Tenant mix variety in regional shopping centres: some UK empirical analyses

The variety and quality of the tenant mix within a shopping centre is a key concern in shopping centre management. Tenant mix determines the extent of externalities between outlets in the centre, helps establish the image of the centre and, as a result, determines the attractiveness of the centre for consumers. This then translates into sales and rents. However, the management of tenant mix has largely been based on perceived “optimum” arrangements and industry rules of thumb. This paper attempts to model the impact of tenant mix on the rent paid by retailers in larger UK shopping centres and, hence, the returns made by shopping centre landlords. It extends work on shopping centre rent determination (see Working Paper 10/03) utilising a database of 148 regional shopping centres in the UK, with detailed data for over 1900 tenants. Econometric models test the relationship between rental levels and the levels of retail concentration and diversity, while controlling for a range of continuous and qualitative characteristics of each tenant, each retail product, and each shopping centre. Factor analysis is then used to extract the core retail and service categories from the tenant lists of the 148 shopping centres. The factor scores from these core retailer factors are then tested against rent payable. The results from the empirical analysis allow us to generate some clear analytical and empirical implications for optimal retail management.

Necessary and sufficient conditions for realizability of point processes

We give necessary and sufficient conditions for a pair of (generali- zed) functions 1(r1) and 2(r1, r2), ri 2X, to be the density and pair correlations of some point process in a topological space X, for ex- ample, Rd, Zd or a subset of these. This is an infinite-dimensional version of the classical “truncated moment” problem. Standard tech- niques apply in the case in which there can be only a bounded num- ber of points in any compact subset of X. Without this restriction we obtain, for compact X, strengthened conditions which are necessary and sufficient for the existence of a process satisfying a further re- quirement—the existence of a finite third order moment. We general- ize the latter conditions in two distinct ways when X is not compact.

Self-tuning property of state-space self tuners

The basic assumption from implicit self-tuning theory is that, for self tuning to occur, the control input obtained from the estimated system model converges to the value whic would be obtained if the system parameters were known. As as direct result of this, only certain control strategies are acceptable. Here a general rule for the self-tuning property of pole-placement self tuners is obtained, and previous strategies are shown to be special cases of this.

Predicting space climate change

The recent decline in the open magnetic flux of the Sun heralds the end of the Grand Solar Maximum (GSM) that has persisted throughout the space age, during which the largest‐fluence Solar Energetic Particle (SEP) events have been rare and Galactic Cosmic Ray (GCR) fluxes have been relatively low. In the absence of a predictive model of the solar dynamo, we here make analogue forecasts by studying past variations of solar activity in order to evaluate how long‐term change in space climate may influence the hazardous energetic particle environment of the Earth in the future. We predict the probable future variations in GCR flux, near‐Earth interplanetary magnetic field (IMF), sunspot number, and the probability of large SEP events, all deduced from cosmogenic isotope abundance changes following 24 GSMs in a 9300‐year record.