimental information is therefore necessary to understand both the network properties and the fundamentals of glass formation. Here we address the problem by investigating topological and chemical ordering in structurally disordered AX2 systems by applying the method of isotopic substitution in neutron diffraction to glassy ZnCl2. This system may be regarded as a prototypical ionic network forming glass, provided that ion polarization effects are taken into account(7), and has thus been the focus of much attention(8-14). By experiment, we show that both the topological and chemical ordering are described by two length scales at distances greater than nearest-neighbour length scales. One of these is associated with the intermediate range, as manifested by the appearance in the measured diffraction patterns of a first sharp diffraction peak at 1.09( 3) angstrom(-1); the other is associated with an extended range, which shows ordering in the glass out to 62( 4) angstrom. We also find that these general features are characteristic of glassy GeSe2, a prototypical covalently bonded network material(15,16). The results therefore offer structural insight into those length scales that determine many important aspects of supercooled liquid and glass phenomenology(11).

Data Independence in the Multi-dimensional Numbered Information Spaces

The concept of data independence designates the techniques that allow data to be changed without affecting the applications that process it. The different structures of the information bases require corresponded tools for supporting data independence. A kind of information bases (the Multi-dimensional Numbered Information Spaces) are pointed in the paper. The data independence in such information bases is discussed.

The Interval [0,1] Admits no Functorial Embedding into a Finite-Dimensional or Metrizable Topological Group

An embedding X ⊂ G of a topological space X into a topological group G is called functorial if every homeomorphism of X extends to a continuous group homomorphism of G. It is shown that the interval [0, 1] admits no functorial embedding into a finite-dimensional or metrizable topological group.

The JNR Property and the Borel Structure of a Banach Space

Research partially supported by a grant of Caja de Ahorros del Mediterraneo.

Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis

*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler.

Some properties of g- and P-spaces

A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with c.c.c. is given. A P−space with c.c.c. is countable and discrete.

Paracompact Spaces and Radon Spaces

We prove that if E is a subset of a Banach space whose density is of measure zero and such that (E, weak) is a paracompact space, then (E, weak) is a Radon space of type (F ) under very general conditions.

An Example Concerning Valdivia Compact Spaces

∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998

Topological Dichotomy and Unconditional Convergence

In this paper, we give a criterion for unconditional convergence with respect to some summability methods, dealing with the topological size of the set of choices of sign providing convergence. We obtain similar results for boundedness. In particular, quasi-sure unconditional convergence implies unconditional convergence.

Descriptive Sets and the Topology of Nonseparable Banach Spaces

This paper was extensively circulated in manuscript form beginning in the Summer of 1989. It is being published here for the first time in its original form except for minor corrections, updated references and some concluding comments.

Boolean Rings that are Baire Spaces

∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.

Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

Continuity of Pseudo-differential Operators on Bessel And Besov Spaces

We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.

Compositions, Generated by Special Nets in Affinely Connected Spaces

Special nets which characterize Cartesian, geodesic, Chebyshevian, geodesic- Chebyshevian and Chebyshevian-geodesic compositions are introduced. Con- ditions for the coefficients of the connectedness in the parameters of these special nets are found.

Co-Connected Spaces

∗ Financial support of the Grant Agency of the Czech Republic under the grant no 201/96/0119 and of the Grant Agency of the Charles University under the grant GAUK 149 is gratefully acknowledged.