On the domain dependence of solutions to the compressible Navier–Stokes equations of a barotropic fluid

We prove a general compactness result for the solution set of the compressible Navier–Stokes equations with respect to the variation of the underlying spatial domain. Among various corollaries, we then prove a general existence theorem for the system in question with no restrictions on smoothness of the spatial domain. Copyright © 2002 John Wiley & Sons, Ltd.     

On the duration of the total eclipse of a satellite of a body

This paper solves the problem of the duration of the total eclipseof a satellite of a body, provided that (a) the body is sphericalin shape and the mass distribution inside the body is sphericallysymmetrical; (b) the satellite is a very small object; (c) thesatellite's orbit around a body is circular and the satellitecan pass through the centre of its shadow; (d) a source of lightis the source of the conical body's shadow (umbra) and it doesnot change its apparent position in the sky; (e) there are noperturbations on the satellite's orbit. The solution presentedrepresents the general discussion of the problem based on utilizationof some parts of the theory of contraction mappings.     

A Positive Doubly Power Bounded Operator with a Nonpositive Inverse Exists on any Infinite-dimensional AL-Space

In this paper we construct a positive doubly power bounded operator with a nonpositive inverse on an AL-space.     

Summing the derivative expansion of the effective action

The derivative expansion of the effective action is a perturbative development in derivatives of the fields. The expansion breaks down when some of the derivatives are too large. We show how to sum exactly the first and second derivatives and treat perturbatively derivatives higher than second.     

Thermodynamic non-additivity in disordered systems with extended phase space

Non-additivity effects in coupled dynamic-stochastic systems are investigated. It is shown that there is a mapping of the replica approach to disordered systems with finite replica indexn on Tsallis non-extensive statistics, if the average thermodynamic entropy of the dynamic subsystem differs from the information entropy for the probability distribution in the stochastic subsystem. The entropic indexq is determined by the entropy difference ΔS. In the case of incomplete information, the entropic indexq=1−n is shown to be related to the degree of lost information.     

The axial Ward identity in the presence of a quark-condensing vacuum

Quark-condensate contributions to triangle amplitudes arising from the nonperturbative content of the QCD vacuum are shown to uphold the anomalous axial Ward identity to leading and next-to-leading order in both the expansion parameter [m _quark/momentum]², as well as in the expansion parameter [m _π/m _quark]² appropriate forπ ⁰→ kinematics.     

An externally cooled beetle type scanning tunneling microscope for imaging in cryogenic liquids

We describe a variable temperature cryogenic scanning tunneling microscope designed for imaging and research in cryogenic liquids. It has an external Dewar type large scale cooling system with a temperature control range of roughly 85-110 K using pressure controlled liquid nitrogen cooling. The liquid nitrogen is kept in a closed chamber surrounding the STM and maintained at a pressure to suit the chosen temperature. Several gases have triple points in this temperature range and can therefore be liquified, such as argon, methane, silane and germane. The STM is based on a beetle type design built into a small cube vacuum chamber to fit into the cooling dewar. The system has been used for atomic resolution of highly oriented graphite submerged in a methane liquid at a temperature of 100 K.     

A modular scanning tunneling microscope with an interchangeable elastic closed cell and external actuators

We introduce a novel modular cell based scanning tunneling microscope with external piezoelectric actuators. A tip and a sample are contained in a closed interchangeable cell, consisting of a stiff top plate and a bottom part, fastened together by an elastic material. The bottom part, containing a scanning tip, is fastened to a base unit while the top plate, containing a sample, is capable of scanning motion by external piezoelectric actuators mounted in the same base unit. The actuators are pre-loaded by the deformation of the elastic material of the cell, giving an increased stability. This design is expected to simplify the scanning tunneling microscope (STM) operation in difficult environments greatly by enclosing only the tip and sample in a small cell-module, which is pluggable to a scanning mechanism and other supportive functionalities. A frequency characterization and an image scan showing atomic resolution of highly oriented graphite in air, at room temperature, is presented.     

2-Dimension from the Topological Viewpoint

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset.