Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

Molecular recognition between functionalized gold nanoparticles and healable, supramolecular polymer blends – a route to property enhancement

A new, healable, supramolecular nanocomposite material has been developed and evaluated. The material comprises a blend of three components: a pyrene-functionalized polyamide, a polydiimide and pyrenefunctionalized gold nanoparticles (P-AuNPs). The polymeric components interact by forming well-defined p–p stacked complexes between p-electron rich pyrenyl residues and p-electron deficient polydiimide residues. Solution studies in the mixed solvent chloroform–hexafluoroisopropanol (6 : 1, v/v) show that mixing the three components (each of which is soluble in isolation), results in the precipitation of a supramolecular, polymer nanocomposite network. The precipitate thus formed can be re-dissolved on heating, with the thermoreversible dissolution/precipitation procedure repeatable over at least 5 cycles. Robust, self-supporting composite films containing up to 15 wt% P-AuNPs could be cast from 2,2,2- trichloroethanol. Addition of as little as 1.25 wt% P-AuNPs resulted in significantly enhanced mechanical properties compared to the supramolecular blend without nanoparticles. The nanocomposites showed a linear increase in both tensile moduli and ultimate tensile strength with increasing P-AuNP content. All compositions up to 10 wt% P-AuNPs exhibited essentially quantitative healing efficiencies. Control experiments on an analogous nanocomposite material containing dodecylamine-functionalized AuNPs (5 wt%) exhibited a tensile modulus approximately half that of the corresponding nanocomposite that incorporated 5 wt% pyrene functionalized-AuNPs, clearly demonstrating the importance of the designed interactions between the gold filler and the supramolecular polymer matrix.

The creativity of action: Property, Kin and the social in African artisanal mining

Analyses of neo-liberal change in African mining tend to frame discussion through the lens of an overarching structural perspective. Far less attention has been paid to the way change is enacted within social relations in mining communities. To this end, our chapter considers how development in the Tanzanian mineral sector transforms people’s relationships and stimulates new iterations of power and agency within local trajectories of development, focusing on the case of artisanal gold mining in Mgusu village in Geita region, Tanzania. The aim is to trace how neo-liberal change configures market rationality and property relations in ways that can fundamentally alter social relationships within the local community, occupational groups and families, raising both opportunities for wealth accumulation and the potential to entrench poverty. The creative action involved in these processes generates new associational ties and repertoires of practice, as miners’ respond to change and the need to protect their livelihoods.

A modified PNN algorithm with optimal PD modeling using the orthogonal least squares method

In this paper a modified algorithm is suggested for developing polynomial neural network (PNN) models. Optimal partial description (PD) modeling is introduced at each layer of the PNN expansion, a task accomplished using the orthogonal least squares (OLS) method. Based on the initial PD models determined by the polynomial order and the number of PD inputs, OLS selects the most significant regressor terms reducing the output error variance. The method produces PNN models exhibiting a high level of accuracy and superior generalization capabilities. Additionally, parsimonious models are obtained comprising a considerably smaller number of parameters compared to the ones generated by means of the conventional PNN algorithm. Three benchmark examples are elaborated, including modeling of the gas furnace process as well as the iris and wine classification problems. Extensive simulation results and comparison with other methods in the literature, demonstrate the effectiveness of the suggested modeling approach.

Non-orthogonal version of the arbitrary polygonal C-grid and a new diamond grid

Quasi-uniform grids of the sphere have become popular recently since they avoid parallel scaling bottle- necks associated with the poles of latitude–longitude grids. However quasi-uniform grids of the sphere are often non- orthogonal. A version of the C-grid for arbitrary non- orthogonal grids is presented which gives some of the mimetic properties of the orthogonal C-grid. Exact energy conservation is sacrificed for improved accuracy and the re- sulting scheme numerically conserves energy and potential enstrophy well. The non-orthogonal nature means that the scheme can be used on a cubed sphere. The advantage of the cubed sphere is that it does not admit the computa- tional modes of the hexagonal or triangular C-grids. On var- ious shallow-water test cases, the non-orthogonal scheme on a cubed sphere has accuracy less than or equal to the orthog- onal scheme on an orthogonal hexagonal icosahedron. A new diamond grid is presented consisting of quasi- uniform quadrilaterals which is more nearly orthogonal than the equal-angle cubed sphere but with otherwise similar properties. It performs better than the cubed sphere in ev- ery way and should be used instead in codes which allow a flexible grid structure.

