In this paper we investigate the Margulis–Ruelle inequality for general Riemannian manifolds (possibly non-compact and with a boundary) and show that it always holds under an integrable condition.

A mechanical model is developed to explain the influence of grain rotation on nanovoid growth in nanocrystalline solids in the current paper. In the framework of the mechanical model, the dislocations released from the nanovoid surface will be affected by four stresses: the driving stress induced by far-field stress, the stress arising from grain rotation, the image stress caused by the free surface of the nanovoid, and the back stress generated by the previously emitted dislocations. Furthermore, under the condition of different rotational strength and surface effects, we analyzed in detail the influence of the important parameters such as nanovoid radius, nucleation radius, dislocation emission angle, relative distance, rotation grain size, rotation coefficient, and direction angle on the critical stress. Finally, we discuss the effect of the coupling of rotational deformation and the grain boundary on the growth of the nanovoid. As a conclusion, the high stress nearby the nanovoid can be released by grain rotation, which inhibits the growth of the nanovoid.

Natural samples of the substituted basic Cu(II) chloride series, Cu4–xMx2+(OH)6Cl2(M = Zn, Ni, or Mg) were investigated by single-crystal X-ray diffraction in order to elucidate compositional boundaries associated with paratacamite and its congeners. The compositional ranges examined are Cu3.65Zn0.35(OH)6Cl2 – Cu3.36Zn0.64(OH)6Cl2 and Cu3.61Ni0.39(OH)6Cl2 – Cu3.13Ni0.87(OH)6Cl2, along with a single Mg-bearing phase. The majority of samples studied have trigonal symmetry (R3̄m) analogous to that of herbertsmithite (Zn) and gillardite (Ni), with a ≈ 6.8, c ≈ 14.0 Å. Crystallographic variations for these samples caused by composition are compared with both published and new data for the R3̄m sub-cell of paratacamite, paratacamite-(Mg) and paratacamite-(Ni). The observed trends suggest that the composition of end-members associated with the paratacamite congeners depend upon the nature of the substituting cation.

This article contributes to the communities of practice (CoP) literature by focusing on the neglected role of the boundary in constructing community. It takes issue with advocates of International Relations’ (IR) most recent ‘practice turn’ who have overrated inclusive practices of linking to the detriment of taking account of exclusive practices of demarcation. A conceptual turn to the boundary, understood as a ‘site of difference’, highlights how the two sets of practices operate simultaneously in creating shared senses of belonging to a community. The article empirically probes this turn to the boundary by studying how the postmodern community of the European Union (EU) is (re)constructed by EU diplomats in its neighbouring state Ukraine. As a borderland, it symbolises an interstitial zone of high connectivity where the EU’s otherwise latent order is unearthed. A reconstructive analysis of interviews with members of this ‘community of practice’ reveals that they function as ‘boundary workers’ who engage in both boundary-spanning and boundary-drawing practices on an everyday basis. Zooming in on the ‘boundary work’ by EU diplomats exposes the complex process of community-building and thereby helps grasp community as an emergent structure of possibilities whose meaning is contextually mediated by its members’ social experience of the boundary.

Let Γ be an Ã2 subgroup of PGL3(), where is a local field with residue field of order q. The module of coinvariants C(,ℤ)Γ is shown to be finite, where is the projective plane over . If the group Γ is of Tits type and if q ≢ 1 (mod 3) then the exact value of the order of the class [1]K0 in the K-theory of the (full) crossed product C*-algebra C(Ω) ⋊ Γ is determined, where Ω is the Furstenberg boundary of PGL3(). For groups of Tits type, this verifies a conjecture of G. Robertson and T. Steger.

