Least energy solutions of a critical Neumann problem with a weight

We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.

On a semilinear Schrodinger equation with critical Sobolev exponent

We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an element of W-1,W-2 (R-N), where N greater than or equal to4, V, K, g are periodic in x(j) for 1 less than or equal toj less than or equal toN, K>0, g is of subcritical growth and 0 is in a gap of the spectrum of -Delta +V. We show that under suitable hypotheses this equation has a solution u not equal 0. In particular, such a solution exists if K equivalent to 1 and g equivalent to 0.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Two-body and three-body abrasion: A critical discussion

It is argued that the common classification of abrasive wear into 'two-body abrasion' and 'three-body abrasion' is seriously flawed. No definitions have been agreed upon for these terms, and indeed there are two quite different interpretations, the implications of which are mutually inconsistent. In the dominant interpretation, the primary thrust of the two-body/three-body concept is to describe whether the abrasive particles are constrained (two-body) or free to roll (three-body). In this view, two-body abrasion is generally much more severe than three-body. The alternative interpretation emphasises the presence (three-body) or absence (two-body) of a rigid counterface backing the abrasive. In this view, three-body abrasion is equated to high-stress (or grinding) abrasion and is generally more severe than two-body (low-stress) abrasion. This paper recommends that the 'two-body/three-body' terminology be abandoned, to be replaced by an alternative classification scheme based directly upon the manifest severity of wear. (C) 1998 Elsevier Science S.A.

Critical sets for families of Latin squares

In this paper I give details of new constructions for critical sets in latin squares. These latin squares, of order n, are such that they can be partitioned into four subsquares each of which is based on the addition table of the integers module n/2, an isotopism of this or a conjugate.

Critical values for unit root and cointegration test statistics - the use of response surface equations

This note considers the value of surface response equations which can be used to calculate critical values for a range of unit root and cointegration tests popular in applied economic research.

The politics and ethics of relocated art

At the end of Word War II, Soviet occupation forces removed countless art objects from German soil. Some of them were returned during the 1950s, but most either disappeared for good or were stored away secretly in cellars of Soviet museums. The Cold War then covered the issue with silence. After the collapse of the Soviet Union, museums in St Petersburg and Moscow started to exhibit some of the relocated art for the first time in half a century. The unusual quality of the paintings-mostly impressionist masterpieces-not only attracted the attention of the international art community, but also triggered a diplomatic row between Russia and Germany. Both governments advanced moral and legal claims to ownership. To make things even more complicated, many of the paintings once belonged to private collectors, some of whom were Jews. Their descendants also entered the dispute. The basic premise of this article is that the political and ethical dimensions of relocated art can be understood most adequately by eschewing a single authorial standpoint. Various positions, sometimes incommensurable ones, are thus explored in an attempt to outline possibilities for an ethics of representation and a dialogical solution to the international problem that relocated art has become.

Paramagnetic limiting of the upper critical field of the layered organic superconductor kappa-(BEDT-TTF)(2)Cu(SCN)(2)

We report detailed measurements of the interlayer magnetoresistance of the layered organic superconductor kappa-(BEDT-TTF)(2)Cu(SCN)(2) for temperatures down to 0.5 K and fields up to 30 T. The upper critical field is determined from the resistive transition for a wide range of temperatures and field directions. For magnetic fields parallel to the layers, the upper critical field increases approximately linearly with decreasing temperature. The upper critical field at low temperatures is compared to the Pauli paramagnetic limit, at which singlet superconductivity should be destroyed by the Zeeman splitting of the electron spins. The measured value is comparable to a value for the paramagnetic limit calculated from thermodynamic quantities but exceeds the limit calculated from BCS theory. The angular dependence of the upper critical field shows a cusplike feature for fields close to the layers, consistent with decoupled layers.

Overview, critical assessment, and conservation implications of koala distribution and abundance

Regional and national surveys provide a broadscale description of the koala's present distribution in Australia. A detailed understanding of its distribution is precluded, however, by past and continuing land clearing across large parts of the koala's range. Koala population density increased in some regions during the late 1800s and then declined dramatically in the early 1900s. The decline was associated with habitat loss, hunting, disease, fire, and drought. Declines are continuing in Queensland and New South Wales. In contrast, dense koala populations in habitat isolates in Victoria and South Australia are managed to reduce population size and browse damage. Current understanding of koala distribution and abundance suggests that the species does not meet Australian criteria as endangered or vulnerable fauna. Its conservation status needs to be reviewed, however, in light of the extensive land clearing in New South Wales and Queensland since the last (1980s) broadscale surveys. Consequently, we recommend that broadacre clearing by curtailed in New South Wales and Queensland and that regular, comprehensive, standardized, national koala surveys be undertaken. Given the fragmentation of koala habitat and regional differences in the status of the koala, we recommended that studies on regional variation in the koala be intensified and that koala ecology in fragmented and naturally restricted habitats be developed. More generally, the National Koala Conservation Strategy should be implemented.