Conscience, discretion and the creation of property rights

This paper considers the utility of the concept of conscience or unconscionable conduct as a contemporary rationale for intervention in two principles applied where a person seeks to renege on an informal agreement relating to land: the principle in Rochefoucauld v Boustead; and transfers 'subject to' rights in favour of a claimant. By analysing the concept in light of our current understanding of the nature of judicial discretion and the use of general principles, it responds to arguments that unconscionability is too general a concept on which to base intervention. In doing so, it considers the nature of the discretion that is actually in issue when the court intervenes through conscience in these principles. However, the paper questions the use of constructive trusts as a response to unconscionability. It argues that there is a need, in limited circumstances, to separate the finding of unconscionability from the imposition of a constructive trust. In these limited circumstances, once unconscionability is found, the courts should have a discretion as to the remedy, modelled on that developed in the context of proprietary estoppel. The message underlying this paper is that many of the concerns expressed about unconscionability that have led to suggestions of alternative rationales for intervention can in fact be addressed whilst retaining an unconscionability analysis. Unconscionability remains a preferable rationale for intervention as it provides a common thread that links apparently separate principles and can assist our understanding of their scope.

Housing or property? The dynamics of housing policy and property principles in the right to buy

This paper examines the interplay and tension between housing law and policy and property law, in the specific context of the right to buy (RTB). It focuses on funding arrangements between the RTB tenant and another party. It first examines how courts determine the parties' respective entitlements in the home, highlighting the difficulty of categorising, under traditional property law principles, a contribution in the form of the statutory discount conferred on the RTB tenant. Secondly, it considers possible exploitation of the RTB scheme, both at the macro level of exploitation of the policy underpinning the legislation and, at the micro level, of exploitation of the tenant. The measures contained in the Housing Act 2004 intended to curb exploitation of the RTB are analysed to determine what can be considered to be legitimate and illegitimate uses of the scheme. It is argued that, despite the government's implicit approval, certain funding arrangements by non-resident relatives fail to give effect to the spirit of the scheme.

The "value" of property rights in social security law

This article provides a critical examination of the way that property rules are applied judicially in the context of social security law concerned with the assessment of capital, and especially in connection with the determination of ownership and the valuation of assets, which can have a critical bearing on entitlement to various means-tested benefits.

The dynamics and measurement of commercial property depreciation in the UK

Beginning with an extensive literature review, this new research summary report analyses the process of rental depreciation, its effect on the performance of rents, and the impacts of capital expenditure on depreciation. It is based on an analysis of more than 700 commercial and industrial properties and newer property types and it is the most comprehensive national study of rental depreciation since the 1986 CALUS report. The report will be of interest to valuers, fund managers, institutional investors and their advisors and researchers.

Destination UK: international property investment and the role of taxation

This research examines whether or not foreign property investors enjoy tax and other advantages over their UK counterparts and how, if such advantages exists, UK quoted property companies can redress the balance. Current issues such as lack of liquidity, inequalities amongst asset classes, and differences in tax burden are examined in detail. The report will be of interest to property investment specialists, valuers, fund managers, institutional investors and their advisers.

Future shock or e-hype?: the impact of online shopping on UK retail property

This research examines the impact of ecommerce on sales and rental values and on the future space and ownership/leasing requirements of UK retailers for 2000-2005. The independent study, commissioned by BCSC (and funded by BCSC Educational Trust with support from the RICS Education Trust), included a major postal survey, follow-up interviews, a retail focus group, and shopper survey and case study of Cyberton, a town in the South East of England. The study was conducted by the Research Department of The College of Estate Management between June and December 2000.

eRPUK 2003: eCommerce and Retail Property in the UK: third annual benchmarking survey

This new survey, which has just been completed and includes brand new data, has been funded by the RICS Education Trust and the European Shopping Centre Trust. It follows up our 2000 survey of UK retailers, investors and developers. The report presents results from our new 2001 survey. This continuing benchmark series of studies includes an extensive review of developments in ecommerce and retail in Europe and the USA. The survey reveals a cooling in attitude towards ecommerce in the UK, but there is rapid growth in some sectors and polarisation and marginalisation of secondary centres are likely to increase. In Europe the growth of a three tier system of ecommerce 'pioneers', 'followers' and 'laggards' is becoming established, and the research also reveals results from a recent joint survey on US and UK retailers conducted with Colorado State University. There is a danger of complacency as UK online sales (in percentage terms) now outstrip USA.

Building the web: the Internet and the property profession

The report examines the development of the Internet and Intranets in the world of business and commerce, drawing on previous literature and research. The new technology is explained, and key issues examined, such as the impact of the Internet on the surveyor's role as 'information broker' and its likely effect on clients' property requirements. The research is based on an analysis of 261 postal questionnaire responses and eight case study interviews from a sample of general practice and quantity surveying practices and corporates. For the first time the property profession is examined in detail and the key drivers, barriers and benefits of Internet use are identified for a range of different sized organisations.