Most of the land surface of Melville Island, Australia's second largest island, is covered in Eucalyptus savanna. One exception is an area at Yapilika where a large tract of savanna is dominated by Acacia shrubs. An ordination analysis of 122 quadrats revealed that the boundary of Eucalyptus dominance did not correspond to a major change in floristic composition. Detailed transect studies at one site on the boundary showed that Eucalyptus trees were abruptly replaced by a band of Grevillea trees which gradually gave way to Acacia shrub dominance. There was a gradual change in the floristic composition of the savanna across the boundary. The distributional limit of Eucalyptus was found to be independent of any hydrological discontinuity. There was a slight decrease (<2.5 m) in altitude from Eucalyptus to Acacia savanna. The Acacia savanna soils were sandier and their surface soil had significantly lower concentrations of Ca and Mg and significantly greater concentration of Al compared with the Eucalyptus savanna soils. Eucalyptus seedlings planted in the three savanna communities were not found to be under drought stress (pre-dawn leaf xylem potentials of > – 0.9 MPa) during the dry season. Over a 12 month period Eucalyptus tetrodonta and E. miniata seedling growth was not significantly different on the Acacia or Eucalyptus savanna, although this result may be due to the counteracting effects of greater soil fertility and tree competition in the Eucalyptus savanna and lower soil fertility in the treeless, and hence competition-free, Acacia savanna. This hypothesis is supported by the significantly greater growth of Eucalyptus seedlings on fertilized Acacia savanna soils. The limited production, dispersal and establishment of Eucalyptus seeds and the greater frequency of fires in the Acacia savanna probably explains the abrupt limit to Eucalyptus dominance along the edaphic gradient.

The current financial crisis has raised queries about the adequacy of the present regulatory regime. Whilst the immediate priority may be to plug the obvious holes in the system, there are some long-term generic problems with almost any system of financial regulation. This paper explores one such concern, i.e. the boundary problem. This arises because effective regulation, one that actually bites, is likely to penalise those within the regulated sector, relative to those just outside, causing substitution flows towards the unregulated. This boundary problem impacts on many proposals, such as ‘narrow banking’ and my own, with Avinash Persaud, for state and time-varying capital adequacy requirements. The question of how and where to set the boundary is considered. Such boundaries will always be criticised as leading to disintermediation, competitive inequality (no level-playing-field), inefficiency and higher spreads and borrowing rates; and such criticisms will be valid up to a point. The paper ends by discussing how best to respond.

Adélie penguins Pygoscelis adeliae were tested as to whether they jump with optimal energy efficiency when moving out of the sea to the land. Adélie penguins risk predation if the jump fails. Swimming penguins usually launch up the side of sea ice to a surface higher than sea level. Analysis of jumping behaviour recorded by a video camera showed that the trajectory of the centre of gravity of the birds during the aerial phase of jumping was parabolic, indicating that the success of landing depends on three parameters at the time of take-off from water: speed, angle and distance from the point of emergence to the ice edge. There was a negative relationship between distance and the take-off angle, suggesting that penguins adjust their take-off angle to the distance from the ice edge. The comparison among hypotheses revealed that penguins did not jump with optimal energy efficiency. Instead, they aimed for the refracted image of the edge of the cliff, which from underwater appears higher than it actually is. This direction-dependent rule seems to be more robust and reliable than the optimal energetic strategy.

In lowland England, badgers Meles meles form social groups of up to 30 individuals. They share a main den (sett) and a core feeding range, but largely forage alone. Faeces are deposited in discrete hinterland and border ‘latrines’. Border latrines are shared with neighbouring groups. We demonstrate that there is a highly significant tendency for neighbouring groups to place a similar quantity of faeces at shared latrines. There are also significant tendencies to place more faeces in boundary latrines close to the sett, and for reduced separation of latrines close to the sett. We also demonstrate that badgers tend to defecate most frequently on the boundary closest to their current feeding site. These observations are consistent with the hypothesis that faeces at border latrines are used to promote range exclusion. We propose that faecal volume represents a reliable signal of the encounter likelihood and/or foraging pressure of badgers along a particular border. According to the ‘active territorial defence’ hypothesis, this indicates a stand-off position in terms of each group's resource holding potential by signalling encounter likelihood across the boundary. By the ‘passive range exclusion’ hypothesis, this border is an isopleth (equal contour) of resource depletion between groups, and crossing over such a contour deep into a neighbouring range reduces foraging efficiency. By either hypothesis, the matched faecal volume and sett proximity effects suggest a simple mechanism that is capable of allowing reliable information to be passed by individuals between adjacent sectors of neighbouring territories to deter intrusion. This is a ‘bottom–up’ process of inter-dependent, parallel, individual responses, which is capable of generating the emergent complexity of co-ordinated group ranges without central control.

In this paper we prove a uniqueness theorem for minimal discs in R3 spanning a polygonal boundary.

A space X is a D-space if, for every neighborhood assignment f there is a closed discrete set D such that f(D) = X. In this paper we give some necessary conditions and some sufficient conditions for a resolution of a topological space to be a D-space. In particular, if a space X is resolved at each x ∊ X into a D-space Yx by continuous mappings fx: X − {x} → Yx, then the resolution is a D-space if and only if {x} × Bd(Yx) is a D-space.